Non-MonoAbelian4folds.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We investigate abelian varieties of dimension 4. For the relevant Weil polynomials, we use the LMFDB."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "def numbirred(n,p): #The number of irred. polys of degree n in F_p[x].\n",
    "    L = []\n",
    "    for i in range(1,n+1):\n",
    "        if ZZ(i).divides(ZZ(n)):\n",
    "            L.append(p^i*moebius(n/i))\n",
    "        else:\n",
    "            pass\n",
    "    return 1/n*sum(L)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(i, index)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "var('i,index')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ordGSp(g,n): #This is the order of GSp_{2g}(n).\n",
    "    primeorders = []\n",
    "    h = factor(n)\n",
    "    for i in range(0,len(h)):\n",
    "        l = h[i][0]\n",
    "        e = h[i][1]\n",
    "        primeorders.append((l-1)*l^(g^2)*product(l^(2*index)-1,index,1,g)*(l^(2*g^2+g+1))^(e-1)) #I've used product to try to make things easy to change as I increase my dimension g.\n",
    "    return product(primeorders)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "37440000"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ordGSp(2,5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "GSpOrders = [0,0]\n",
    "for n in range(2,1001):\n",
    "    GSpOrders.append(ordGSp(4,ZZ(n))) #g=4."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Frobmatrix4(a7,a6,a5,a4,p): #This is for the minimal order Z[pi,v].\n",
    "    frob = Matrix([[0,0,0,0,-p*a5,p,0,0],[1,0,0,0,-a4,0,0,0],[0,1,0,0,-a5,0,0,0],[0,0,1,0,-a6,0,0,0],[0,0,0,1,-a7,0,0,0],[0,0,0,0,-p*a6,0,p,0],[0,0,0,0,-p*a7,0,0,p],[0,0,0,0,-p,0,0,0]])\n",
    "    return frob"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[ 0  0  0  0  0  2  0  0]\n",
       "[ 1  0  0  0 -1  0  0  0]\n",
       "[ 0  1  0  0  0  0  0  0]\n",
       "[ 0  0  1  0 -2  0  0  0]\n",
       "[ 0  0  0  1  3  0  0  0]\n",
       "[ 0  0  0  0 -4  0  2  0]\n",
       "[ 0  0  0  0  6  0  0  2]\n",
       "[ 0  0  0  0 -2  0  0  0]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "testFrob = Frobmatrix4(-3, 2, 0, 1,2);testFrob"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "LPolys2 = [ \\\n",
    "16*x^8 - 40*x^7 + 48*x^6 - 40*x^5 + 29*x^4 - 20*x^3 + 12*x^2 - 5*x + 1,\\\n",
    "16*x^8 - 40*x^7 + 52*x^6 - 50*x^5 + 39*x^4 - 25*x^3 + 13*x^2 - 5*x + 1,\\\n",
    "16*x^8 - 32*x^7 + 16*x^6 + 14*x^5 - 21*x^4 + 7*x^3 + 4*x^2 - 4*x + 1,\\\n",
    "16*x^8 - 32*x^7 + 20*x^6 + 4*x^5 - 11*x^4 + 2*x^3 + 5*x^2 - 4*x + 1,\\\n",
    "16*x^8 - 32*x^7 + 24*x^6 - 8*x^5 + 2*x^4 - 4*x^3 + 6*x^2 - 4*x + 1,\\\n",
    "16*x^8 - 32*x^7 + 32*x^6 - 24*x^5 + 17*x^4 - 12*x^3 + 8*x^2 - 4*x + 1,\\\n",
    "16*x^8 - 32*x^7 + 36*x^6 - 34*x^5 + 27*x^4 - 17*x^3 + 9*x^2 - 4*x + 1,\\\n",
    "16*x^8 - 32*x^7 + 40*x^6 - 38*x^5 + 29*x^4 - 19*x^3 + 10*x^2 - 4*x + 1,\\\n",
    "16*x^8 - 24*x^7 + 8*x^6 + x^4 + 2*x^2 - 3*x + 1,\\\n",
    "16*x^8 - 24*x^7 + 8*x^6 + 8*x^5 - 10*x^4 + 4*x^3 + 2*x^2 - 3*x + 1,\\\n",
    "16*x^8 - 24*x^7 + 8*x^6 + 10*x^5 - 13*x^4 + 5*x^3 + 2*x^2 - 3*x + 1,\\\n",
    "16*x^8 - 24*x^7 + 8*x^6 + 12*x^5 - 15*x^4 + 6*x^3 + 2*x^2 - 3*x + 1,\\\n",
    "16*x^8 - 24*x^7 + 12*x^6 - 4*x^5 + 3*x^4 - 2*x^3 + 3*x^2 - 3*x + 1,\\\n",
    "16*x^8 - 24*x^7 + 12*x^6 - 2*x^5 - x^3 + 3*x^2 - 3*x + 1,\\\n",
    "16*x^8 - 24*x^7 + 12*x^6 - 3*x^4 + 3*x^2 - 3*x + 1,\\\n",
    "16*x^8 - 24*x^7 + 12*x^6 + 2*x^5 - 5*x^4 + x^3 + 3*x^2 - 3*x + 1,\\\n",
    "16*x^8 - 24*x^7 + 12*x^6 + 4*x^5 - 7*x^4 + 2*x^3 + 3*x^2 - 3*x + 1,\\\n",
    "16*x^8 - 24*x^7 + 12*x^6 + 6*x^5 - 11*x^4 + 3*x^3 + 3*x^2 - 3*x + 1,\\\n",
    "16*x^8 - 24*x^7 + 16*x^6 - 12*x^5 + 10*x^4 - 6*x^3 + 4*x^2 - 3*x + 1,\\\n",
    "16*x^8 - 24*x^7 + 16*x^6 - 8*x^5 + 5*x^4 - 4*x^3 + 4*x^2 - 3*x + 1,\\\n",
    "16*x^8 - 24*x^7 + 16*x^6 - 4*x^5 - x^4 - 2*x^3 + 4*x^2 - 3*x + 1,\\\n",
    "16*x^8 - 24*x^7 + 20*x^6 - 18*x^5 + 15*x^4 - 9*x^3 + 5*x^2 - 3*x + 1,\\\n",
    "16*x^8 - 24*x^7 + 20*x^6 - 16*x^5 + 13*x^4 - 8*x^3 + 5*x^2 - 3*x + 1,\\\n",
    "16*x^8 - 24*x^7 + 20*x^6 - 14*x^5 + 9*x^4 - 7*x^3 + 5*x^2 - 3*x + 1,\\\n",
    "16*x^8 - 24*x^7 + 20*x^6 - 14*x^5 + 11*x^4 - 7*x^3 + 5*x^2 - 3*x + 1,\\\n",
    "16*x^8 - 24*x^7 + 20*x^6 - 12*x^5 + 6*x^4 - 6*x^3 + 5*x^2 - 3*x + 1,\\\n",
    "16*x^8 - 24*x^7 + 20*x^6 - 12*x^5 + 7*x^4 - 6*x^3 + 5*x^2 - 3*x + 1,\\\n",
    "16*x^8 - 24*x^7 + 20*x^6 - 10*x^5 + 5*x^4 - 5*x^3 + 5*x^2 - 3*x + 1,\\\n",
    "16*x^8 - 24*x^7 + 24*x^6 - 24*x^5 + 19*x^4 - 12*x^3 + 6*x^2 - 3*x + 1,\\\n",
    "16*x^8 - 24*x^7 + 24*x^6 - 22*x^5 + 17*x^4 - 11*x^3 + 6*x^2 - 3*x + 1,\\\n",
    "16*x^8 - 24*x^7 + 24*x^6 - 20*x^5 + 14*x^4 - 10*x^3 + 6*x^2 - 3*x + 1,\\\n",
    "16*x^8 - 24*x^7 + 24*x^6 - 20*x^5 + 15*x^4 - 10*x^3 + 6*x^2 - 3*x + 1,\\\n",
    "16*x^8 - 24*x^7 + 24*x^6 - 18*x^5 + 12*x^4 - 9*x^3 + 6*x^2 - 3*x + 1,\\\n",
    "16*x^8 - 24*x^7 + 24*x^6 - 16*x^5 + 11*x^4 - 8*x^3 + 6*x^2 - 3*x + 1,\\\n",
    "16*x^8 - 24*x^7 + 28*x^6 - 26*x^5 + 19*x^4 - 13*x^3 + 7*x^2 - 3*x + 1,\\\n",
    "16*x^8 - 24*x^7 + 28*x^6 - 26*x^5 + 21*x^4 - 13*x^3 + 7*x^2 - 3*x + 1,\\\n",
    "16*x^8 - 24*x^7 + 28*x^6 - 24*x^5 + 19*x^4 - 12*x^3 + 7*x^2 - 3*x + 1,\\\n",
    "16*x^8 - 24*x^7 + 28*x^6 - 22*x^5 + 17*x^4 - 11*x^3 + 7*x^2 - 3*x + 1,\\\n",
    "16*x^8 - 24*x^7 + 32*x^6 - 28*x^5 + 23*x^4 - 14*x^3 + 8*x^2 - 3*x + 1,\\\n",
    "16*x^8 - 16*x^7 - 4*x^6 + 6*x^5 - x^4 + 3*x^3 - x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 - 4*x^5 + 9*x^4 - 2*x^3 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 2*x^5 + x^4 + x^3 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 4*x^5 - 2*x^4 + 2*x^3 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 6*x^5 - 5*x^4 + 3*x^3 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 6*x^5 - 4*x^4 + 3*x^3 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 8*x^5 - 7*x^4 + 4*x^3 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 8*x^5 - 6*x^4 + 4*x^3 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 4*x^6 - 6*x^5 + 8*x^4 - 3*x^3 + x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 4*x^6 - 4*x^5 + 5*x^4 - 2*x^3 + x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 4*x^6 - 2*x^5 + 3*x^4 - x^3 + x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 4*x^6 - 2*x^5 + 4*x^4 - x^3 + x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 4*x^6 + x^4 + x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 4*x^6 + 2*x^5 - 3*x^4 + x^3 + x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 4*x^6 + 2*x^5 - x^4 + x^3 + x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 4*x^6 + 4*x^5 - 6*x^4 + 2*x^3 + x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 4*x^6 + 4*x^5 - 5*x^4 + 2*x^3 + x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 4*x^6 + 4*x^5 - 3*x^4 + 2*x^3 + x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 4*x^6 + 6*x^5 - 9*x^4 + 3*x^3 + x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 4*x^6 + 6*x^5 - 8*x^4 + 3*x^3 + x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 4*x^6 + 6*x^5 - 7*x^4 + 3*x^3 + x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 4*x^6 + 8*x^5 - 11*x^4 + 4*x^3 + x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 4*x^6 + 8*x^5 - 10*x^4 + 4*x^3 + x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 8*x^6 - 10*x^5 + 11*x^4 - 5*x^3 + 2*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 8*x^6 - 8*x^5 + 7*x^4 - 4*x^3 + 2*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 8*x^6 - 8*x^5 + 9*x^4 - 4*x^3 + 2*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 8*x^6 - 6*x^5 + 4*x^4 - 3*x^3 + 2*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 8*x^6 - 6*x^5 + 5*x^4 - 3*x^3 + 2*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 8*x^6 - 6*x^5 + 7*x^4 - 3*x^3 + 2*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 8*x^6 - 4*x^5 + x^4 - 2*x^3 + 2*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 8*x^6 - 4*x^5 + 2*x^4 - 2*x^3 + 2*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 8*x^6 - 4*x^5 + 3*x^4 - 2*x^3 + 2*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 8*x^6 - 2*x^5 - x^4 - x^3 + 2*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 8*x^6 - 2*x^5 + x^4 - x^3 + 2*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 8*x^6 - 4*x^4 + 2*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 8*x^6 - 3*x^4 + 2*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 8*x^6 - 2*x^4 + 2*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 8*x^6 - x^4 + 2*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 8*x^6 + 2*x^5 - 5*x^4 + x^3 + 2*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 8*x^6 + 2*x^5 - 3*x^4 + x^3 + 2*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 8*x^6 + 4*x^5 - 6*x^4 + 2*x^3 + 2*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 8*x^6 + 4*x^5 - 5*x^4 + 2*x^3 + 2*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 8*x^6 + 6*x^5 - 7*x^4 + 3*x^3 + 2*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 12*x^6 - 12*x^5 + 11*x^4 - 6*x^3 + 3*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 12*x^6 - 10*x^5 + 7*x^4 - 5*x^3 + 3*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 12*x^6 - 10*x^5 + 8*x^4 - 5*x^3 + 3*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 12*x^6 - 10*x^5 + 9*x^4 - 5*x^3 + 3*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 12*x^6 - 8*x^5 + 3*x^4 - 4*x^3 + 3*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 12*x^6 - 8*x^5 + 5*x^4 - 4*x^3 + 3*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 12*x^6 - 8*x^5 + 6*x^4 - 4*x^3 + 3*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 12*x^6 - 8*x^5 + 7*x^4 - 4*x^3 + 3*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 12*x^6 - 6*x^5 + 2*x^4 - 3*x^3 + 3*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 12*x^6 - 6*x^5 + 3*x^4 - 3*x^3 + 3*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 12*x^6 - 6*x^5 + 5*x^4 - 3*x^3 + 3*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 12*x^6 - 4*x^5 + 2*x^4 - 2*x^3 + 3*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 12*x^6 - 4*x^5 + 3*x^4 - 2*x^3 + 3*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 12*x^6 - 2*x^5 - x^3 + 3*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 12*x^6 - 2*x^5 + x^4 - x^3 + 3*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 12*x^6 - x^4 + 3*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 16*x^6 - 16*x^5 + 10*x^4 - 8*x^3 + 4*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 16*x^6 - 16*x^5 + 11*x^4 - 8*x^3 + 4*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 16*x^6 - 14*x^5 + 9*x^4 - 7*x^3 + 4*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 16*x^6 - 14*x^5 + 10*x^4 - 7*x^3 + 4*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 16*x^6 - 14*x^5 + 11*x^4 - 7*x^3 + 4*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 16*x^6 - 14*x^5 + 13*x^4 - 7*x^3 + 4*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 16*x^6 - 12*x^5 + 9*x^4 - 6*x^3 + 4*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 16*x^6 - 12*x^5 + 10*x^4 - 6*x^3 + 4*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 16*x^6 - 10*x^5 + 7*x^4 - 5*x^3 + 4*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 16*x^6 - 10*x^5 + 9*x^4 - 5*x^3 + 4*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 16*x^6 - 8*x^5 + 6*x^4 - 4*x^3 + 4*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 16*x^6 - 8*x^5 + 7*x^4 - 4*x^3 + 4*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 16*x^6 - 6*x^5 + 5*x^4 - 3*x^3 + 4*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 20*x^6 - 20*x^5 + 13*x^4 - 10*x^3 + 5*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 20*x^6 - 18*x^5 + 14*x^4 - 9*x^3 + 5*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 20*x^6 - 16*x^5 + 13*x^4 - 8*x^3 + 5*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 20*x^6 - 14*x^5 + 13*x^4 - 7*x^3 + 5*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 20*x^6 - 12*x^5 + 11*x^4 - 6*x^3 + 5*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 16*x^7 + 24*x^6 - 18*x^5 + 17*x^4 - 9*x^3 + 6*x^2 - 2*x + 1,\\\n",
    "16*x^8 - 8*x^7 - 12*x^6 + 2*x^5 + 7*x^4 + x^3 - 3*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 - 12*x^6 + 4*x^5 + 5*x^4 + 2*x^3 - 3*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 - 8*x^6 + 6*x^4 - 2*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 - 8*x^6 + 7*x^4 - 2*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 - 8*x^6 + 2*x^5 + 3*x^4 + x^3 - 2*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 - 8*x^6 + 2*x^5 + 4*x^4 + x^3 - 2*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 - 8*x^6 + 4*x^5 + x^4 + 2*x^3 - 2*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 - 8*x^6 + 4*x^5 + 2*x^4 + 2*x^3 - 2*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 - 8*x^6 + 4*x^5 + 3*x^4 + 2*x^3 - 2*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 - 4*x^6 - 2*x^5 + 5*x^4 - x^3 - x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 - 4*x^6 - 2*x^5 + 7*x^4 - x^3 - x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 - 4*x^6 + 2*x^4 - x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 - 4*x^6 + 3*x^4 - x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 - 4*x^6 + 5*x^4 - x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 - 4*x^6 + 2*x^5 - x^4 + x^3 - x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 - 4*x^6 + 2*x^5 + x^3 - x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 - 4*x^6 + 2*x^5 + x^4 + x^3 - x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 - 4*x^6 + 2*x^5 + 3*x^4 + x^3 - x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 - 4*x^6 + 4*x^5 - 3*x^4 + 2*x^3 - x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 - 4*x^6 + 4*x^5 - x^4 + 2*x^3 - x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 - 4*x^6 + 4*x^5 + x^4 + 2*x^3 - x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 - 4*x^6 + 6*x^5 - x^4 + 3*x^3 - x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 - 4*x^5 + 4*x^4 - 2*x^3 - x + 1,\\\n",
    "16*x^8 - 8*x^7 - 4*x^5 + 5*x^4 - 2*x^3 - x + 1,\\\n",
    "16*x^8 - 8*x^7 - 4*x^5 + 6*x^4 - 2*x^3 - x + 1,\\\n",
    "16*x^8 - 8*x^7 - 4*x^5 + 7*x^4 - 2*x^3 - x + 1,\\\n",
    "16*x^8 - 8*x^7 - 2*x^5 + x^4 - x^3 - x + 1,\\\n",
    "16*x^8 - 8*x^7 - 2*x^5 + 2*x^4 - x^3 - x + 1,\\\n",
    "16*x^8 - 8*x^7 - 2*x^5 + 4*x^4 - x^3 - x + 1,\\\n",
    "16*x^8 - 8*x^7 - 2*x^5 + 5*x^4 - x^3 - x + 1,\\\n",
    "16*x^8 - 8*x^7 - 2*x^4 - x + 1,\\\n",
    "16*x^8 - 8*x^7 - x^4 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + x^4 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 2*x^4 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 3*x^4 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 2*x^5 - 5*x^4 + x^3 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 2*x^5 - 4*x^4 + x^3 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 2*x^5 - 3*x^4 + x^3 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 2*x^5 - 2*x^4 + x^3 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 2*x^5 + x^3 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 2*x^5 + x^4 + x^3 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 4*x^5 - 7*x^4 + 2*x^3 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 4*x^5 - 6*x^4 + 2*x^3 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 4*x^5 - 5*x^4 + 2*x^3 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 4*x^5 - 4*x^4 + 2*x^3 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 4*x^5 - 3*x^4 + 2*x^3 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 4*x^5 - 2*x^4 + 2*x^3 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 4*x^5 - x^4 + 2*x^3 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 6*x^5 - 5*x^4 + 3*x^3 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 6*x^5 - 4*x^4 + 3*x^3 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 4*x^6 - 8*x^5 + 5*x^4 - 4*x^3 + x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 4*x^6 - 6*x^5 + 3*x^4 - 3*x^3 + x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 4*x^6 - 6*x^5 + 5*x^4 - 3*x^3 + x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 4*x^6 - 6*x^5 + 7*x^4 - 3*x^3 + x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 4*x^6 - 4*x^5 - 2*x^3 + x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 4*x^6 - 4*x^5 + x^4 - 2*x^3 + x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 4*x^6 - 4*x^5 + 3*x^4 - 2*x^3 + x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 4*x^6 - 4*x^5 + 4*x^4 - 2*x^3 + x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 4*x^6 - 4*x^5 + 6*x^4 - 2*x^3 + x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 4*x^6 - 4*x^5 + 7*x^4 - 2*x^3 + x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 4*x^6 - 2*x^5 - 3*x^4 - x^3 + x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 4*x^6 - 2*x^5 - x^4 - x^3 + x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 4*x^6 - 2*x^5 - x^3 + x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 4*x^6 - 2*x^5 + x^4 - x^3 + x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 4*x^6 - 2*x^5 + 2*x^4 - x^3 + x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 4*x^6 - 2*x^5 + 3*x^4 - x^3 + x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 4*x^6 - 2*x^5 + 4*x^4 - x^3 + x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 4*x^6 - 2*x^5 + 5*x^4 - x^3 + x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 4*x^6 - 5*x^4 + x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 4*x^6 - 2*x^4 + x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 4*x^6 - x^4 + x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 4*x^6 + x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 4*x^6 + x^4 + x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 4*x^6 + 3*x^4 + x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 4*x^6 + 2*x^5 - 5*x^4 + x^3 + x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 4*x^6 + 2*x^5 - 3*x^4 + x^3 + x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 4*x^6 + 2*x^5 - 2*x^4 + x^3 + x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 4*x^6 + 2*x^5 - x^4 + x^3 + x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 4*x^6 + 2*x^5 + x^4 + x^3 + x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 4*x^6 + 4*x^5 - 3*x^4 + 2*x^3 + x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 4*x^6 + 4*x^5 - 2*x^4 + 2*x^3 + x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 4*x^6 + 4*x^5 - x^4 + 2*x^3 + x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 4*x^6 + 6*x^5 - 5*x^4 + 3*x^3 + x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 4*x^6 + 6*x^5 - 3*x^4 + 3*x^3 + x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 4*x^6 + 8*x^5 - 6*x^4 + 4*x^3 + x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 4*x^6 + 8*x^5 - 5*x^4 + 4*x^3 + x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 8*x^6 - 10*x^5 + 4*x^4 - 5*x^3 + 2*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 8*x^6 - 10*x^5 + 6*x^4 - 5*x^3 + 2*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 8*x^6 - 8*x^5 + x^4 - 4*x^3 + 2*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 8*x^6 - 8*x^5 + 2*x^4 - 4*x^3 + 2*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 8*x^6 - 8*x^5 + 3*x^4 - 4*x^3 + 2*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 8*x^6 - 8*x^5 + 5*x^4 - 4*x^3 + 2*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 8*x^6 - 8*x^5 + 7*x^4 - 4*x^3 + 2*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 8*x^6 - 6*x^5 + x^4 - 3*x^3 + 2*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 8*x^6 - 6*x^5 + 2*x^4 - 3*x^3 + 2*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 8*x^6 - 6*x^5 + 4*x^4 - 3*x^3 + 2*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 8*x^6 - 6*x^5 + 5*x^4 - 3*x^3 + 2*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 8*x^6 - 6*x^5 + 8*x^4 - 3*x^3 + 2*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 8*x^6 - 4*x^5 + x^4 - 2*x^3 + 2*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 8*x^6 - 4*x^5 + 3*x^4 - 2*x^3 + 2*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 8*x^6 - 4*x^5 + 4*x^4 - 2*x^3 + 2*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 8*x^6 - 4*x^5 + 5*x^4 - 2*x^3 + 2*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 8*x^6 - 4*x^5 + 6*x^4 - 2*x^3 + 2*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 8*x^6 - 4*x^5 + 7*x^4 - 2*x^3 + 2*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 8*x^6 - 2*x^5 + 2*x^4 - x^3 + 2*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 8*x^6 - 2*x^5 + 4*x^4 - x^3 + 2*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 8*x^6 - x^4 + 2*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 8*x^6 + x^4 + 2*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 8*x^6 + 2*x^4 + 2*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 8*x^6 + 3*x^4 + 2*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 8*x^6 + 2*x^5 + x^4 + x^3 + 2*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 8*x^6 + 4*x^5 - x^4 + 2*x^3 + 2*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 12*x^6 - 12*x^5 + 5*x^4 - 6*x^3 + 3*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 12*x^6 - 10*x^5 + 5*x^4 - 5*x^3 + 3*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 12*x^6 - 10*x^5 + 6*x^4 - 5*x^3 + 3*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 12*x^6 - 10*x^5 + 7*x^4 - 5*x^3 + 3*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 12*x^6 - 8*x^5 + 5*x^4 - 4*x^3 + 3*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 12*x^6 - 8*x^5 + 6*x^4 - 4*x^3 + 3*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 12*x^6 - 8*x^5 + 8*x^4 - 4*x^3 + 3*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 12*x^6 - 6*x^5 + 5*x^4 - 3*x^3 + 3*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 12*x^6 - 6*x^5 + 7*x^4 - 3*x^3 + 3*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 12*x^6 - 6*x^5 + 8*x^4 - 3*x^3 + 3*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 12*x^6 - 6*x^5 + 9*x^4 - 3*x^3 + 3*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 12*x^6 - 4*x^5 + 6*x^4 - 2*x^3 + 3*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 12*x^6 - 4*x^5 + 7*x^4 - 2*x^3 + 3*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 12*x^6 - 2*x^5 + 3*x^4 - x^3 + 3*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 12*x^6 - 2*x^5 + 5*x^4 - x^3 + 3*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 12*x^6 + 2*x^5 + 3*x^4 + x^3 + 3*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 16*x^6 - 12*x^5 + 9*x^4 - 6*x^3 + 4*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 16*x^6 - 10*x^5 + 10*x^4 - 5*x^3 + 4*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 16*x^6 - 8*x^5 + 9*x^4 - 4*x^3 + 4*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 16*x^6 - 8*x^5 + 11*x^4 - 4*x^3 + 4*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 16*x^6 - 4*x^5 + 9*x^4 - 2*x^3 + 4*x^2 - x + 1,\\\n",
    "16*x^8 - 8*x^7 + 20*x^6 - 10*x^5 + 13*x^4 - 5*x^3 + 5*x^2 - x + 1,\\\n",
    "16*x^8 - 20*x^6 + 13*x^4 - 5*x^2 + 1,\\\n",
    "16*x^8 - 16*x^6 + 9*x^4 - 4*x^2 + 1,\\\n",
    "16*x^8 - 16*x^6 + 10*x^4 - 4*x^2 + 1,\\\n",
    "16*x^8 - 12*x^6 - 2*x^5 + 7*x^4 - x^3 - 3*x^2 + 1,\\\n",
    "16*x^8 - 12*x^6 + 6*x^4 - 3*x^2 + 1,\\\n",
    "16*x^8 - 12*x^6 + 7*x^4 - 3*x^2 + 1,\\\n",
    "16*x^8 - 12*x^6 + 9*x^4 - 3*x^2 + 1,\\\n",
    "16*x^8 - 12*x^6 + 2*x^5 + 7*x^4 + x^3 - 3*x^2 + 1,\\\n",
    "16*x^8 - 8*x^6 - 2*x^5 + 3*x^4 - x^3 - 2*x^2 + 1,\\\n",
    "16*x^8 - 8*x^6 - 2*x^5 + 5*x^4 - x^3 - 2*x^2 + 1,\\\n",
    "16*x^8 - 8*x^6 + x^4 - 2*x^2 + 1,\\\n",
    "16*x^8 - 8*x^6 + 2*x^4 - 2*x^2 + 1,\\\n",
    "16*x^8 - 8*x^6 + 3*x^4 - 2*x^2 + 1,\\\n",
    "16*x^8 - 8*x^6 + 4*x^4 - 2*x^2 + 1,\\\n",
    "16*x^8 - 8*x^6 + 6*x^4 - 2*x^2 + 1,\\\n",
    "16*x^8 - 8*x^6 + 7*x^4 - 2*x^2 + 1,\\\n",
    "16*x^8 - 8*x^6 + 2*x^5 + 3*x^4 + x^3 - 2*x^2 + 1,\\\n",
    "16*x^8 - 8*x^6 + 2*x^5 + 5*x^4 + x^3 - 2*x^2 + 1,\\\n",
    "16*x^8 - 4*x^6 - 4*x^5 + 2*x^4 - 2*x^3 - x^2 + 1,\\\n",
    "16*x^8 - 4*x^6 - 2*x^5 - x^4 - x^3 - x^2 + 1,\\\n",
    "16*x^8 - 4*x^6 - 2*x^5 - x^3 - x^2 + 1,\\\n",
    "16*x^8 - 4*x^6 - 2*x^5 + x^4 - x^3 - x^2 + 1,\\\n",
    "16*x^8 - 4*x^6 - 2*x^5 + 2*x^4 - x^3 - x^2 + 1,\\\n",
    "16*x^8 - 4*x^6 - 2*x^5 + 3*x^4 - x^3 - x^2 + 1,\\\n",
    "16*x^8 - 4*x^6 - 2*x^5 + 4*x^4 - x^3 - x^2 + 1,\\\n",
    "16*x^8 - 4*x^6 - 2*x^5 + 5*x^4 - x^3 - x^2 + 1,\\\n",
    "16*x^8 - 4*x^6 - 3*x^4 - x^2 + 1,\\\n",
    "16*x^8 - 4*x^6 - 2*x^4 - x^2 + 1,\\\n",
    "16*x^8 - 4*x^6 - x^4 - x^2 + 1,\\\n",
    "16*x^8 - 4*x^6 - x^2 + 1,\\\n",
    "16*x^8 - 4*x^6 + x^4 - x^2 + 1,\\\n",
    "16*x^8 - 4*x^6 + 3*x^4 - x^2 + 1,\\\n",
    "16*x^8 - 4*x^6 + 5*x^4 - x^2 + 1,\\\n",
    "16*x^8 - 4*x^6 + 7*x^4 - x^2 + 1,\\\n",
    "16*x^8 - 4*x^6 + 2*x^5 - x^4 + x^3 - x^2 + 1,\\\n",
    "16*x^8 - 4*x^6 + 2*x^5 + x^3 - x^2 + 1,\\\n",
    "16*x^8 - 4*x^6 + 2*x^5 + x^4 + x^3 - x^2 + 1,\\\n",
    "16*x^8 - 4*x^6 + 2*x^5 + 2*x^4 + x^3 - x^2 + 1,\\\n",
    "16*x^8 - 4*x^6 + 2*x^5 + 3*x^4 + x^3 - x^2 + 1,\\\n",
    "16*x^8 - 4*x^6 + 2*x^5 + 4*x^4 + x^3 - x^2 + 1,\\\n",
    "16*x^8 - 4*x^6 + 2*x^5 + 5*x^4 + x^3 - x^2 + 1,\\\n",
    "16*x^8 - 4*x^6 + 4*x^5 + 2*x^4 + 2*x^3 - x^2 + 1,\\\n",
    "16*x^8 - 6*x^5 + x^4 - 3*x^3 + 1,\\\n",
    "16*x^8 - 4*x^5 - 2*x^4 - 2*x^3 + 1,\\\n",
    "16*x^8 - 4*x^5 - x^4 - 2*x^3 + 1,\\\n",
    "16*x^8 - 4*x^5 - 2*x^3 + 1,\\\n",
    "16*x^8 - 4*x^5 + 2*x^4 - 2*x^3 + 1,\\\n",
    "16*x^8 - 4*x^5 + 3*x^4 - 2*x^3 + 1,\\\n",
    "16*x^8 - 2*x^5 - 5*x^4 - x^3 + 1,\\\n",
    "16*x^8 - 2*x^5 - 4*x^4 - x^3 + 1,\\\n",
    "16*x^8 - 2*x^5 - 3*x^4 - x^3 + 1,\\\n",
    "16*x^8 - 2*x^5 - x^4 - x^3 + 1,\\\n",
    "16*x^8 - 2*x^5 + x^4 - x^3 + 1,\\\n",
    "16*x^8 - 2*x^5 + 2*x^4 - x^3 + 1,\\\n",
    "16*x^8 - 2*x^5 + 3*x^4 - x^3 + 1,\\\n",
    "16*x^8 - 2*x^5 + 5*x^4 - x^3 + 1,\\\n",
    "16*x^8 - 7*x^4 + 1,\\\n",
    "16*x^8 - 6*x^4 + 1,\\\n",
    "16*x^8 - 5*x^4 + 1,\\\n",
    "16*x^8 - 3*x^4 + 1,\\\n",
    "16*x^8 - 2*x^4 + 1,\\\n",
    "16*x^8 + 1,\\\n",
    "16*x^8 + x^4 + 1,\\\n",
    "16*x^8 + 2*x^4 + 1,\\\n",
    "16*x^8 + 3*x^4 + 1,\\\n",
    "16*x^8 + 5*x^4 + 1,\\\n",
    "16*x^8 + 6*x^4 + 1,\\\n",
    "16*x^8 + 2*x^5 - 5*x^4 + x^3 + 1,\\\n",
    "16*x^8 + 2*x^5 - 4*x^4 + x^3 + 1,\\\n",
    "16*x^8 + 2*x^5 - 3*x^4 + x^3 + 1,\\\n",
    "16*x^8 + 2*x^5 - x^4 + x^3 + 1,\\\n",
    "16*x^8 + 2*x^5 + x^4 + x^3 + 1,\\\n",
    "16*x^8 + 2*x^5 + 2*x^4 + x^3 + 1,\\\n",
    "16*x^8 + 2*x^5 + 3*x^4 + x^3 + 1,\\\n",
    "16*x^8 + 2*x^5 + 5*x^4 + x^3 + 1,\\\n",
    "16*x^8 + 4*x^5 - 2*x^4 + 2*x^3 + 1,\\\n",
    "16*x^8 + 4*x^5 - x^4 + 2*x^3 + 1,\\\n",
    "16*x^8 + 4*x^5 + 2*x^3 + 1,\\\n",
    "16*x^8 + 4*x^5 + 2*x^4 + 2*x^3 + 1,\\\n",
    "16*x^8 + 4*x^5 + 3*x^4 + 2*x^3 + 1,\\\n",
    "16*x^8 + 6*x^5 + x^4 + 3*x^3 + 1,\\\n",
    "16*x^8 + 4*x^6 - 6*x^5 - 3*x^4 - 3*x^3 + x^2 + 1,\\\n",
    "16*x^8 + 4*x^6 - 6*x^5 - 2*x^4 - 3*x^3 + x^2 + 1,\\\n",
    "16*x^8 + 4*x^6 - 6*x^5 - 3*x^3 + x^2 + 1,\\\n",
    "16*x^8 + 4*x^6 - 6*x^5 + x^4 - 3*x^3 + x^2 + 1,\\\n",
    "16*x^8 + 4*x^6 - 4*x^5 - 3*x^4 - 2*x^3 + x^2 + 1,\\\n",
    "16*x^8 + 4*x^6 - 4*x^5 - x^4 - 2*x^3 + x^2 + 1,\\\n",
    "16*x^8 + 4*x^6 - 4*x^5 + x^4 - 2*x^3 + x^2 + 1,\\\n",
    "16*x^8 + 4*x^6 - 4*x^5 + 2*x^4 - 2*x^3 + x^2 + 1,\\\n",
    "16*x^8 + 4*x^6 - 4*x^5 + 3*x^4 - 2*x^3 + x^2 + 1,\\\n",
    "16*x^8 + 4*x^6 - 2*x^5 - 3*x^4 - x^3 + x^2 + 1,\\\n",
    "16*x^8 + 4*x^6 - 2*x^5 - 2*x^4 - x^3 + x^2 + 1,\\\n",
    "16*x^8 + 4*x^6 - 2*x^5 - x^4 - x^3 + x^2 + 1,\\\n",
    "16*x^8 + 4*x^6 - 2*x^5 - x^3 + x^2 + 1,\\\n",
    "16*x^8 + 4*x^6 - 2*x^5 + 2*x^4 - x^3 + x^2 + 1,\\\n",
    "16*x^8 + 4*x^6 - 2*x^5 + 4*x^4 - x^3 + x^2 + 1,\\\n",
    "16*x^8 + 4*x^6 - 2*x^5 + 5*x^4 - x^3 + x^2 + 1,\\\n",
    "16*x^8 + 4*x^6 - 2*x^4 + x^2 + 1,\\\n",
    "16*x^8 + 4*x^6 - x^4 + x^2 + 1,\\\n",
    "16*x^8 + 4*x^6 + x^2 + 1,\\\n",
    "16*x^8 + 4*x^6 + x^4 + x^2 + 1,\\\n",
    "16*x^8 + 4*x^6 + 3*x^4 + x^2 + 1,\\\n",
    "16*x^8 + 4*x^6 + 4*x^4 + x^2 + 1,\\\n",
    "16*x^8 + 4*x^6 + 7*x^4 + x^2 + 1,\\\n",
    "16*x^8 + 4*x^6 + 2*x^5 - 3*x^4 + x^3 + x^2 + 1,\\\n",
    "16*x^8 + 4*x^6 + 2*x^5 - 2*x^4 + x^3 + x^2 + 1,\\\n",
    "16*x^8 + 4*x^6 + 2*x^5 - x^4 + x^3 + x^2 + 1,\\\n",
    "16*x^8 + 4*x^6 + 2*x^5 + x^3 + x^2 + 1,\\\n",
    "16*x^8 + 4*x^6 + 2*x^5 + 2*x^4 + x^3 + x^2 + 1,\\\n",
    "16*x^8 + 4*x^6 + 2*x^5 + 4*x^4 + x^3 + x^2 + 1,\\\n",
    "16*x^8 + 4*x^6 + 2*x^5 + 5*x^4 + x^3 + x^2 + 1,\\\n",
    "16*x^8 + 4*x^6 + 4*x^5 - 3*x^4 + 2*x^3 + x^2 + 1,\\\n",
    "16*x^8 + 4*x^6 + 4*x^5 - x^4 + 2*x^3 + x^2 + 1,\\\n",
    "16*x^8 + 4*x^6 + 4*x^5 + x^4 + 2*x^3 + x^2 + 1,\\\n",
    "16*x^8 + 4*x^6 + 4*x^5 + 2*x^4 + 2*x^3 + x^2 + 1,\\\n",
    "16*x^8 + 4*x^6 + 4*x^5 + 3*x^4 + 2*x^3 + x^2 + 1,\\\n",
    "16*x^8 + 4*x^6 + 6*x^5 - 3*x^4 + 3*x^3 + x^2 + 1,\\\n",
    "16*x^8 + 4*x^6 + 6*x^5 - 2*x^4 + 3*x^3 + x^2 + 1,\\\n",
    "16*x^8 + 4*x^6 + 6*x^5 + 3*x^3 + x^2 + 1,\\\n",
    "16*x^8 + 4*x^6 + 6*x^5 + x^4 + 3*x^3 + x^2 + 1,\\\n",
    "16*x^8 + 8*x^6 - 10*x^5 - x^4 - 5*x^3 + 2*x^2 + 1,\\\n",
    "16*x^8 + 8*x^6 - 8*x^5 + 2*x^4 - 4*x^3 + 2*x^2 + 1,\\\n",
    "16*x^8 + 8*x^6 - 6*x^5 + x^4 - 3*x^3 + 2*x^2 + 1,\\\n",
    "16*x^8 + 8*x^6 - 6*x^5 + 3*x^4 - 3*x^3 + 2*x^2 + 1,\\\n",
    "16*x^8 + 8*x^6 - 4*x^5 + x^4 - 2*x^3 + 2*x^2 + 1,\\\n",
    "16*x^8 + 8*x^6 - 4*x^5 + 2*x^4 - 2*x^3 + 2*x^2 + 1,\\\n",
    "16*x^8 + 8*x^6 - 4*x^5 + 5*x^4 - 2*x^3 + 2*x^2 + 1,\\\n",
    "16*x^8 + 8*x^6 - 2*x^5 + x^4 - x^3 + 2*x^2 + 1,\\\n",
    "16*x^8 + 8*x^6 - 2*x^5 + 2*x^4 - x^3 + 2*x^2 + 1,\\\n",
    "16*x^8 + 8*x^6 - 2*x^5 + 3*x^4 - x^3 + 2*x^2 + 1,\\\n",
    "16*x^8 + 8*x^6 - 2*x^5 + 5*x^4 - x^3 + 2*x^2 + 1,\\\n",
    "16*x^8 + 8*x^6 - 2*x^5 + 7*x^4 - x^3 + 2*x^2 + 1,\\\n",
    "16*x^8 + 8*x^6 + 2*x^4 + 2*x^2 + 1,\\\n",
    "16*x^8 + 8*x^6 + 3*x^4 + 2*x^2 + 1,\\\n",
    "16*x^8 + 8*x^6 + 4*x^4 + 2*x^2 + 1,\\\n",
    "16*x^8 + 8*x^6 + 6*x^4 + 2*x^2 + 1,\\\n",
    "16*x^8 + 8*x^6 + 7*x^4 + 2*x^2 + 1,\\\n",
    "16*x^8 + 8*x^6 + 2*x^5 + x^4 + x^3 + 2*x^2 + 1,\\\n",
    "16*x^8 + 8*x^6 + 2*x^5 + 2*x^4 + x^3 + 2*x^2 + 1,\\\n",
    "16*x^8 + 8*x^6 + 2*x^5 + 3*x^4 + x^3 + 2*x^2 + 1,\\\n",
    "16*x^8 + 8*x^6 + 2*x^5 + 5*x^4 + x^3 + 2*x^2 + 1,\\\n",
    "16*x^8 + 8*x^6 + 2*x^5 + 7*x^4 + x^3 + 2*x^2 + 1,\\\n",
    "16*x^8 + 8*x^6 + 4*x^5 + x^4 + 2*x^3 + 2*x^2 + 1,\\\n",
    "16*x^8 + 8*x^6 + 4*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 1,\\\n",
    "16*x^8 + 8*x^6 + 4*x^5 + 5*x^4 + 2*x^3 + 2*x^2 + 1,\\\n",
    "16*x^8 + 8*x^6 + 6*x^5 + x^4 + 3*x^3 + 2*x^2 + 1,\\\n",
    "16*x^8 + 8*x^6 + 6*x^5 + 3*x^4 + 3*x^3 + 2*x^2 + 1,\\\n",
    "16*x^8 + 8*x^6 + 8*x^5 + 2*x^4 + 4*x^3 + 2*x^2 + 1,\\\n",
    "16*x^8 + 8*x^6 + 10*x^5 - x^4 + 5*x^3 + 2*x^2 + 1,\\\n",
    "16*x^8 + 12*x^6 - 4*x^5 + 5*x^4 - 2*x^3 + 3*x^2 + 1,\\\n",
    "16*x^8 + 12*x^6 - 2*x^5 + 5*x^4 - x^3 + 3*x^2 + 1,\\\n",
    "16*x^8 + 12*x^6 - 2*x^5 + 8*x^4 - x^3 + 3*x^2 + 1,\\\n",
    "16*x^8 + 12*x^6 + 5*x^4 + 3*x^2 + 1,\\\n",
    "16*x^8 + 12*x^6 + 6*x^4 + 3*x^2 + 1,\\\n",
    "16*x^8 + 12*x^6 + 7*x^4 + 3*x^2 + 1,\\\n",
    "16*x^8 + 12*x^6 + 9*x^4 + 3*x^2 + 1,\\\n",
    "16*x^8 + 12*x^6 + 2*x^5 + 5*x^4 + x^3 + 3*x^2 + 1,\\\n",
    "16*x^8 + 12*x^6 + 2*x^5 + 8*x^4 + x^3 + 3*x^2 + 1,\\\n",
    "16*x^8 + 12*x^6 + 4*x^5 + 5*x^4 + 2*x^3 + 3*x^2 + 1,\\\n",
    "16*x^8 + 16*x^6 - 2*x^5 + 9*x^4 - x^3 + 4*x^2 + 1,\\\n",
    "16*x^8 + 16*x^6 + 9*x^4 + 4*x^2 + 1,\\\n",
    "16*x^8 + 16*x^6 + 10*x^4 + 4*x^2 + 1,\\\n",
    "16*x^8 + 16*x^6 + 2*x^5 + 9*x^4 + x^3 + 4*x^2 + 1,\\\n",
    "16*x^8 + 8*x^7 - 12*x^6 - 4*x^5 + 5*x^4 - 2*x^3 - 3*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 - 12*x^6 - 2*x^5 + 7*x^4 - x^3 - 3*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 - 8*x^6 - 4*x^5 + x^4 - 2*x^3 - 2*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 - 8*x^6 - 4*x^5 + 2*x^4 - 2*x^3 - 2*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 - 8*x^6 - 4*x^5 + 3*x^4 - 2*x^3 - 2*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 - 8*x^6 - 2*x^5 + 3*x^4 - x^3 - 2*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 - 8*x^6 - 2*x^5 + 4*x^4 - x^3 - 2*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 - 8*x^6 + 6*x^4 - 2*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 - 8*x^6 + 7*x^4 - 2*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 - 4*x^6 - 6*x^5 - x^4 - 3*x^3 - x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 - 4*x^6 - 4*x^5 - 3*x^4 - 2*x^3 - x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 - 4*x^6 - 4*x^5 - x^4 - 2*x^3 - x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 - 4*x^6 - 4*x^5 + x^4 - 2*x^3 - x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 - 4*x^6 - 2*x^5 - x^4 - x^3 - x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 - 4*x^6 - 2*x^5 - x^3 - x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 - 4*x^6 - 2*x^5 + x^4 - x^3 - x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 - 4*x^6 - 2*x^5 + 3*x^4 - x^3 - x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 - 4*x^6 + 2*x^4 - x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 - 4*x^6 + 3*x^4 - x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 - 4*x^6 + 5*x^4 - x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 - 4*x^6 + 2*x^5 + 5*x^4 + x^3 - x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 - 4*x^6 + 2*x^5 + 7*x^4 + x^3 - x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 - 6*x^5 - 5*x^4 - 3*x^3 + x + 1,\\\n",
    "16*x^8 + 8*x^7 - 6*x^5 - 4*x^4 - 3*x^3 + x + 1,\\\n",
    "16*x^8 + 8*x^7 - 4*x^5 - 7*x^4 - 2*x^3 + x + 1,\\\n",
    "16*x^8 + 8*x^7 - 4*x^5 - 6*x^4 - 2*x^3 + x + 1,\\\n",
    "16*x^8 + 8*x^7 - 4*x^5 - 5*x^4 - 2*x^3 + x + 1,\\\n",
    "16*x^8 + 8*x^7 - 4*x^5 - 4*x^4 - 2*x^3 + x + 1,\\\n",
    "16*x^8 + 8*x^7 - 4*x^5 - 3*x^4 - 2*x^3 + x + 1,\\\n",
    "16*x^8 + 8*x^7 - 4*x^5 - 2*x^4 - 2*x^3 + x + 1,\\\n",
    "16*x^8 + 8*x^7 - 4*x^5 - x^4 - 2*x^3 + x + 1,\\\n",
    "16*x^8 + 8*x^7 - 2*x^5 - 5*x^4 - x^3 + x + 1,\\\n",
    "16*x^8 + 8*x^7 - 2*x^5 - 4*x^4 - x^3 + x + 1,\\\n",
    "16*x^8 + 8*x^7 - 2*x^5 - 3*x^4 - x^3 + x + 1,\\\n",
    "16*x^8 + 8*x^7 - 2*x^5 - 2*x^4 - x^3 + x + 1,\\\n",
    "16*x^8 + 8*x^7 - 2*x^5 - x^3 + x + 1,\\\n",
    "16*x^8 + 8*x^7 - 2*x^5 + x^4 - x^3 + x + 1,\\\n",
    "16*x^8 + 8*x^7 - 2*x^4 + x + 1,\\\n",
    "16*x^8 + 8*x^7 - x^4 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + x^4 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 2*x^4 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 3*x^4 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 2*x^5 + x^4 + x^3 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 2*x^5 + 2*x^4 + x^3 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 2*x^5 + 4*x^4 + x^3 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 2*x^5 + 5*x^4 + x^3 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 4*x^5 + 4*x^4 + 2*x^3 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 4*x^5 + 5*x^4 + 2*x^3 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 4*x^5 + 6*x^4 + 2*x^3 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 4*x^5 + 7*x^4 + 2*x^3 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 4*x^6 - 8*x^5 - 6*x^4 - 4*x^3 + x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 4*x^6 - 8*x^5 - 5*x^4 - 4*x^3 + x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 4*x^6 - 6*x^5 - 5*x^4 - 3*x^3 + x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 4*x^6 - 6*x^5 - 3*x^4 - 3*x^3 + x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 4*x^6 - 4*x^5 - 3*x^4 - 2*x^3 + x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 4*x^6 - 4*x^5 - 2*x^4 - 2*x^3 + x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 4*x^6 - 4*x^5 - x^4 - 2*x^3 + x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 4*x^6 - 2*x^5 - 5*x^4 - x^3 + x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 4*x^6 - 2*x^5 - 3*x^4 - x^3 + x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 4*x^6 - 2*x^5 - 2*x^4 - x^3 + x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 4*x^6 - 2*x^5 - x^4 - x^3 + x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 4*x^6 - 2*x^5 + x^4 - x^3 + x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 4*x^6 - 5*x^4 + x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 4*x^6 - 2*x^4 + x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 4*x^6 - x^4 + x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 4*x^6 + x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 4*x^6 + x^4 + x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 4*x^6 + 3*x^4 + x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 4*x^6 + 2*x^5 - 3*x^4 + x^3 + x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 4*x^6 + 2*x^5 - x^4 + x^3 + x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 4*x^6 + 2*x^5 + x^3 + x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 4*x^6 + 2*x^5 + x^4 + x^3 + x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 4*x^6 + 2*x^5 + 2*x^4 + x^3 + x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 4*x^6 + 2*x^5 + 3*x^4 + x^3 + x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 4*x^6 + 2*x^5 + 4*x^4 + x^3 + x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 4*x^6 + 2*x^5 + 5*x^4 + x^3 + x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 4*x^6 + 4*x^5 + 2*x^3 + x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 4*x^6 + 4*x^5 + x^4 + 2*x^3 + x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 4*x^6 + 4*x^5 + 3*x^4 + 2*x^3 + x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 4*x^6 + 4*x^5 + 4*x^4 + 2*x^3 + x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 4*x^6 + 4*x^5 + 6*x^4 + 2*x^3 + x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 4*x^6 + 4*x^5 + 7*x^4 + 2*x^3 + x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 4*x^6 + 6*x^5 + 3*x^4 + 3*x^3 + x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 4*x^6 + 6*x^5 + 5*x^4 + 3*x^3 + x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 4*x^6 + 6*x^5 + 7*x^4 + 3*x^3 + x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 4*x^6 + 8*x^5 + 5*x^4 + 4*x^3 + x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 8*x^6 - 4*x^5 - x^4 - 2*x^3 + 2*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 8*x^6 - 2*x^5 + x^4 - x^3 + 2*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 8*x^6 - x^4 + 2*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 8*x^6 + x^4 + 2*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 8*x^6 + 2*x^4 + 2*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 8*x^6 + 3*x^4 + 2*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 8*x^6 + 2*x^5 + 2*x^4 + x^3 + 2*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 8*x^6 + 2*x^5 + 4*x^4 + x^3 + 2*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 8*x^6 + 4*x^5 + x^4 + 2*x^3 + 2*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 8*x^6 + 4*x^5 + 3*x^4 + 2*x^3 + 2*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 8*x^6 + 4*x^5 + 4*x^4 + 2*x^3 + 2*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 8*x^6 + 4*x^5 + 5*x^4 + 2*x^3 + 2*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 8*x^6 + 4*x^5 + 6*x^4 + 2*x^3 + 2*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 8*x^6 + 4*x^5 + 7*x^4 + 2*x^3 + 2*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 8*x^6 + 6*x^5 + x^4 + 3*x^3 + 2*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 8*x^6 + 6*x^5 + 2*x^4 + 3*x^3 + 2*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 8*x^6 + 6*x^5 + 4*x^4 + 3*x^3 + 2*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 8*x^6 + 6*x^5 + 5*x^4 + 3*x^3 + 2*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 8*x^6 + 6*x^5 + 8*x^4 + 3*x^3 + 2*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 8*x^6 + 8*x^5 + x^4 + 4*x^3 + 2*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 8*x^6 + 8*x^5 + 2*x^4 + 4*x^3 + 2*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 8*x^6 + 8*x^5 + 3*x^4 + 4*x^3 + 2*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 8*x^6 + 8*x^5 + 5*x^4 + 4*x^3 + 2*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 8*x^6 + 8*x^5 + 7*x^4 + 4*x^3 + 2*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 8*x^6 + 10*x^5 + 4*x^4 + 5*x^3 + 2*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 8*x^6 + 10*x^5 + 6*x^4 + 5*x^3 + 2*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 12*x^6 - 2*x^5 + 3*x^4 - x^3 + 3*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 12*x^6 + 2*x^5 + 3*x^4 + x^3 + 3*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 12*x^6 + 2*x^5 + 5*x^4 + x^3 + 3*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 12*x^6 + 4*x^5 + 6*x^4 + 2*x^3 + 3*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 12*x^6 + 4*x^5 + 7*x^4 + 2*x^3 + 3*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 12*x^6 + 6*x^5 + 5*x^4 + 3*x^3 + 3*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 12*x^6 + 6*x^5 + 7*x^4 + 3*x^3 + 3*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 12*x^6 + 6*x^5 + 8*x^4 + 3*x^3 + 3*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 12*x^6 + 6*x^5 + 9*x^4 + 3*x^3 + 3*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 12*x^6 + 8*x^5 + 5*x^4 + 4*x^3 + 3*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 12*x^6 + 8*x^5 + 6*x^4 + 4*x^3 + 3*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 12*x^6 + 8*x^5 + 8*x^4 + 4*x^3 + 3*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 12*x^6 + 10*x^5 + 5*x^4 + 5*x^3 + 3*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 12*x^6 + 10*x^5 + 6*x^4 + 5*x^3 + 3*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 12*x^6 + 10*x^5 + 7*x^4 + 5*x^3 + 3*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 12*x^6 + 12*x^5 + 5*x^4 + 6*x^3 + 3*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 16*x^6 + 4*x^5 + 9*x^4 + 2*x^3 + 4*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 16*x^6 + 8*x^5 + 9*x^4 + 4*x^3 + 4*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 16*x^6 + 8*x^5 + 11*x^4 + 4*x^3 + 4*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 16*x^6 + 10*x^5 + 10*x^4 + 5*x^3 + 4*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 16*x^6 + 12*x^5 + 9*x^4 + 6*x^3 + 4*x^2 + x + 1,\\\n",
    "16*x^8 + 8*x^7 + 20*x^6 + 10*x^5 + 13*x^4 + 5*x^3 + 5*x^2 + x + 1,\\\n",
    "16*x^8 + 16*x^7 - 4*x^6 - 6*x^5 - x^4 - 3*x^3 - x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 - 8*x^5 - 7*x^4 - 4*x^3 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 - 8*x^5 - 6*x^4 - 4*x^3 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 - 6*x^5 - 5*x^4 - 3*x^3 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 - 6*x^5 - 4*x^4 - 3*x^3 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 - 4*x^5 - 2*x^4 - 2*x^3 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 - 2*x^5 + x^4 - x^3 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 4*x^5 + 9*x^4 + 2*x^3 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 4*x^6 - 8*x^5 - 11*x^4 - 4*x^3 + x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 4*x^6 - 8*x^5 - 10*x^4 - 4*x^3 + x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 4*x^6 - 6*x^5 - 9*x^4 - 3*x^3 + x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 4*x^6 - 6*x^5 - 8*x^4 - 3*x^3 + x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 4*x^6 - 6*x^5 - 7*x^4 - 3*x^3 + x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 4*x^6 - 4*x^5 - 6*x^4 - 2*x^3 + x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 4*x^6 - 4*x^5 - 5*x^4 - 2*x^3 + x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 4*x^6 - 4*x^5 - 3*x^4 - 2*x^3 + x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 4*x^6 - 2*x^5 - 3*x^4 - x^3 + x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 4*x^6 - 2*x^5 - x^4 - x^3 + x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 4*x^6 + x^4 + x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 4*x^6 + 2*x^5 + 3*x^4 + x^3 + x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 4*x^6 + 2*x^5 + 4*x^4 + x^3 + x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 4*x^6 + 4*x^5 + 5*x^4 + 2*x^3 + x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 4*x^6 + 6*x^5 + 8*x^4 + 3*x^3 + x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 8*x^6 - 6*x^5 - 7*x^4 - 3*x^3 + 2*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 8*x^6 - 4*x^5 - 6*x^4 - 2*x^3 + 2*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 8*x^6 - 4*x^5 - 5*x^4 - 2*x^3 + 2*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 8*x^6 - 2*x^5 - 5*x^4 - x^3 + 2*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 8*x^6 - 2*x^5 - 3*x^4 - x^3 + 2*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 8*x^6 - 4*x^4 + 2*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 8*x^6 - 3*x^4 + 2*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 8*x^6 - 2*x^4 + 2*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 8*x^6 - x^4 + 2*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 8*x^6 + 2*x^5 - x^4 + x^3 + 2*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 8*x^6 + 2*x^5 + x^4 + x^3 + 2*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 8*x^6 + 4*x^5 + x^4 + 2*x^3 + 2*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 8*x^6 + 4*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 8*x^6 + 4*x^5 + 3*x^4 + 2*x^3 + 2*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 8*x^6 + 6*x^5 + 4*x^4 + 3*x^3 + 2*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 8*x^6 + 6*x^5 + 5*x^4 + 3*x^3 + 2*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 8*x^6 + 6*x^5 + 7*x^4 + 3*x^3 + 2*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 8*x^6 + 8*x^5 + 7*x^4 + 4*x^3 + 2*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 8*x^6 + 8*x^5 + 9*x^4 + 4*x^3 + 2*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 8*x^6 + 10*x^5 + 11*x^4 + 5*x^3 + 2*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 12*x^6 - x^4 + 3*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 12*x^6 + 2*x^5 + x^3 + 3*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 12*x^6 + 2*x^5 + x^4 + x^3 + 3*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 12*x^6 + 4*x^5 + 2*x^4 + 2*x^3 + 3*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 12*x^6 + 4*x^5 + 3*x^4 + 2*x^3 + 3*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 12*x^6 + 6*x^5 + 2*x^4 + 3*x^3 + 3*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 12*x^6 + 6*x^5 + 3*x^4 + 3*x^3 + 3*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 12*x^6 + 6*x^5 + 5*x^4 + 3*x^3 + 3*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 12*x^6 + 8*x^5 + 3*x^4 + 4*x^3 + 3*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 12*x^6 + 8*x^5 + 5*x^4 + 4*x^3 + 3*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 12*x^6 + 8*x^5 + 6*x^4 + 4*x^3 + 3*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 12*x^6 + 8*x^5 + 7*x^4 + 4*x^3 + 3*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 12*x^6 + 10*x^5 + 7*x^4 + 5*x^3 + 3*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 12*x^6 + 10*x^5 + 8*x^4 + 5*x^3 + 3*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 12*x^6 + 10*x^5 + 9*x^4 + 5*x^3 + 3*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 12*x^6 + 12*x^5 + 11*x^4 + 6*x^3 + 3*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 16*x^6 + 6*x^5 + 5*x^4 + 3*x^3 + 4*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 16*x^6 + 8*x^5 + 6*x^4 + 4*x^3 + 4*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 16*x^6 + 8*x^5 + 7*x^4 + 4*x^3 + 4*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 16*x^6 + 10*x^5 + 7*x^4 + 5*x^3 + 4*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 16*x^6 + 10*x^5 + 9*x^4 + 5*x^3 + 4*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 16*x^6 + 12*x^5 + 9*x^4 + 6*x^3 + 4*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 16*x^6 + 12*x^5 + 10*x^4 + 6*x^3 + 4*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 16*x^6 + 14*x^5 + 9*x^4 + 7*x^3 + 4*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 16*x^6 + 14*x^5 + 10*x^4 + 7*x^3 + 4*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 16*x^6 + 14*x^5 + 11*x^4 + 7*x^3 + 4*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 16*x^6 + 14*x^5 + 13*x^4 + 7*x^3 + 4*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 16*x^6 + 16*x^5 + 10*x^4 + 8*x^3 + 4*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 16*x^6 + 16*x^5 + 11*x^4 + 8*x^3 + 4*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 20*x^6 + 12*x^5 + 11*x^4 + 6*x^3 + 5*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 20*x^6 + 14*x^5 + 13*x^4 + 7*x^3 + 5*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 20*x^6 + 16*x^5 + 13*x^4 + 8*x^3 + 5*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 20*x^6 + 18*x^5 + 14*x^4 + 9*x^3 + 5*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 20*x^6 + 20*x^5 + 13*x^4 + 10*x^3 + 5*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 16*x^7 + 24*x^6 + 18*x^5 + 17*x^4 + 9*x^3 + 6*x^2 + 2*x + 1,\\\n",
    "16*x^8 + 24*x^7 + 8*x^6 - 12*x^5 - 15*x^4 - 6*x^3 + 2*x^2 + 3*x + 1,\\\n",
    "16*x^8 + 24*x^7 + 8*x^6 - 10*x^5 - 13*x^4 - 5*x^3 + 2*x^2 + 3*x + 1,\\\n",
    "16*x^8 + 24*x^7 + 8*x^6 - 8*x^5 - 10*x^4 - 4*x^3 + 2*x^2 + 3*x + 1,\\\n",
    "16*x^8 + 24*x^7 + 8*x^6 + x^4 + 2*x^2 + 3*x + 1,\\\n",
    "16*x^8 + 24*x^7 + 12*x^6 - 6*x^5 - 11*x^4 - 3*x^3 + 3*x^2 + 3*x + 1,\\\n",
    "16*x^8 + 24*x^7 + 12*x^6 - 4*x^5 - 7*x^4 - 2*x^3 + 3*x^2 + 3*x + 1,\\\n",
    "16*x^8 + 24*x^7 + 12*x^6 - 2*x^5 - 5*x^4 - x^3 + 3*x^2 + 3*x + 1,\\\n",
    "16*x^8 + 24*x^7 + 12*x^6 - 3*x^4 + 3*x^2 + 3*x + 1,\\\n",
    "16*x^8 + 24*x^7 + 12*x^6 + 2*x^5 + x^3 + 3*x^2 + 3*x + 1,\\\n",
    "16*x^8 + 24*x^7 + 12*x^6 + 4*x^5 + 3*x^4 + 2*x^3 + 3*x^2 + 3*x + 1,\\\n",
    "16*x^8 + 24*x^7 + 16*x^6 + 4*x^5 - x^4 + 2*x^3 + 4*x^2 + 3*x + 1,\\\n",
    "16*x^8 + 24*x^7 + 16*x^6 + 8*x^5 + 5*x^4 + 4*x^3 + 4*x^2 + 3*x + 1,\\\n",
    "16*x^8 + 24*x^7 + 16*x^6 + 12*x^5 + 10*x^4 + 6*x^3 + 4*x^2 + 3*x + 1,\\\n",
    "16*x^8 + 24*x^7 + 20*x^6 + 10*x^5 + 5*x^4 + 5*x^3 + 5*x^2 + 3*x + 1,\\\n",
    "16*x^8 + 24*x^7 + 20*x^6 + 12*x^5 + 6*x^4 + 6*x^3 + 5*x^2 + 3*x + 1,\\\n",
    "16*x^8 + 24*x^7 + 20*x^6 + 12*x^5 + 7*x^4 + 6*x^3 + 5*x^2 + 3*x + 1,\\\n",
    "16*x^8 + 24*x^7 + 20*x^6 + 14*x^5 + 9*x^4 + 7*x^3 + 5*x^2 + 3*x + 1,\\\n",
    "16*x^8 + 24*x^7 + 20*x^6 + 14*x^5 + 11*x^4 + 7*x^3 + 5*x^2 + 3*x + 1,\\\n",
    "16*x^8 + 24*x^7 + 20*x^6 + 16*x^5 + 13*x^4 + 8*x^3 + 5*x^2 + 3*x + 1,\\\n",
    "16*x^8 + 24*x^7 + 20*x^6 + 18*x^5 + 15*x^4 + 9*x^3 + 5*x^2 + 3*x + 1,\\\n",
    "16*x^8 + 24*x^7 + 24*x^6 + 16*x^5 + 11*x^4 + 8*x^3 + 6*x^2 + 3*x + 1,\\\n",
    "16*x^8 + 24*x^7 + 24*x^6 + 18*x^5 + 12*x^4 + 9*x^3 + 6*x^2 + 3*x + 1,\\\n",
    "16*x^8 + 24*x^7 + 24*x^6 + 20*x^5 + 14*x^4 + 10*x^3 + 6*x^2 + 3*x + 1,\\\n",
    "16*x^8 + 24*x^7 + 24*x^6 + 20*x^5 + 15*x^4 + 10*x^3 + 6*x^2 + 3*x + 1,\\\n",
    "16*x^8 + 24*x^7 + 24*x^6 + 22*x^5 + 17*x^4 + 11*x^3 + 6*x^2 + 3*x + 1,\\\n",
    "16*x^8 + 24*x^7 + 24*x^6 + 24*x^5 + 19*x^4 + 12*x^3 + 6*x^2 + 3*x + 1,\\\n",
    "16*x^8 + 24*x^7 + 28*x^6 + 22*x^5 + 17*x^4 + 11*x^3 + 7*x^2 + 3*x + 1,\\\n",
    "16*x^8 + 24*x^7 + 28*x^6 + 24*x^5 + 19*x^4 + 12*x^3 + 7*x^2 + 3*x + 1,\\\n",
    "16*x^8 + 24*x^7 + 28*x^6 + 26*x^5 + 19*x^4 + 13*x^3 + 7*x^2 + 3*x + 1,\\\n",
    "16*x^8 + 24*x^7 + 28*x^6 + 26*x^5 + 21*x^4 + 13*x^3 + 7*x^2 + 3*x + 1,\\\n",
    "16*x^8 + 24*x^7 + 32*x^6 + 28*x^5 + 23*x^4 + 14*x^3 + 8*x^2 + 3*x + 1,\\\n",
    "16*x^8 + 32*x^7 + 16*x^6 - 14*x^5 - 21*x^4 - 7*x^3 + 4*x^2 + 4*x + 1,\\\n",
    "16*x^8 + 32*x^7 + 20*x^6 - 4*x^5 - 11*x^4 - 2*x^3 + 5*x^2 + 4*x + 1,\\\n",
    "16*x^8 + 32*x^7 + 24*x^6 + 8*x^5 + 2*x^4 + 4*x^3 + 6*x^2 + 4*x + 1,\\\n",
    "16*x^8 + 32*x^7 + 32*x^6 + 24*x^5 + 17*x^4 + 12*x^3 + 8*x^2 + 4*x + 1,\\\n",
    "16*x^8 + 32*x^7 + 36*x^6 + 34*x^5 + 27*x^4 + 17*x^3 + 9*x^2 + 4*x + 1,\\\n",
    "16*x^8 + 32*x^7 + 40*x^6 + 38*x^5 + 29*x^4 + 19*x^3 + 10*x^2 + 4*x + 1,\\\n",
    "16*x^8 + 40*x^7 + 48*x^6 + 40*x^5 + 29*x^4 + 20*x^3 + 12*x^2 + 5*x + 1,\\\n",
    "16*x^8 + 40*x^7 + 52*x^6 + 50*x^5 + 39*x^4 + 25*x^3 + 13*x^2 + 5*x + 1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-5"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f = LPolys2[0];f.coefficient(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "WP2 = []\n",
    "for n in range(0,len(LPolys2)):\n",
    "    WP2.append((LPolys2[n].coefficient(x),LPolys2[n].coefficient(x^2),LPolys2[n].coefficient(x^3),LPolys2[n].coefficient(x^4)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(-5, 12, -20, 29),\n",
       " (-5, 13, -25, 39),\n",
       " (-4, 4, 7, -21),\n",
       " (-4, 5, 2, -11),\n",
       " (-4, 6, -4, 2),\n",
       " (-4, 8, -12, 17),\n",
       " (-4, 9, -17, 27),\n",
       " (-4, 10, -19, 29),\n",
       " (-3, 2, 0, 1),\n",
       " (-3, 2, 4, -10),\n",
       " (-3, 2, 5, -13),\n",
       " (-3, 2, 6, -15),\n",
       " (-3, 3, -2, 3),\n",
       " (-3, 3, -1, 0),\n",
       " (-3, 3, 0, -3),\n",
       " (-3, 3, 1, -5),\n",
       " (-3, 3, 2, -7),\n",
       " (-3, 3, 3, -11),\n",
       " (-3, 4, -6, 10),\n",
       " (-3, 4, -4, 5),\n",
       " (-3, 4, -2, -1),\n",
       " (-3, 5, -9, 15),\n",
       " (-3, 5, -8, 13),\n",
       " (-3, 5, -7, 9),\n",
       " (-3, 5, -7, 11),\n",
       " (-3, 5, -6, 6),\n",
       " (-3, 5, -6, 7),\n",
       " (-3, 5, -5, 5),\n",
       " (-3, 6, -12, 19),\n",
       " (-3, 6, -11, 17),\n",
       " (-3, 6, -10, 14),\n",
       " (-3, 6, -10, 15),\n",
       " (-3, 6, -9, 12),\n",
       " (-3, 6, -8, 11),\n",
       " (-3, 7, -13, 19),\n",
       " (-3, 7, -13, 21),\n",
       " (-3, 7, -12, 19),\n",
       " (-3, 7, -11, 17),\n",
       " (-3, 8, -14, 23),\n",
       " (-2, -1, 3, -1),\n",
       " (-2, 0, -2, 9),\n",
       " (-2, 0, 1, 1),\n",
       " (-2, 0, 2, -2),\n",
       " (-2, 0, 3, -5),\n",
       " (-2, 0, 3, -4),\n",
       " (-2, 0, 4, -7),\n",
       " (-2, 0, 4, -6),\n",
       " (-2, 1, -3, 8),\n",
       " (-2, 1, -2, 5),\n",
       " (-2, 1, -1, 3),\n",
       " (-2, 1, -1, 4),\n",
       " (-2, 1, 0, 1),\n",
       " (-2, 1, 1, -3),\n",
       " (-2, 1, 1, -1),\n",
       " (-2, 1, 2, -6),\n",
       " (-2, 1, 2, -5),\n",
       " (-2, 1, 2, -3),\n",
       " (-2, 1, 3, -9),\n",
       " (-2, 1, 3, -8),\n",
       " (-2, 1, 3, -7),\n",
       " (-2, 1, 4, -11),\n",
       " (-2, 1, 4, -10),\n",
       " (-2, 2, -5, 11),\n",
       " (-2, 2, -4, 7),\n",
       " (-2, 2, -4, 9),\n",
       " (-2, 2, -3, 4),\n",
       " (-2, 2, -3, 5),\n",
       " (-2, 2, -3, 7),\n",
       " (-2, 2, -2, 1),\n",
       " (-2, 2, -2, 2),\n",
       " (-2, 2, -2, 3),\n",
       " (-2, 2, -1, -1),\n",
       " (-2, 2, -1, 1),\n",
       " (-2, 2, 0, -4),\n",
       " (-2, 2, 0, -3),\n",
       " (-2, 2, 0, -2),\n",
       " (-2, 2, 0, -1),\n",
       " (-2, 2, 1, -5),\n",
       " (-2, 2, 1, -3),\n",
       " (-2, 2, 2, -6),\n",
       " (-2, 2, 2, -5),\n",
       " (-2, 2, 3, -7),\n",
       " (-2, 3, -6, 11),\n",
       " (-2, 3, -5, 7),\n",
       " (-2, 3, -5, 8),\n",
       " (-2, 3, -5, 9),\n",
       " (-2, 3, -4, 3),\n",
       " (-2, 3, -4, 5),\n",
       " (-2, 3, -4, 6),\n",
       " (-2, 3, -4, 7),\n",
       " (-2, 3, -3, 2),\n",
       " (-2, 3, -3, 3),\n",
       " (-2, 3, -3, 5),\n",
       " (-2, 3, -2, 2),\n",
       " (-2, 3, -2, 3),\n",
       " (-2, 3, -1, 0),\n",
       " (-2, 3, -1, 1),\n",
       " (-2, 3, 0, -1),\n",
       " (-2, 4, -8, 10),\n",
       " (-2, 4, -8, 11),\n",
       " (-2, 4, -7, 9),\n",
       " (-2, 4, -7, 10),\n",
       " (-2, 4, -7, 11),\n",
       " (-2, 4, -7, 13),\n",
       " (-2, 4, -6, 9),\n",
       " (-2, 4, -6, 10),\n",
       " (-2, 4, -5, 7),\n",
       " (-2, 4, -5, 9),\n",
       " (-2, 4, -4, 6),\n",
       " (-2, 4, -4, 7),\n",
       " (-2, 4, -3, 5),\n",
       " (-2, 5, -10, 13),\n",
       " (-2, 5, -9, 14),\n",
       " (-2, 5, -8, 13),\n",
       " (-2, 5, -7, 13),\n",
       " (-2, 5, -6, 11),\n",
       " (-2, 6, -9, 17),\n",
       " (-1, -3, 1, 7),\n",
       " (-1, -3, 2, 5),\n",
       " (-1, -2, 0, 6),\n",
       " (-1, -2, 0, 7),\n",
       " (-1, -2, 1, 3),\n",
       " (-1, -2, 1, 4),\n",
       " (-1, -2, 2, 1),\n",
       " (-1, -2, 2, 2),\n",
       " (-1, -2, 2, 3),\n",
       " (-1, -1, -1, 5),\n",
       " (-1, -1, -1, 7),\n",
       " (-1, -1, 0, 2),\n",
       " (-1, -1, 0, 3),\n",
       " (-1, -1, 0, 5),\n",
       " (-1, -1, 1, -1),\n",
       " (-1, -1, 1, 0),\n",
       " (-1, -1, 1, 1),\n",
       " (-1, -1, 1, 3),\n",
       " (-1, -1, 2, -3),\n",
       " (-1, -1, 2, -1),\n",
       " (-1, -1, 2, 1),\n",
       " (-1, -1, 3, -1),\n",
       " (-1, 0, -2, 4),\n",
       " (-1, 0, -2, 5),\n",
       " (-1, 0, -2, 6),\n",
       " (-1, 0, -2, 7),\n",
       " (-1, 0, -1, 1),\n",
       " (-1, 0, -1, 2),\n",
       " (-1, 0, -1, 4),\n",
       " (-1, 0, -1, 5),\n",
       " (-1, 0, 0, -2),\n",
       " (-1, 0, 0, -1),\n",
       " (-1, 0, 0, 1),\n",
       " (-1, 0, 0, 2),\n",
       " (-1, 0, 0, 3),\n",
       " (-1, 0, 1, -5),\n",
       " (-1, 0, 1, -4),\n",
       " (-1, 0, 1, -3),\n",
       " (-1, 0, 1, -2),\n",
       " (-1, 0, 1, 0),\n",
       " (-1, 0, 1, 1),\n",
       " (-1, 0, 2, -7),\n",
       " (-1, 0, 2, -6),\n",
       " (-1, 0, 2, -5),\n",
       " (-1, 0, 2, -4),\n",
       " (-1, 0, 2, -3),\n",
       " (-1, 0, 2, -2),\n",
       " (-1, 0, 2, -1),\n",
       " (-1, 0, 3, -5),\n",
       " (-1, 0, 3, -4),\n",
       " (-1, 1, -4, 5),\n",
       " (-1, 1, -3, 3),\n",
       " (-1, 1, -3, 5),\n",
       " (-1, 1, -3, 7),\n",
       " (-1, 1, -2, 0),\n",
       " (-1, 1, -2, 1),\n",
       " (-1, 1, -2, 3),\n",
       " (-1, 1, -2, 4),\n",
       " (-1, 1, -2, 6),\n",
       " (-1, 1, -2, 7),\n",
       " (-1, 1, -1, -3),\n",
       " (-1, 1, -1, -1),\n",
       " (-1, 1, -1, 0),\n",
       " (-1, 1, -1, 1),\n",
       " (-1, 1, -1, 2),\n",
       " (-1, 1, -1, 3),\n",
       " (-1, 1, -1, 4),\n",
       " (-1, 1, -1, 5),\n",
       " (-1, 1, 0, -5),\n",
       " (-1, 1, 0, -2),\n",
       " (-1, 1, 0, -1),\n",
       " (-1, 1, 0, 0),\n",
       " (-1, 1, 0, 1),\n",
       " (-1, 1, 0, 3),\n",
       " (-1, 1, 1, -5),\n",
       " (-1, 1, 1, -3),\n",
       " (-1, 1, 1, -2),\n",
       " (-1, 1, 1, -1),\n",
       " (-1, 1, 1, 1),\n",
       " (-1, 1, 2, -3),\n",
       " (-1, 1, 2, -2),\n",
       " (-1, 1, 2, -1),\n",
       " (-1, 1, 3, -5),\n",
       " (-1, 1, 3, -3),\n",
       " (-1, 1, 4, -6),\n",
       " (-1, 1, 4, -5),\n",
       " (-1, 2, -5, 4),\n",
       " (-1, 2, -5, 6),\n",
       " (-1, 2, -4, 1),\n",
       " (-1, 2, -4, 2),\n",
       " (-1, 2, -4, 3),\n",
       " (-1, 2, -4, 5),\n",
       " (-1, 2, -4, 7),\n",
       " (-1, 2, -3, 1),\n",
       " (-1, 2, -3, 2),\n",
       " (-1, 2, -3, 4),\n",
       " (-1, 2, -3, 5),\n",
       " (-1, 2, -3, 8),\n",
       " (-1, 2, -2, 1),\n",
       " (-1, 2, -2, 3),\n",
       " (-1, 2, -2, 4),\n",
       " (-1, 2, -2, 5),\n",
       " (-1, 2, -2, 6),\n",
       " (-1, 2, -2, 7),\n",
       " (-1, 2, -1, 2),\n",
       " (-1, 2, -1, 4),\n",
       " (-1, 2, 0, -1),\n",
       " (-1, 2, 0, 1),\n",
       " (-1, 2, 0, 2),\n",
       " (-1, 2, 0, 3),\n",
       " (-1, 2, 1, 1),\n",
       " (-1, 2, 2, -1),\n",
       " (-1, 3, -6, 5),\n",
       " (-1, 3, -5, 5),\n",
       " (-1, 3, -5, 6),\n",
       " (-1, 3, -5, 7),\n",
       " (-1, 3, -4, 5),\n",
       " (-1, 3, -4, 6),\n",
       " (-1, 3, -4, 8),\n",
       " (-1, 3, -3, 5),\n",
       " (-1, 3, -3, 7),\n",
       " (-1, 3, -3, 8),\n",
       " (-1, 3, -3, 9),\n",
       " (-1, 3, -2, 6),\n",
       " (-1, 3, -2, 7),\n",
       " (-1, 3, -1, 3),\n",
       " (-1, 3, -1, 5),\n",
       " (-1, 3, 1, 3),\n",
       " (-1, 4, -6, 9),\n",
       " (-1, 4, -5, 10),\n",
       " (-1, 4, -4, 9),\n",
       " (-1, 4, -4, 11),\n",
       " (-1, 4, -2, 9),\n",
       " (-1, 5, -5, 13),\n",
       " (0, -5, 0, 13),\n",
       " (0, -4, 0, 9),\n",
       " (0, -4, 0, 10),\n",
       " (0, -3, -1, 7),\n",
       " (0, -3, 0, 6),\n",
       " (0, -3, 0, 7),\n",
       " (0, -3, 0, 9),\n",
       " (0, -3, 1, 7),\n",
       " (0, -2, -1, 3),\n",
       " (0, -2, -1, 5),\n",
       " (0, -2, 0, 1),\n",
       " (0, -2, 0, 2),\n",
       " (0, -2, 0, 3),\n",
       " (0, -2, 0, 4),\n",
       " (0, -2, 0, 6),\n",
       " (0, -2, 0, 7),\n",
       " (0, -2, 1, 3),\n",
       " (0, -2, 1, 5),\n",
       " (0, -1, -2, 2),\n",
       " (0, -1, -1, -1),\n",
       " (0, -1, -1, 0),\n",
       " (0, -1, -1, 1),\n",
       " (0, -1, -1, 2),\n",
       " (0, -1, -1, 3),\n",
       " (0, -1, -1, 4),\n",
       " (0, -1, -1, 5),\n",
       " (0, -1, 0, -3),\n",
       " (0, -1, 0, -2),\n",
       " (0, -1, 0, -1),\n",
       " (0, -1, 0, 0),\n",
       " (0, -1, 0, 1),\n",
       " (0, -1, 0, 3),\n",
       " (0, -1, 0, 5),\n",
       " (0, -1, 0, 7),\n",
       " (0, -1, 1, -1),\n",
       " (0, -1, 1, 0),\n",
       " (0, -1, 1, 1),\n",
       " (0, -1, 1, 2),\n",
       " (0, -1, 1, 3),\n",
       " (0, -1, 1, 4),\n",
       " (0, -1, 1, 5),\n",
       " (0, -1, 2, 2),\n",
       " (0, 0, -3, 1),\n",
       " (0, 0, -2, -2),\n",
       " (0, 0, -2, -1),\n",
       " (0, 0, -2, 0),\n",
       " (0, 0, -2, 2),\n",
       " (0, 0, -2, 3),\n",
       " (0, 0, -1, -5),\n",
       " (0, 0, -1, -4),\n",
       " (0, 0, -1, -3),\n",
       " (0, 0, -1, -1),\n",
       " (0, 0, -1, 1),\n",
       " (0, 0, -1, 2),\n",
       " (0, 0, -1, 3),\n",
       " (0, 0, -1, 5),\n",
       " (0, 0, 0, -7),\n",
       " (0, 0, 0, -6),\n",
       " (0, 0, 0, -5),\n",
       " (0, 0, 0, -3),\n",
       " (0, 0, 0, -2),\n",
       " (0, 0, 0, 0),\n",
       " (0, 0, 0, 1),\n",
       " (0, 0, 0, 2),\n",
       " (0, 0, 0, 3),\n",
       " (0, 0, 0, 5),\n",
       " (0, 0, 0, 6),\n",
       " (0, 0, 1, -5),\n",
       " (0, 0, 1, -4),\n",
       " (0, 0, 1, -3),\n",
       " (0, 0, 1, -1),\n",
       " (0, 0, 1, 1),\n",
       " (0, 0, 1, 2),\n",
       " (0, 0, 1, 3),\n",
       " (0, 0, 1, 5),\n",
       " (0, 0, 2, -2),\n",
       " (0, 0, 2, -1),\n",
       " (0, 0, 2, 0),\n",
       " (0, 0, 2, 2),\n",
       " (0, 0, 2, 3),\n",
       " (0, 0, 3, 1),\n",
       " (0, 1, -3, -3),\n",
       " (0, 1, -3, -2),\n",
       " (0, 1, -3, 0),\n",
       " (0, 1, -3, 1),\n",
       " (0, 1, -2, -3),\n",
       " (0, 1, -2, -1),\n",
       " (0, 1, -2, 1),\n",
       " (0, 1, -2, 2),\n",
       " (0, 1, -2, 3),\n",
       " (0, 1, -1, -3),\n",
       " (0, 1, -1, -2),\n",
       " (0, 1, -1, -1),\n",
       " (0, 1, -1, 0),\n",
       " (0, 1, -1, 2),\n",
       " (0, 1, -1, 4),\n",
       " (0, 1, -1, 5),\n",
       " (0, 1, 0, -2),\n",
       " (0, 1, 0, -1),\n",
       " (0, 1, 0, 0),\n",
       " (0, 1, 0, 1),\n",
       " (0, 1, 0, 3),\n",
       " (0, 1, 0, 4),\n",
       " (0, 1, 0, 7),\n",
       " (0, 1, 1, -3),\n",
       " (0, 1, 1, -2),\n",
       " (0, 1, 1, -1),\n",
       " (0, 1, 1, 0),\n",
       " (0, 1, 1, 2),\n",
       " (0, 1, 1, 4),\n",
       " (0, 1, 1, 5),\n",
       " (0, 1, 2, -3),\n",
       " (0, 1, 2, -1),\n",
       " (0, 1, 2, 1),\n",
       " (0, 1, 2, 2),\n",
       " (0, 1, 2, 3),\n",
       " (0, 1, 3, -3),\n",
       " (0, 1, 3, -2),\n",
       " (0, 1, 3, 0),\n",
       " (0, 1, 3, 1),\n",
       " (0, 2, -5, -1),\n",
       " (0, 2, -4, 2),\n",
       " (0, 2, -3, 1),\n",
       " (0, 2, -3, 3),\n",
       " (0, 2, -2, 1),\n",
       " (0, 2, -2, 2),\n",
       " (0, 2, -2, 5),\n",
       " (0, 2, -1, 1),\n",
       " (0, 2, -1, 2),\n",
       " (0, 2, -1, 3),\n",
       " (0, 2, -1, 5),\n",
       " (0, 2, -1, 7),\n",
       " (0, 2, 0, 2),\n",
       " (0, 2, 0, 3),\n",
       " (0, 2, 0, 4),\n",
       " (0, 2, 0, 6),\n",
       " (0, 2, 0, 7),\n",
       " (0, 2, 1, 1),\n",
       " (0, 2, 1, 2),\n",
       " (0, 2, 1, 3),\n",
       " (0, 2, 1, 5),\n",
       " (0, 2, 1, 7),\n",
       " (0, 2, 2, 1),\n",
       " (0, 2, 2, 2),\n",
       " (0, 2, 2, 5),\n",
       " (0, 2, 3, 1),\n",
       " (0, 2, 3, 3),\n",
       " (0, 2, 4, 2),\n",
       " (0, 2, 5, -1),\n",
       " (0, 3, -2, 5),\n",
       " (0, 3, -1, 5),\n",
       " (0, 3, -1, 8),\n",
       " (0, 3, 0, 5),\n",
       " (0, 3, 0, 6),\n",
       " (0, 3, 0, 7),\n",
       " (0, 3, 0, 9),\n",
       " (0, 3, 1, 5),\n",
       " (0, 3, 1, 8),\n",
       " (0, 3, 2, 5),\n",
       " (0, 4, -1, 9),\n",
       " (0, 4, 0, 9),\n",
       " (0, 4, 0, 10),\n",
       " (0, 4, 1, 9),\n",
       " (1, -3, -2, 5),\n",
       " (1, -3, -1, 7),\n",
       " (1, -2, -2, 1),\n",
       " (1, -2, -2, 2),\n",
       " (1, -2, -2, 3),\n",
       " (1, -2, -1, 3),\n",
       " (1, -2, -1, 4),\n",
       " (1, -2, 0, 6),\n",
       " (1, -2, 0, 7),\n",
       " (1, -1, -3, -1),\n",
       " (1, -1, -2, -3),\n",
       " (1, -1, -2, -1),\n",
       " (1, -1, -2, 1),\n",
       " (1, -1, -1, -1),\n",
       " (1, -1, -1, 0),\n",
       " (1, -1, -1, 1),\n",
       " (1, -1, -1, 3),\n",
       " (1, -1, 0, 2),\n",
       " (1, -1, 0, 3),\n",
       " (1, -1, 0, 5),\n",
       " (1, -1, 1, 5),\n",
       " (1, -1, 1, 7),\n",
       " (1, 0, -3, -5),\n",
       " (1, 0, -3, -4),\n",
       " (1, 0, -2, -7),\n",
       " (1, 0, -2, -6),\n",
       " (1, 0, -2, -5),\n",
       " (1, 0, -2, -4),\n",
       " (1, 0, -2, -3),\n",
       " (1, 0, -2, -2),\n",
       " (1, 0, -2, -1),\n",
       " (1, 0, -1, -5),\n",
       " (1, 0, -1, -4),\n",
       " (1, 0, -1, -3),\n",
       " (1, 0, -1, -2),\n",
       " (1, 0, -1, 0),\n",
       " (1, 0, -1, 1),\n",
       " (1, 0, 0, -2),\n",
       " (1, 0, 0, -1),\n",
       " (1, 0, 0, 1),\n",
       " (1, 0, 0, 2),\n",
       " (1, 0, 0, 3),\n",
       " (1, 0, 1, 1),\n",
       " (1, 0, 1, 2),\n",
       " (1, 0, 1, 4),\n",
       " (1, 0, 1, 5),\n",
       " (1, 0, 2, 4),\n",
       " (1, 0, 2, 5),\n",
       " (1, 0, 2, 6),\n",
       " (1, 0, 2, 7),\n",
       " (1, 1, -4, -6),\n",
       " (1, 1, -4, -5),\n",
       " (1, 1, -3, -5),\n",
       " (1, 1, -3, -3),\n",
       " (1, 1, -2, -3),\n",
       " (1, 1, -2, -2),\n",
       " (1, 1, -2, -1),\n",
       " (1, 1, -1, -5),\n",
       " (1, 1, -1, -3),\n",
       " (1, 1, -1, -2),\n",
       " (1, 1, -1, -1),\n",
       " (1, 1, -1, 1),\n",
       " (1, 1, 0, -5),\n",
       " (1, 1, 0, -2),\n",
       " (1, 1, 0, -1),\n",
       " (1, 1, 0, 0),\n",
       " (1, 1, 0, 1),\n",
       " (1, 1, 0, 3),\n",
       " (1, 1, 1, -3),\n",
       " (1, 1, 1, -1),\n",
       " (1, 1, 1, 0),\n",
       " (1, 1, 1, 1),\n",
       " (1, 1, 1, 2),\n",
       " (1, 1, 1, 3),\n",
       " (1, 1, 1, 4),\n",
       " (1, 1, 1, 5),\n",
       " (1, 1, 2, 0),\n",
       " (1, 1, 2, 1),\n",
       " (1, 1, 2, 3),\n",
       " (1, 1, 2, 4),\n",
       " (1, 1, 2, 6),\n",
       " (1, 1, 2, 7),\n",
       " (1, 1, 3, 3),\n",
       " (1, 1, 3, 5),\n",
       " (1, 1, 3, 7),\n",
       " (1, 1, 4, 5),\n",
       " (1, 2, -2, -1),\n",
       " (1, 2, -1, 1),\n",
       " (1, 2, 0, -1),\n",
       " (1, 2, 0, 1),\n",
       " (1, 2, 0, 2),\n",
       " (1, 2, 0, 3),\n",
       " (1, 2, 1, 2),\n",
       " (1, 2, 1, 4),\n",
       " (1, 2, 2, 1),\n",
       " (1, 2, 2, 3),\n",
       " (1, 2, 2, 4),\n",
       " (1, 2, 2, 5),\n",
       " (1, 2, 2, 6),\n",
       " (1, 2, 2, 7),\n",
       " (1, 2, 3, 1),\n",
       " (1, 2, 3, 2),\n",
       " (1, 2, 3, 4),\n",
       " (1, 2, 3, 5),\n",
       " (1, 2, 3, 8),\n",
       " (1, 2, 4, 1),\n",
       " (1, 2, 4, 2),\n",
       " (1, 2, 4, 3),\n",
       " (1, 2, 4, 5),\n",
       " (1, 2, 4, 7),\n",
       " (1, 2, 5, 4),\n",
       " (1, 2, 5, 6),\n",
       " (1, 3, -1, 3),\n",
       " (1, 3, 1, 3),\n",
       " (1, 3, 1, 5),\n",
       " (1, 3, 2, 6),\n",
       " (1, 3, 2, 7),\n",
       " (1, 3, 3, 5),\n",
       " (1, 3, 3, 7),\n",
       " (1, 3, 3, 8),\n",
       " (1, 3, 3, 9),\n",
       " (1, 3, 4, 5),\n",
       " (1, 3, 4, 6),\n",
       " (1, 3, 4, 8),\n",
       " (1, 3, 5, 5),\n",
       " (1, 3, 5, 6),\n",
       " (1, 3, 5, 7),\n",
       " (1, 3, 6, 5),\n",
       " (1, 4, 2, 9),\n",
       " (1, 4, 4, 9),\n",
       " (1, 4, 4, 11),\n",
       " (1, 4, 5, 10),\n",
       " (1, 4, 6, 9),\n",
       " (1, 5, 5, 13),\n",
       " (2, -1, -3, -1),\n",
       " (2, 0, -4, -7),\n",
       " (2, 0, -4, -6),\n",
       " (2, 0, -3, -5),\n",
       " (2, 0, -3, -4),\n",
       " (2, 0, -2, -2),\n",
       " (2, 0, -1, 1),\n",
       " (2, 0, 2, 9),\n",
       " (2, 1, -4, -11),\n",
       " (2, 1, -4, -10),\n",
       " (2, 1, -3, -9),\n",
       " (2, 1, -3, -8),\n",
       " (2, 1, -3, -7),\n",
       " (2, 1, -2, -6),\n",
       " (2, 1, -2, -5),\n",
       " (2, 1, -2, -3),\n",
       " (2, 1, -1, -3),\n",
       " (2, 1, -1, -1),\n",
       " (2, 1, 0, 1),\n",
       " (2, 1, 1, 3),\n",
       " (2, 1, 1, 4),\n",
       " (2, 1, 2, 5),\n",
       " (2, 1, 3, 8),\n",
       " (2, 2, -3, -7),\n",
       " (2, 2, -2, -6),\n",
       " (2, 2, -2, -5),\n",
       " (2, 2, -1, -5),\n",
       " (2, 2, -1, -3),\n",
       " (2, 2, 0, -4),\n",
       " (2, 2, 0, -3),\n",
       " (2, 2, 0, -2),\n",
       " (2, 2, 0, -1),\n",
       " (2, 2, 1, -1),\n",
       " (2, 2, 1, 1),\n",
       " (2, 2, 2, 1),\n",
       " (2, 2, 2, 2),\n",
       " (2, 2, 2, 3),\n",
       " (2, 2, 3, 4),\n",
       " (2, 2, 3, 5),\n",
       " (2, 2, 3, 7),\n",
       " (2, 2, 4, 7),\n",
       " (2, 2, 4, 9),\n",
       " (2, 2, 5, 11),\n",
       " (2, 3, 0, -1),\n",
       " (2, 3, 1, 0),\n",
       " (2, 3, 1, 1),\n",
       " (2, 3, 2, 2),\n",
       " (2, 3, 2, 3),\n",
       " (2, 3, 3, 2),\n",
       " (2, 3, 3, 3),\n",
       " (2, 3, 3, 5),\n",
       " (2, 3, 4, 3),\n",
       " (2, 3, 4, 5),\n",
       " (2, 3, 4, 6),\n",
       " (2, 3, 4, 7),\n",
       " (2, 3, 5, 7),\n",
       " (2, 3, 5, 8),\n",
       " (2, 3, 5, 9),\n",
       " (2, 3, 6, 11),\n",
       " (2, 4, 3, 5),\n",
       " (2, 4, 4, 6),\n",
       " (2, 4, 4, 7),\n",
       " (2, 4, 5, 7),\n",
       " (2, 4, 5, 9),\n",
       " (2, 4, 6, 9),\n",
       " (2, 4, 6, 10),\n",
       " (2, 4, 7, 9),\n",
       " (2, 4, 7, 10),\n",
       " (2, 4, 7, 11),\n",
       " (2, 4, 7, 13),\n",
       " (2, 4, 8, 10),\n",
       " (2, 4, 8, 11),\n",
       " (2, 5, 6, 11),\n",
       " (2, 5, 7, 13),\n",
       " (2, 5, 8, 13),\n",
       " (2, 5, 9, 14),\n",
       " (2, 5, 10, 13),\n",
       " (2, 6, 9, 17),\n",
       " (3, 2, -6, -15),\n",
       " (3, 2, -5, -13),\n",
       " (3, 2, -4, -10),\n",
       " (3, 2, 0, 1),\n",
       " (3, 3, -3, -11),\n",
       " (3, 3, -2, -7),\n",
       " (3, 3, -1, -5),\n",
       " (3, 3, 0, -3),\n",
       " (3, 3, 1, 0),\n",
       " (3, 3, 2, 3),\n",
       " (3, 4, 2, -1),\n",
       " (3, 4, 4, 5),\n",
       " (3, 4, 6, 10),\n",
       " (3, 5, 5, 5),\n",
       " (3, 5, 6, 6),\n",
       " (3, 5, 6, 7),\n",
       " (3, 5, 7, 9),\n",
       " (3, 5, 7, 11),\n",
       " (3, 5, 8, 13),\n",
       " (3, 5, 9, 15),\n",
       " (3, 6, 8, 11),\n",
       " (3, 6, 9, 12),\n",
       " (3, 6, 10, 14),\n",
       " (3, 6, 10, 15),\n",
       " (3, 6, 11, 17),\n",
       " (3, 6, 12, 19),\n",
       " (3, 7, 11, 17),\n",
       " (3, 7, 12, 19),\n",
       " (3, 7, 13, 19),\n",
       " (3, 7, 13, 21),\n",
       " (3, 8, 14, 23),\n",
       " (4, 4, -7, -21),\n",
       " (4, 5, -2, -11),\n",
       " (4, 6, 4, 2),\n",
       " (4, 8, 12, 17),\n",
       " (4, 9, 17, 27),\n",
       " (4, 10, 19, 29),\n",
       " (5, 12, 20, 29),\n",
       " (5, 13, 25, 39)]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "WP2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "665"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(WP2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For $p=3$ the LMFDB says there are around 6,700 polynomials to consider, so we will stop with 2 for now."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Mono4(bound,a7,a6,a5,a4,p):\n",
    "    #bound is the arbitrary upper bound.\n",
    "    print(a7,a6,a5,a4)\n",
    "    nonmono = [] #This is to get my list on non-monogenic stuff easily.\n",
    "    Frob = Frobmatrix4(a7,a6,a5,a4,p)\n",
    "    #print Frob\n",
    "    print(\"****************\")\n",
    "    #print latex(Frob)\n",
    "    if ZZ(a4).valuation(p) == 0:\n",
    "        prank = 4\n",
    "    elif ZZ(a5).valuation(p) == 0:\n",
    "        prank = 3\n",
    "    elif ZZ(a6).valuation(p) == 0:\n",
    "        prank = 2\n",
    "    elif ZZ(a7).valuation(p) == 0:\n",
    "        prank = 1\n",
    "    else:\n",
    "        prank = 0\n",
    "    print(\"p-rank is %i.\" % prank)\n",
    "    for n in range(2,bound):\n",
    "        #print n\n",
    "        try:\n",
    "            if gcd(Frob.determinant(),n)!=1:\n",
    "                #print \"n is %i and the determinant is not 1.\" % n\n",
    "                pass\n",
    "            else:\n",
    "                GSpsize = GSpOrders[n]\n",
    "                #print \"GSpsize is %i.\" % GSpsize\n",
    "                R = Integers(ZZ(n)) #This works better than the quotient ring I was using.\n",
    "                V = GL(2*4,R) #I will need to change this for different g.\n",
    "                F = V(Frob)\n",
    "                Fj = F\n",
    "                j=1\n",
    "                while GSpsize/numbirred(j,p)>j:\n",
    "                    if not Fj.is_one():\n",
    "                        #print \"j is %i.\" % j\n",
    "                        Fj = Fj*F\n",
    "                        j = j+1\n",
    "                    else:\n",
    "                        ord = j\n",
    "                        print(\"***********************************\")\n",
    "                        print(\"n is %i.\" % n)\n",
    "                        print(\"The order of the Frobenius is %i.\" % ord)\n",
    "                        print(\"We have %i polys of the proper degree in Z/%iZ[x].\" % (numbirred(ord,p),p))\n",
    "                        split = GSpsize/ord\n",
    "                        print(\"The number of primes %i splits into has to be %s.\" % (p,split))\n",
    "                        nonmono.append(str(n))\n",
    "                        break\n",
    "                pass\n",
    "        except:\n",
    "            pass\n",
    "    print(nonmono)\n",
    "    return \"%i & %i & %i & %i & %i & %s \\\\\\\\ \\\\hline\" %(a7,a6,a5,a4,prank,\", \".join(nonmono)) #join concatenates and the quotes tell it what to put between the elts of the list."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 0 0 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 12.\n",
      "We have 335 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 21928252218163200.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 12.\n",
      "We have 335 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4648852845000000000000000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 36.\n",
      "We have 1908866960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 3291313019385817508292770634547200.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 7663773114740251530029566811151360000.\n",
      "***********************************\n",
      "n is 13.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1795849439724535843832505615198484070400.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 12.\n",
      "We have 335 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1223294612523426635931648000000000000000000.\n",
      "***********************************\n",
      "n is 17.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 21898183327078294518532490120366252674252800.\n",
      "***********************************\n",
      "n is 23.\n",
      "The order of the Frobenius is 88.\n",
      "We have 3516875111605994051576550 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2626145600901025089133169289252654740978201395200.\n",
      "***********************************\n",
      "n is 25.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 67649712509592063724994659423828125000000000000000.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 108.\n",
      "We have 3004801422763210266376748072960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 494008427292979276777256641360443463387130633011200.\n",
      "***********************************\n",
      "n is 29.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 22119769862896408048724133628291257570336870021120000.\n",
      "***********************************\n",
      "n is 31.\n",
      "The order of the Frobenius is 160.\n",
      "We have 9134385233318143238773022648690396281390393344 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 91531298760533254792138099902184797220606149918720000.\n",
      "***********************************\n",
      "n is 33.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 672212599211209667518297404327639289429185527808000000.\n",
      "***********************************\n",
      "n is 35.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 5173195923195119279491622026331750400000000000000000000.\n",
      "***********************************\n",
      "n is 37.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 142532692134702083741989049522003954470918246973906534400.\n",
      "***********************************\n",
      "n is 39.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 472558073521520316661244245520244932920642328969871360000.\n",
      "***********************************\n",
      "n is 43.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 15942974011631826897035608561733270862886349685046778880000.\n",
      "***********************************\n",
      "n is 45.\n",
      "The order of the Frobenius is 36.\n",
      "We have 1908866960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 183609958727487574512931894288166472081408000000000000000000.\n",
      "***********************************\n",
      "n is 51.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 5762266645388988177055757955028906434770113986349781483520000.\n",
      "***********************************\n",
      "n is 53.\n",
      "The order of the Frobenius is 104.\n",
      "We have 195023169265881403080265614570 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 59257949449230365265985592681009875476724801536661098254745600.\n",
      "***********************************\n",
      "n is 55.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 142511013791578919045574218416554310646476800000000000000000000.\n",
      "***********************************\n",
      "n is 57.\n",
      "The order of the Frobenius is 180.\n",
      "We have 8513864115921604768657483477290939684335762639067568 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 284516105414669267553699888956242226862813564308744149401600000.\n",
      "***********************************\n",
      "n is 65.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 100183677324660773686862633192327374924394643456000000000000000000.\n",
      "***********************************\n",
      "n is 75.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 17801279500758779408812522888183593750000000000000000000000000000000.\n",
      "***********************************\n",
      "n is 85.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1221617182325033940122732063051988554240267850350592000000000000000000.\n",
      "***********************************\n",
      "n is 87.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1940191570245270648561170916393031739899543577133125296126427136000000.\n",
      "***********************************\n",
      "n is 91.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 13988820289661471406276180147610678520451975960277619306498359296000000.\n",
      "***********************************\n",
      "n is 95.\n",
      "The order of the Frobenius is 180.\n",
      "We have 8513864115921604768657483477290939684335762639067568 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 60318236626708121028581519834220024877651722159759360000000000000000000.\n",
      "***********************************\n",
      "n is 105.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1361269739733554370743425992932878713927836746383360000000000000000000000.\n",
      "***********************************\n",
      "n is 109.\n",
      "The order of the Frobenius is 216.\n",
      "We have 487556905872949938416287165202176425001580704867851135635947520 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 11124676016228016239945581539791488845995911570661528270949831363409920000.\n",
      "***********************************\n",
      "n is 111.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 37505913869562641495290517939751452007764101332862699307851618147368960000.\n",
      "***********************************\n",
      "n is 113.\n",
      "The order of the Frobenius is 112.\n",
      "We have 46359793379775246039936627600240 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 81431034063756427448794551716946384916329899203940049515686122682633420800.\n",
      "***********************************\n",
      "n is 117.\n",
      "The order of the Frobenius is 252.\n",
      "We have 28718276100524850055449153027948389844223426388382068626139450471822065680 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 70928431701865089031698782309242744003144227114417502235598229403074560000.\n",
      "***********************************\n",
      "n is 129.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4195218662816206311756137462620843176489086894014484192132582281838592000000.\n",
      "***********************************\n",
      "n is 135.\n",
      "The order of the Frobenius is 108.\n",
      "We have 3004801422763210266376748072960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 27558869792099308312463903621803707182746986955929216442368000000000000000000.\n",
      "***********************************\n",
      "n is 137.\n",
      "The order of the Frobenius is 136.\n",
      "We have 640531514204119460634770232333480215490 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 83544387016804736144300813742373748009123654663428044114785921775725956300800.\n",
      "***********************************\n",
      "n is 145.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 411326220231484905990368348952167940977953383224315688345600000000000000000000.\n",
      "***********************************\n",
      "n is 153.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2594655931871168226307942669720087819224942925222599375343152043042547957760000.\n",
      "***********************************\n",
      "n is 165.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 37500209451454521824807291731975934673559770803796568965120000000000000000000000.\n",
      "***********************************\n",
      "n is 171.\n",
      "The order of the Frobenius is 180.\n",
      "We have 8513864115921604768657483477290939684335762639067568 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 128113023235012021733070122104771185991088237547924589798177816206503627980800000.\n",
      "***********************************\n",
      "n is 185.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 7951362136031026862776488465950567686120545146484696398514364416000000000000000000.\n",
      "***********************************\n",
      "n is 193.\n",
      "The order of the Frobenius is 192.\n",
      "We have 32693238205138962311644736578793949237341897722922270720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 19056865314605004399864707730533056457117507087225053163746706571699947569152000000.\n",
      "***********************************\n",
      "n is 195.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 26362235334218866714031114544320029938059547003108148694640230400000000000000000000.\n",
      "['3', '5', '9', '11', '13', '15', '17', '23', '25', '27', '29', '31', '33', '35', '37', '39', '43', '45', '51', '53', '55', '57', '65', '75', '85', '87', '91', '95', '105', '109', '111', '113', '117', '129', '135', '137', '145', '153', '165', '171', '185', '193', '195']\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "'0 & 0 & 0 & 1 & 4 & 3, 5, 9, 11, 13, 15, 17, 23, 25, 27, 29, 31, 33, 35, 37, 39, 43, 45, 51, 53, 55, 57, 65, 75, 85, 87, 91, 95, 105, 109, 111, 113, 117, 129, 135, 137, 145, 153, 165, 171, 185, 193, 195 \\\\\\\\ \\\\hline'"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Mono4(200,0,0,0,1,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-5 12 -20 29\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1394655853500000000000000.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 5109182076493501020019711207434240000.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 80.\n",
      "We have 15111572745169120787664 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 183494191878513995389747200000000000000000.\n",
      "***********************************\n",
      "n is 55.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 142511013791578919045574218416554310646476800000000000000000000.\n",
      "***********************************\n",
      "n is 99.\n",
      "The order of the Frobenius is 240.\n",
      "We have 7361862769909934706597072919762160477076066254539558997491267234955536 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 151343257380981531068227153985461530090635137663735205377345585152000000.\n",
      "['5', '11', '15', '55', '99']\n",
      "-5 13 -25 39\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1394655853500000000000000.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 122329461252342663593164800000000000000000.\n",
      "***********************************\n",
      "n is 19.\n",
      "The order of the Frobenius is 90.\n",
      "We have 13754889325392723216145164 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2162477448301482392501266615671936620802048000.\n",
      "***********************************\n",
      "n is 31.\n",
      "The order of the Frobenius is 30.\n",
      "We have 35790267 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 488166926722844025558069866144985585176566132899840000.\n",
      "***********************************\n",
      "n is 33.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 672212599211209667518297404327639289429185527808000000.\n",
      "***********************************\n",
      "n is 55.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 142511013791578919045574218416554310646476800000000000000000000.\n",
      "***********************************\n",
      "n is 57.\n",
      "The order of the Frobenius is 180.\n",
      "We have 8513864115921604768657483477290939684335762639067568 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 284516105414669267553699888956242226862813564308744149401600000.\n",
      "***********************************\n",
      "n is 61.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 18696370204190757357625820678773810243630816396158668004618240000.\n",
      "***********************************\n",
      "n is 85.\n",
      "The order of the Frobenius is 160.\n",
      "We have 9134385233318143238773022648690396281390393344 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1099455464092530546110458856746789698816241065315532800000000000000000.\n",
      "***********************************\n",
      "n is 93.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 64227884962464700902917774250382921619285555237312489068406243328000000.\n",
      "['5', '11', '15', '19', '31', '33', '55', '57', '61', '85', '93']\n",
      "-4 4 7 -21\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 122329461252342663593164800000000000000000.\n",
      "***********************************\n",
      "n is 19.\n",
      "The order of the Frobenius is 90.\n",
      "We have 13754889325392723216145164 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2162477448301482392501266615671936620802048000.\n",
      "***********************************\n",
      "n is 31.\n",
      "The order of the Frobenius is 30.\n",
      "We have 35790267 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 488166926722844025558069866144985585176566132899840000.\n",
      "***********************************\n",
      "n is 33.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 672212599211209667518297404327639289429185527808000000.\n",
      "***********************************\n",
      "n is 55.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 142511013791578919045574218416554310646476800000000000000000000.\n",
      "***********************************\n",
      "n is 57.\n",
      "The order of the Frobenius is 180.\n",
      "We have 8513864115921604768657483477290939684335762639067568 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 284516105414669267553699888956242226862813564308744149401600000.\n",
      "***********************************\n",
      "n is 61.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 18696370204190757357625820678773810243630816396158668004618240000.\n",
      "***********************************\n",
      "n is 93.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 64227884962464700902917774250382921619285555237312489068406243328000000.\n",
      "['11', '15', '19', '31', '33', '55', '57', '61', '93']\n",
      "-4 5 2 -11\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 13.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1795849439724535843832505615198484070400.\n",
      "***********************************\n",
      "n is 97.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 667984314469131063089064298074943230765904451874459405272918408980070400.\n",
      "['13', '97']\n",
      "-4 6 -4 2\n",
      "****************\n",
      "p-rank is 0.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 324563685115292090914037760000.\n",
      "***********************************\n",
      "n is 89.\n",
      "The order of the Frobenius is 88.\n",
      "We have 3516875111605994051576550 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 15065564203696702099946252489589827058925193934062868227323646115840000.\n",
      "['7', '89']\n",
      "-4 8 -12 17\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 52.\n",
      "We have 86607683851185 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1072812195000000000000000.\n",
      "***********************************\n",
      "n is 47.\n",
      "The order of the Frobenius is 184.\n",
      "We have 133260481814425118118117132768767319460642961170332270 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 391982030717821598324589325979762941685518502555015498956800.\n",
      "***********************************\n",
      "n is 89.\n",
      "The order of the Frobenius is 44.\n",
      "We have 399822314775 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 30131128407393404199892504979179654117850387868125736454647292231680000.\n",
      "***********************************\n",
      "n is 91.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 13988820289661471406276180147610678520451975960277619306498359296000000.\n",
      "***********************************\n",
      "n is 93.\n",
      "The order of the Frobenius is 240.\n",
      "We have 7361862769909934706597072919762160477076066254539558997491267234955536 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 16056971240616175225729443562595730404821388809328122267101560832000000.\n",
      "['3', '5', '47', '89', '91', '93']\n",
      "-4 9 -17 27\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-4 10 -19 29\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "['3', '9']\n",
      "-3 2 0 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 20.\n",
      "We have 52377 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 13156951330897920.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 20.\n",
      "We have 52377 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2789311707000000000000000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1974787811631490504975662380728320.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 20.\n",
      "We have 52377 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 733976767514055981558988800000000000000000.\n",
      "***********************************\n",
      "n is 25.\n",
      "The order of the Frobenius is 100.\n",
      "We have 12676506002282282755967953152 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 40589827505755238234996795654296875000000000000000.\n",
      "***********************************\n",
      "n is 31.\n",
      "The order of the Frobenius is 160.\n",
      "We have 9134385233318143238773022648690396281390393344 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 91531298760533254792138099902184797220606149918720000.\n",
      "***********************************\n",
      "n is 33.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 672212599211209667518297404327639289429185527808000000.\n",
      "***********************************\n",
      "n is 45.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 110165975236492544707759136572899883248844800000000000000000.\n",
      "***********************************\n",
      "n is 55.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 142511013791578919045574218416554310646476800000000000000000000.\n",
      "***********************************\n",
      "n is 75.\n",
      "The order of the Frobenius is 100.\n",
      "We have 12676506002282282755967953152 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10680767700455267645287513732910156250000000000000000000000000000000.\n",
      "***********************************\n",
      "n is 93.\n",
      "The order of the Frobenius is 160.\n",
      "We have 9134385233318143238773022648690396281390393344 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 24085456860924262838594165343893595607232083213992183400652341248000000.\n",
      "***********************************\n",
      "n is 99.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 302686514761963062136454307970923060181270275327470410754691170304000000.\n",
      "['3', '5', '9', '11', '15', '25', '31', '33', '45', '55', '75', '93', '99']\n",
      "-3 2 4 -10\n",
      "****************\n",
      "p-rank is 1.\n",
      "[]\n",
      "-3 2 5 -13\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-3 2 6 -15\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 18.\n",
      "We have 14532 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 14618834812108800.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 54.\n",
      "We have 333599969907456 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2194208679590545005528513756364800.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 162.\n",
      "We have 36086460181009948597621832796379474289919787008 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 329338951528652851184837760906962308924753755340800.\n",
      "['3', '9', '27']\n",
      "-3 3 -2 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-3 3 -1 0\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "-3 3 0 -3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 16.\n",
      "We have 4080 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 16446189163622400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2468484764539363131219577975910400.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 370506320469734457582942481020332597540347974758400.\n",
      "['3', '9', '27']\n",
      "-3 3 1 -5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 122329461252342663593164800000000000000000.\n",
      "***********************************\n",
      "n is 17.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 21898183327078294518532490120366252674252800.\n",
      "***********************************\n",
      "n is 45.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 55082987618246272353879568286449941624422400000000000000000.\n",
      "['3', '15', '17', '45']\n",
      "-3 3 2 -7\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-3 3 3 -11\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 12.\n",
      "We have 335 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 21928252218163200.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 996182752500000000000000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 36.\n",
      "We have 1908866960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 3291313019385817508292770634547200.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 108.\n",
      "We have 3004801422763210266376748072960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 494008427292979276777256641360443463387130633011200.\n",
      "['3', '5', '9', '27']\n",
      "-3 4 -6 10\n",
      "****************\n",
      "p-rank is 1.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 10.\n",
      "We have 99 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 26313902661795840.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 30.\n",
      "We have 35790267 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 3949575623262981009951324761456640.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 90.\n",
      "We have 13754889325392723216145164 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 592810112751575132132707969632532156064556759613440.\n",
      "['3', '9', '27']\n",
      "-3 4 -4 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "-3 4 -2 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "-3 5 -9 15\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 18.\n",
      "We have 14532 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 14618834812108800.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 54.\n",
      "We have 333599969907456 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2194208679590545005528513756364800.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 162.\n",
      "We have 36086460181009948597621832796379474289919787008 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 329338951528652851184837760906962308924753755340800.\n",
      "['3', '9', '27']\n",
      "-3 5 -8 13\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-3 5 -7 9\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "['3', '9']\n",
      "-3 5 -7 11\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 17.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 21898183327078294518532490120366252674252800.\n",
      "['17']\n",
      "-3 5 -6 6\n",
      "****************\n",
      "p-rank is 2.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 18.\n",
      "We have 14532 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 14618834812108800.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 54.\n",
      "We have 333599969907456 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2194208679590545005528513756364800.\n",
      "***********************************\n",
      "n is 13.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1795849439724535843832505615198484070400.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 162.\n",
      "We have 36086460181009948597621832796379474289919787008 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 329338951528652851184837760906962308924753755340800.\n",
      "***********************************\n",
      "n is 97.\n",
      "The order of the Frobenius is 96.\n",
      "We have 825293359523583917857003520 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 333992157234565531544532149037471615382952225937229702636459204490035200.\n",
      "['3', '9', '13', '27', '97']\n",
      "-3 5 -6 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 20.\n",
      "We have 52377 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 13156951330897920.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1974787811631490504975662380728320.\n",
      "['3', '9']\n",
      "-3 5 -5 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-3 6 -12 19\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 12.\n",
      "We have 335 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 21928252218163200.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 36.\n",
      "We have 1908866960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 3291313019385817508292770634547200.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 108.\n",
      "We have 3004801422763210266376748072960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 494008427292979276777256641360443463387130633011200.\n",
      "['3', '9', '27']\n",
      "-3 6 -11 17\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-3 6 -10 14\n",
      "****************\n",
      "p-rank is 1.\n",
      "[]\n",
      "-3 6 -10 15\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-3 6 -9 12\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 16.\n",
      "We have 4080 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 16446189163622400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2468484764539363131219577975910400.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 370506320469734457582942481020332597540347974758400.\n",
      "['3', '9', '27']\n",
      "-3 6 -8 11\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-3 7 -13 19\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 774808807500000000000000.\n",
      "['5']\n",
      "-3 7 -13 21\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 52.\n",
      "We have 86607683851185 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1072812195000000000000000.\n",
      "['3', '5']\n",
      "-3 7 -12 19\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 10.\n",
      "We have 99 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 26313902661795840.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 30.\n",
      "We have 35790267 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 3949575623262981009951324761456640.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 90.\n",
      "We have 13754889325392723216145164 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 592810112751575132132707969632532156064556759613440.\n",
      "['3', '9', '27']\n",
      "-3 7 -11 17\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "-3 8 -14 23\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "***********************************\n",
      "n is 99.\n",
      "The order of the Frobenius is 240.\n",
      "We have 7361862769909934706597072919762160477076066254539558997491267234955536 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 151343257380981531068227153985461530090635137663735205377345585152000000.\n",
      "['11', '99']\n",
      "-2 -1 3 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "['3']\n",
      "-2 0 -2 9\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "-2 0 1 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "***********************************\n",
      "n is 39.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 236279036760760158330622122760122466460321164484935680000.\n",
      "['3', '9', '39']\n",
      "-2 0 2 -2\n",
      "****************\n",
      "p-rank is 0.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 75.\n",
      "We have 503719091506095041632 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 207720758473786938184984166400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "***********************************\n",
      "n is 45.\n",
      "The order of the Frobenius is 156.\n",
      "We have 585537514956291233254679485982745394048986165 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 42371528937112517195291975604961493557248000000000000000000.\n",
      "['3', '7', '9', '45']\n",
      "-2 0 3 -5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "['3', '9']\n",
      "-2 0 3 -4\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "-2 0 4 -7\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-2 0 4 -6\n",
      "****************\n",
      "p-rank is 0.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "-2 1 -3 8\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "-2 1 -2 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "['3', '9']\n",
      "-2 1 -1 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 122329461252342663593164800000000000000000.\n",
      "['15']\n",
      "-2 1 -1 4\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "-2 1 0 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 104.\n",
      "We have 195023169265881403080265614570 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 141149378368087688761344000000000000000000.\n",
      "['15']\n",
      "-2 1 1 -3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "***********************************\n",
      "n is 33.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 672212599211209667518297404327639289429185527808000000.\n",
      "['3', '9', '11', '33']\n",
      "-2 1 1 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 104.\n",
      "We have 195023169265881403080265614570 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 141149378368087688761344000000000000000000.\n",
      "['3', '9', '15']\n",
      "-2 1 2 -6\n",
      "****************\n",
      "p-rank is 2.\n",
      "[]\n",
      "-2 1 2 -5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2324426422500000000000000.\n",
      "***********************************\n",
      "n is 25.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 33824856254796031862497329711914062500000000000000.\n",
      "['5', '25']\n",
      "-2 1 2 -3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1974787811631490504975662380728320.\n",
      "***********************************\n",
      "n is 13.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1795849439724535843832505615198484070400.\n",
      "***********************************\n",
      "n is 47.\n",
      "The order of the Frobenius is 138.\n",
      "We have 2524993795123485410042792044415965268769 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 522642707623762131099452434639683922247358003406687331942400.\n",
      "***********************************\n",
      "n is 91.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 13988820289661471406276180147610678520451975960277619306498359296000000.\n",
      "***********************************\n",
      "n is 93.\n",
      "The order of the Frobenius is 240.\n",
      "We have 7361862769909934706597072919762160477076066254539558997491267234955536 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 16056971240616175225729443562595730404821388809328122267101560832000000.\n",
      "['9', '13', '47', '91', '93']\n",
      "-2 1 3 -9\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "-2 1 3 -8\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 23.\n",
      "The order of the Frobenius is 132.\n",
      "We have 41246347505568298601062172159252055475 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1750763733934016726088779526168436493985467596800.\n",
      "['23']\n",
      "-2 1 3 -7\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1974787811631490504975662380728320.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "***********************************\n",
      "n is 33.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 672212599211209667518297404327639289429185527808000000.\n",
      "***********************************\n",
      "n is 99.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 302686514761963062136454307970923060181270275327470410754691170304000000.\n",
      "['9', '11', '33', '99']\n",
      "-2 1 4 -11\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 324563685115292090914037760000.\n",
      "['3', '7']\n",
      "-2 1 4 -10\n",
      "****************\n",
      "p-rank is 2.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "['3', '9']\n",
      "-2 2 -5 11\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 20.\n",
      "We have 52377 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2789311707000000000000000.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 75.\n",
      "We have 503719091506095041632 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 207720758473786938184984166400.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 244658922504685327186329600000000000000000.\n",
      "***********************************\n",
      "n is 25.\n",
      "The order of the Frobenius is 100.\n",
      "We have 12676506002282282755967953152 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 40589827505755238234996795654296875000000000000000.\n",
      "***********************************\n",
      "n is 31.\n",
      "The order of the Frobenius is 160.\n",
      "We have 9134385233318143238773022648690396281390393344 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 91531298760533254792138099902184797220606149918720000.\n",
      "***********************************\n",
      "n is 33.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 672212599211209667518297404327639289429185527808000000.\n",
      "***********************************\n",
      "n is 45.\n",
      "The order of the Frobenius is 180.\n",
      "We have 8513864115921604768657483477290939684335762639067568 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 36721991745497514902586378857633294416281600000000000000000.\n",
      "***********************************\n",
      "n is 55.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 142511013791578919045574218416554310646476800000000000000000000.\n",
      "['5', '7', '11', '15', '25', '31', '33', '45', '55']\n",
      "-2 2 -4 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-2 2 -4 9\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "-2 2 -3 4\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "-2 2 -3 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "['3']\n",
      "-2 2 -3 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-2 2 -2 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 52.\n",
      "We have 86607683851185 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1072812195000000000000000.\n",
      "***********************************\n",
      "n is 13.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1795849439724535843832505615198484070400.\n",
      "***********************************\n",
      "n is 97.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 667984314469131063089064298074943230765904451874459405272918408980070400.\n",
      "['5', '13', '97']\n",
      "-2 2 -2 2\n",
      "****************\n",
      "p-rank is 0.\n",
      "[]\n",
      "-2 2 -2 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "['3']\n",
      "-2 2 -1 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 122329461252342663593164800000000000000000.\n",
      "['3', '9', '15']\n",
      "-2 2 -1 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "['11']\n",
      "-2 2 0 -4\n",
      "****************\n",
      "p-rank is 0.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 20.\n",
      "We have 52377 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2789311707000000000000000.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 7663773114740251530029566811151360000.\n",
      "***********************************\n",
      "n is 13.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2514189215614350181365507861277877698560.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 366988383757027990779494400000000000000000.\n",
      "***********************************\n",
      "n is 17.\n",
      "The order of the Frobenius is 80.\n",
      "We have 15111572745169120787664 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 39416729988740930133358482216659254813655040.\n",
      "***********************************\n",
      "n is 21.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 34162148870710205624229224771006028683673600000.\n",
      "***********************************\n",
      "n is 25.\n",
      "The order of the Frobenius is 20.\n",
      "We have 52377 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 202949137528776191174983978271484375000000000000000.\n",
      "***********************************\n",
      "n is 29.\n",
      "The order of the Frobenius is 140.\n",
      "We have 9955689820772599616748584288712892238241 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 8847907945158563219489653451316503028134748008448000.\n",
      "***********************************\n",
      "n is 31.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 366125195042133019168552399608739188882424599674880000.\n",
      "***********************************\n",
      "n is 33.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2016637797633629002554892212982917868287556583424000000.\n",
      "***********************************\n",
      "n is 35.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 7242474292473166991288270836864450560000000000000000000.\n",
      "***********************************\n",
      "n is 37.\n",
      "The order of the Frobenius is 180.\n",
      "We have 8513864115921604768657483477290939684335762639067568 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 57013076853880833496795619808801581788367298789562613760.\n",
      "***********************************\n",
      "n is 39.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 330790651465064221662870971864171453044449630278909952000.\n",
      "***********************************\n",
      "n is 41.\n",
      "The order of the Frobenius is 20.\n",
      "We have 52377 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 22960971106711927848077898123151125260963223347451002880000.\n",
      "***********************************\n",
      "n is 45.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 55082987618246272353879568286449941624422400000000000000000.\n",
      "***********************************\n",
      "n is 51.\n",
      "The order of the Frobenius is 80.\n",
      "We have 15111572745169120787664 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10372079961700178718700364319052031582586205175429606670336000.\n",
      "***********************************\n",
      "n is 55.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 427533041374736757136722655249662931939430400000000000000000000.\n",
      "***********************************\n",
      "n is 61.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 18696370204190757357625820678773810243630816396158668004618240000.\n",
      "***********************************\n",
      "n is 63.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 15382665827133116070047119093387333552727208767663538752716800000.\n",
      "***********************************\n",
      "n is 65.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 140257148254525083161607686469258324894152500838400000000000000000.\n",
      "***********************************\n",
      "n is 75.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 26701919251138169113218784332275390625000000000000000000000000000000.\n",
      "***********************************\n",
      "n is 77.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 39798119104121540497639612482387096066538777321240513845657600000000.\n",
      "***********************************\n",
      "n is 85.\n",
      "The order of the Frobenius is 80.\n",
      "We have 15111572745169120787664 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2198910928185061092220917713493579397632482130631065600000000000000000.\n",
      "***********************************\n",
      "n is 91.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 19584348405526059968786652206654949928632766344388667029097703014400000.\n",
      "***********************************\n",
      "n is 93.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 96341827443697051354376661375574382428928332855968733602609364992000000.\n",
      "***********************************\n",
      "n is 99.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 302686514761963062136454307970923060181270275327470410754691170304000000.\n",
      "['3', '5', '11', '13', '15', '17', '21', '25', '29', '31', '33', '35', '37', '39', '41', '45', '51', '55', '61', '63', '65', '75', '77', '85', '91', '93', '99']\n",
      "-2 2 0 -3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "['3', '9']\n",
      "-2 2 0 -2\n",
      "****************\n",
      "p-rank is 0.\n",
      "[]\n",
      "-2 2 0 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 70.\n",
      "We have 16865594581186450683 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4379298922708715160016895320657920000.\n",
      "['3', '11']\n",
      "-2 2 1 -5\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-2 2 1 -3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "['3']\n",
      "-2 2 2 -6\n",
      "****************\n",
      "p-rank is 0.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "['3', '11']\n",
      "-2 2 2 -5\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-2 2 3 -7\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "['3']\n",
      "-2 3 -6 11\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-2 3 -5 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "['3', '9']\n",
      "-2 3 -5 8\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "-2 3 -5 9\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "-2 3 -4 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-2 3 -4 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "['3']\n",
      "-2 3 -4 6\n",
      "****************\n",
      "p-rank is 2.\n",
      "***********************************\n",
      "n is 17.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 21898183327078294518532490120366252674252800.\n",
      "['17']\n",
      "-2 3 -4 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "***********************************\n",
      "n is 17.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 21898183327078294518532490120366252674252800.\n",
      "['3', '9', '17']\n",
      "-2 3 -3 2\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "-2 3 -3 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-2 3 -3 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2324426422500000000000000.\n",
      "***********************************\n",
      "n is 25.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 33824856254796031862497329711914062500000000000000.\n",
      "['5', '25']\n",
      "-2 3 -2 2\n",
      "****************\n",
      "p-rank is 2.\n",
      "[]\n",
      "-2 3 -2 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "***********************************\n",
      "n is 39.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 236279036760760158330622122760122466460321164484935680000.\n",
      "['3', '39']\n",
      "-2 3 -1 0\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "***********************************\n",
      "n is 55.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 142511013791578919045574218416554310646476800000000000000000000.\n",
      "['11', '55']\n",
      "-2 3 -1 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "['3', '9']\n",
      "-2 3 0 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-2 4 -8 10\n",
      "****************\n",
      "p-rank is 0.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "-2 4 -8 11\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "['3', '9']\n",
      "-2 4 -7 9\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-2 4 -7 10\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "['11']\n",
      "-2 4 -7 11\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "***********************************\n",
      "n is 33.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 672212599211209667518297404327639289429185527808000000.\n",
      "['3', '9', '11', '33']\n",
      "-2 4 -7 13\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-2 4 -6 9\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 75.\n",
      "We have 503719091506095041632 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 207720758473786938184984166400.\n",
      "['3', '7']\n",
      "-2 4 -6 10\n",
      "****************\n",
      "p-rank is 0.\n",
      "[]\n",
      "-2 4 -5 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "['3', '11']\n",
      "-2 4 -5 9\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "***********************************\n",
      "n is 13.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1795849439724535843832505615198484070400.\n",
      "***********************************\n",
      "n is 39.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 236279036760760158330622122760122466460321164484935680000.\n",
      "['3', '9', '13', '39']\n",
      "-2 4 -4 6\n",
      "****************\n",
      "p-rank is 0.\n",
      "[]\n",
      "-2 4 -4 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-2 4 -3 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1974787811631490504975662380728320.\n",
      "['9']\n",
      "-2 5 -10 13\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 17.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 21898183327078294518532490120366252674252800.\n",
      "['17']\n",
      "-2 5 -9 14\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "['3']\n",
      "-2 5 -8 13\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 13.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1795849439724535843832505615198484070400.\n",
      "***********************************\n",
      "n is 97.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 667984314469131063089064298074943230765904451874459405272918408980070400.\n",
      "['13', '97']\n",
      "-2 5 -7 13\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-2 5 -6 11\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "***********************************\n",
      "n is 73.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 12009956792259882194266685541781102395654590129409543206404345036800.\n",
      "['3', '73']\n",
      "-2 6 -9 17\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "['11']\n",
      "-1 -3 1 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "['3', '9']\n",
      "-1 -3 2 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-1 -2 0 6\n",
      "****************\n",
      "p-rank is 1.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 52.\n",
      "We have 86607683851185 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1072812195000000000000000.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "['3', '5', '11']\n",
      "-1 -2 0 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-1 -2 1 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 929770569000000000000000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1974787811631490504975662380728320.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 244658922504685327186329600000000000000000.\n",
      "***********************************\n",
      "n is 33.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 672212599211209667518297404327639289429185527808000000.\n",
      "***********************************\n",
      "n is 45.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 110165975236492544707759136572899883248844800000000000000000.\n",
      "***********************************\n",
      "n is 55.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 142511013791578919045574218416554310646476800000000000000000000.\n",
      "***********************************\n",
      "n is 59.\n",
      "The order of the Frobenius is 174.\n",
      "We have 137616338080629387424420529565983194224941889694755 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1876836103979097573472933781074997082407915824380650873671680000.\n",
      "***********************************\n",
      "n is 99.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 302686514761963062136454307970923060181270275327470410754691170304000000.\n",
      "['5', '9', '11', '15', '33', '45', '55', '59', '99']\n",
      "-1 -2 1 4\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "-1 -2 2 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "-1 -2 2 2\n",
      "****************\n",
      "p-rank is 1.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 52.\n",
      "We have 86607683851185 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1072812195000000000000000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 52.\n",
      "We have 86607683851185 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 282298756736175377522688000000000000000000.\n",
      "***********************************\n",
      "n is 17.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 21898183327078294518532490120366252674252800.\n",
      "***********************************\n",
      "n is 45.\n",
      "The order of the Frobenius is 156.\n",
      "We have 585537514956291233254679485982745394048986165 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 42371528937112517195291975604961493557248000000000000000000.\n",
      "['3', '5', '9', '15', '17', '45']\n",
      "-1 -2 2 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "***********************************\n",
      "n is 13.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1795849439724535843832505615198484070400.\n",
      "***********************************\n",
      "n is 39.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 236279036760760158330622122760122466460321164484935680000.\n",
      "['3', '9', '13', '39']\n",
      "-1 -1 -1 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 17.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 65694549981234883555597470361098758022758400.\n",
      "['17']\n",
      "-1 -1 -1 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-1 -1 0 2\n",
      "****************\n",
      "p-rank is 2.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "['3']\n",
      "-1 -1 0 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "***********************************\n",
      "n is 93.\n",
      "The order of the Frobenius is 240.\n",
      "We have 7361862769909934706597072919762160477076066254539558997491267234955536 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 16056971240616175225729443562595730404821388809328122267101560832000000.\n",
      "['3', '9', '93']\n",
      "-1 -1 0 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "['3']\n",
      "-1 -1 1 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "***********************************\n",
      "n is 83.\n",
      "The order of the Frobenius is 82.\n",
      "We have 58971991200686800921575 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1221091674167727563038312344538739590181881499754147861874537112371200.\n",
      "['3', '9', '83']\n",
      "-1 -1 1 0\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "-1 -1 1 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-1 -1 1 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "-1 -1 2 -3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "['3']\n",
      "-1 -1 2 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-1 -1 2 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1394655853500000000000000.\n",
      "['5']\n",
      "-1 -1 3 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 10.\n",
      "We have 99 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 30655092458961006120118267244605440000.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 122329461252342663593164800000000000000000.\n",
      "***********************************\n",
      "n is 23.\n",
      "The order of the Frobenius is 55.\n",
      "We have 655069036708398 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4201832961441640142613070862804247585565122232320.\n",
      "***********************************\n",
      "n is 25.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 33824856254796031862497329711914062500000000000000.\n",
      "***********************************\n",
      "n is 29.\n",
      "The order of the Frobenius is 140.\n",
      "We have 9955689820772599616748584288712892238241 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 8847907945158563219489653451316503028134748008448000.\n",
      "***********************************\n",
      "n is 31.\n",
      "The order of the Frobenius is 160.\n",
      "We have 9134385233318143238773022648690396281390393344 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 91531298760533254792138099902184797220606149918720000.\n",
      "***********************************\n",
      "n is 33.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2016637797633629002554892212982917868287556583424000000.\n",
      "***********************************\n",
      "n is 37.\n",
      "The order of the Frobenius is 180.\n",
      "We have 8513864115921604768657483477290939684335762639067568 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 57013076853880833496795619808801581788367298789562613760.\n",
      "***********************************\n",
      "n is 45.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 55082987618246272353879568286449941624422400000000000000000.\n",
      "***********************************\n",
      "n is 55.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 142511013791578919045574218416554310646476800000000000000000000.\n",
      "***********************************\n",
      "n is 71.\n",
      "The order of the Frobenius is 70.\n",
      "We have 16865594581186450683 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4417884685101844093339615138147356028825028252460368993846231040000.\n",
      "***********************************\n",
      "n is 75.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 8900639750379389704406261444091796875000000000000000000000000000000.\n",
      "***********************************\n",
      "n is 77.\n",
      "The order of the Frobenius is 210.\n",
      "We have 7835735987243838295976043726463380667445368484290985174649363 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 22741782345212308855794064275649769180879301326423150768947200000000.\n",
      "***********************************\n",
      "n is 93.\n",
      "The order of the Frobenius is 160.\n",
      "We have 9134385233318143238773022648690396281390393344 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 24085456860924262838594165343893595607232083213992183400652341248000000.\n",
      "***********************************\n",
      "n is 99.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 302686514761963062136454307970923060181270275327470410754691170304000000.\n",
      "['3', '11', '15', '23', '25', '29', '31', '33', '37', '45', '55', '71', '75', '77', '93', '99']\n",
      "-1 0 -2 4\n",
      "****************\n",
      "p-rank is 1.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "***********************************\n",
      "n is 45.\n",
      "The order of the Frobenius is 156.\n",
      "We have 585537514956291233254679485982745394048986165 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 42371528937112517195291975604961493557248000000000000000000.\n",
      "['3', '9', '45']\n",
      "-1 0 -2 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "['3']\n",
      "-1 0 -2 6\n",
      "****************\n",
      "p-rank is 1.\n",
      "[]\n",
      "-1 0 -2 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "['3', '9']\n",
      "-1 0 -1 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "['3', '9']\n",
      "-1 0 -1 2\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "-1 0 -1 4\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "['3', '9']\n",
      "-1 0 -1 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-1 0 0 -2\n",
      "****************\n",
      "p-rank is 1.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "['3', '9']\n",
      "-1 0 0 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 649127370230584181828075520000.\n",
      "***********************************\n",
      "n is 35.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 7242474292473166991288270836864450560000000000000000000.\n",
      "***********************************\n",
      "n is 49.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1721311070532199434768105504686408634459537165592406507520000.\n",
      "['7', '35', '49']\n",
      "-1 0 0 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "['3', '9']\n",
      "-1 0 0 2\n",
      "****************\n",
      "p-rank is 1.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2324426422500000000000000.\n",
      "***********************************\n",
      "n is 25.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 33824856254796031862497329711914062500000000000000.\n",
      "['5', '25']\n",
      "-1 0 0 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "***********************************\n",
      "n is 33.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 672212599211209667518297404327639289429185527808000000.\n",
      "['11', '33']\n",
      "-1 0 1 -5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "['3', '9']\n",
      "-1 0 1 -4\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "['3']\n",
      "-1 0 1 -3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1394655853500000000000000.\n",
      "['5']\n",
      "-1 0 1 -2\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "***********************************\n",
      "n is 17.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 21898183327078294518532490120366252674252800.\n",
      "['3', '9', '17']\n",
      "-1 0 1 0\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "-1 0 1 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "['3', '9']\n",
      "-1 0 2 -7\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 29.\n",
      "The order of the Frobenius is 140.\n",
      "We have 9955689820772599616748584288712892238241 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 8847907945158563219489653451316503028134748008448000.\n",
      "['29']\n",
      "-1 0 2 -6\n",
      "****************\n",
      "p-rank is 1.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "-1 0 2 -5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "['3', '9']\n",
      "-1 0 2 -4\n",
      "****************\n",
      "p-rank is 1.\n",
      "[]\n",
      "-1 0 2 -3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "-1 0 2 -2\n",
      "****************\n",
      "p-rank is 1.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "['3', '9']\n",
      "-1 0 2 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 185464962923024051950878720000.\n",
      "['7']\n",
      "-1 0 3 -5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 75.\n",
      "We have 503719091506095041632 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 207720758473786938184984166400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4936969529078726262439155951820800.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 741012640939468915165884962040665195080695949516800.\n",
      "***********************************\n",
      "n is 81.\n",
      "The order of the Frobenius is 216.\n",
      "We have 487556905872949938416287165202176425001580704867851135635947520 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 111222022092275746924580349840573900526036783282962743442749974732800.\n",
      "['3', '7', '9', '27', '81']\n",
      "-1 0 3 -4\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "['11']\n",
      "-1 1 -4 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 104.\n",
      "We have 195023169265881403080265614570 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 141149378368087688761344000000000000000000.\n",
      "['3', '9', '15']\n",
      "-1 1 -3 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "***********************************\n",
      "n is 63.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10987618447952225764319370780990952537662291976902527680512000000.\n",
      "['3', '63']\n",
      "-1 1 -3 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 122329461252342663593164800000000000000000.\n",
      "['15']\n",
      "-1 1 -3 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-1 1 -2 0\n",
      "****************\n",
      "p-rank is 2.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 57.\n",
      "We have 2528336632900554 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 273316787465509129190768640000.\n",
      "['7']\n",
      "-1 1 -2 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-1 1 -2 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-1 1 -2 4\n",
      "****************\n",
      "p-rank is 2.\n",
      "[]\n",
      "-1 1 -2 6\n",
      "****************\n",
      "p-rank is 2.\n",
      "[]\n",
      "-1 1 -2 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 57.\n",
      "We have 2528336632900554 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 273316787465509129190768640000.\n",
      "['7']\n",
      "-1 1 -1 -3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "***********************************\n",
      "n is 13.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1795849439724535843832505615198484070400.\n",
      "***********************************\n",
      "n is 39.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 236279036760760158330622122760122466460321164484935680000.\n",
      "['3', '9', '13', '39']\n",
      "-1 1 -1 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "['3', '9']\n",
      "-1 1 -1 0\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "['3', '9']\n",
      "-1 1 -1 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "-1 1 -1 2\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "['3', '9', '11']\n",
      "-1 1 -1 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "['3', '9']\n",
      "-1 1 -1 4\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "-1 1 -1 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "***********************************\n",
      "n is 13.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1795849439724535843832505615198484070400.\n",
      "['3', '9', '13']\n",
      "-1 1 0 -5\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-1 1 0 -2\n",
      "****************\n",
      "p-rank is 2.\n",
      "[]\n",
      "-1 1 0 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-1 1 0 0\n",
      "****************\n",
      "p-rank is 2.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "-1 1 0 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "['11']\n",
      "-1 1 0 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "***********************************\n",
      "n is 31.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 122041731680711006389517466536246396294141533224960000.\n",
      "['3', '31']\n",
      "-1 1 1 -5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "['11']\n",
      "-1 1 1 -3\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-1 1 1 -2\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "-1 1 1 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4936969529078726262439155951820800.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 741012640939468915165884962040665195080695949516800.\n",
      "***********************************\n",
      "n is 81.\n",
      "The order of the Frobenius is 216.\n",
      "We have 487556905872949938416287165202176425001580704867851135635947520 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 111222022092275746924580349840573900526036783282962743442749974732800.\n",
      "['3', '9', '27', '81']\n",
      "-1 1 1 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2324426422500000000000000.\n",
      "***********************************\n",
      "n is 25.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 33824856254796031862497329711914062500000000000000.\n",
      "['5', '25']\n",
      "-1 1 2 -3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "['3', '9']\n",
      "-1 1 2 -2\n",
      "****************\n",
      "p-rank is 2.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "-1 1 2 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "['3', '9']\n",
      "-1 1 3 -5\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-1 1 3 -3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "-1 1 4 -6\n",
      "****************\n",
      "p-rank is 2.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 324563685115292090914037760000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1974787811631490504975662380728320.\n",
      "***********************************\n",
      "n is 47.\n",
      "The order of the Frobenius is 138.\n",
      "We have 2524993795123485410042792044415965268769 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 522642707623762131099452434639683922247358003406687331942400.\n",
      "['7', '9', '47']\n",
      "-1 1 4 -5\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-1 2 -5 4\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "-1 2 -5 6\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "***********************************\n",
      "n is 19.\n",
      "The order of the Frobenius is 90.\n",
      "We have 13754889325392723216145164 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2162477448301482392501266615671936620802048000.\n",
      "['3', '19']\n",
      "-1 2 -4 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 324563685115292090914037760000.\n",
      "***********************************\n",
      "n is 21.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 28468457392258504686857687309171690569728000000.\n",
      "['7', '21']\n",
      "-1 2 -4 2\n",
      "****************\n",
      "p-rank is 1.\n",
      "[]\n",
      "-1 2 -4 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "['3']\n",
      "-1 2 -4 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-1 2 -4 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-1 2 -3 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-1 2 -3 2\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "['3']\n",
      "-1 2 -3 4\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "-1 2 -3 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "['3']\n",
      "-1 2 -3 8\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 774808807500000000000000.\n",
      "['3', '5']\n",
      "-1 2 -2 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-1 2 -2 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 75.\n",
      "We have 503719091506095041632 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 207720758473786938184984166400.\n",
      "['3', '7']\n",
      "-1 2 -2 4\n",
      "****************\n",
      "p-rank is 1.\n",
      "[]\n",
      "-1 2 -2 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "***********************************\n",
      "n is 33.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 672212599211209667518297404327639289429185527808000000.\n",
      "['3', '9', '11', '33']\n",
      "-1 2 -2 6\n",
      "****************\n",
      "p-rank is 1.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "-1 2 -2 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 774808807500000000000000.\n",
      "['5']\n",
      "-1 2 -1 2\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "-1 2 -1 4\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "-1 2 0 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "['3']\n",
      "-1 2 0 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "['11']\n",
      "-1 2 0 2\n",
      "****************\n",
      "p-rank is 1.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 996182752500000000000000.\n",
      "['3', '5']\n",
      "-1 2 0 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "['3', '9']\n",
      "-1 2 1 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-1 2 2 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-1 3 -6 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-1 3 -5 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 75.\n",
      "We have 503719091506095041632 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 207720758473786938184984166400.\n",
      "['3', '7']\n",
      "-1 3 -5 6\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 52.\n",
      "We have 86607683851185 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1072812195000000000000000.\n",
      "['5']\n",
      "-1 3 -5 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "['3', '9']\n",
      "-1 3 -4 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-1 3 -4 6\n",
      "****************\n",
      "p-rank is 2.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "-1 3 -4 8\n",
      "****************\n",
      "p-rank is 2.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 929770569000000000000000.\n",
      "['5']\n",
      "-1 3 -3 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-1 3 -3 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 52.\n",
      "We have 86607683851185 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1072812195000000000000000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4936969529078726262439155951820800.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 741012640939468915165884962040665195080695949516800.\n",
      "***********************************\n",
      "n is 81.\n",
      "The order of the Frobenius is 216.\n",
      "We have 487556905872949938416287165202176425001580704867851135635947520 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 111222022092275746924580349840573900526036783282962743442749974732800.\n",
      "['3', '5', '9', '27', '81']\n",
      "-1 3 -3 8\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "-1 3 -3 9\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "-1 3 -2 6\n",
      "****************\n",
      "p-rank is 2.\n",
      "[]\n",
      "-1 3 -2 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "['3', '9']\n",
      "-1 3 -1 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "-1 3 -1 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 35.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 5173195923195119279491622026331750400000000000000000000.\n",
      "['35']\n",
      "-1 3 1 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 929770569000000000000000.\n",
      "['5']\n",
      "-1 4 -6 9\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "-1 4 -5 10\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "-1 4 -4 9\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "['3', '9']\n",
      "-1 4 -4 11\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "['3', '9']\n",
      "-1 4 -2 9\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 122329461252342663593164800000000000000000.\n",
      "***********************************\n",
      "n is 19.\n",
      "The order of the Frobenius is 90.\n",
      "We have 13754889325392723216145164 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2162477448301482392501266615671936620802048000.\n",
      "***********************************\n",
      "n is 33.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 672212599211209667518297404327639289429185527808000000.\n",
      "***********************************\n",
      "n is 55.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 142511013791578919045574218416554310646476800000000000000000000.\n",
      "***********************************\n",
      "n is 57.\n",
      "The order of the Frobenius is 180.\n",
      "We have 8513864115921604768657483477290939684335762639067568 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 284516105414669267553699888956242226862813564308744149401600000.\n",
      "***********************************\n",
      "n is 61.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 18696370204190757357625820678773810243630816396158668004618240000.\n",
      "['11', '15', '19', '33', '55', '57', '61']\n",
      "-1 5 -5 13\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "0 -5 0 13\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 10.\n",
      "We have 99 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 26313902661795840.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 20.\n",
      "We have 52377 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2789311707000000000000000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 30.\n",
      "We have 35790267 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 3949575623262981009951324761456640.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 20.\n",
      "We have 52377 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 733976767514055981558988800000000000000000.\n",
      "***********************************\n",
      "n is 25.\n",
      "The order of the Frobenius is 100.\n",
      "We have 12676506002282282755967953152 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 40589827505755238234996795654296875000000000000000.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 90.\n",
      "We have 13754889325392723216145164 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 592810112751575132132707969632532156064556759613440.\n",
      "***********************************\n",
      "n is 31.\n",
      "The order of the Frobenius is 160.\n",
      "We have 9134385233318143238773022648690396281390393344 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 91531298760533254792138099902184797220606149918720000.\n",
      "***********************************\n",
      "n is 33.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 672212599211209667518297404327639289429185527808000000.\n",
      "***********************************\n",
      "n is 45.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 110165975236492544707759136572899883248844800000000000000000.\n",
      "***********************************\n",
      "n is 55.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 142511013791578919045574218416554310646476800000000000000000000.\n",
      "***********************************\n",
      "n is 59.\n",
      "The order of the Frobenius is 116.\n",
      "We have 716178877039286566967737630308705 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2815254155968646360209400671612495623611873736570976310507520000.\n",
      "***********************************\n",
      "n is 75.\n",
      "The order of the Frobenius is 100.\n",
      "We have 12676506002282282755967953152 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10680767700455267645287513732910156250000000000000000000000000000000.\n",
      "***********************************\n",
      "n is 93.\n",
      "The order of the Frobenius is 160.\n",
      "We have 9134385233318143238773022648690396281390393344 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 24085456860924262838594165343893595607232083213992183400652341248000000.\n",
      "***********************************\n",
      "n is 99.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 302686514761963062136454307970923060181270275327470410754691170304000000.\n",
      "['3', '5', '9', '11', '15', '25', '27', '31', '33', '45', '55', '59', '75', '93', '99']\n",
      "0 -4 0 9\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 18.\n",
      "We have 14532 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 14618834812108800.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 54.\n",
      "We have 333599969907456 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2194208679590545005528513756364800.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 110.\n",
      "We have 11800674678488244282762064174071 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2786826587178273283647115204055040000.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 162.\n",
      "We have 36086460181009948597621832796379474289919787008 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 329338951528652851184837760906962308924753755340800.\n",
      "***********************************\n",
      "n is 97.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 667984314469131063089064298074943230765904451874459405272918408980070400.\n",
      "['3', '9', '11', '27', '97']\n",
      "0 -4 0 10\n",
      "****************\n",
      "p-rank is 0.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 20.\n",
      "We have 52377 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 13156951330897920.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 324563685115292090914037760000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1974787811631490504975662380728320.\n",
      "***********************************\n",
      "n is 47.\n",
      "The order of the Frobenius is 92.\n",
      "We have 53823479968928812291873035 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 783964061435643196649178651959525883371037005110030997913600.\n",
      "***********************************\n",
      "n is 89.\n",
      "The order of the Frobenius is 176.\n",
      "We have 544210064227943486632935732314825648606966627338800 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 7532782101848351049973126244794913529462596967031434113661823057920000.\n",
      "['3', '7', '9', '47', '89']\n",
      "0 -3 -1 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "['3']\n",
      "0 -3 0 6\n",
      "****************\n",
      "p-rank is 2.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 16.\n",
      "We have 4080 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 16446189163622400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2468484764539363131219577975910400.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 370506320469734457582942481020332597540347974758400.\n",
      "['3', '9', '27']\n",
      "0 -3 0 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 12.\n",
      "We have 335 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 21928252218163200.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1162213211250000000000000.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 96.\n",
      "We have 825293359523583917857003520 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 162281842557646045457018880000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 36.\n",
      "We have 1908866960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 3291313019385817508292770634547200.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 305823653130856658982912000000000000000000.\n",
      "***********************************\n",
      "n is 17.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 21898183327078294518532490120366252674252800.\n",
      "***********************************\n",
      "n is 21.\n",
      "The order of the Frobenius is 96.\n",
      "We have 825293359523583917857003520 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 42702686088387757030286530963757535854592000000.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 108.\n",
      "We have 3004801422763210266376748072960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 494008427292979276777256641360443463387130633011200.\n",
      "***********************************\n",
      "n is 33.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 672212599211209667518297404327639289429185527808000000.\n",
      "***********************************\n",
      "n is 35.\n",
      "The order of the Frobenius is 96.\n",
      "We have 825293359523583917857003520 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 9053092865591458739110338546080563200000000000000000000.\n",
      "***********************************\n",
      "n is 39.\n",
      "The order of the Frobenius is 156.\n",
      "We have 585537514956291233254679485982745394048986165 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 254454347280818632048362286049362656188038177137623040000.\n",
      "***********************************\n",
      "n is 43.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 31885948023263653794071217123466541725772699370093557760000.\n",
      "***********************************\n",
      "n is 45.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 45902489681871893628232973572041618020352000000000000000000.\n",
      "***********************************\n",
      "n is 51.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 5762266645388988177055757955028906434770113986349781483520000.\n",
      "***********************************\n",
      "n is 61.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 9348185102095378678812910339386905121815408198079334002309120000.\n",
      "***********************************\n",
      "n is 79.\n",
      "The order of the Frobenius is 156.\n",
      "We have 585537514956291233254679485982745394048986165 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 103151533014311705289524690254069332149432933578964636349872209920000.\n",
      "***********************************\n",
      "n is 85.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1221617182325033940122732063051988554240267850350592000000000000000000.\n",
      "['3', '5', '7', '9', '11', '15', '17', '21', '27', '33', '35', '39', '43', '45', '51', '61', '79', '85']\n",
      "0 -3 0 9\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 16.\n",
      "We have 4080 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 16446189163622400.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1394655853500000000000000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2468484764539363131219577975910400.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 5109182076493501020019711207434240000.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 80.\n",
      "We have 15111572745169120787664 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 183494191878513995389747200000000000000000.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 370506320469734457582942481020332597540347974758400.\n",
      "***********************************\n",
      "n is 55.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 142511013791578919045574218416554310646476800000000000000000000.\n",
      "***********************************\n",
      "n is 59.\n",
      "The order of the Frobenius is 116.\n",
      "We have 716178877039286566967737630308705 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2815254155968646360209400671612495623611873736570976310507520000.\n",
      "***********************************\n",
      "n is 99.\n",
      "The order of the Frobenius is 240.\n",
      "We have 7361862769909934706597072919762160477076066254539558997491267234955536 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 151343257380981531068227153985461530090635137663735205377345585152000000.\n",
      "['3', '5', '9', '11', '15', '27', '55', '59', '99']\n",
      "0 -3 1 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "['3']\n",
      "0 -2 -1 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "0 -2 -1 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "['3', '11']\n",
      "0 -2 0 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 10.\n",
      "We have 99 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 26313902661795840.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 649127370230584181828075520000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 30.\n",
      "We have 35790267 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 3949575623262981009951324761456640.\n",
      "***********************************\n",
      "n is 13.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1795849439724535843832505615198484070400.\n",
      "***********************************\n",
      "n is 21.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 34162148870710205624229224771006028683673600000.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 90.\n",
      "We have 13754889325392723216145164 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 592810112751575132132707969632532156064556759613440.\n",
      "***********************************\n",
      "n is 47.\n",
      "The order of the Frobenius is 92.\n",
      "We have 53823479968928812291873035 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 783964061435643196649178651959525883371037005110030997913600.\n",
      "***********************************\n",
      "n is 49.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1721311070532199434768105504686408634459537165592406507520000.\n",
      "***********************************\n",
      "n is 63.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 15382665827133116070047119093387333552727208767663538752716800000.\n",
      "***********************************\n",
      "n is 89.\n",
      "The order of the Frobenius is 88.\n",
      "We have 3516875111605994051576550 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 15065564203696702099946252489589827058925193934062868227323646115840000.\n",
      "***********************************\n",
      "n is 91.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 13988820289661471406276180147610678520451975960277619306498359296000000.\n",
      "***********************************\n",
      "n is 93.\n",
      "The order of the Frobenius is 240.\n",
      "We have 7361862769909934706597072919762160477076066254539558997491267234955536 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 16056971240616175225729443562595730404821388809328122267101560832000000.\n",
      "['3', '7', '9', '13', '21', '27', '47', '49', '63', '89', '91', '93']\n",
      "0 -2 0 2\n",
      "****************\n",
      "p-rank is 0.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1162213211250000000000000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 80.\n",
      "We have 15111572745169120787664 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 3831886557370125765014783405575680000.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 305823653130856658982912000000000000000000.\n",
      "***********************************\n",
      "n is 17.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 43796366654156589037064980240732505348505600.\n",
      "***********************************\n",
      "n is 29.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 22119769862896408048724133628291257570336870021120000.\n",
      "***********************************\n",
      "n is 37.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 142532692134702083741989049522003954470918246973906534400.\n",
      "***********************************\n",
      "n is 45.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 45902489681871893628232973572041618020352000000000000000000.\n",
      "***********************************\n",
      "n is 51.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 11524533290777976354111515910057812869540227972699562967040000.\n",
      "***********************************\n",
      "n is 53.\n",
      "The order of the Frobenius is 104.\n",
      "We have 195023169265881403080265614570 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 59257949449230365265985592681009875476724801536661098254745600.\n",
      "***********************************\n",
      "n is 85.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1221617182325033940122732063051988554240267850350592000000000000000000.\n",
      "***********************************\n",
      "n is 87.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1940191570245270648561170916393031739899543577133125296126427136000000.\n",
      "['3', '5', '9', '11', '15', '17', '29', '37', '45', '51', '53', '85', '87']\n",
      "0 -2 0 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 36.\n",
      "We have 1908866960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 7309417406054400.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2324426422500000000000000.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 96.\n",
      "We have 825293359523583917857003520 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 162281842557646045457018880000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 108.\n",
      "We have 3004801422763210266376748072960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1097104339795272502764256878182400.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 203882435420571105988608000000000000000000.\n",
      "***********************************\n",
      "n is 25.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 33824856254796031862497329711914062500000000000000.\n",
      "***********************************\n",
      "n is 29.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 22119769862896408048724133628291257570336870021120000.\n",
      "***********************************\n",
      "n is 35.\n",
      "The order of the Frobenius is 96.\n",
      "We have 825293359523583917857003520 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 9053092865591458739110338546080563200000000000000000000.\n",
      "***********************************\n",
      "n is 71.\n",
      "The order of the Frobenius is 70.\n",
      "We have 16865594581186450683 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4417884685101844093339615138147356028825028252460368993846231040000.\n",
      "['3', '5', '7', '9', '15', '25', '29', '35', '71']\n",
      "0 -2 0 4\n",
      "****************\n",
      "p-rank is 0.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 10.\n",
      "We have 99 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 26313902661795840.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1394655853500000000000000.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 259650948092233672731230208000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 30.\n",
      "We have 35790267 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 3949575623262981009951324761456640.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 10.\n",
      "We have 99 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 30655092458961006120118267244605440000.\n",
      "***********************************\n",
      "n is 13.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1257094607807175090682753930638938849280.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 366988383757027990779494400000000000000000.\n",
      "***********************************\n",
      "n is 17.\n",
      "The order of the Frobenius is 80.\n",
      "We have 15111572745169120787664 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 39416729988740930133358482216659254813655040.\n",
      "***********************************\n",
      "n is 19.\n",
      "The order of the Frobenius is 90.\n",
      "We have 13754889325392723216145164 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2162477448301482392501266615671936620802048000.\n",
      "***********************************\n",
      "n is 21.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 68324297741420411248458449542012057367347200000.\n",
      "***********************************\n",
      "n is 25.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 101474568764388095587491989135742187500000000000000.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 90.\n",
      "We have 13754889325392723216145164 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 592810112751575132132707969632532156064556759613440.\n",
      "***********************************\n",
      "n is 31.\n",
      "The order of the Frobenius is 20.\n",
      "We have 52377 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 732250390084266038337104799217478377764849199349760000.\n",
      "***********************************\n",
      "n is 33.\n",
      "The order of the Frobenius is 10.\n",
      "We have 99 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 8066551190534516010219568851931671473150226333696000000.\n",
      "***********************************\n",
      "n is 35.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 7242474292473166991288270836864450560000000000000000000.\n",
      "***********************************\n",
      "n is 39.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 330790651465064221662870971864171453044449630278909952000.\n",
      "***********************************\n",
      "n is 41.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 11480485553355963924038949061575562630481611673725501440000.\n",
      "***********************************\n",
      "n is 43.\n",
      "The order of the Frobenius is 70.\n",
      "We have 16865594581186450683 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 38263137627916384552885460548159850070927239244112269312000.\n",
      "***********************************\n",
      "n is 45.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 55082987618246272353879568286449941624422400000000000000000.\n",
      "***********************************\n",
      "n is 51.\n",
      "The order of the Frobenius is 80.\n",
      "We have 15111572745169120787664 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10372079961700178718700364319052031582586205175429606670336000.\n",
      "***********************************\n",
      "n is 55.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 427533041374736757136722655249662931939430400000000000000000000.\n",
      "***********************************\n",
      "n is 57.\n",
      "The order of the Frobenius is 90.\n",
      "We have 13754889325392723216145164 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 569032210829338535107399777912484453725627128617488298803200000.\n",
      "***********************************\n",
      "n is 61.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 9348185102095378678812910339386905121815408198079334002309120000.\n",
      "***********************************\n",
      "n is 63.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 30765331654266232140094238186774667105454417535327077505433600000.\n",
      "***********************************\n",
      "n is 65.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 70128574127262541580803843234629162447076250419200000000000000000.\n",
      "***********************************\n",
      "n is 69.\n",
      "The order of the Frobenius is 220.\n",
      "We have 7659075757713249941666765649721480086491394966826721044785047445 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 276416558871251679222360549403058606948397568740829137702223872000.\n",
      "***********************************\n",
      "n is 71.\n",
      "The order of the Frobenius is 140.\n",
      "We have 9955689820772599616748584288712892238241 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2208942342550922046669807569073678014412514126230184496923115520000.\n",
      "***********************************\n",
      "n is 73.\n",
      "The order of the Frobenius is 180.\n",
      "We have 8513864115921604768657483477290939684335762639067568 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4803982716903952877706674216712440958261836051763817282561738014720.\n",
      "***********************************\n",
      "n is 75.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 26701919251138169113218784332275390625000000000000000000000000000000.\n",
      "***********************************\n",
      "n is 77.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 79596238208243080995279224964774192133077554642481027691315200000000.\n",
      "***********************************\n",
      "n is 85.\n",
      "The order of the Frobenius is 80.\n",
      "We have 15111572745169120787664 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2198910928185061092220917713493579397632482130631065600000000000000000.\n",
      "***********************************\n",
      "n is 89.\n",
      "The order of the Frobenius is 220.\n",
      "We have 7659075757713249941666765649721480086491394966826721044785047445 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6026225681478680839978500995835930823570077573625147290929458446336000.\n",
      "***********************************\n",
      "n is 91.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 19584348405526059968786652206654949928632766344388667029097703014400000.\n",
      "***********************************\n",
      "n is 93.\n",
      "The order of the Frobenius is 20.\n",
      "We have 52377 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 192683654887394102708753322751148764857856665711937467205218729984000000.\n",
      "***********************************\n",
      "n is 99.\n",
      "The order of the Frobenius is 30.\n",
      "We have 35790267 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1210746059047852248545817231883692240725081101309881643018764681216000000.\n",
      "['3', '5', '7', '9', '11', '13', '15', '17', '19', '21', '25', '27', '31', '33', '35', '39', '41', '43', '45', '51', '55', '57', '61', '63', '65', '69', '71', '73', '75', '77', '85', '89', '91', '93', '99']\n",
      "0 -2 0 6\n",
      "****************\n",
      "p-rank is 0.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 36.\n",
      "We have 1908866960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 7309417406054400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 108.\n",
      "We have 3004801422763210266376748072960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1097104339795272502764256878182400.\n",
      "***********************************\n",
      "n is 97.\n",
      "The order of the Frobenius is 192.\n",
      "We have 32693238205138962311644736578793949237341897722922270720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 166996078617282765772266074518735807691476112968614851318229602245017600.\n",
      "['3', '9', '97']\n",
      "0 -2 0 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 10.\n",
      "We have 99 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 26313902661795840.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1162213211250000000000000.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 42.\n",
      "We have 104715342801 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 370929925846048103901757440000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 30.\n",
      "We have 35790267 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 3949575623262981009951324761456640.\n",
      "***********************************\n",
      "n is 17.\n",
      "The order of the Frobenius is 32.\n",
      "We have 134215680 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 98541824971852325333396205541648137034137600.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 90.\n",
      "We have 13754889325392723216145164 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 592810112751575132132707969632532156064556759613440.\n",
      "***********************************\n",
      "n is 51.\n",
      "The order of the Frobenius is 160.\n",
      "We have 9134385233318143238773022648690396281390393344 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 5186039980850089359350182159526015791293102587714803335168000.\n",
      "***********************************\n",
      "n is 63.\n",
      "The order of the Frobenius is 210.\n",
      "We have 7835735987243838295976043726463380667445368484290985174649363 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 8790094758361780611455496624792762030129833581522022144409600000.\n",
      "***********************************\n",
      "n is 85.\n",
      "The order of the Frobenius is 96.\n",
      "We have 825293359523583917857003520 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1832425773487550910184098094577982831360401775525888000000000000000000.\n",
      "['3', '5', '7', '9', '17', '27', '51', '63', '85']\n",
      "0 -2 1 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "0 -2 1 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "['3', '11']\n",
      "0 -1 -2 2\n",
      "****************\n",
      "p-rank is 2.\n",
      "[]\n",
      "0 -1 -1 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "0 -1 -1 0\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 122329461252342663593164800000000000000000.\n",
      "['3', '9', '15']\n",
      "0 -1 -1 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 996182752500000000000000.\n",
      "***********************************\n",
      "n is 53.\n",
      "The order of the Frobenius is 156.\n",
      "We have 585537514956291233254679485982745394048986165 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 39505299632820243510657061787339916984483201024440732169830400.\n",
      "['5', '53']\n",
      "0 -1 -1 2\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "0 -1 -1 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "['3', '9']\n",
      "0 -1 -1 4\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "0 -1 -1 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "0 -1 0 -3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 18.\n",
      "We have 14532 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 14618834812108800.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 324563685115292090914037760000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 54.\n",
      "We have 333599969907456 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2194208679590545005528513756364800.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "***********************************\n",
      "n is 17.\n",
      "The order of the Frobenius is 96.\n",
      "We have 825293359523583917857003520 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 32847274990617441777798735180549379011379200.\n",
      "***********************************\n",
      "n is 19.\n",
      "The order of the Frobenius is 36.\n",
      "We have 1908866960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 5406193620753705981253166539179841552005120000.\n",
      "***********************************\n",
      "n is 21.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 28468457392258504686857687309171690569728000000.\n",
      "***********************************\n",
      "n is 23.\n",
      "The order of the Frobenius is 66.\n",
      "We have 1117984489185516357 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 3501527467868033452177559052336872987970935193600.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 162.\n",
      "We have 36086460181009948597621832796379474289919787008 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 329338951528652851184837760906962308924753755340800.\n",
      "***********************************\n",
      "n is 31.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 244083463361422012779034933072492792588283066449920000.\n",
      "***********************************\n",
      "n is 47.\n",
      "The order of the Frobenius is 138.\n",
      "We have 2524993795123485410042792044415965268769 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 522642707623762131099452434639683922247358003406687331942400.\n",
      "***********************************\n",
      "n is 55.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 142511013791578919045574218416554310646476800000000000000000000.\n",
      "***********************************\n",
      "n is 57.\n",
      "The order of the Frobenius is 36.\n",
      "We have 1908866960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1422580527073346337768499444781211134314067821543720747008000000.\n",
      "***********************************\n",
      "n is 61.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 18696370204190757357625820678773810243630816396158668004618240000.\n",
      "***********************************\n",
      "n is 69.\n",
      "The order of the Frobenius is 198.\n",
      "We have 2028962177094684691340861227700286996617994175599311154996 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 307129509856946310247067277114509563275997298600921264113582080000.\n",
      "***********************************\n",
      "n is 79.\n",
      "The order of the Frobenius is 156.\n",
      "We have 585537514956291233254679485982745394048986165 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 103151533014311705289524690254069332149432933578964636349872209920000.\n",
      "***********************************\n",
      "n is 93.\n",
      "The order of the Frobenius is 180.\n",
      "We have 8513864115921604768657483477290939684335762639067568 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 21409294987488233634305924750127640539761851745770829689468747776000000.\n",
      "['3', '7', '9', '11', '17', '19', '21', '23', '27', '31', '47', '55', '57', '61', '69', '79', '93']\n",
      "0 -1 0 -2\n",
      "****************\n",
      "p-rank is 2.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 20.\n",
      "We have 52377 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 13156951330897920.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1394655853500000000000000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1974787811631490504975662380728320.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 366988383757027990779494400000000000000000.\n",
      "***********************************\n",
      "n is 45.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 55082987618246272353879568286449941624422400000000000000000.\n",
      "***********************************\n",
      "n is 59.\n",
      "The order of the Frobenius is 116.\n",
      "We have 716178877039286566967737630308705 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2815254155968646360209400671612495623611873736570976310507520000.\n",
      "***********************************\n",
      "n is 75.\n",
      "The order of the Frobenius is 200.\n",
      "We have 8034690221294951377709810461699474759609873821900983107584 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 5340383850227633822643756866455078125000000000000000000000000000000.\n",
      "***********************************\n",
      "n is 99.\n",
      "The order of the Frobenius is 240.\n",
      "We have 7361862769909934706597072919762160477076066254539558997491267234955536 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 151343257380981531068227153985461530090635137663735205377345585152000000.\n",
      "['3', '5', '9', '15', '45', '59', '75', '99']\n",
      "0 -1 0 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 324563685115292090914037760000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 110.\n",
      "We have 11800674678488244282762064174071 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2786826587178273283647115204055040000.\n",
      "***********************************\n",
      "n is 21.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 85405372176775514060573061927515071709184000000.\n",
      "***********************************\n",
      "n is 41.\n",
      "The order of the Frobenius is 80.\n",
      "We have 15111572745169120787664 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 5740242776677981962019474530787781315240805836862750720000.\n",
      "***********************************\n",
      "n is 63.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 12818888189277596725039265911156111293939340639719615627264000000.\n",
      "***********************************\n",
      "n is 83.\n",
      "The order of the Frobenius is 164.\n",
      "We have 142585525593258821288164344437544206438891596725 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 610545837083863781519156172269369795090940749877073930937268556185600.\n",
      "['3', '7', '9', '11', '21', '41', '63', '83']\n",
      "0 -1 0 0\n",
      "****************\n",
      "p-rank is 2.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 18.\n",
      "We have 14532 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 14618834812108800.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 54.\n",
      "We have 333599969907456 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2194208679590545005528513756364800.\n",
      "***********************************\n",
      "n is 13.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1795849439724535843832505615198484070400.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 162.\n",
      "We have 36086460181009948597621832796379474289919787008 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 329338951528652851184837760906962308924753755340800.\n",
      "***********************************\n",
      "n is 97.\n",
      "The order of the Frobenius is 96.\n",
      "We have 825293359523583917857003520 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 333992157234565531544532149037471615382952225937229702636459204490035200.\n",
      "['3', '9', '13', '27', '97']\n",
      "0 -1 0 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 20.\n",
      "We have 52377 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 13156951330897920.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 324563685115292090914037760000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1974787811631490504975662380728320.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 122329461252342663593164800000000000000000.\n",
      "***********************************\n",
      "n is 45.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 55082987618246272353879568286449941624422400000000000000000.\n",
      "***********************************\n",
      "n is 67.\n",
      "The order of the Frobenius is 132.\n",
      "We have 41246347505568298601062172159252055475 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 273883659998363740992418941722706278797682072780049411537588633600.\n",
      "***********************************\n",
      "n is 83.\n",
      "The order of the Frobenius is 164.\n",
      "We have 142585525593258821288164344437544206438891596725 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 610545837083863781519156172269369795090940749877073930937268556185600.\n",
      "['3', '7', '9', '15', '45', '67', '83']\n",
      "0 -1 0 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 18.\n",
      "We have 14532 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 14618834812108800.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1394655853500000000000000.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 42.\n",
      "We have 104715342801 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 370929925846048103901757440000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 54.\n",
      "We have 333599969907456 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2194208679590545005528513756364800.\n",
      "***********************************\n",
      "n is 21.\n",
      "The order of the Frobenius is 126.\n",
      "We have 675163426430433459179525995420973028 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 32535379876866862499265928353339074936832000000.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 162.\n",
      "We have 36086460181009948597621832796379474289919787008 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 329338951528652851184837760906962308924753755340800.\n",
      "***********************************\n",
      "n is 41.\n",
      "The order of the Frobenius is 80.\n",
      "We have 15111572745169120787664 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 5740242776677981962019474530787781315240805836862750720000.\n",
      "***********************************\n",
      "n is 59.\n",
      "The order of the Frobenius is 116.\n",
      "We have 716178877039286566967737630308705 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2815254155968646360209400671612495623611873736570976310507520000.\n",
      "['3', '5', '7', '9', '21', '27', '41', '59']\n",
      "0 -1 0 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "***********************************\n",
      "n is 19.\n",
      "The order of the Frobenius is 90.\n",
      "We have 13754889325392723216145164 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2162477448301482392501266615671936620802048000.\n",
      "['3', '9', '19']\n",
      "0 -1 0 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 20.\n",
      "We have 52377 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 13156951330897920.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1974787811631490504975662380728320.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 122329461252342663593164800000000000000000.\n",
      "***********************************\n",
      "n is 29.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 22119769862896408048724133628291257570336870021120000.\n",
      "***********************************\n",
      "n is 41.\n",
      "The order of the Frobenius is 80.\n",
      "We have 15111572745169120787664 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 5740242776677981962019474530787781315240805836862750720000.\n",
      "***********************************\n",
      "n is 45.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 55082987618246272353879568286449941624422400000000000000000.\n",
      "['3', '9', '15', '29', '41', '45']\n",
      "0 -1 1 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "0 -1 1 0\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 122329461252342663593164800000000000000000.\n",
      "['3', '9', '15']\n",
      "0 -1 1 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 996182752500000000000000.\n",
      "***********************************\n",
      "n is 53.\n",
      "The order of the Frobenius is 156.\n",
      "We have 585537514956291233254679485982745394048986165 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 39505299632820243510657061787339916984483201024440732169830400.\n",
      "['5', '53']\n",
      "0 -1 1 2\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "0 -1 1 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "['3', '9']\n",
      "0 -1 1 4\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "0 -1 1 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "0 -1 2 2\n",
      "****************\n",
      "p-rank is 2.\n",
      "[]\n",
      "0 0 -3 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 12.\n",
      "We have 335 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 21928252218163200.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 36.\n",
      "We have 1908866960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 3291313019385817508292770634547200.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 108.\n",
      "We have 3004801422763210266376748072960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 494008427292979276777256641360443463387130633011200.\n",
      "['3', '9', '27']\n",
      "0 0 -2 -2\n",
      "****************\n",
      "p-rank is 0.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "['3']\n",
      "0 0 -2 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "['11']\n",
      "0 0 -2 0\n",
      "****************\n",
      "p-rank is 0.\n",
      "[]\n",
      "0 0 -2 2\n",
      "****************\n",
      "p-rank is 0.\n",
      "[]\n",
      "0 0 -2 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "0 0 -1 -5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "***********************************\n",
      "n is 29.\n",
      "The order of the Frobenius is 140.\n",
      "We have 9955689820772599616748584288712892238241 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 8847907945158563219489653451316503028134748008448000.\n",
      "['3', '29']\n",
      "0 0 -1 -4\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "0 0 -1 -3\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "0 0 -1 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "0 0 -1 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "['3']\n",
      "0 0 -1 2\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "0 0 -1 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 17.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 21898183327078294518532490120366252674252800.\n",
      "['17']\n",
      "0 0 -1 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "0 0 0 -7\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 20.\n",
      "We have 52377 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2789311707000000000000000.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 324563685115292090914037760000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 5109182076493501020019711207434240000.\n",
      "***********************************\n",
      "n is 13.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1795849439724535843832505615198484070400.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 122329461252342663593164800000000000000000.\n",
      "***********************************\n",
      "n is 17.\n",
      "The order of the Frobenius is 32.\n",
      "We have 134215680 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 98541824971852325333396205541648137034137600.\n",
      "***********************************\n",
      "n is 19.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2703096810376852990626583269589920776002560000.\n",
      "***********************************\n",
      "n is 21.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 85405372176775514060573061927515071709184000000.\n",
      "***********************************\n",
      "n is 23.\n",
      "The order of the Frobenius is 88.\n",
      "We have 3516875111605994051576550 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2626145600901025089133169289252654740978201395200.\n",
      "***********************************\n",
      "n is 25.\n",
      "The order of the Frobenius is 100.\n",
      "We have 12676506002282282755967953152 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 40589827505755238234996795654296875000000000000000.\n",
      "***********************************\n",
      "n is 31.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 122041731680711006389517466536246396294141533224960000.\n",
      "***********************************\n",
      "n is 33.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 672212599211209667518297404327639289429185527808000000.\n",
      "***********************************\n",
      "n is 39.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 236279036760760158330622122760122466460321164484935680000.\n",
      "***********************************\n",
      "n is 47.\n",
      "The order of the Frobenius is 184.\n",
      "We have 133260481814425118118117132768767319460642961170332270 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 391982030717821598324589325979762941685518502555015498956800.\n",
      "***********************************\n",
      "n is 51.\n",
      "The order of the Frobenius is 96.\n",
      "We have 825293359523583917857003520 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 8643399968083482265583636932543359652155170979524672225280000.\n",
      "***********************************\n",
      "n is 53.\n",
      "The order of the Frobenius is 52.\n",
      "We have 86607683851185 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 118515898898460730531971185362019750953449603073322196509491200.\n",
      "***********************************\n",
      "n is 55.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 285022027583157838091148436833108621292953600000000000000000000.\n",
      "***********************************\n",
      "n is 57.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 711290263536673168884249722390605567157033910771860373504000000.\n",
      "***********************************\n",
      "n is 61.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 9348185102095378678812910339386905121815408198079334002309120000.\n",
      "***********************************\n",
      "n is 63.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 12818888189277596725039265911156111293939340639719615627264000000.\n",
      "***********************************\n",
      "n is 85.\n",
      "The order of the Frobenius is 160.\n",
      "We have 9134385233318143238773022648690396281390393344 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1099455464092530546110458856746789698816241065315532800000000000000000.\n",
      "***********************************\n",
      "n is 93.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 32113942481232350451458887125191460809642777618656244534203121664000000.\n",
      "['3', '5', '7', '9', '11', '13', '15', '17', '19', '21', '23', '25', '31', '33', '39', '47', '51', '53', '55', '57', '61', '63', '85', '93']\n",
      "0 0 0 -6\n",
      "****************\n",
      "p-rank is 0.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 16.\n",
      "We have 4080 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 16446189163622400.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2324426422500000000000000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2468484764539363131219577975910400.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 20.\n",
      "We have 52377 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 15327546229480503060059133622302720000.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 305823653130856658982912000000000000000000.\n",
      "***********************************\n",
      "n is 17.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 21898183327078294518532490120366252674252800.\n",
      "***********************************\n",
      "n is 23.\n",
      "The order of the Frobenius is 88.\n",
      "We have 3516875111605994051576550 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2626145600901025089133169289252654740978201395200.\n",
      "***********************************\n",
      "n is 25.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 33824856254796031862497329711914062500000000000000.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 370506320469734457582942481020332597540347974758400.\n",
      "***********************************\n",
      "n is 29.\n",
      "The order of the Frobenius is 112.\n",
      "We have 46359793379775246039936627600240 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 11059884931448204024362066814145628785168435010560000.\n",
      "***********************************\n",
      "n is 33.\n",
      "The order of the Frobenius is 80.\n",
      "We have 15111572745169120787664 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1008318898816814501277446106491458934143778291712000000.\n",
      "***********************************\n",
      "n is 35.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 5173195923195119279491622026331750400000000000000000000.\n",
      "***********************************\n",
      "n is 37.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 71266346067351041870994524761001977235459123486953267200.\n",
      "***********************************\n",
      "n is 43.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 31885948023263653794071217123466541725772699370093557760000.\n",
      "***********************************\n",
      "n is 45.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 137707469045615680884698920716124854061056000000000000000000.\n",
      "***********************************\n",
      "n is 51.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 5762266645388988177055757955028906434770113986349781483520000.\n",
      "***********************************\n",
      "n is 53.\n",
      "The order of the Frobenius is 208.\n",
      "We have 1977769900626449569897799498265948768442693820855629897047120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 29628974724615182632992796340504937738362400768330549127372800.\n",
      "***********************************\n",
      "n is 55.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 142511013791578919045574218416554310646476800000000000000000000.\n",
      "***********************************\n",
      "n is 65.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 50091838662330386843431316596163687462197321728000000000000000000.\n",
      "***********************************\n",
      "n is 67.\n",
      "The order of the Frobenius is 132.\n",
      "We have 41246347505568298601062172159252055475 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 273883659998363740992418941722706278797682072780049411537588633600.\n",
      "***********************************\n",
      "n is 69.\n",
      "The order of the Frobenius is 176.\n",
      "We have 544210064227943486632935732314825648606966627338800 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 345520698589064599027950686753823258685496960926036422127779840000.\n",
      "***********************************\n",
      "n is 85.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1221617182325033940122732063051988554240267850350592000000000000000000.\n",
      "***********************************\n",
      "n is 87.\n",
      "The order of the Frobenius is 112.\n",
      "We have 46359793379775246039936627600240 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2910287355367905972841756374589547609849315365699687944189640704000000.\n",
      "***********************************\n",
      "n is 91.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 13988820289661471406276180147610678520451975960277619306498359296000000.\n",
      "***********************************\n",
      "n is 99.\n",
      "The order of the Frobenius is 240.\n",
      "We have 7361862769909934706597072919762160477076066254539558997491267234955536 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 151343257380981531068227153985461530090635137663735205377345585152000000.\n",
      "['3', '5', '9', '11', '15', '17', '23', '25', '27', '29', '33', '35', '37', '43', '45', '51', '53', '55', '65', '67', '69', '85', '87', '91', '99']\n",
      "0 0 0 -5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 12.\n",
      "We have 335 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 21928252218163200.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 16.\n",
      "We have 4080 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 3486639633750000000000000.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 96.\n",
      "We have 825293359523583917857003520 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 162281842557646045457018880000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 12.\n",
      "We have 335 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 9873939058157452524878311903641600.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 7663773114740251530029566811151360000.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 305823653130856658982912000000000000000000.\n",
      "***********************************\n",
      "n is 17.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 21898183327078294518532490120366252674252800.\n",
      "***********************************\n",
      "n is 21.\n",
      "The order of the Frobenius is 96.\n",
      "We have 825293359523583917857003520 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 42702686088387757030286530963757535854592000000.\n",
      "***********************************\n",
      "n is 25.\n",
      "The order of the Frobenius is 80.\n",
      "We have 15111572745169120787664 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 50737284382194047793745994567871093750000000000000.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 36.\n",
      "We have 1908866960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1482025281878937830331769924081330390161391899033600.\n",
      "***********************************\n",
      "n is 33.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 672212599211209667518297404327639289429185527808000000.\n",
      "***********************************\n",
      "n is 35.\n",
      "The order of the Frobenius is 96.\n",
      "We have 825293359523583917857003520 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 9053092865591458739110338546080563200000000000000000000.\n",
      "***********************************\n",
      "n is 39.\n",
      "The order of the Frobenius is 156.\n",
      "We have 585537514956291233254679485982745394048986165 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 254454347280818632048362286049362656188038177137623040000.\n",
      "***********************************\n",
      "n is 41.\n",
      "The order of the Frobenius is 160.\n",
      "We have 9134385233318143238773022648690396281390393344 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2870121388338990981009737265393890657620402918431375360000.\n",
      "***********************************\n",
      "n is 43.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 31885948023263653794071217123466541725772699370093557760000.\n",
      "***********************************\n",
      "n is 45.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 137707469045615680884698920716124854061056000000000000000000.\n",
      "***********************************\n",
      "n is 47.\n",
      "The order of the Frobenius is 184.\n",
      "We have 133260481814425118118117132768767319460642961170332270 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 391982030717821598324589325979762941685518502555015498956800.\n",
      "***********************************\n",
      "n is 51.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 5762266645388988177055757955028906434770113986349781483520000.\n",
      "***********************************\n",
      "n is 55.\n",
      "The order of the Frobenius is 80.\n",
      "We have 15111572745169120787664 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 213766520687368378568361327624831465969715200000000000000000000.\n",
      "***********************************\n",
      "n is 61.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 9348185102095378678812910339386905121815408198079334002309120000.\n",
      "***********************************\n",
      "n is 63.\n",
      "The order of the Frobenius is 96.\n",
      "We have 825293359523583917857003520 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 19228332283916395087558898866734166940909010959579423440896000000.\n",
      "***********************************\n",
      "n is 79.\n",
      "The order of the Frobenius is 156.\n",
      "We have 585537514956291233254679485982745394048986165 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 103151533014311705289524690254069332149432933578964636349872209920000.\n",
      "***********************************\n",
      "n is 81.\n",
      "The order of the Frobenius is 108.\n",
      "We have 3004801422763210266376748072960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 222444044184551493849160699681147801052073566565925486885499949465600.\n",
      "***********************************\n",
      "n is 85.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1221617182325033940122732063051988554240267850350592000000000000000000.\n",
      "***********************************\n",
      "n is 99.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 302686514761963062136454307970923060181270275327470410754691170304000000.\n",
      "['3', '5', '7', '9', '11', '15', '17', '21', '25', '27', '33', '35', '39', '41', '43', '45', '47', '51', '55', '61', '63', '79', '81', '85', '99']\n",
      "0 0 0 -3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 16.\n",
      "We have 4080 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 16446189163622400.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1394655853500000000000000.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 12.\n",
      "We have 335 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1298254740461168363656151040000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2468484764539363131219577975910400.\n",
      "***********************************\n",
      "n is 13.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 3142736519517937726706884826597347123200.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 80.\n",
      "We have 15111572745169120787664 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 183494191878513995389747200000000000000000.\n",
      "***********************************\n",
      "n is 17.\n",
      "The order of the Frobenius is 64.\n",
      "We have 288230376084602880 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 49270912485926162666698102770824068517068800.\n",
      "***********************************\n",
      "n is 21.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 85405372176775514060573061927515071709184000000.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 370506320469734457582942481020332597540347974758400.\n",
      "***********************************\n",
      "n is 31.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 122041731680711006389517466536246396294141533224960000.\n",
      "***********************************\n",
      "n is 35.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 7242474292473166991288270836864450560000000000000000000.\n",
      "***********************************\n",
      "n is 39.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 826976628662660554157177429660428632611124075697274880000.\n",
      "***********************************\n",
      "n is 41.\n",
      "The order of the Frobenius is 140.\n",
      "We have 9955689820772599616748584288712892238241 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 3280138729530275406868271160450160751566174763921571840000.\n",
      "***********************************\n",
      "n is 43.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 31885948023263653794071217123466541725772699370093557760000.\n",
      "***********************************\n",
      "n is 49.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 3442622141064398869536211009372817268919074331184813015040000.\n",
      "***********************************\n",
      "n is 51.\n",
      "The order of the Frobenius is 64.\n",
      "We have 288230376084602880 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 12965099952125223398375455398815039478232756469287008337920000.\n",
      "***********************************\n",
      "n is 63.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 38456664567832790175117797733468333881818021919158846881792000000.\n",
      "***********************************\n",
      "n is 83.\n",
      "The order of the Frobenius is 164.\n",
      "We have 142585525593258821288164344437544206438891596725 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 610545837083863781519156172269369795090940749877073930937268556185600.\n",
      "***********************************\n",
      "n is 89.\n",
      "The order of the Frobenius is 176.\n",
      "We have 544210064227943486632935732314825648606966627338800 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 7532782101848351049973126244794913529462596967031434113661823057920000.\n",
      "***********************************\n",
      "n is 91.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 48960871013815149921966630516637374821581915860971667572744257536000000.\n",
      "***********************************\n",
      "n is 93.\n",
      "The order of the Frobenius is 240.\n",
      "We have 7361862769909934706597072919762160477076066254539558997491267234955536 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 16056971240616175225729443562595730404821388809328122267101560832000000.\n",
      "['3', '5', '7', '9', '13', '15', '17', '21', '27', '31', '35', '39', '41', '43', '49', '51', '63', '83', '89', '91', '93']\n",
      "0 0 0 -2\n",
      "****************\n",
      "p-rank is 0.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 12.\n",
      "We have 335 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 21928252218163200.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 20.\n",
      "We have 52377 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2789311707000000000000000.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 96.\n",
      "We have 825293359523583917857003520 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 162281842557646045457018880000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 36.\n",
      "We have 1908866960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 3291313019385817508292770634547200.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 244658922504685327186329600000000000000000.\n",
      "***********************************\n",
      "n is 17.\n",
      "The order of the Frobenius is 64.\n",
      "We have 288230376084602880 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 49270912485926162666698102770824068517068800.\n",
      "***********************************\n",
      "n is 19.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2703096810376852990626583269589920776002560000.\n",
      "***********************************\n",
      "n is 21.\n",
      "The order of the Frobenius is 96.\n",
      "We have 825293359523583917857003520 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 42702686088387757030286530963757535854592000000.\n",
      "***********************************\n",
      "n is 23.\n",
      "The order of the Frobenius is 88.\n",
      "We have 3516875111605994051576550 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2626145600901025089133169289252654740978201395200.\n",
      "***********************************\n",
      "n is 25.\n",
      "The order of the Frobenius is 100.\n",
      "We have 12676506002282282755967953152 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 40589827505755238234996795654296875000000000000000.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 108.\n",
      "We have 3004801422763210266376748072960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 494008427292979276777256641360443463387130633011200.\n",
      "***********************************\n",
      "n is 31.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 244083463361422012779034933072492792588283066449920000.\n",
      "***********************************\n",
      "n is 39.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 236279036760760158330622122760122466460321164484935680000.\n",
      "***********************************\n",
      "n is 45.\n",
      "The order of the Frobenius is 180.\n",
      "We have 8513864115921604768657483477290939684335762639067568 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 36721991745497514902586378857633294416281600000000000000000.\n",
      "***********************************\n",
      "n is 47.\n",
      "The order of the Frobenius is 184.\n",
      "We have 133260481814425118118117132768767319460642961170332270 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 391982030717821598324589325979762941685518502555015498956800.\n",
      "***********************************\n",
      "n is 51.\n",
      "The order of the Frobenius is 192.\n",
      "We have 32693238205138962311644736578793949237341897722922270720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4321699984041741132791818466271679826077585489762336112640000.\n",
      "***********************************\n",
      "n is 53.\n",
      "The order of the Frobenius is 52.\n",
      "We have 86607683851185 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 118515898898460730531971185362019750953449603073322196509491200.\n",
      "***********************************\n",
      "n is 57.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 711290263536673168884249722390605567157033910771860373504000000.\n",
      "***********************************\n",
      "n is 79.\n",
      "The order of the Frobenius is 156.\n",
      "We have 585537514956291233254679485982745394048986165 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 103151533014311705289524690254069332149432933578964636349872209920000.\n",
      "***********************************\n",
      "n is 83.\n",
      "The order of the Frobenius is 164.\n",
      "We have 142585525593258821288164344437544206438891596725 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 610545837083863781519156172269369795090940749877073930937268556185600.\n",
      "***********************************\n",
      "n is 93.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 64227884962464700902917774250382921619285555237312489068406243328000000.\n",
      "['3', '5', '7', '9', '15', '17', '19', '21', '23', '25', '27', '31', '39', '45', '47', '51', '53', '57', '79', '83', '93']\n",
      "0 0 0 0\n",
      "****************\n",
      "p-rank is 0.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 16.\n",
      "We have 4080 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 16446189163622400.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 16.\n",
      "We have 4080 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 3486639633750000000000000.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 324563685115292090914037760000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2468484764539363131219577975910400.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 80.\n",
      "We have 15111572745169120787664 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 3831886557370125765014783405575680000.\n",
      "***********************************\n",
      "n is 13.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 3142736519517937726706884826597347123200.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 16.\n",
      "We have 4080 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 917470959392569976948736000000000000000000.\n",
      "***********************************\n",
      "n is 17.\n",
      "The order of the Frobenius is 8.\n",
      "We have 30 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 394167299887409301333584822166592548136550400.\n",
      "***********************************\n",
      "n is 19.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1351548405188426495313291634794960388001280000.\n",
      "***********************************\n",
      "n is 21.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 85405372176775514060573061927515071709184000000.\n",
      "***********************************\n",
      "n is 25.\n",
      "The order of the Frobenius is 80.\n",
      "We have 15111572745169120787664 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 50737284382194047793745994567871093750000000000000.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 370506320469734457582942481020332597540347974758400.\n",
      "***********************************\n",
      "n is 29.\n",
      "The order of the Frobenius is 112.\n",
      "We have 46359793379775246039936627600240 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 11059884931448204024362066814145628785168435010560000.\n",
      "***********************************\n",
      "n is 31.\n",
      "The order of the Frobenius is 80.\n",
      "We have 15111572745169120787664 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 183062597521066509584276199804369594441212299837440000.\n",
      "***********************************\n",
      "n is 33.\n",
      "The order of the Frobenius is 80.\n",
      "We have 15111572745169120787664 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1008318898816814501277446106491458934143778291712000000.\n",
      "***********************************\n",
      "n is 35.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 18106185731182917478220677092161126400000000000000000000.\n",
      "***********************************\n",
      "n is 37.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 71266346067351041870994524761001977235459123486953267200.\n",
      "***********************************\n",
      "n is 39.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 826976628662660554157177429660428632611124075697274880000.\n",
      "***********************************\n",
      "n is 41.\n",
      "The order of the Frobenius is 80.\n",
      "We have 15111572745169120787664 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 5740242776677981962019474530787781315240805836862750720000.\n",
      "***********************************\n",
      "n is 43.\n",
      "The order of the Frobenius is 112.\n",
      "We have 46359793379775246039936627600240 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 23914461017447740345553412842599906294329524527570168320000.\n",
      "***********************************\n",
      "n is 45.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 137707469045615680884698920716124854061056000000000000000000.\n",
      "***********************************\n",
      "n is 51.\n",
      "The order of the Frobenius is 16.\n",
      "We have 4080 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 51860399808500893593501821595260157912931025877148033351680000.\n",
      "***********************************\n",
      "n is 53.\n",
      "The order of the Frobenius is 208.\n",
      "We have 1977769900626449569897799498265948768442693820855629897047120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 29628974724615182632992796340504937738362400768330549127372800.\n",
      "***********************************\n",
      "n is 55.\n",
      "The order of the Frobenius is 80.\n",
      "We have 15111572745169120787664 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 213766520687368378568361327624831465969715200000000000000000000.\n",
      "***********************************\n",
      "n is 57.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 355645131768336584442124861195302783578516955385930186752000000.\n",
      "***********************************\n",
      "n is 63.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 38456664567832790175117797733468333881818021919158846881792000000.\n",
      "***********************************\n",
      "n is 65.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 175321435318156353952009608086572906117690626048000000000000000000.\n",
      "***********************************\n",
      "n is 69.\n",
      "The order of the Frobenius is 176.\n",
      "We have 544210064227943486632935732314825648606966627338800 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 345520698589064599027950686753823258685496960926036422127779840000.\n",
      "***********************************\n",
      "n is 73.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6004978396129941097133342770890551197827295064704771603202172518400.\n",
      "***********************************\n",
      "n is 75.\n",
      "The order of the Frobenius is 80.\n",
      "We have 15111572745169120787664 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 13350959625569084556609392166137695312500000000000000000000000000000.\n",
      "***********************************\n",
      "n is 85.\n",
      "The order of the Frobenius is 16.\n",
      "We have 4080 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10994554640925305461104588567467896988162410653155328000000000000000000.\n",
      "***********************************\n",
      "n is 87.\n",
      "The order of the Frobenius is 112.\n",
      "We have 46359793379775246039936627600240 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2910287355367905972841756374589547609849315365699687944189640704000000.\n",
      "***********************************\n",
      "n is 89.\n",
      "The order of the Frobenius is 176.\n",
      "We have 544210064227943486632935732314825648606966627338800 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 7532782101848351049973126244794913529462596967031434113661823057920000.\n",
      "***********************************\n",
      "n is 91.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 48960871013815149921966630516637374821581915860971667572744257536000000.\n",
      "***********************************\n",
      "n is 93.\n",
      "The order of the Frobenius is 80.\n",
      "We have 15111572745169120787664 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 48170913721848525677188330687787191214464166427984366801304682496000000.\n",
      "***********************************\n",
      "n is 95.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 75397795783385151285726899792775031097064652699699200000000000000000000.\n",
      "***********************************\n",
      "n is 97.\n",
      "The order of the Frobenius is 96.\n",
      "We have 825293359523583917857003520 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 333992157234565531544532149037471615382952225937229702636459204490035200.\n",
      "***********************************\n",
      "n is 99.\n",
      "The order of the Frobenius is 240.\n",
      "We have 7361862769909934706597072919762160477076066254539558997491267234955536 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 151343257380981531068227153985461530090635137663735205377345585152000000.\n",
      "['3', '5', '7', '9', '11', '13', '15', '17', '19', '21', '25', '27', '29', '31', '33', '35', '37', '39', '41', '43', '45', '51', '53', '55', '57', '63', '65', '69', '73', '75', '85', '87', '89', '91', '93', '95', '97', '99']\n",
      "0 0 0 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 12.\n",
      "We have 335 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 21928252218163200.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 12.\n",
      "We have 335 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4648852845000000000000000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 36.\n",
      "We have 1908866960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 3291313019385817508292770634547200.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 7663773114740251530029566811151360000.\n",
      "***********************************\n",
      "n is 13.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1795849439724535843832505615198484070400.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 12.\n",
      "We have 335 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1223294612523426635931648000000000000000000.\n",
      "***********************************\n",
      "n is 17.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 21898183327078294518532490120366252674252800.\n",
      "***********************************\n",
      "n is 23.\n",
      "The order of the Frobenius is 88.\n",
      "We have 3516875111605994051576550 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2626145600901025089133169289252654740978201395200.\n",
      "***********************************\n",
      "n is 25.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 67649712509592063724994659423828125000000000000000.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 108.\n",
      "We have 3004801422763210266376748072960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 494008427292979276777256641360443463387130633011200.\n",
      "***********************************\n",
      "n is 29.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 22119769862896408048724133628291257570336870021120000.\n",
      "***********************************\n",
      "n is 31.\n",
      "The order of the Frobenius is 160.\n",
      "We have 9134385233318143238773022648690396281390393344 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 91531298760533254792138099902184797220606149918720000.\n",
      "***********************************\n",
      "n is 33.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 672212599211209667518297404327639289429185527808000000.\n",
      "***********************************\n",
      "n is 35.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 5173195923195119279491622026331750400000000000000000000.\n",
      "***********************************\n",
      "n is 37.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 142532692134702083741989049522003954470918246973906534400.\n",
      "***********************************\n",
      "n is 39.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 472558073521520316661244245520244932920642328969871360000.\n",
      "***********************************\n",
      "n is 43.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 15942974011631826897035608561733270862886349685046778880000.\n",
      "***********************************\n",
      "n is 45.\n",
      "The order of the Frobenius is 36.\n",
      "We have 1908866960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 183609958727487574512931894288166472081408000000000000000000.\n",
      "***********************************\n",
      "n is 51.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 5762266645388988177055757955028906434770113986349781483520000.\n",
      "***********************************\n",
      "n is 53.\n",
      "The order of the Frobenius is 104.\n",
      "We have 195023169265881403080265614570 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 59257949449230365265985592681009875476724801536661098254745600.\n",
      "***********************************\n",
      "n is 55.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 142511013791578919045574218416554310646476800000000000000000000.\n",
      "***********************************\n",
      "n is 57.\n",
      "The order of the Frobenius is 180.\n",
      "We have 8513864115921604768657483477290939684335762639067568 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 284516105414669267553699888956242226862813564308744149401600000.\n",
      "***********************************\n",
      "n is 65.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 100183677324660773686862633192327374924394643456000000000000000000.\n",
      "***********************************\n",
      "n is 75.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 17801279500758779408812522888183593750000000000000000000000000000000.\n",
      "***********************************\n",
      "n is 85.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1221617182325033940122732063051988554240267850350592000000000000000000.\n",
      "***********************************\n",
      "n is 87.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1940191570245270648561170916393031739899543577133125296126427136000000.\n",
      "***********************************\n",
      "n is 91.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 13988820289661471406276180147610678520451975960277619306498359296000000.\n",
      "***********************************\n",
      "n is 95.\n",
      "The order of the Frobenius is 180.\n",
      "We have 8513864115921604768657483477290939684335762639067568 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 60318236626708121028581519834220024877651722159759360000000000000000000.\n",
      "['3', '5', '9', '11', '13', '15', '17', '23', '25', '27', '29', '31', '33', '35', '37', '39', '43', '45', '51', '53', '55', '57', '65', '75', '85', '87', '91', '95']\n",
      "0 0 0 2\n",
      "****************\n",
      "p-rank is 0.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1394655853500000000000000.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 96.\n",
      "We have 825293359523583917857003520 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 162281842557646045457018880000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "***********************************\n",
      "n is 13.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1795849439724535843832505615198484070400.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 122329461252342663593164800000000000000000.\n",
      "***********************************\n",
      "n is 17.\n",
      "The order of the Frobenius is 64.\n",
      "We have 288230376084602880 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 49270912485926162666698102770824068517068800.\n",
      "***********************************\n",
      "n is 19.\n",
      "The order of the Frobenius is 36.\n",
      "We have 1908866960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 5406193620753705981253166539179841552005120000.\n",
      "***********************************\n",
      "n is 21.\n",
      "The order of the Frobenius is 96.\n",
      "We have 825293359523583917857003520 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 42702686088387757030286530963757535854592000000.\n",
      "***********************************\n",
      "n is 23.\n",
      "The order of the Frobenius is 44.\n",
      "We have 399822314775 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 5252291201802050178266338578505309481956402790400.\n",
      "***********************************\n",
      "n is 31.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 122041731680711006389517466536246396294141533224960000.\n",
      "***********************************\n",
      "n is 39.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 236279036760760158330622122760122466460321164484935680000.\n",
      "***********************************\n",
      "n is 47.\n",
      "The order of the Frobenius is 92.\n",
      "We have 53823479968928812291873035 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 783964061435643196649178651959525883371037005110030997913600.\n",
      "***********************************\n",
      "n is 51.\n",
      "The order of the Frobenius is 192.\n",
      "We have 32693238205138962311644736578793949237341897722922270720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4321699984041741132791818466271679826077585489762336112640000.\n",
      "***********************************\n",
      "n is 53.\n",
      "The order of the Frobenius is 104.\n",
      "We have 195023169265881403080265614570 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 59257949449230365265985592681009875476724801536661098254745600.\n",
      "***********************************\n",
      "n is 57.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 711290263536673168884249722390605567157033910771860373504000000.\n",
      "***********************************\n",
      "n is 93.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 32113942481232350451458887125191460809642777618656244534203121664000000.\n",
      "['3', '5', '7', '9', '13', '15', '17', '19', '21', '23', '31', '39', '47', '51', '53', '57', '93']\n",
      "0 0 0 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 16.\n",
      "We have 4080 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 16446189163622400.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 20.\n",
      "We have 52377 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2789311707000000000000000.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 649127370230584181828075520000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2468484764539363131219577975910400.\n",
      "***********************************\n",
      "n is 13.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 3142736519517937726706884826597347123200.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 80.\n",
      "We have 15111572745169120787664 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 183494191878513995389747200000000000000000.\n",
      "***********************************\n",
      "n is 17.\n",
      "The order of the Frobenius is 64.\n",
      "We have 288230376084602880 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 49270912485926162666698102770824068517068800.\n",
      "***********************************\n",
      "n is 21.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 85405372176775514060573061927515071709184000000.\n",
      "***********************************\n",
      "n is 25.\n",
      "The order of the Frobenius is 100.\n",
      "We have 12676506002282282755967953152 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 40589827505755238234996795654296875000000000000000.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 370506320469734457582942481020332597540347974758400.\n",
      "***********************************\n",
      "n is 31.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 244083463361422012779034933072492792588283066449920000.\n",
      "***********************************\n",
      "n is 35.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 7242474292473166991288270836864450560000000000000000000.\n",
      "***********************************\n",
      "n is 39.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 826976628662660554157177429660428632611124075697274880000.\n",
      "***********************************\n",
      "n is 43.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 15942974011631826897035608561733270862886349685046778880000.\n",
      "***********************************\n",
      "n is 49.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1721311070532199434768105504686408634459537165592406507520000.\n",
      "***********************************\n",
      "n is 51.\n",
      "The order of the Frobenius is 64.\n",
      "We have 288230376084602880 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 12965099952125223398375455398815039478232756469287008337920000.\n",
      "***********************************\n",
      "n is 59.\n",
      "The order of the Frobenius is 116.\n",
      "We have 716178877039286566967737630308705 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2815254155968646360209400671612495623611873736570976310507520000.\n",
      "***********************************\n",
      "n is 63.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 38456664567832790175117797733468333881818021919158846881792000000.\n",
      "***********************************\n",
      "n is 71.\n",
      "The order of the Frobenius is 140.\n",
      "We have 9955689820772599616748584288712892238241 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2208942342550922046669807569073678014412514126230184496923115520000.\n",
      "***********************************\n",
      "n is 89.\n",
      "The order of the Frobenius is 176.\n",
      "We have 544210064227943486632935732314825648606966627338800 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 7532782101848351049973126244794913529462596967031434113661823057920000.\n",
      "***********************************\n",
      "n is 91.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 48960871013815149921966630516637374821581915860971667572744257536000000.\n",
      "***********************************\n",
      "n is 93.\n",
      "The order of the Frobenius is 240.\n",
      "We have 7361862769909934706597072919762160477076066254539558997491267234955536 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 16056971240616175225729443562595730404821388809328122267101560832000000.\n",
      "***********************************\n",
      "n is 95.\n",
      "The order of the Frobenius is 180.\n",
      "We have 8513864115921604768657483477290939684335762639067568 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 60318236626708121028581519834220024877651722159759360000000000000000000.\n",
      "['3', '5', '7', '9', '13', '15', '17', '21', '25', '27', '31', '35', '39', '43', '49', '51', '59', '63', '71', '89', '91', '93', '95']\n",
      "0 0 0 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 16.\n",
      "We have 4080 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 3486639633750000000000000.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 96.\n",
      "We have 825293359523583917857003520 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 162281842557646045457018880000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4936969529078726262439155951820800.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 20.\n",
      "We have 52377 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 15327546229480503060059133622302720000.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 305823653130856658982912000000000000000000.\n",
      "***********************************\n",
      "n is 17.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 21898183327078294518532490120366252674252800.\n",
      "***********************************\n",
      "n is 21.\n",
      "The order of the Frobenius is 96.\n",
      "We have 825293359523583917857003520 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 42702686088387757030286530963757535854592000000.\n",
      "***********************************\n",
      "n is 25.\n",
      "The order of the Frobenius is 80.\n",
      "We have 15111572745169120787664 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 50737284382194047793745994567871093750000000000000.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 741012640939468915165884962040665195080695949516800.\n",
      "***********************************\n",
      "n is 29.\n",
      "The order of the Frobenius is 140.\n",
      "We have 9955689820772599616748584288712892238241 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 8847907945158563219489653451316503028134748008448000.\n",
      "***********************************\n",
      "n is 33.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 672212599211209667518297404327639289429185527808000000.\n",
      "***********************************\n",
      "n is 35.\n",
      "The order of the Frobenius is 96.\n",
      "We have 825293359523583917857003520 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 9053092865591458739110338546080563200000000000000000000.\n",
      "***********************************\n",
      "n is 41.\n",
      "The order of the Frobenius is 160.\n",
      "We have 9134385233318143238773022648690396281390393344 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2870121388338990981009737265393890657620402918431375360000.\n",
      "***********************************\n",
      "n is 43.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 15942974011631826897035608561733270862886349685046778880000.\n",
      "***********************************\n",
      "n is 45.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 137707469045615680884698920716124854061056000000000000000000.\n",
      "***********************************\n",
      "n is 47.\n",
      "The order of the Frobenius is 92.\n",
      "We have 53823479968928812291873035 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 783964061435643196649178651959525883371037005110030997913600.\n",
      "***********************************\n",
      "n is 51.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 5762266645388988177055757955028906434770113986349781483520000.\n",
      "***********************************\n",
      "n is 55.\n",
      "The order of the Frobenius is 80.\n",
      "We have 15111572745169120787664 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 213766520687368378568361327624831465969715200000000000000000000.\n",
      "***********************************\n",
      "n is 59.\n",
      "The order of the Frobenius is 116.\n",
      "We have 716178877039286566967737630308705 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2815254155968646360209400671612495623611873736570976310507520000.\n",
      "***********************************\n",
      "n is 61.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 18696370204190757357625820678773810243630816396158668004618240000.\n",
      "***********************************\n",
      "n is 63.\n",
      "The order of the Frobenius is 96.\n",
      "We have 825293359523583917857003520 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 19228332283916395087558898866734166940909010959579423440896000000.\n",
      "***********************************\n",
      "n is 71.\n",
      "The order of the Frobenius is 140.\n",
      "We have 9955689820772599616748584288712892238241 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2208942342550922046669807569073678014412514126230184496923115520000.\n",
      "***********************************\n",
      "n is 81.\n",
      "The order of the Frobenius is 216.\n",
      "We have 487556905872949938416287165202176425001580704867851135635947520 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 111222022092275746924580349840573900526036783282962743442749974732800.\n",
      "***********************************\n",
      "n is 83.\n",
      "The order of the Frobenius is 164.\n",
      "We have 142585525593258821288164344437544206438891596725 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 610545837083863781519156172269369795090940749877073930937268556185600.\n",
      "***********************************\n",
      "n is 85.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1221617182325033940122732063051988554240267850350592000000000000000000.\n",
      "***********************************\n",
      "n is 99.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 302686514761963062136454307970923060181270275327470410754691170304000000.\n",
      "['3', '5', '7', '9', '11', '15', '17', '21', '25', '27', '29', '33', '35', '41', '43', '45', '47', '51', '55', '59', '61', '63', '71', '81', '83', '85', '99']\n",
      "0 0 0 6\n",
      "****************\n",
      "p-rank is 0.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 16.\n",
      "We have 4080 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 16446189163622400.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 12.\n",
      "We have 335 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4648852845000000000000000.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 185464962923024051950878720000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2468484764539363131219577975910400.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 7663773114740251530029566811151360000.\n",
      "***********************************\n",
      "n is 13.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1795849439724535843832505615198484070400.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 305823653130856658982912000000000000000000.\n",
      "***********************************\n",
      "n is 17.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 21898183327078294518532490120366252674252800.\n",
      "***********************************\n",
      "n is 23.\n",
      "The order of the Frobenius is 44.\n",
      "We have 399822314775 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 5252291201802050178266338578505309481956402790400.\n",
      "***********************************\n",
      "n is 25.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 67649712509592063724994659423828125000000000000000.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 370506320469734457582942481020332597540347974758400.\n",
      "***********************************\n",
      "n is 29.\n",
      "The order of the Frobenius is 112.\n",
      "We have 46359793379775246039936627600240 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 11059884931448204024362066814145628785168435010560000.\n",
      "***********************************\n",
      "n is 33.\n",
      "The order of the Frobenius is 80.\n",
      "We have 15111572745169120787664 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1008318898816814501277446106491458934143778291712000000.\n",
      "***********************************\n",
      "n is 35.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10346391846390238558983244052663500800000000000000000000.\n",
      "***********************************\n",
      "n is 37.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 71266346067351041870994524761001977235459123486953267200.\n",
      "***********************************\n",
      "n is 43.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 15942974011631826897035608561733270862886349685046778880000.\n",
      "***********************************\n",
      "n is 45.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 137707469045615680884698920716124854061056000000000000000000.\n",
      "***********************************\n",
      "n is 51.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 5762266645388988177055757955028906434770113986349781483520000.\n",
      "***********************************\n",
      "n is 53.\n",
      "The order of the Frobenius is 208.\n",
      "We have 1977769900626449569897799498265948768442693820855629897047120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 29628974724615182632992796340504937738362400768330549127372800.\n",
      "***********************************\n",
      "n is 55.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 142511013791578919045574218416554310646476800000000000000000000.\n",
      "***********************************\n",
      "n is 65.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 100183677324660773686862633192327374924394643456000000000000000000.\n",
      "***********************************\n",
      "n is 69.\n",
      "The order of the Frobenius is 176.\n",
      "We have 544210064227943486632935732314825648606966627338800 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 345520698589064599027950686753823258685496960926036422127779840000.\n",
      "***********************************\n",
      "n is 71.\n",
      "The order of the Frobenius is 140.\n",
      "We have 9955689820772599616748584288712892238241 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2208942342550922046669807569073678014412514126230184496923115520000.\n",
      "***********************************\n",
      "n is 79.\n",
      "The order of the Frobenius is 156.\n",
      "We have 585537514956291233254679485982745394048986165 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 103151533014311705289524690254069332149432933578964636349872209920000.\n",
      "***********************************\n",
      "n is 85.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1221617182325033940122732063051988554240267850350592000000000000000000.\n",
      "***********************************\n",
      "n is 87.\n",
      "The order of the Frobenius is 112.\n",
      "We have 46359793379775246039936627600240 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2910287355367905972841756374589547609849315365699687944189640704000000.\n",
      "***********************************\n",
      "n is 91.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 27977640579322942812552360295221357040903951920555238612996718592000000.\n",
      "***********************************\n",
      "n is 99.\n",
      "The order of the Frobenius is 240.\n",
      "We have 7361862769909934706597072919762160477076066254539558997491267234955536 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 151343257380981531068227153985461530090635137663735205377345585152000000.\n",
      "['3', '5', '7', '9', '11', '13', '15', '17', '23', '25', '27', '29', '33', '35', '37', '43', '45', '51', '53', '55', '65', '69', '71', '79', '85', '87', '91', '99']\n",
      "0 0 1 -5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "***********************************\n",
      "n is 29.\n",
      "The order of the Frobenius is 140.\n",
      "We have 9955689820772599616748584288712892238241 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 8847907945158563219489653451316503028134748008448000.\n",
      "['3', '29']\n",
      "0 0 1 -4\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "0 0 1 -3\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "0 0 1 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "0 0 1 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "['3']\n",
      "0 0 1 2\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "0 0 1 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 17.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 21898183327078294518532490120366252674252800.\n",
      "['17']\n",
      "0 0 1 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "0 0 2 -2\n",
      "****************\n",
      "p-rank is 0.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "['3']\n",
      "0 0 2 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "['11']\n",
      "0 0 2 0\n",
      "****************\n",
      "p-rank is 0.\n",
      "[]\n",
      "0 0 2 2\n",
      "****************\n",
      "p-rank is 0.\n",
      "[]\n",
      "0 0 2 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "0 0 3 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 12.\n",
      "We have 335 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 21928252218163200.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 36.\n",
      "We have 1908866960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 3291313019385817508292770634547200.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 108.\n",
      "We have 3004801422763210266376748072960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 494008427292979276777256641360443463387130633011200.\n",
      "['3', '9', '27']\n",
      "0 1 -3 -3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 36.\n",
      "We have 1908866960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 7309417406054400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 108.\n",
      "We have 3004801422763210266376748072960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1097104339795272502764256878182400.\n",
      "['3', '9']\n",
      "0 1 -3 -2\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 10.\n",
      "We have 99 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 26313902661795840.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 30.\n",
      "We have 35790267 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 3949575623262981009951324761456640.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 90.\n",
      "We have 13754889325392723216145164 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 592810112751575132132707969632532156064556759613440.\n",
      "['3', '9', '27']\n",
      "0 1 -3 0\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 36.\n",
      "We have 1908866960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 7309417406054400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 108.\n",
      "We have 3004801422763210266376748072960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1097104339795272502764256878182400.\n",
      "['3', '9']\n",
      "0 1 -3 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 10.\n",
      "We have 99 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 26313902661795840.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 30.\n",
      "We have 35790267 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 3949575623262981009951324761456640.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 90.\n",
      "We have 13754889325392723216145164 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 592810112751575132132707969632532156064556759613440.\n",
      "['3', '9', '27']\n",
      "0 1 -2 -3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "0 1 -2 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "***********************************\n",
      "n is 17.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 26277819992493953422238988144439503209103360.\n",
      "['3', '11', '17']\n",
      "0 1 -2 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "0 1 -2 2\n",
      "****************\n",
      "p-rank is 2.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "0 1 -2 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "0 1 -1 -3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "0 1 -1 -2\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 21.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 34162148870710205624229224771006028683673600000.\n",
      "['21']\n",
      "0 1 -1 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "***********************************\n",
      "n is 39.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 236279036760760158330622122760122466460321164484935680000.\n",
      "['3', '11', '39']\n",
      "0 1 -1 0\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "0 1 -1 2\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "0 1 -1 4\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "0 1 -1 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "0 1 0 -2\n",
      "****************\n",
      "p-rank is 2.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 10.\n",
      "We have 99 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 26313902661795840.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1394655853500000000000000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 30.\n",
      "We have 35790267 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 3949575623262981009951324761456640.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 366988383757027990779494400000000000000000.\n",
      "***********************************\n",
      "n is 21.\n",
      "The order of the Frobenius is 150.\n",
      "We have 9514984618039732540388321270110041855160272 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 27329719096568164499383379816804822946938880000.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 90.\n",
      "We have 13754889325392723216145164 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 592810112751575132132707969632532156064556759613440.\n",
      "***********************************\n",
      "n is 45.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 55082987618246272353879568286449941624422400000000000000000.\n",
      "***********************************\n",
      "n is 59.\n",
      "The order of the Frobenius is 116.\n",
      "We have 716178877039286566967737630308705 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2815254155968646360209400671612495623611873736570976310507520000.\n",
      "***********************************\n",
      "n is 63.\n",
      "The order of the Frobenius is 150.\n",
      "We have 9514984618039732540388321270110041855160272 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 12306132661706492856037695274709866842181767014130831002173440000.\n",
      "***********************************\n",
      "n is 75.\n",
      "The order of the Frobenius is 200.\n",
      "We have 8034690221294951377709810461699474759609873821900983107584 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 5340383850227633822643756866455078125000000000000000000000000000000.\n",
      "***********************************\n",
      "n is 99.\n",
      "The order of the Frobenius is 240.\n",
      "We have 7361862769909934706597072919762160477076066254539558997491267234955536 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 151343257380981531068227153985461530090635137663735205377345585152000000.\n",
      "['3', '5', '9', '15', '21', '27', '45', '59', '63', '75', '99']\n",
      "0 1 0 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 324563685115292090914037760000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "***********************************\n",
      "n is 21.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 85405372176775514060573061927515071709184000000.\n",
      "***********************************\n",
      "n is 41.\n",
      "The order of the Frobenius is 80.\n",
      "We have 15111572745169120787664 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 5740242776677981962019474530787781315240805836862750720000.\n",
      "***********************************\n",
      "n is 63.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 12818888189277596725039265911156111293939340639719615627264000000.\n",
      "***********************************\n",
      "n is 83.\n",
      "The order of the Frobenius is 82.\n",
      "We have 58971991200686800921575 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1221091674167727563038312344538739590181881499754147861874537112371200.\n",
      "['3', '7', '9', '21', '41', '63', '83']\n",
      "0 1 0 0\n",
      "****************\n",
      "p-rank is 2.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 36.\n",
      "We have 1908866960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 7309417406054400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 108.\n",
      "We have 3004801422763210266376748072960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1097104339795272502764256878182400.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 110.\n",
      "We have 11800674678488244282762064174071 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2786826587178273283647115204055040000.\n",
      "***********************************\n",
      "n is 13.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1795849439724535843832505615198484070400.\n",
      "***********************************\n",
      "n is 97.\n",
      "The order of the Frobenius is 96.\n",
      "We have 825293359523583917857003520 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 333992157234565531544532149037471615382952225937229702636459204490035200.\n",
      "['3', '9', '11', '13', '97']\n",
      "0 1 0 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 10.\n",
      "We have 99 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 26313902661795840.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 324563685115292090914037760000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 30.\n",
      "We have 35790267 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 3949575623262981009951324761456640.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 122329461252342663593164800000000000000000.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 90.\n",
      "We have 13754889325392723216145164 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 592810112751575132132707969632532156064556759613440.\n",
      "***********************************\n",
      "n is 45.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 55082987618246272353879568286449941624422400000000000000000.\n",
      "***********************************\n",
      "n is 67.\n",
      "The order of the Frobenius is 132.\n",
      "We have 41246347505568298601062172159252055475 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 273883659998363740992418941722706278797682072780049411537588633600.\n",
      "***********************************\n",
      "n is 83.\n",
      "The order of the Frobenius is 164.\n",
      "We have 142585525593258821288164344437544206438891596725 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 610545837083863781519156172269369795090940749877073930937268556185600.\n",
      "['3', '7', '9', '15', '27', '45', '67', '83']\n",
      "0 1 0 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 36.\n",
      "We have 1908866960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 7309417406054400.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1394655853500000000000000.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 185464962923024051950878720000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 108.\n",
      "We have 3004801422763210266376748072960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1097104339795272502764256878182400.\n",
      "***********************************\n",
      "n is 41.\n",
      "The order of the Frobenius is 80.\n",
      "We have 15111572745169120787664 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 5740242776677981962019474530787781315240805836862750720000.\n",
      "***********************************\n",
      "n is 59.\n",
      "The order of the Frobenius is 58.\n",
      "We have 4969489234738635 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 5630508311937292720418801343224991247223747473141952621015040000.\n",
      "['3', '5', '7', '9', '41', '59']\n",
      "0 1 0 4\n",
      "****************\n",
      "p-rank is 2.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 10.\n",
      "We have 99 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 26313902661795840.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 324563685115292090914037760000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 30.\n",
      "We have 35790267 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 3949575623262981009951324761456640.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 90.\n",
      "We have 13754889325392723216145164 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 592810112751575132132707969632532156064556759613440.\n",
      "***********************************\n",
      "n is 47.\n",
      "The order of the Frobenius is 92.\n",
      "We have 53823479968928812291873035 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 783964061435643196649178651959525883371037005110030997913600.\n",
      "***********************************\n",
      "n is 89.\n",
      "The order of the Frobenius is 88.\n",
      "We have 3516875111605994051576550 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 15065564203696702099946252489589827058925193934062868227323646115840000.\n",
      "['3', '7', '9', '27', '47', '89']\n",
      "0 1 0 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 10.\n",
      "We have 99 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 26313902661795840.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 30.\n",
      "We have 35790267 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 3949575623262981009951324761456640.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 122329461252342663593164800000000000000000.\n",
      "***********************************\n",
      "n is 21.\n",
      "The order of the Frobenius is 150.\n",
      "We have 9514984618039732540388321270110041855160272 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 27329719096568164499383379816804822946938880000.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 90.\n",
      "We have 13754889325392723216145164 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 592810112751575132132707969632532156064556759613440.\n",
      "***********************************\n",
      "n is 29.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 22119769862896408048724133628291257570336870021120000.\n",
      "***********************************\n",
      "n is 41.\n",
      "The order of the Frobenius is 80.\n",
      "We have 15111572745169120787664 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 5740242776677981962019474530787781315240805836862750720000.\n",
      "***********************************\n",
      "n is 45.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 55082987618246272353879568286449941624422400000000000000000.\n",
      "***********************************\n",
      "n is 63.\n",
      "The order of the Frobenius is 150.\n",
      "We have 9514984618039732540388321270110041855160272 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 12306132661706492856037695274709866842181767014130831002173440000.\n",
      "['3', '9', '15', '21', '27', '29', '41', '45', '63']\n",
      "0 1 1 -3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "0 1 1 -2\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 21.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 34162148870710205624229224771006028683673600000.\n",
      "['21']\n",
      "0 1 1 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "***********************************\n",
      "n is 39.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 236279036760760158330622122760122466460321164484935680000.\n",
      "['3', '11', '39']\n",
      "0 1 1 0\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "0 1 1 2\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "0 1 1 4\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "0 1 1 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "0 1 2 -3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "0 1 2 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "***********************************\n",
      "n is 17.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 26277819992493953422238988144439503209103360.\n",
      "['3', '11', '17']\n",
      "0 1 2 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "0 1 2 2\n",
      "****************\n",
      "p-rank is 2.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "0 1 2 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "0 1 3 -3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 36.\n",
      "We have 1908866960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 7309417406054400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 108.\n",
      "We have 3004801422763210266376748072960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1097104339795272502764256878182400.\n",
      "['3', '9']\n",
      "0 1 3 -2\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 10.\n",
      "We have 99 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 26313902661795840.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 30.\n",
      "We have 35790267 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 3949575623262981009951324761456640.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 90.\n",
      "We have 13754889325392723216145164 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 592810112751575132132707969632532156064556759613440.\n",
      "['3', '9', '27']\n",
      "0 1 3 0\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 36.\n",
      "We have 1908866960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 7309417406054400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 108.\n",
      "We have 3004801422763210266376748072960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1097104339795272502764256878182400.\n",
      "['3', '9']\n",
      "0 1 3 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 10.\n",
      "We have 99 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 26313902661795840.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 30.\n",
      "We have 35790267 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 3949575623262981009951324761456640.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 90.\n",
      "We have 13754889325392723216145164 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 592810112751575132132707969632532156064556759613440.\n",
      "['3', '9', '27']\n",
      "0 2 -5 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1394655853500000000000000.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 5109182076493501020019711207434240000.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 80.\n",
      "We have 15111572745169120787664 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 183494191878513995389747200000000000000000.\n",
      "***********************************\n",
      "n is 55.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 142511013791578919045574218416554310646476800000000000000000000.\n",
      "***********************************\n",
      "n is 99.\n",
      "The order of the Frobenius is 240.\n",
      "We have 7361862769909934706597072919762160477076066254539558997491267234955536 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 151343257380981531068227153985461530090635137663735205377345585152000000.\n",
      "['5', '11', '15', '55', '99']\n",
      "0 2 -4 2\n",
      "****************\n",
      "p-rank is 0.\n",
      "***********************************\n",
      "n is 89.\n",
      "The order of the Frobenius is 88.\n",
      "We have 3516875111605994051576550 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 15065564203696702099946252489589827058925193934062868227323646115840000.\n",
      "['89']\n",
      "0 2 -3 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 20.\n",
      "We have 52377 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 13156951330897920.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1974787811631490504975662380728320.\n",
      "['3', '9']\n",
      "0 2 -3 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 18.\n",
      "We have 14532 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 14618834812108800.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 57.\n",
      "We have 2528336632900554 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 273316787465509129190768640000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 54.\n",
      "We have 333599969907456 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2194208679590545005528513756364800.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 162.\n",
      "We have 36086460181009948597621832796379474289919787008 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 329338951528652851184837760906962308924753755340800.\n",
      "['3', '7', '9', '27']\n",
      "0 2 -2 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "0 2 -2 2\n",
      "****************\n",
      "p-rank is 0.\n",
      "[]\n",
      "0 2 -2 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 774808807500000000000000.\n",
      "['5']\n",
      "0 2 -1 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "0 2 -1 2\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "0 2 -1 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "['3', '9']\n",
      "0 2 -1 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2324426422500000000000000.\n",
      "***********************************\n",
      "n is 25.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 33824856254796031862497329711914062500000000000000.\n",
      "***********************************\n",
      "n is 65.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 50091838662330386843431316596163687462197321728000000000000000000.\n",
      "['5', '25', '65']\n",
      "0 2 -1 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 36.\n",
      "We have 1908866960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 432751580153722787885383680000.\n",
      "['7']\n",
      "0 2 0 2\n",
      "****************\n",
      "p-rank is 0.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1162213211250000000000000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 80.\n",
      "We have 15111572745169120787664 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 3831886557370125765014783405575680000.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 305823653130856658982912000000000000000000.\n",
      "***********************************\n",
      "n is 17.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 43796366654156589037064980240732505348505600.\n",
      "***********************************\n",
      "n is 29.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 22119769862896408048724133628291257570336870021120000.\n",
      "***********************************\n",
      "n is 37.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 142532692134702083741989049522003954470918246973906534400.\n",
      "***********************************\n",
      "n is 45.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 45902489681871893628232973572041618020352000000000000000000.\n",
      "***********************************\n",
      "n is 51.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 11524533290777976354111515910057812869540227972699562967040000.\n",
      "***********************************\n",
      "n is 53.\n",
      "The order of the Frobenius is 104.\n",
      "We have 195023169265881403080265614570 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 59257949449230365265985592681009875476724801536661098254745600.\n",
      "***********************************\n",
      "n is 85.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1221617182325033940122732063051988554240267850350592000000000000000000.\n",
      "***********************************\n",
      "n is 87.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1940191570245270648561170916393031739899543577133125296126427136000000.\n",
      "['3', '5', '9', '11', '15', '17', '29', '37', '45', '51', '53', '85', '87']\n",
      "0 2 0 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 18.\n",
      "We have 14532 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 14618834812108800.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2324426422500000000000000.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 96.\n",
      "We have 825293359523583917857003520 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 162281842557646045457018880000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 54.\n",
      "We have 333599969907456 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2194208679590545005528513756364800.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 203882435420571105988608000000000000000000.\n",
      "***********************************\n",
      "n is 25.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 33824856254796031862497329711914062500000000000000.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 162.\n",
      "We have 36086460181009948597621832796379474289919787008 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 329338951528652851184837760906962308924753755340800.\n",
      "***********************************\n",
      "n is 29.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 22119769862896408048724133628291257570336870021120000.\n",
      "***********************************\n",
      "n is 35.\n",
      "The order of the Frobenius is 96.\n",
      "We have 825293359523583917857003520 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 9053092865591458739110338546080563200000000000000000000.\n",
      "***********************************\n",
      "n is 71.\n",
      "The order of the Frobenius is 140.\n",
      "We have 9955689820772599616748584288712892238241 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2208942342550922046669807569073678014412514126230184496923115520000.\n",
      "['3', '5', '7', '9', '15', '25', '27', '29', '35', '71']\n",
      "0 2 0 4\n",
      "****************\n",
      "p-rank is 0.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 20.\n",
      "We have 52377 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 13156951330897920.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1394655853500000000000000.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 30.\n",
      "We have 35790267 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 519301896184467345462460416000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1974787811631490504975662380728320.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 20.\n",
      "We have 52377 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 15327546229480503060059133622302720000.\n",
      "***********************************\n",
      "n is 13.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1257094607807175090682753930638938849280.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 366988383757027990779494400000000000000000.\n",
      "***********************************\n",
      "n is 17.\n",
      "The order of the Frobenius is 80.\n",
      "We have 15111572745169120787664 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 39416729988740930133358482216659254813655040.\n",
      "***********************************\n",
      "n is 21.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 68324297741420411248458449542012057367347200000.\n",
      "***********************************\n",
      "n is 23.\n",
      "The order of the Frobenius is 110.\n",
      "We have 11800674678488244282762064174071 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2100916480720820071306535431402123792782561116160.\n",
      "***********************************\n",
      "n is 25.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 101474568764388095587491989135742187500000000000000.\n",
      "***********************************\n",
      "n is 31.\n",
      "The order of the Frobenius is 10.\n",
      "We have 99 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1464500780168532076674209598434956755529698398699520000.\n",
      "***********************************\n",
      "n is 33.\n",
      "The order of the Frobenius is 20.\n",
      "We have 52377 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4033275595267258005109784425965835736575113166848000000.\n",
      "***********************************\n",
      "n is 35.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 7242474292473166991288270836864450560000000000000000000.\n",
      "***********************************\n",
      "n is 39.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 330790651465064221662870971864171453044449630278909952000.\n",
      "***********************************\n",
      "n is 41.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 11480485553355963924038949061575562630481611673725501440000.\n",
      "***********************************\n",
      "n is 43.\n",
      "The order of the Frobenius is 140.\n",
      "We have 9955689820772599616748584288712892238241 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 19131568813958192276442730274079925035463619622056134656000.\n",
      "***********************************\n",
      "n is 45.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 55082987618246272353879568286449941624422400000000000000000.\n",
      "***********************************\n",
      "n is 51.\n",
      "The order of the Frobenius is 80.\n",
      "We have 15111572745169120787664 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10372079961700178718700364319052031582586205175429606670336000.\n",
      "***********************************\n",
      "n is 55.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 427533041374736757136722655249662931939430400000000000000000000.\n",
      "***********************************\n",
      "n is 57.\n",
      "The order of the Frobenius is 180.\n",
      "We have 8513864115921604768657483477290939684335762639067568 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 284516105414669267553699888956242226862813564308744149401600000.\n",
      "***********************************\n",
      "n is 61.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 9348185102095378678812910339386905121815408198079334002309120000.\n",
      "***********************************\n",
      "n is 63.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 30765331654266232140094238186774667105454417535327077505433600000.\n",
      "***********************************\n",
      "n is 65.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 70128574127262541580803843234629162447076250419200000000000000000.\n",
      "***********************************\n",
      "n is 69.\n",
      "The order of the Frobenius is 220.\n",
      "We have 7659075757713249941666765649721480086491394966826721044785047445 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 276416558871251679222360549403058606948397568740829137702223872000.\n",
      "***********************************\n",
      "n is 71.\n",
      "The order of the Frobenius is 70.\n",
      "We have 16865594581186450683 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4417884685101844093339615138147356028825028252460368993846231040000.\n",
      "***********************************\n",
      "n is 73.\n",
      "The order of the Frobenius is 90.\n",
      "We have 13754889325392723216145164 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 9607965433807905755413348433424881916523672103527634565123476029440.\n",
      "***********************************\n",
      "n is 75.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 26701919251138169113218784332275390625000000000000000000000000000000.\n",
      "***********************************\n",
      "n is 77.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 79596238208243080995279224964774192133077554642481027691315200000000.\n",
      "***********************************\n",
      "n is 85.\n",
      "The order of the Frobenius is 80.\n",
      "We have 15111572745169120787664 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2198910928185061092220917713493579397632482130631065600000000000000000.\n",
      "***********************************\n",
      "n is 89.\n",
      "The order of the Frobenius is 110.\n",
      "We have 11800674678488244282762064174071 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 12052451362957361679957001991671861647140155147250294581858916892672000.\n",
      "***********************************\n",
      "n is 91.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 19584348405526059968786652206654949928632766344388667029097703014400000.\n",
      "***********************************\n",
      "n is 93.\n",
      "The order of the Frobenius is 20.\n",
      "We have 52377 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 192683654887394102708753322751148764857856665711937467205218729984000000.\n",
      "***********************************\n",
      "n is 99.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 605373029523926124272908615941846120362540550654940821509382340608000000.\n",
      "['3', '5', '7', '9', '11', '13', '15', '17', '21', '23', '25', '31', '33', '35', '39', '41', '43', '45', '51', '55', '57', '61', '63', '65', '69', '71', '73', '75', '77', '85', '89', '91', '93', '99']\n",
      "0 2 0 6\n",
      "****************\n",
      "p-rank is 0.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 18.\n",
      "We have 14532 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 14618834812108800.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 54.\n",
      "We have 333599969907456 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2194208679590545005528513756364800.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 162.\n",
      "We have 36086460181009948597621832796379474289919787008 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 329338951528652851184837760906962308924753755340800.\n",
      "***********************************\n",
      "n is 97.\n",
      "The order of the Frobenius is 192.\n",
      "We have 32693238205138962311644736578793949237341897722922270720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 166996078617282765772266074518735807691476112968614851318229602245017600.\n",
      "['3', '9', '27', '97']\n",
      "0 2 0 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 20.\n",
      "We have 52377 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 13156951330897920.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1162213211250000000000000.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 185464962923024051950878720000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1974787811631490504975662380728320.\n",
      "***********************************\n",
      "n is 17.\n",
      "The order of the Frobenius is 32.\n",
      "We have 134215680 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 98541824971852325333396205541648137034137600.\n",
      "***********************************\n",
      "n is 51.\n",
      "The order of the Frobenius is 160.\n",
      "We have 9134385233318143238773022648690396281390393344 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 5186039980850089359350182159526015791293102587714803335168000.\n",
      "***********************************\n",
      "n is 85.\n",
      "The order of the Frobenius is 96.\n",
      "We have 825293359523583917857003520 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1832425773487550910184098094577982831360401775525888000000000000000000.\n",
      "['3', '5', '7', '9', '17', '51', '85']\n",
      "0 2 1 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "0 2 1 2\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "0 2 1 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "['3', '9']\n",
      "0 2 1 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2324426422500000000000000.\n",
      "***********************************\n",
      "n is 25.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 33824856254796031862497329711914062500000000000000.\n",
      "***********************************\n",
      "n is 65.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 50091838662330386843431316596163687462197321728000000000000000000.\n",
      "['5', '25', '65']\n",
      "0 2 1 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 36.\n",
      "We have 1908866960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 432751580153722787885383680000.\n",
      "['7']\n",
      "0 2 2 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "0 2 2 2\n",
      "****************\n",
      "p-rank is 0.\n",
      "[]\n",
      "0 2 2 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 774808807500000000000000.\n",
      "['5']\n",
      "0 2 3 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 20.\n",
      "We have 52377 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 13156951330897920.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1974787811631490504975662380728320.\n",
      "['3', '9']\n",
      "0 2 3 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 18.\n",
      "We have 14532 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 14618834812108800.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 54.\n",
      "We have 333599969907456 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2194208679590545005528513756364800.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 162.\n",
      "We have 36086460181009948597621832796379474289919787008 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 329338951528652851184837760906962308924753755340800.\n",
      "['3', '9', '27']\n",
      "0 2 4 2\n",
      "****************\n",
      "p-rank is 0.\n",
      "***********************************\n",
      "n is 89.\n",
      "The order of the Frobenius is 88.\n",
      "We have 3516875111605994051576550 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 15065564203696702099946252489589827058925193934062868227323646115840000.\n",
      "['89']\n",
      "0 2 5 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1394655853500000000000000.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 5109182076493501020019711207434240000.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 80.\n",
      "We have 15111572745169120787664 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 183494191878513995389747200000000000000000.\n",
      "***********************************\n",
      "n is 55.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 142511013791578919045574218416554310646476800000000000000000000.\n",
      "***********************************\n",
      "n is 99.\n",
      "The order of the Frobenius is 240.\n",
      "We have 7361862769909934706597072919762160477076066254539558997491267234955536 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 151343257380981531068227153985461530090635137663735205377345585152000000.\n",
      "['5', '11', '15', '55', '99']\n",
      "0 3 -2 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "0 3 -1 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "0 3 -1 8\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "0 3 0 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 185464962923024051950878720000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4936969529078726262439155951820800.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 5109182076493501020019711207434240000.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 122329461252342663593164800000000000000000.\n",
      "***********************************\n",
      "n is 17.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 21898183327078294518532490120366252674252800.\n",
      "***********************************\n",
      "n is 23.\n",
      "The order of the Frobenius is 132.\n",
      "We have 41246347505568298601062172159252055475 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1750763733934016726088779526168436493985467596800.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 741012640939468915165884962040665195080695949516800.\n",
      "***********************************\n",
      "n is 29.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 14746513241930938699149422418860838380224580014080000.\n",
      "***********************************\n",
      "n is 33.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 672212599211209667518297404327639289429185527808000000.\n",
      "***********************************\n",
      "n is 37.\n",
      "The order of the Frobenius is 36.\n",
      "We have 1908866960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 285065384269404167483978099044007908941836493947813068800.\n",
      "***********************************\n",
      "n is 39.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 236279036760760158330622122760122466460321164484935680000.\n",
      "***********************************\n",
      "n is 43.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 31885948023263653794071217123466541725772699370093557760000.\n",
      "***********************************\n",
      "n is 45.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 55082987618246272353879568286449941624422400000000000000000.\n",
      "***********************************\n",
      "n is 51.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 5762266645388988177055757955028906434770113986349781483520000.\n",
      "***********************************\n",
      "n is 53.\n",
      "The order of the Frobenius is 156.\n",
      "We have 585537514956291233254679485982745394048986165 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 39505299632820243510657061787339916984483201024440732169830400.\n",
      "***********************************\n",
      "n is 55.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 142511013791578919045574218416554310646476800000000000000000000.\n",
      "***********************************\n",
      "n is 63.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10987618447952225764319370780990952537662291976902527680512000000.\n",
      "***********************************\n",
      "n is 67.\n",
      "The order of the Frobenius is 132.\n",
      "We have 41246347505568298601062172159252055475 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 273883659998363740992418941722706278797682072780049411537588633600.\n",
      "***********************************\n",
      "n is 79.\n",
      "The order of the Frobenius is 156.\n",
      "We have 585537514956291233254679485982745394048986165 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 103151533014311705289524690254069332149432933578964636349872209920000.\n",
      "***********************************\n",
      "n is 81.\n",
      "The order of the Frobenius is 216.\n",
      "We have 487556905872949938416287165202176425001580704867851135635947520 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 111222022092275746924580349840573900526036783282962743442749974732800.\n",
      "***********************************\n",
      "n is 87.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1940191570245270648561170916393031739899543577133125296126427136000000.\n",
      "***********************************\n",
      "n is 91.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 13988820289661471406276180147610678520451975960277619306498359296000000.\n",
      "***********************************\n",
      "n is 99.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 302686514761963062136454307970923060181270275327470410754691170304000000.\n",
      "['3', '7', '9', '11', '15', '17', '23', '27', '29', '33', '37', '39', '43', '45', '51', '53', '55', '63', '67', '79', '81', '87', '91', '99']\n",
      "0 3 0 6\n",
      "****************\n",
      "p-rank is 2.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 16.\n",
      "We have 4080 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 16446189163622400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2468484764539363131219577975910400.\n",
      "***********************************\n",
      "n is 19.\n",
      "The order of the Frobenius is 90.\n",
      "We have 13754889325392723216145164 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2162477448301482392501266615671936620802048000.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 370506320469734457582942481020332597540347974758400.\n",
      "['3', '9', '19', '27']\n",
      "0 3 0 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 12.\n",
      "We have 335 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 21928252218163200.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1162213211250000000000000.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 96.\n",
      "We have 825293359523583917857003520 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 162281842557646045457018880000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 36.\n",
      "We have 1908866960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 3291313019385817508292770634547200.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 305823653130856658982912000000000000000000.\n",
      "***********************************\n",
      "n is 17.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 21898183327078294518532490120366252674252800.\n",
      "***********************************\n",
      "n is 21.\n",
      "The order of the Frobenius is 96.\n",
      "We have 825293359523583917857003520 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 42702686088387757030286530963757535854592000000.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 108.\n",
      "We have 3004801422763210266376748072960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 494008427292979276777256641360443463387130633011200.\n",
      "***********************************\n",
      "n is 33.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 672212599211209667518297404327639289429185527808000000.\n",
      "***********************************\n",
      "n is 35.\n",
      "The order of the Frobenius is 96.\n",
      "We have 825293359523583917857003520 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 9053092865591458739110338546080563200000000000000000000.\n",
      "***********************************\n",
      "n is 39.\n",
      "The order of the Frobenius is 156.\n",
      "We have 585537514956291233254679485982745394048986165 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 254454347280818632048362286049362656188038177137623040000.\n",
      "***********************************\n",
      "n is 43.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 31885948023263653794071217123466541725772699370093557760000.\n",
      "***********************************\n",
      "n is 45.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 45902489681871893628232973572041618020352000000000000000000.\n",
      "***********************************\n",
      "n is 51.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 5762266645388988177055757955028906434770113986349781483520000.\n",
      "***********************************\n",
      "n is 61.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 9348185102095378678812910339386905121815408198079334002309120000.\n",
      "***********************************\n",
      "n is 79.\n",
      "The order of the Frobenius is 156.\n",
      "We have 585537514956291233254679485982745394048986165 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 103151533014311705289524690254069332149432933578964636349872209920000.\n",
      "***********************************\n",
      "n is 85.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1221617182325033940122732063051988554240267850350592000000000000000000.\n",
      "['3', '5', '7', '9', '11', '15', '17', '21', '27', '33', '35', '39', '43', '45', '51', '61', '79', '85']\n",
      "0 3 0 9\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 16.\n",
      "We have 4080 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 16446189163622400.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1394655853500000000000000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2468484764539363131219577975910400.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 5109182076493501020019711207434240000.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 80.\n",
      "We have 15111572745169120787664 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 183494191878513995389747200000000000000000.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 370506320469734457582942481020332597540347974758400.\n",
      "***********************************\n",
      "n is 55.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 142511013791578919045574218416554310646476800000000000000000000.\n",
      "***********************************\n",
      "n is 59.\n",
      "The order of the Frobenius is 58.\n",
      "We have 4969489234738635 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 5630508311937292720418801343224991247223747473141952621015040000.\n",
      "***********************************\n",
      "n is 99.\n",
      "The order of the Frobenius is 240.\n",
      "We have 7361862769909934706597072919762160477076066254539558997491267234955536 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 151343257380981531068227153985461530090635137663735205377345585152000000.\n",
      "['3', '5', '9', '11', '15', '27', '55', '59', '99']\n",
      "0 3 1 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "0 3 1 8\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "0 3 2 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "0 4 -1 9\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "0 4 0 9\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 36.\n",
      "We have 1908866960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 7309417406054400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 108.\n",
      "We have 3004801422763210266376748072960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1097104339795272502764256878182400.\n",
      "***********************************\n",
      "n is 97.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 667984314469131063089064298074943230765904451874459405272918408980070400.\n",
      "['3', '9', '97']\n",
      "0 4 0 10\n",
      "****************\n",
      "p-rank is 0.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 10.\n",
      "We have 99 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 26313902661795840.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 324563685115292090914037760000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 30.\n",
      "We have 35790267 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 3949575623262981009951324761456640.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 90.\n",
      "We have 13754889325392723216145164 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 592810112751575132132707969632532156064556759613440.\n",
      "***********************************\n",
      "n is 47.\n",
      "The order of the Frobenius is 46.\n",
      "We have 1529755125849 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1567928122871286393298357303919051766742074010220061995827200.\n",
      "***********************************\n",
      "n is 89.\n",
      "The order of the Frobenius is 176.\n",
      "We have 544210064227943486632935732314825648606966627338800 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 7532782101848351049973126244794913529462596967031434113661823057920000.\n",
      "['3', '7', '9', '27', '47', '89']\n",
      "0 4 1 9\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "1 -3 -2 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "1 -3 -1 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "['3', '9']\n",
      "1 -2 -2 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "1 -2 -2 2\n",
      "****************\n",
      "p-rank is 1.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 52.\n",
      "We have 86607683851185 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1072812195000000000000000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 52.\n",
      "We have 86607683851185 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 282298756736175377522688000000000000000000.\n",
      "***********************************\n",
      "n is 17.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 21898183327078294518532490120366252674252800.\n",
      "***********************************\n",
      "n is 45.\n",
      "The order of the Frobenius is 156.\n",
      "We have 585537514956291233254679485982745394048986165 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 42371528937112517195291975604961493557248000000000000000000.\n",
      "['3', '5', '9', '15', '17', '45']\n",
      "1 -2 -2 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "***********************************\n",
      "n is 13.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1795849439724535843832505615198484070400.\n",
      "***********************************\n",
      "n is 39.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 236279036760760158330622122760122466460321164484935680000.\n",
      "['3', '9', '13', '39']\n",
      "1 -2 -1 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 929770569000000000000000.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 75.\n",
      "We have 503719091506095041632 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 207720758473786938184984166400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1974787811631490504975662380728320.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 244658922504685327186329600000000000000000.\n",
      "***********************************\n",
      "n is 33.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 672212599211209667518297404327639289429185527808000000.\n",
      "***********************************\n",
      "n is 45.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 110165975236492544707759136572899883248844800000000000000000.\n",
      "***********************************\n",
      "n is 55.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 142511013791578919045574218416554310646476800000000000000000000.\n",
      "***********************************\n",
      "n is 59.\n",
      "The order of the Frobenius is 174.\n",
      "We have 137616338080629387424420529565983194224941889694755 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1876836103979097573472933781074997082407915824380650873671680000.\n",
      "***********************************\n",
      "n is 99.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 302686514761963062136454307970923060181270275327470410754691170304000000.\n",
      "['5', '7', '9', '11', '15', '33', '45', '55', '59', '99']\n",
      "1 -2 -1 4\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "1 -2 0 6\n",
      "****************\n",
      "p-rank is 1.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 52.\n",
      "We have 86607683851185 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1072812195000000000000000.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "['3', '5', '11']\n",
      "1 -2 0 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "1 -1 -3 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 10.\n",
      "We have 99 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 30655092458961006120118267244605440000.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 122329461252342663593164800000000000000000.\n",
      "***********************************\n",
      "n is 23.\n",
      "The order of the Frobenius is 110.\n",
      "We have 11800674678488244282762064174071 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2100916480720820071306535431402123792782561116160.\n",
      "***********************************\n",
      "n is 25.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 33824856254796031862497329711914062500000000000000.\n",
      "***********************************\n",
      "n is 29.\n",
      "The order of the Frobenius is 140.\n",
      "We have 9955689820772599616748584288712892238241 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 8847907945158563219489653451316503028134748008448000.\n",
      "***********************************\n",
      "n is 31.\n",
      "The order of the Frobenius is 160.\n",
      "We have 9134385233318143238773022648690396281390393344 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 91531298760533254792138099902184797220606149918720000.\n",
      "***********************************\n",
      "n is 33.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2016637797633629002554892212982917868287556583424000000.\n",
      "***********************************\n",
      "n is 37.\n",
      "The order of the Frobenius is 180.\n",
      "We have 8513864115921604768657483477290939684335762639067568 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 57013076853880833496795619808801581788367298789562613760.\n",
      "***********************************\n",
      "n is 45.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 55082987618246272353879568286449941624422400000000000000000.\n",
      "***********************************\n",
      "n is 55.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 142511013791578919045574218416554310646476800000000000000000000.\n",
      "***********************************\n",
      "n is 71.\n",
      "The order of the Frobenius is 35.\n",
      "We have 981706806 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 8835769370203688186679230276294712057650056504920737987692462080000.\n",
      "***********************************\n",
      "n is 75.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 8900639750379389704406261444091796875000000000000000000000000000000.\n",
      "***********************************\n",
      "n is 77.\n",
      "The order of the Frobenius is 210.\n",
      "We have 7835735987243838295976043726463380667445368484290985174649363 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 22741782345212308855794064275649769180879301326423150768947200000000.\n",
      "***********************************\n",
      "n is 79.\n",
      "The order of the Frobenius is 195.\n",
      "We have 257522122477402287747109309670058109378368974702641544418 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 82521226411449364231619752203255465719546346863171709079897767936000.\n",
      "***********************************\n",
      "n is 89.\n",
      "The order of the Frobenius is 165.\n",
      "We have 283442741785387232621320694829824367273843833006 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 8034967575304907786638001327781241098093436764833529721239277928448000.\n",
      "***********************************\n",
      "n is 93.\n",
      "The order of the Frobenius is 160.\n",
      "We have 9134385233318143238773022648690396281390393344 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 24085456860924262838594165343893595607232083213992183400652341248000000.\n",
      "***********************************\n",
      "n is 99.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 302686514761963062136454307970923060181270275327470410754691170304000000.\n",
      "['3', '11', '15', '23', '25', '29', '31', '33', '37', '45', '55', '71', '75', '77', '79', '89', '93', '99']\n",
      "1 -1 -2 -3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "['3']\n",
      "1 -1 -2 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "1 -1 -2 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1394655853500000000000000.\n",
      "['5']\n",
      "1 -1 -1 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "***********************************\n",
      "n is 83.\n",
      "The order of the Frobenius is 82.\n",
      "We have 58971991200686800921575 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1221091674167727563038312344538739590181881499754147861874537112371200.\n",
      "['3', '9', '83']\n",
      "1 -1 -1 0\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "1 -1 -1 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "1 -1 -1 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "1 -1 0 2\n",
      "****************\n",
      "p-rank is 2.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "['3']\n",
      "1 -1 0 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "***********************************\n",
      "n is 93.\n",
      "The order of the Frobenius is 240.\n",
      "We have 7361862769909934706597072919762160477076066254539558997491267234955536 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 16056971240616175225729443562595730404821388809328122267101560832000000.\n",
      "['3', '9', '93']\n",
      "1 -1 0 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "['3']\n",
      "1 -1 1 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 17.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 65694549981234883555597470361098758022758400.\n",
      "['17']\n",
      "1 -1 1 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "1 0 -3 -5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4936969529078726262439155951820800.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 741012640939468915165884962040665195080695949516800.\n",
      "***********************************\n",
      "n is 81.\n",
      "The order of the Frobenius is 216.\n",
      "We have 487556905872949938416287165202176425001580704867851135635947520 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 111222022092275746924580349840573900526036783282962743442749974732800.\n",
      "['3', '9', '27', '81']\n",
      "1 0 -3 -4\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "['11']\n",
      "1 0 -2 -7\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 29.\n",
      "The order of the Frobenius is 140.\n",
      "We have 9955689820772599616748584288712892238241 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 8847907945158563219489653451316503028134748008448000.\n",
      "['29']\n",
      "1 0 -2 -6\n",
      "****************\n",
      "p-rank is 1.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "1 0 -2 -5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "['3', '9']\n",
      "1 0 -2 -4\n",
      "****************\n",
      "p-rank is 1.\n",
      "[]\n",
      "1 0 -2 -3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "1 0 -2 -2\n",
      "****************\n",
      "p-rank is 1.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "['3', '9']\n",
      "1 0 -2 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 185464962923024051950878720000.\n",
      "['7']\n",
      "1 0 -1 -5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "['3', '9']\n",
      "1 0 -1 -4\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "['3']\n",
      "1 0 -1 -3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1394655853500000000000000.\n",
      "['5']\n",
      "1 0 -1 -2\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "***********************************\n",
      "n is 17.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 21898183327078294518532490120366252674252800.\n",
      "['3', '9', '17']\n",
      "1 0 -1 0\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "1 0 -1 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "['3', '9']\n",
      "1 0 0 -2\n",
      "****************\n",
      "p-rank is 1.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "['3', '9']\n",
      "1 0 0 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 649127370230584181828075520000.\n",
      "***********************************\n",
      "n is 35.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 7242474292473166991288270836864450560000000000000000000.\n",
      "***********************************\n",
      "n is 49.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1721311070532199434768105504686408634459537165592406507520000.\n",
      "['7', '35', '49']\n",
      "1 0 0 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "['3', '9']\n",
      "1 0 0 2\n",
      "****************\n",
      "p-rank is 1.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2324426422500000000000000.\n",
      "***********************************\n",
      "n is 25.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 33824856254796031862497329711914062500000000000000.\n",
      "['5', '25']\n",
      "1 0 0 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "***********************************\n",
      "n is 33.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 672212599211209667518297404327639289429185527808000000.\n",
      "['11', '33']\n",
      "1 0 1 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "['3', '9']\n",
      "1 0 1 2\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "1 0 1 4\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "['3', '9']\n",
      "1 0 1 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "1 0 2 4\n",
      "****************\n",
      "p-rank is 1.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 75.\n",
      "We have 503719091506095041632 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 207720758473786938184984166400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "***********************************\n",
      "n is 45.\n",
      "The order of the Frobenius is 156.\n",
      "We have 585537514956291233254679485982745394048986165 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 42371528937112517195291975604961493557248000000000000000000.\n",
      "['3', '7', '9', '45']\n",
      "1 0 2 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "['3']\n",
      "1 0 2 6\n",
      "****************\n",
      "p-rank is 1.\n",
      "[]\n",
      "1 0 2 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "['3', '9']\n",
      "1 1 -4 -6\n",
      "****************\n",
      "p-rank is 2.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 324563685115292090914037760000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1974787811631490504975662380728320.\n",
      "***********************************\n",
      "n is 47.\n",
      "The order of the Frobenius is 69.\n",
      "We have 8555011744328945842 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1045285415247524262198904869279367844494716006813374663884800.\n",
      "['7', '9', '47']\n",
      "1 1 -4 -5\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "1 1 -3 -5\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "1 1 -3 -3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "1 1 -2 -3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "['3', '9']\n",
      "1 1 -2 -2\n",
      "****************\n",
      "p-rank is 2.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "1 1 -2 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "['3', '9']\n",
      "1 1 -1 -5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "['11']\n",
      "1 1 -1 -3\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "1 1 -1 -2\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "1 1 -1 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4936969529078726262439155951820800.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 741012640939468915165884962040665195080695949516800.\n",
      "***********************************\n",
      "n is 81.\n",
      "The order of the Frobenius is 216.\n",
      "We have 487556905872949938416287165202176425001580704867851135635947520 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 111222022092275746924580349840573900526036783282962743442749974732800.\n",
      "['3', '9', '27', '81']\n",
      "1 1 -1 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2324426422500000000000000.\n",
      "***********************************\n",
      "n is 25.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 33824856254796031862497329711914062500000000000000.\n",
      "['5', '25']\n",
      "1 1 0 -5\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "1 1 0 -2\n",
      "****************\n",
      "p-rank is 2.\n",
      "[]\n",
      "1 1 0 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "1 1 0 0\n",
      "****************\n",
      "p-rank is 2.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "1 1 0 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "['11']\n",
      "1 1 0 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "***********************************\n",
      "n is 31.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 122041731680711006389517466536246396294141533224960000.\n",
      "['3', '31']\n",
      "1 1 1 -3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "***********************************\n",
      "n is 13.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1795849439724535843832505615198484070400.\n",
      "***********************************\n",
      "n is 39.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 236279036760760158330622122760122466460321164484935680000.\n",
      "['3', '9', '13', '39']\n",
      "1 1 1 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "['3', '9']\n",
      "1 1 1 0\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 75.\n",
      "We have 503719091506095041632 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 207720758473786938184984166400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "['3', '7', '9']\n",
      "1 1 1 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "1 1 1 2\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "['3', '9', '11']\n",
      "1 1 1 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "['3', '9']\n",
      "1 1 1 4\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "1 1 1 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "***********************************\n",
      "n is 13.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1795849439724535843832505615198484070400.\n",
      "['3', '9', '13']\n",
      "1 1 2 0\n",
      "****************\n",
      "p-rank is 2.\n",
      "[]\n",
      "1 1 2 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "1 1 2 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "1 1 2 4\n",
      "****************\n",
      "p-rank is 2.\n",
      "[]\n",
      "1 1 2 6\n",
      "****************\n",
      "p-rank is 2.\n",
      "[]\n",
      "1 1 2 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "1 1 3 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "***********************************\n",
      "n is 63.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10987618447952225764319370780990952537662291976902527680512000000.\n",
      "['3', '63']\n",
      "1 1 3 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 122329461252342663593164800000000000000000.\n",
      "['15']\n",
      "1 1 3 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "1 1 4 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 104.\n",
      "We have 195023169265881403080265614570 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 141149378368087688761344000000000000000000.\n",
      "['3', '9', '15']\n",
      "1 2 -2 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "1 2 -1 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "1 2 0 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "['3']\n",
      "1 2 0 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "['11']\n",
      "1 2 0 2\n",
      "****************\n",
      "p-rank is 1.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 996182752500000000000000.\n",
      "['3', '5']\n",
      "1 2 0 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "['3', '9']\n",
      "1 2 1 2\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "1 2 1 4\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "1 2 2 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "1 2 2 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "1 2 2 4\n",
      "****************\n",
      "p-rank is 1.\n",
      "[]\n",
      "1 2 2 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "***********************************\n",
      "n is 33.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 672212599211209667518297404327639289429185527808000000.\n",
      "['3', '9', '11', '33']\n",
      "1 2 2 6\n",
      "****************\n",
      "p-rank is 1.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "1 2 2 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 774808807500000000000000.\n",
      "['5']\n",
      "1 2 3 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "1 2 3 2\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "['3']\n",
      "1 2 3 4\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "1 2 3 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "['3']\n",
      "1 2 3 8\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 774808807500000000000000.\n",
      "['3', '5']\n",
      "1 2 4 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 324563685115292090914037760000.\n",
      "***********************************\n",
      "n is 21.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 28468457392258504686857687309171690569728000000.\n",
      "['7', '21']\n",
      "1 2 4 2\n",
      "****************\n",
      "p-rank is 1.\n",
      "[]\n",
      "1 2 4 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "['3']\n",
      "1 2 4 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "1 2 4 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "1 2 5 4\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "1 2 5 6\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "***********************************\n",
      "n is 19.\n",
      "The order of the Frobenius is 90.\n",
      "We have 13754889325392723216145164 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2162477448301482392501266615671936620802048000.\n",
      "['3', '19']\n",
      "1 3 -1 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 929770569000000000000000.\n",
      "['5']\n",
      "1 3 1 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "1 3 1 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 35.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 5173195923195119279491622026331750400000000000000000000.\n",
      "['35']\n",
      "1 3 2 6\n",
      "****************\n",
      "p-rank is 2.\n",
      "[]\n",
      "1 3 2 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "['3', '9']\n",
      "1 3 3 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "1 3 3 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 52.\n",
      "We have 86607683851185 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1072812195000000000000000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4936969529078726262439155951820800.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 741012640939468915165884962040665195080695949516800.\n",
      "***********************************\n",
      "n is 81.\n",
      "The order of the Frobenius is 216.\n",
      "We have 487556905872949938416287165202176425001580704867851135635947520 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 111222022092275746924580349840573900526036783282962743442749974732800.\n",
      "['3', '5', '9', '27', '81']\n",
      "1 3 3 8\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "1 3 3 9\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "1 3 4 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "1 3 4 6\n",
      "****************\n",
      "p-rank is 2.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "1 3 4 8\n",
      "****************\n",
      "p-rank is 2.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 929770569000000000000000.\n",
      "['5']\n",
      "1 3 5 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "['3']\n",
      "1 3 5 6\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 52.\n",
      "We have 86607683851185 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1072812195000000000000000.\n",
      "['5']\n",
      "1 3 5 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "['3', '9']\n",
      "1 3 6 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "1 4 2 9\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 122329461252342663593164800000000000000000.\n",
      "***********************************\n",
      "n is 19.\n",
      "The order of the Frobenius is 90.\n",
      "We have 13754889325392723216145164 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2162477448301482392501266615671936620802048000.\n",
      "***********************************\n",
      "n is 33.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 672212599211209667518297404327639289429185527808000000.\n",
      "***********************************\n",
      "n is 55.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 142511013791578919045574218416554310646476800000000000000000000.\n",
      "***********************************\n",
      "n is 57.\n",
      "The order of the Frobenius is 180.\n",
      "We have 8513864115921604768657483477290939684335762639067568 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 284516105414669267553699888956242226862813564308744149401600000.\n",
      "***********************************\n",
      "n is 61.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 18696370204190757357625820678773810243630816396158668004618240000.\n",
      "['11', '15', '19', '33', '55', '57', '61']\n",
      "1 4 4 9\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "['3', '9']\n",
      "1 4 4 11\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "['3', '9']\n",
      "1 4 5 10\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "1 4 6 9\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "1 5 5 13\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "2 -1 -3 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "['3']\n",
      "2 0 -4 -7\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "2 0 -4 -6\n",
      "****************\n",
      "p-rank is 0.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "2 0 -3 -5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "['3', '9']\n",
      "2 0 -3 -4\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "2 0 -2 -2\n",
      "****************\n",
      "p-rank is 0.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "***********************************\n",
      "n is 45.\n",
      "The order of the Frobenius is 156.\n",
      "We have 585537514956291233254679485982745394048986165 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 42371528937112517195291975604961493557248000000000000000000.\n",
      "['3', '9', '45']\n",
      "2 0 -1 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "***********************************\n",
      "n is 39.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 236279036760760158330622122760122466460321164484935680000.\n",
      "['3', '9', '39']\n",
      "2 0 2 9\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "2 1 -4 -11\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 324563685115292090914037760000.\n",
      "['3', '7']\n",
      "2 1 -4 -10\n",
      "****************\n",
      "p-rank is 2.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "['3', '9']\n",
      "2 1 -3 -9\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "2 1 -3 -8\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 23.\n",
      "The order of the Frobenius is 132.\n",
      "We have 41246347505568298601062172159252055475 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1750763733934016726088779526168436493985467596800.\n",
      "['23']\n",
      "2 1 -3 -7\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1974787811631490504975662380728320.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "***********************************\n",
      "n is 33.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 672212599211209667518297404327639289429185527808000000.\n",
      "***********************************\n",
      "n is 99.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 302686514761963062136454307970923060181270275327470410754691170304000000.\n",
      "['9', '11', '33', '99']\n",
      "2 1 -2 -6\n",
      "****************\n",
      "p-rank is 2.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 57.\n",
      "We have 2528336632900554 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 273316787465509129190768640000.\n",
      "['7']\n",
      "2 1 -2 -5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2324426422500000000000000.\n",
      "***********************************\n",
      "n is 25.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 33824856254796031862497329711914062500000000000000.\n",
      "['5', '25']\n",
      "2 1 -2 -3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1974787811631490504975662380728320.\n",
      "***********************************\n",
      "n is 13.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1795849439724535843832505615198484070400.\n",
      "***********************************\n",
      "n is 47.\n",
      "The order of the Frobenius is 138.\n",
      "We have 2524993795123485410042792044415965268769 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 522642707623762131099452434639683922247358003406687331942400.\n",
      "***********************************\n",
      "n is 91.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 13988820289661471406276180147610678520451975960277619306498359296000000.\n",
      "***********************************\n",
      "n is 93.\n",
      "The order of the Frobenius is 240.\n",
      "We have 7361862769909934706597072919762160477076066254539558997491267234955536 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 16056971240616175225729443562595730404821388809328122267101560832000000.\n",
      "['9', '13', '47', '91', '93']\n",
      "2 1 -1 -3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "***********************************\n",
      "n is 33.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 672212599211209667518297404327639289429185527808000000.\n",
      "['3', '9', '11', '33']\n",
      "2 1 -1 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 104.\n",
      "We have 195023169265881403080265614570 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 141149378368087688761344000000000000000000.\n",
      "['3', '9', '15']\n",
      "2 1 0 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 104.\n",
      "We have 195023169265881403080265614570 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 141149378368087688761344000000000000000000.\n",
      "['15']\n",
      "2 1 1 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 122329461252342663593164800000000000000000.\n",
      "['15']\n",
      "2 1 1 4\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "2 1 2 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "['3', '9']\n",
      "2 1 3 8\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "2 2 -3 -7\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "['3']\n",
      "2 2 -2 -6\n",
      "****************\n",
      "p-rank is 0.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "['3', '11']\n",
      "2 2 -2 -5\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "2 2 -1 -5\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "2 2 -1 -3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "['3']\n",
      "2 2 0 -4\n",
      "****************\n",
      "p-rank is 0.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 20.\n",
      "We have 52377 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2789311707000000000000000.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 7663773114740251530029566811151360000.\n",
      "***********************************\n",
      "n is 13.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2514189215614350181365507861277877698560.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 366988383757027990779494400000000000000000.\n",
      "***********************************\n",
      "n is 17.\n",
      "The order of the Frobenius is 80.\n",
      "We have 15111572745169120787664 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 39416729988740930133358482216659254813655040.\n",
      "***********************************\n",
      "n is 21.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 34162148870710205624229224771006028683673600000.\n",
      "***********************************\n",
      "n is 25.\n",
      "The order of the Frobenius is 20.\n",
      "We have 52377 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 202949137528776191174983978271484375000000000000000.\n",
      "***********************************\n",
      "n is 29.\n",
      "The order of the Frobenius is 140.\n",
      "We have 9955689820772599616748584288712892238241 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 8847907945158563219489653451316503028134748008448000.\n",
      "***********************************\n",
      "n is 31.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 366125195042133019168552399608739188882424599674880000.\n",
      "***********************************\n",
      "n is 33.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2016637797633629002554892212982917868287556583424000000.\n",
      "***********************************\n",
      "n is 35.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 7242474292473166991288270836864450560000000000000000000.\n",
      "***********************************\n",
      "n is 37.\n",
      "The order of the Frobenius is 180.\n",
      "We have 8513864115921604768657483477290939684335762639067568 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 57013076853880833496795619808801581788367298789562613760.\n",
      "***********************************\n",
      "n is 39.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 330790651465064221662870971864171453044449630278909952000.\n",
      "***********************************\n",
      "n is 41.\n",
      "The order of the Frobenius is 20.\n",
      "We have 52377 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 22960971106711927848077898123151125260963223347451002880000.\n",
      "***********************************\n",
      "n is 45.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 55082987618246272353879568286449941624422400000000000000000.\n",
      "***********************************\n",
      "n is 51.\n",
      "The order of the Frobenius is 80.\n",
      "We have 15111572745169120787664 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10372079961700178718700364319052031582586205175429606670336000.\n",
      "***********************************\n",
      "n is 55.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 427533041374736757136722655249662931939430400000000000000000000.\n",
      "***********************************\n",
      "n is 61.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 18696370204190757357625820678773810243630816396158668004618240000.\n",
      "***********************************\n",
      "n is 63.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 15382665827133116070047119093387333552727208767663538752716800000.\n",
      "***********************************\n",
      "n is 65.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 140257148254525083161607686469258324894152500838400000000000000000.\n",
      "***********************************\n",
      "n is 75.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 26701919251138169113218784332275390625000000000000000000000000000000.\n",
      "***********************************\n",
      "n is 77.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 39798119104121540497639612482387096066538777321240513845657600000000.\n",
      "***********************************\n",
      "n is 85.\n",
      "The order of the Frobenius is 80.\n",
      "We have 15111572745169120787664 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2198910928185061092220917713493579397632482130631065600000000000000000.\n",
      "***********************************\n",
      "n is 91.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 19584348405526059968786652206654949928632766344388667029097703014400000.\n",
      "***********************************\n",
      "n is 93.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 96341827443697051354376661375574382428928332855968733602609364992000000.\n",
      "***********************************\n",
      "n is 99.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 302686514761963062136454307970923060181270275327470410754691170304000000.\n",
      "['3', '5', '11', '13', '15', '17', '21', '25', '29', '31', '33', '35', '37', '39', '41', '45', '51', '55', '61', '63', '65', '75', '77', '85', '91', '93', '99']\n",
      "2 2 0 -3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "['3', '9']\n",
      "2 2 0 -2\n",
      "****************\n",
      "p-rank is 0.\n",
      "[]\n",
      "2 2 0 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 70.\n",
      "We have 16865594581186450683 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4379298922708715160016895320657920000.\n",
      "['3', '11']\n",
      "2 2 1 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 122329461252342663593164800000000000000000.\n",
      "['3', '9', '15']\n",
      "2 2 1 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "['11']\n",
      "2 2 2 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 52.\n",
      "We have 86607683851185 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1072812195000000000000000.\n",
      "***********************************\n",
      "n is 13.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1795849439724535843832505615198484070400.\n",
      "***********************************\n",
      "n is 97.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 667984314469131063089064298074943230765904451874459405272918408980070400.\n",
      "['5', '13', '97']\n",
      "2 2 2 2\n",
      "****************\n",
      "p-rank is 0.\n",
      "[]\n",
      "2 2 2 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "['3']\n",
      "2 2 3 4\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "2 2 3 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "['3']\n",
      "2 2 3 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "2 2 4 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "2 2 4 9\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "2 2 5 11\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 20.\n",
      "We have 52377 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2789311707000000000000000.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 244658922504685327186329600000000000000000.\n",
      "***********************************\n",
      "n is 25.\n",
      "The order of the Frobenius is 100.\n",
      "We have 12676506002282282755967953152 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 40589827505755238234996795654296875000000000000000.\n",
      "***********************************\n",
      "n is 31.\n",
      "The order of the Frobenius is 160.\n",
      "We have 9134385233318143238773022648690396281390393344 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 91531298760533254792138099902184797220606149918720000.\n",
      "***********************************\n",
      "n is 33.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 672212599211209667518297404327639289429185527808000000.\n",
      "***********************************\n",
      "n is 45.\n",
      "The order of the Frobenius is 180.\n",
      "We have 8513864115921604768657483477290939684335762639067568 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 36721991745497514902586378857633294416281600000000000000000.\n",
      "***********************************\n",
      "n is 55.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 142511013791578919045574218416554310646476800000000000000000000.\n",
      "['5', '11', '15', '25', '31', '33', '45', '55']\n",
      "2 3 0 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "2 3 1 0\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "***********************************\n",
      "n is 55.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 142511013791578919045574218416554310646476800000000000000000000.\n",
      "['11', '55']\n",
      "2 3 1 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "['3', '9']\n",
      "2 3 2 2\n",
      "****************\n",
      "p-rank is 2.\n",
      "[]\n",
      "2 3 2 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "***********************************\n",
      "n is 39.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 236279036760760158330622122760122466460321164484935680000.\n",
      "['3', '39']\n",
      "2 3 3 2\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "2 3 3 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "2 3 3 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2324426422500000000000000.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 75.\n",
      "We have 503719091506095041632 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 207720758473786938184984166400.\n",
      "***********************************\n",
      "n is 25.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 33824856254796031862497329711914062500000000000000.\n",
      "['5', '7', '25']\n",
      "2 3 4 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "2 3 4 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "['3']\n",
      "2 3 4 6\n",
      "****************\n",
      "p-rank is 2.\n",
      "***********************************\n",
      "n is 17.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 21898183327078294518532490120366252674252800.\n",
      "['17']\n",
      "2 3 4 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "***********************************\n",
      "n is 17.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 21898183327078294518532490120366252674252800.\n",
      "['3', '9', '17']\n",
      "2 3 5 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "['3', '9']\n",
      "2 3 5 8\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "2 3 5 9\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "2 3 6 11\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "2 4 3 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1974787811631490504975662380728320.\n",
      "['9']\n",
      "2 4 4 6\n",
      "****************\n",
      "p-rank is 0.\n",
      "[]\n",
      "2 4 4 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "2 4 5 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "['3', '11']\n",
      "2 4 5 9\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "***********************************\n",
      "n is 13.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1795849439724535843832505615198484070400.\n",
      "***********************************\n",
      "n is 39.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 236279036760760158330622122760122466460321164484935680000.\n",
      "['3', '9', '13', '39']\n",
      "2 4 6 9\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "2 4 6 10\n",
      "****************\n",
      "p-rank is 0.\n",
      "[]\n",
      "2 4 7 9\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "2 4 7 10\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "['11']\n",
      "2 4 7 11\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "***********************************\n",
      "n is 33.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 672212599211209667518297404327639289429185527808000000.\n",
      "['3', '9', '11', '33']\n",
      "2 4 7 13\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "2 4 8 10\n",
      "****************\n",
      "p-rank is 0.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "2 4 8 11\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "['3', '9']\n",
      "2 5 6 11\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "***********************************\n",
      "n is 73.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 12009956792259882194266685541781102395654590129409543206404345036800.\n",
      "['3', '73']\n",
      "2 5 7 13\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "2 5 8 13\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 13.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1795849439724535843832505615198484070400.\n",
      "***********************************\n",
      "n is 97.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 667984314469131063089064298074943230765904451874459405272918408980070400.\n",
      "['13', '97']\n",
      "2 5 9 14\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "['3']\n",
      "2 5 10 13\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 17.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 21898183327078294518532490120366252674252800.\n",
      "['17']\n",
      "2 6 9 17\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "['11']\n",
      "3 2 -6 -15\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 18.\n",
      "We have 14532 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 14618834812108800.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 57.\n",
      "We have 2528336632900554 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 273316787465509129190768640000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 54.\n",
      "We have 333599969907456 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2194208679590545005528513756364800.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 162.\n",
      "We have 36086460181009948597621832796379474289919787008 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 329338951528652851184837760906962308924753755340800.\n",
      "['3', '7', '9', '27']\n",
      "3 2 -5 -13\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "3 2 -4 -10\n",
      "****************\n",
      "p-rank is 1.\n",
      "[]\n",
      "3 2 0 1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 20.\n",
      "We have 52377 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 13156951330897920.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 20.\n",
      "We have 52377 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2789311707000000000000000.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 75.\n",
      "We have 503719091506095041632 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 207720758473786938184984166400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1974787811631490504975662380728320.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 20.\n",
      "We have 52377 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 733976767514055981558988800000000000000000.\n",
      "***********************************\n",
      "n is 25.\n",
      "The order of the Frobenius is 100.\n",
      "We have 12676506002282282755967953152 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 40589827505755238234996795654296875000000000000000.\n",
      "***********************************\n",
      "n is 31.\n",
      "The order of the Frobenius is 160.\n",
      "We have 9134385233318143238773022648690396281390393344 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 91531298760533254792138099902184797220606149918720000.\n",
      "***********************************\n",
      "n is 33.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 672212599211209667518297404327639289429185527808000000.\n",
      "***********************************\n",
      "n is 45.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 110165975236492544707759136572899883248844800000000000000000.\n",
      "***********************************\n",
      "n is 55.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 142511013791578919045574218416554310646476800000000000000000000.\n",
      "***********************************\n",
      "n is 75.\n",
      "The order of the Frobenius is 100.\n",
      "We have 12676506002282282755967953152 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10680767700455267645287513732910156250000000000000000000000000000000.\n",
      "***********************************\n",
      "n is 93.\n",
      "The order of the Frobenius is 160.\n",
      "We have 9134385233318143238773022648690396281390393344 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 24085456860924262838594165343893595607232083213992183400652341248000000.\n",
      "***********************************\n",
      "n is 99.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 302686514761963062136454307970923060181270275327470410754691170304000000.\n",
      "['3', '5', '7', '9', '11', '15', '25', '31', '33', '45', '55', '75', '93', '99']\n",
      "3 3 -3 -11\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 12.\n",
      "We have 335 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 21928252218163200.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 996182752500000000000000.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 36.\n",
      "We have 1908866960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 3291313019385817508292770634547200.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 108.\n",
      "We have 3004801422763210266376748072960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 494008427292979276777256641360443463387130633011200.\n",
      "['3', '5', '9', '27']\n",
      "3 3 -2 -7\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "3 3 -1 -5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 122329461252342663593164800000000000000000.\n",
      "***********************************\n",
      "n is 17.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 21898183327078294518532490120366252674252800.\n",
      "***********************************\n",
      "n is 45.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 55082987618246272353879568286449941624422400000000000000000.\n",
      "['3', '15', '17', '45']\n",
      "3 3 0 -3\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 16.\n",
      "We have 4080 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 16446189163622400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2468484764539363131219577975910400.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 370506320469734457582942481020332597540347974758400.\n",
      "['3', '9', '27']\n",
      "3 3 1 0\n",
      "****************\n",
      "p-rank is 3.\n",
      "[]\n",
      "3 3 2 3\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "3 4 2 -1\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "3 4 4 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "3 4 6 10\n",
      "****************\n",
      "p-rank is 1.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 10.\n",
      "We have 99 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 26313902661795840.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 30.\n",
      "We have 35790267 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 3949575623262981009951324761456640.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 90.\n",
      "We have 13754889325392723216145164 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 592810112751575132132707969632532156064556759613440.\n",
      "['3', '9', '27']\n",
      "3 5 5 5\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "3 5 6 6\n",
      "****************\n",
      "p-rank is 2.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 18.\n",
      "We have 14532 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 14618834812108800.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 54.\n",
      "We have 333599969907456 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2194208679590545005528513756364800.\n",
      "***********************************\n",
      "n is 13.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1795849439724535843832505615198484070400.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 162.\n",
      "We have 36086460181009948597621832796379474289919787008 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 329338951528652851184837760906962308924753755340800.\n",
      "***********************************\n",
      "n is 97.\n",
      "The order of the Frobenius is 96.\n",
      "We have 825293359523583917857003520 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 333992157234565531544532149037471615382952225937229702636459204490035200.\n",
      "['3', '9', '13', '27', '97']\n",
      "3 5 6 7\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 20.\n",
      "We have 52377 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 13156951330897920.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1974787811631490504975662380728320.\n",
      "['3', '9']\n",
      "3 5 7 9\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 24.\n",
      "We have 698870 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10964126109081600.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1645656509692908754146385317273600.\n",
      "['3', '9']\n",
      "3 5 7 11\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 17.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 21898183327078294518532490120366252674252800.\n",
      "['17']\n",
      "3 5 8 13\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "3 5 9 15\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 18.\n",
      "We have 14532 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 14618834812108800.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 54.\n",
      "We have 333599969907456 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2194208679590545005528513756364800.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 162.\n",
      "We have 36086460181009948597621832796379474289919787008 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 329338951528652851184837760906962308924753755340800.\n",
      "['3', '9', '27']\n",
      "3 6 8 11\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "3 6 9 12\n",
      "****************\n",
      "p-rank is 3.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 16.\n",
      "We have 4080 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 16446189163622400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2468484764539363131219577975910400.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 144.\n",
      "We have 154866286100907105149520804901972339589120 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 370506320469734457582942481020332597540347974758400.\n",
      "['3', '9', '27']\n",
      "3 6 10 14\n",
      "****************\n",
      "p-rank is 1.\n",
      "[]\n",
      "3 6 10 15\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "3 6 11 17\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "3 6 12 19\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 12.\n",
      "We have 335 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 21928252218163200.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 36.\n",
      "We have 1908866960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 3291313019385817508292770634547200.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 108.\n",
      "We have 3004801422763210266376748072960 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 494008427292979276777256641360443463387130633011200.\n",
      "['3', '9', '27']\n",
      "3 7 11 17\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "['3']\n",
      "3 7 12 19\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 10.\n",
      "We have 99 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 26313902661795840.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 30.\n",
      "We have 35790267 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 3949575623262981009951324761456640.\n",
      "***********************************\n",
      "n is 27.\n",
      "The order of the Frobenius is 90.\n",
      "We have 13754889325392723216145164 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 592810112751575132132707969632532156064556759613440.\n",
      "['3', '9', '27']\n",
      "3 7 13 19\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 72.\n",
      "We have 65588423372234846720 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 774808807500000000000000.\n",
      "['5']\n",
      "3 7 13 21\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 56.\n",
      "We have 1286742745883790 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 4698911189606400.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 52.\n",
      "We have 86607683851185 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1072812195000000000000000.\n",
      "['3', '5']\n",
      "3 8 14 23\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "***********************************\n",
      "n is 99.\n",
      "The order of the Frobenius is 240.\n",
      "We have 7361862769909934706597072919762160477076066254539558997491267234955536 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 151343257380981531068227153985461530090635137663735205377345585152000000.\n",
      "['11', '99']\n",
      "4 4 -7 -21\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 122329461252342663593164800000000000000000.\n",
      "***********************************\n",
      "n is 19.\n",
      "The order of the Frobenius is 90.\n",
      "We have 13754889325392723216145164 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2162477448301482392501266615671936620802048000.\n",
      "***********************************\n",
      "n is 31.\n",
      "The order of the Frobenius is 30.\n",
      "We have 35790267 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 488166926722844025558069866144985585176566132899840000.\n",
      "***********************************\n",
      "n is 33.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 672212599211209667518297404327639289429185527808000000.\n",
      "***********************************\n",
      "n is 55.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 142511013791578919045574218416554310646476800000000000000000000.\n",
      "***********************************\n",
      "n is 57.\n",
      "The order of the Frobenius is 180.\n",
      "We have 8513864115921604768657483477290939684335762639067568 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 284516105414669267553699888956242226862813564308744149401600000.\n",
      "***********************************\n",
      "n is 61.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 18696370204190757357625820678773810243630816396158668004618240000.\n",
      "***********************************\n",
      "n is 93.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 64227884962464700902917774250382921619285555237312489068406243328000000.\n",
      "['11', '15', '19', '31', '33', '55', '57', '61', '93']\n",
      "4 5 -2 -11\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 13.\n",
      "The order of the Frobenius is 84.\n",
      "We have 230271584688448434290055 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1795849439724535843832505615198484070400.\n",
      "***********************************\n",
      "n is 97.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 667984314469131063089064298074943230765904451874459405272918408980070400.\n",
      "['13', '97']\n",
      "4 6 4 2\n",
      "****************\n",
      "p-rank is 0.\n",
      "***********************************\n",
      "n is 7.\n",
      "The order of the Frobenius is 48.\n",
      "We have 5864061663920 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 324563685115292090914037760000.\n",
      "***********************************\n",
      "n is 89.\n",
      "The order of the Frobenius is 88.\n",
      "We have 3516875111605994051576550 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 15065564203696702099946252489589827058925193934062868227323646115840000.\n",
      "['7', '89']\n",
      "4 8 12 17\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 6578475665448960.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 52.\n",
      "We have 86607683851185 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1072812195000000000000000.\n",
      "***********************************\n",
      "n is 47.\n",
      "The order of the Frobenius is 184.\n",
      "We have 133260481814425118118117132768767319460642961170332270 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 391982030717821598324589325979762941685518502555015498956800.\n",
      "***********************************\n",
      "n is 89.\n",
      "The order of the Frobenius is 44.\n",
      "We have 399822314775 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 30131128407393404199892504979179654117850387868125736454647292231680000.\n",
      "***********************************\n",
      "n is 91.\n",
      "The order of the Frobenius is 168.\n",
      "We have 2227050114028042542024662487098543256787250889510 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 13988820289661471406276180147610678520451975960277619306498359296000000.\n",
      "***********************************\n",
      "n is 93.\n",
      "The order of the Frobenius is 240.\n",
      "We have 7361862769909934706597072919762160477076066254539558997491267234955536 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 16056971240616175225729443562595730404821388809328122267101560832000000.\n",
      "['3', '5', '47', '89', '91', '93']\n",
      "4 9 17 27\n",
      "****************\n",
      "p-rank is 4.\n",
      "[]\n",
      "4 10 19 29\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 3.\n",
      "The order of the Frobenius is 26.\n",
      "We have 2580795 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 10120731792998400.\n",
      "***********************************\n",
      "n is 9.\n",
      "The order of the Frobenius is 78.\n",
      "We have 3874762242347531676435 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1519067547408838849981278754406400.\n",
      "['3', '9']\n",
      "5 12 20 29\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1394655853500000000000000.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 5109182076493501020019711207434240000.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 80.\n",
      "We have 15111572745169120787664 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 183494191878513995389747200000000000000000.\n",
      "***********************************\n",
      "n is 55.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 142511013791578919045574218416554310646476800000000000000000000.\n",
      "***********************************\n",
      "n is 99.\n",
      "The order of the Frobenius is 240.\n",
      "We have 7361862769909934706597072919762160477076066254539558997491267234955536 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 151343257380981531068227153985461530090635137663735205377345585152000000.\n",
      "['5', '11', '15', '55', '99']\n",
      "5 13 25 39\n",
      "****************\n",
      "p-rank is 4.\n",
      "***********************************\n",
      "n is 5.\n",
      "The order of the Frobenius is 40.\n",
      "We have 27487764474 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1394655853500000000000000.\n",
      "***********************************\n",
      "n is 11.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2554591038246750510009855603717120000.\n",
      "***********************************\n",
      "n is 15.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 122329461252342663593164800000000000000000.\n",
      "***********************************\n",
      "n is 19.\n",
      "The order of the Frobenius is 90.\n",
      "We have 13754889325392723216145164 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 2162477448301482392501266615671936620802048000.\n",
      "***********************************\n",
      "n is 31.\n",
      "The order of the Frobenius is 30.\n",
      "We have 35790267 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 488166926722844025558069866144985585176566132899840000.\n",
      "***********************************\n",
      "n is 33.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 672212599211209667518297404327639289429185527808000000.\n",
      "***********************************\n",
      "n is 55.\n",
      "The order of the Frobenius is 120.\n",
      "We have 11076899964874298931257370467884546 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 142511013791578919045574218416554310646476800000000000000000000.\n",
      "***********************************\n",
      "n is 57.\n",
      "The order of the Frobenius is 180.\n",
      "We have 8513864115921604768657483477290939684335762639067568 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 284516105414669267553699888956242226862813564308744149401600000.\n",
      "***********************************\n",
      "n is 61.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 18696370204190757357625820678773810243630816396158668004618240000.\n",
      "***********************************\n",
      "n is 85.\n",
      "The order of the Frobenius is 160.\n",
      "We have 9134385233318143238773022648690396281390393344 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 1099455464092530546110458856746789698816241065315532800000000000000000.\n",
      "***********************************\n",
      "n is 93.\n",
      "The order of the Frobenius is 60.\n",
      "We have 19215358392200893 polys of the proper degree in Z/2Z[x].\n",
      "The number of primes 2 splits into has to be 64227884962464700902917774250382921619285555237312489068406243328000000.\n",
      "['5', '11', '15', '19', '31', '33', '55', '57', '61', '85', '93']\n"
     ]
    }
   ],
   "source": [
    "List2=[]\n",
    "for i in range(0, len(WP2)):\n",
    "    List2.append(Mono4(100,WP2[i][0],WP2[i][1],WP2[i][2],WP2[i][3],2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-5 & 12 & -20 & 29 & 4 & 5, 11, 15, 55, 99 \\\\ \\hline\n",
      "-5 & 13 & -25 & 39 & 4 & 5, 11, 15, 19, 31, 33, 55, 57, 61, 85, 93 \\\\ \\hline\n",
      "-4 & 4 & 7 & -21 & 4 & 11, 15, 19, 31, 33, 55, 57, 61, 93 \\\\ \\hline\n",
      "-4 & 5 & 2 & -11 & 4 & 13, 97 \\\\ \\hline\n",
      "-4 & 6 & -4 & 2 & 0 & 7, 89 \\\\ \\hline\n",
      "-4 & 8 & -12 & 17 & 4 & 3, 5, 47, 89, 91, 93 \\\\ \\hline\n",
      "-4 & 9 & -17 & 27 & 4 &  \\\\ \\hline\n",
      "-4 & 10 & -19 & 29 & 4 & 3, 9 \\\\ \\hline\n",
      "-3 & 2 & 0 & 1 & 4 & 3, 5, 9, 11, 15, 25, 31, 33, 45, 55, 75, 93, 99 \\\\ \\hline\n",
      "-3 & 2 & 4 & -10 & 1 &  \\\\ \\hline\n",
      "-3 & 2 & 5 & -13 & 4 &  \\\\ \\hline\n",
      "-3 & 2 & 6 & -15 & 4 & 3, 9, 27 \\\\ \\hline\n",
      "-3 & 3 & -2 & 3 & 4 &  \\\\ \\hline\n",
      "-3 & 3 & -1 & 0 & 3 &  \\\\ \\hline\n",
      "-3 & 3 & 0 & -3 & 4 & 3, 9, 27 \\\\ \\hline\n",
      "-3 & 3 & 1 & -5 & 4 & 3, 15, 17, 45 \\\\ \\hline\n",
      "-3 & 3 & 2 & -7 & 4 &  \\\\ \\hline\n",
      "-3 & 3 & 3 & -11 & 4 & 3, 5, 9, 27 \\\\ \\hline\n",
      "-3 & 4 & -6 & 10 & 1 & 3, 9, 27 \\\\ \\hline\n",
      "-3 & 4 & -4 & 5 & 4 & 3 \\\\ \\hline\n",
      "-3 & 4 & -2 & -1 & 4 & 3 \\\\ \\hline\n",
      "-3 & 5 & -9 & 15 & 4 & 3, 9, 27 \\\\ \\hline\n",
      "-3 & 5 & -8 & 13 & 4 &  \\\\ \\hline\n",
      "-3 & 5 & -7 & 9 & 4 & 3, 9 \\\\ \\hline\n",
      "-3 & 5 & -7 & 11 & 4 & 17 \\\\ \\hline\n",
      "-3 & 5 & -6 & 6 & 2 & 3, 9, 13, 27, 97 \\\\ \\hline\n",
      "-3 & 5 & -6 & 7 & 4 & 3, 9 \\\\ \\hline\n",
      "-3 & 5 & -5 & 5 & 4 &  \\\\ \\hline\n",
      "-3 & 6 & -12 & 19 & 4 & 3, 9, 27 \\\\ \\hline\n",
      "-3 & 6 & -11 & 17 & 4 &  \\\\ \\hline\n",
      "-3 & 6 & -10 & 14 & 1 &  \\\\ \\hline\n",
      "-3 & 6 & -10 & 15 & 4 &  \\\\ \\hline\n",
      "-3 & 6 & -9 & 12 & 3 & 3, 9, 27 \\\\ \\hline\n",
      "-3 & 6 & -8 & 11 & 4 &  \\\\ \\hline\n",
      "-3 & 7 & -13 & 19 & 4 & 5 \\\\ \\hline\n",
      "-3 & 7 & -13 & 21 & 4 & 3, 5 \\\\ \\hline\n",
      "-3 & 7 & -12 & 19 & 4 & 3, 9, 27 \\\\ \\hline\n",
      "-3 & 7 & -11 & 17 & 4 & 3 \\\\ \\hline\n",
      "-3 & 8 & -14 & 23 & 4 & 11, 99 \\\\ \\hline\n",
      "-2 & -1 & 3 & -1 & 4 & 3 \\\\ \\hline\n",
      "-2 & 0 & -2 & 9 & 4 & 3 \\\\ \\hline\n",
      "-2 & 0 & 1 & 1 & 4 & 3, 9, 39 \\\\ \\hline\n",
      "-2 & 0 & 2 & -2 & 0 & 3, 7, 9, 45 \\\\ \\hline\n",
      "-2 & 0 & 3 & -5 & 4 & 3, 9 \\\\ \\hline\n",
      "-2 & 0 & 3 & -4 & 3 &  \\\\ \\hline\n",
      "-2 & 0 & 4 & -7 & 4 &  \\\\ \\hline\n",
      "-2 & 0 & 4 & -6 & 0 & 3 \\\\ \\hline\n",
      "-2 & 1 & -3 & 8 & 3 &  \\\\ \\hline\n",
      "-2 & 1 & -2 & 5 & 4 & 3, 9 \\\\ \\hline\n",
      "-2 & 1 & -1 & 3 & 4 & 15 \\\\ \\hline\n",
      "-2 & 1 & -1 & 4 & 3 &  \\\\ \\hline\n",
      "-2 & 1 & 0 & 1 & 4 & 15 \\\\ \\hline\n",
      "-2 & 1 & 1 & -3 & 4 & 3, 9, 11, 33 \\\\ \\hline\n",
      "-2 & 1 & 1 & -1 & 4 & 3, 9, 15 \\\\ \\hline\n",
      "-2 & 1 & 2 & -6 & 2 &  \\\\ \\hline\n",
      "-2 & 1 & 2 & -5 & 4 & 5, 25 \\\\ \\hline\n",
      "-2 & 1 & 2 & -3 & 4 & 9, 13, 47, 91, 93 \\\\ \\hline\n",
      "-2 & 1 & 3 & -9 & 4 & 3 \\\\ \\hline\n",
      "-2 & 1 & 3 & -8 & 3 & 23 \\\\ \\hline\n",
      "-2 & 1 & 3 & -7 & 4 & 9, 11, 33, 99 \\\\ \\hline\n",
      "-2 & 1 & 4 & -11 & 4 & 3, 7 \\\\ \\hline\n",
      "-2 & 1 & 4 & -10 & 2 & 3, 9 \\\\ \\hline\n",
      "-2 & 2 & -5 & 11 & 4 & 5, 7, 11, 15, 25, 31, 33, 45, 55 \\\\ \\hline\n",
      "-2 & 2 & -4 & 7 & 4 &  \\\\ \\hline\n",
      "-2 & 2 & -4 & 9 & 4 & 3 \\\\ \\hline\n",
      "-2 & 2 & -3 & 4 & 3 &  \\\\ \\hline\n",
      "-2 & 2 & -3 & 5 & 4 & 3 \\\\ \\hline\n",
      "-2 & 2 & -3 & 7 & 4 &  \\\\ \\hline\n",
      "-2 & 2 & -2 & 1 & 4 & 5, 13, 97 \\\\ \\hline\n",
      "-2 & 2 & -2 & 2 & 0 &  \\\\ \\hline\n",
      "-2 & 2 & -2 & 3 & 4 & 3 \\\\ \\hline\n",
      "-2 & 2 & -1 & -1 & 4 & 3, 9, 15 \\\\ \\hline\n",
      "-2 & 2 & -1 & 1 & 4 & 11 \\\\ \\hline\n",
      "-2 & 2 & 0 & -4 & 0 & 3, 5, 11, 13, 15, 17, 21, 25, 29, 31, 33, 35, 37, 39, 41, 45, 51, 55, 61, 63, 65, 75, 77, 85, 91, 93, 99 \\\\ \\hline\n",
      "-2 & 2 & 0 & -3 & 4 & 3, 9 \\\\ \\hline\n",
      "-2 & 2 & 0 & -2 & 0 &  \\\\ \\hline\n",
      "-2 & 2 & 0 & -1 & 4 & 3, 11 \\\\ \\hline\n",
      "-2 & 2 & 1 & -5 & 4 &  \\\\ \\hline\n",
      "-2 & 2 & 1 & -3 & 4 & 3 \\\\ \\hline\n",
      "-2 & 2 & 2 & -6 & 0 & 3, 11 \\\\ \\hline\n",
      "-2 & 2 & 2 & -5 & 4 &  \\\\ \\hline\n",
      "-2 & 2 & 3 & -7 & 4 & 3 \\\\ \\hline\n",
      "-2 & 3 & -6 & 11 & 4 &  \\\\ \\hline\n",
      "-2 & 3 & -5 & 7 & 4 & 3, 9 \\\\ \\hline\n",
      "-2 & 3 & -5 & 8 & 3 &  \\\\ \\hline\n",
      "-2 & 3 & -5 & 9 & 4 & 3 \\\\ \\hline\n",
      "-2 & 3 & -4 & 3 & 4 &  \\\\ \\hline\n",
      "-2 & 3 & -4 & 5 & 4 & 3 \\\\ \\hline\n",
      "-2 & 3 & -4 & 6 & 2 & 17 \\\\ \\hline\n",
      "-2 & 3 & -4 & 7 & 4 & 3, 9, 17 \\\\ \\hline\n",
      "-2 & 3 & -3 & 2 & 3 &  \\\\ \\hline\n",
      "-2 & 3 & -3 & 3 & 4 &  \\\\ \\hline\n",
      "-2 & 3 & -3 & 5 & 4 & 5, 25 \\\\ \\hline\n",
      "-2 & 3 & -2 & 2 & 2 &  \\\\ \\hline\n",
      "-2 & 3 & -2 & 3 & 4 & 3, 39 \\\\ \\hline\n",
      "-2 & 3 & -1 & 0 & 3 & 11, 55 \\\\ \\hline\n",
      "-2 & 3 & -1 & 1 & 4 & 3, 9 \\\\ \\hline\n",
      "-2 & 3 & 0 & -1 & 4 &  \\\\ \\hline\n",
      "-2 & 4 & -8 & 10 & 0 & 3 \\\\ \\hline\n",
      "-2 & 4 & -8 & 11 & 4 & 3, 9 \\\\ \\hline\n",
      "-2 & 4 & -7 & 9 & 4 &  \\\\ \\hline\n",
      "-2 & 4 & -7 & 10 & 3 & 11 \\\\ \\hline\n",
      "-2 & 4 & -7 & 11 & 4 & 3, 9, 11, 33 \\\\ \\hline\n",
      "-2 & 4 & -7 & 13 & 4 &  \\\\ \\hline\n",
      "-2 & 4 & -6 & 9 & 4 & 3, 7 \\\\ \\hline\n",
      "-2 & 4 & -6 & 10 & 0 &  \\\\ \\hline\n",
      "-2 & 4 & -5 & 7 & 4 & 3, 11 \\\\ \\hline\n",
      "-2 & 4 & -5 & 9 & 4 & 3, 9, 13, 39 \\\\ \\hline\n",
      "-2 & 4 & -4 & 6 & 0 &  \\\\ \\hline\n",
      "-2 & 4 & -4 & 7 & 4 &  \\\\ \\hline\n",
      "-2 & 4 & -3 & 5 & 4 & 9 \\\\ \\hline\n",
      "-2 & 5 & -10 & 13 & 4 & 17 \\\\ \\hline\n",
      "-2 & 5 & -9 & 14 & 3 & 3 \\\\ \\hline\n",
      "-2 & 5 & -8 & 13 & 4 & 13, 97 \\\\ \\hline\n",
      "-2 & 5 & -7 & 13 & 4 &  \\\\ \\hline\n",
      "-2 & 5 & -6 & 11 & 4 & 3, 73 \\\\ \\hline\n",
      "-2 & 6 & -9 & 17 & 4 & 11 \\\\ \\hline\n",
      "-1 & -3 & 1 & 7 & 4 & 3, 9 \\\\ \\hline\n",
      "-1 & -3 & 2 & 5 & 4 &  \\\\ \\hline\n",
      "-1 & -2 & 0 & 6 & 1 & 3, 5, 11 \\\\ \\hline\n",
      "-1 & -2 & 0 & 7 & 4 &  \\\\ \\hline\n",
      "-1 & -2 & 1 & 3 & 4 & 5, 9, 11, 15, 33, 45, 55, 59, 99 \\\\ \\hline\n",
      "-1 & -2 & 1 & 4 & 3 &  \\\\ \\hline\n",
      "-1 & -2 & 2 & 1 & 4 & 3 \\\\ \\hline\n",
      "-1 & -2 & 2 & 2 & 1 & 3, 5, 9, 15, 17, 45 \\\\ \\hline\n",
      "-1 & -2 & 2 & 3 & 4 & 3, 9, 13, 39 \\\\ \\hline\n",
      "-1 & -1 & -1 & 5 & 4 & 17 \\\\ \\hline\n",
      "-1 & -1 & -1 & 7 & 4 &  \\\\ \\hline\n",
      "-1 & -1 & 0 & 2 & 2 & 3 \\\\ \\hline\n",
      "-1 & -1 & 0 & 3 & 4 & 3, 9, 93 \\\\ \\hline\n",
      "-1 & -1 & 0 & 5 & 4 & 3 \\\\ \\hline\n",
      "-1 & -1 & 1 & -1 & 4 & 3, 9, 83 \\\\ \\hline\n",
      "-1 & -1 & 1 & 0 & 3 & 3 \\\\ \\hline\n",
      "-1 & -1 & 1 & 1 & 4 &  \\\\ \\hline\n",
      "-1 & -1 & 1 & 3 & 4 & 3 \\\\ \\hline\n",
      "-1 & -1 & 2 & -3 & 4 & 3 \\\\ \\hline\n",
      "-1 & -1 & 2 & -1 & 4 &  \\\\ \\hline\n",
      "-1 & -1 & 2 & 1 & 4 & 5 \\\\ \\hline\n",
      "-1 & -1 & 3 & -1 & 4 & 3, 11, 15, 23, 25, 29, 31, 33, 37, 45, 55, 71, 75, 77, 93, 99 \\\\ \\hline\n",
      "-1 & 0 & -2 & 4 & 1 & 3, 9, 45 \\\\ \\hline\n",
      "-1 & 0 & -2 & 5 & 4 & 3 \\\\ \\hline\n",
      "-1 & 0 & -2 & 6 & 1 &  \\\\ \\hline\n",
      "-1 & 0 & -2 & 7 & 4 & 3, 9 \\\\ \\hline\n",
      "-1 & 0 & -1 & 1 & 4 & 3, 9 \\\\ \\hline\n",
      "-1 & 0 & -1 & 2 & 3 &  \\\\ \\hline\n",
      "-1 & 0 & -1 & 4 & 3 & 3, 9 \\\\ \\hline\n",
      "-1 & 0 & -1 & 5 & 4 &  \\\\ \\hline\n",
      "-1 & 0 & 0 & -2 & 1 & 3, 9 \\\\ \\hline\n",
      "-1 & 0 & 0 & -1 & 4 & 7, 35, 49 \\\\ \\hline\n",
      "-1 & 0 & 0 & 1 & 4 & 3, 9 \\\\ \\hline\n",
      "-1 & 0 & 0 & 2 & 1 & 5, 25 \\\\ \\hline\n",
      "-1 & 0 & 0 & 3 & 4 & 11, 33 \\\\ \\hline\n",
      "-1 & 0 & 1 & -5 & 4 & 3, 9 \\\\ \\hline\n",
      "-1 & 0 & 1 & -4 & 3 & 3 \\\\ \\hline\n",
      "-1 & 0 & 1 & -3 & 4 & 5 \\\\ \\hline\n",
      "-1 & 0 & 1 & -2 & 3 & 3, 9, 17 \\\\ \\hline\n",
      "-1 & 0 & 1 & 0 & 3 &  \\\\ \\hline\n",
      "-1 & 0 & 1 & 1 & 4 & 3, 9 \\\\ \\hline\n",
      "-1 & 0 & 2 & -7 & 4 & 29 \\\\ \\hline\n",
      "-1 & 0 & 2 & -6 & 1 & 3 \\\\ \\hline\n",
      "-1 & 0 & 2 & -5 & 4 & 3, 9 \\\\ \\hline\n",
      "-1 & 0 & 2 & -4 & 1 &  \\\\ \\hline\n",
      "-1 & 0 & 2 & -3 & 4 & 3 \\\\ \\hline\n",
      "-1 & 0 & 2 & -2 & 1 & 3, 9 \\\\ \\hline\n",
      "-1 & 0 & 2 & -1 & 4 & 7 \\\\ \\hline\n",
      "-1 & 0 & 3 & -5 & 4 & 3, 7, 9, 27, 81 \\\\ \\hline\n",
      "-1 & 0 & 3 & -4 & 3 & 11 \\\\ \\hline\n",
      "-1 & 1 & -4 & 5 & 4 & 3, 9, 15 \\\\ \\hline\n",
      "-1 & 1 & -3 & 3 & 4 & 3, 63 \\\\ \\hline\n",
      "-1 & 1 & -3 & 5 & 4 & 15 \\\\ \\hline\n",
      "-1 & 1 & -3 & 7 & 4 &  \\\\ \\hline\n",
      "-1 & 1 & -2 & 0 & 2 & 7 \\\\ \\hline\n",
      "-1 & 1 & -2 & 1 & 4 &  \\\\ \\hline\n",
      "-1 & 1 & -2 & 3 & 4 &  \\\\ \\hline\n",
      "-1 & 1 & -2 & 4 & 2 &  \\\\ \\hline\n",
      "-1 & 1 & -2 & 6 & 2 &  \\\\ \\hline\n",
      "-1 & 1 & -2 & 7 & 4 & 7 \\\\ \\hline\n",
      "-1 & 1 & -1 & -3 & 4 & 3, 9, 13, 39 \\\\ \\hline\n",
      "-1 & 1 & -1 & -1 & 4 & 3, 9 \\\\ \\hline\n",
      "-1 & 1 & -1 & 0 & 3 & 3, 9 \\\\ \\hline\n",
      "-1 & 1 & -1 & 1 & 4 & 3 \\\\ \\hline\n",
      "-1 & 1 & -1 & 2 & 3 & 3, 9, 11 \\\\ \\hline\n",
      "-1 & 1 & -1 & 3 & 4 & 3, 9 \\\\ \\hline\n",
      "-1 & 1 & -1 & 4 & 3 & 3 \\\\ \\hline\n",
      "-1 & 1 & -1 & 5 & 4 & 3, 9, 13 \\\\ \\hline\n",
      "-1 & 1 & 0 & -5 & 4 &  \\\\ \\hline\n",
      "-1 & 1 & 0 & -2 & 2 &  \\\\ \\hline\n",
      "-1 & 1 & 0 & -1 & 4 &  \\\\ \\hline\n",
      "-1 & 1 & 0 & 0 & 2 & 3 \\\\ \\hline\n",
      "-1 & 1 & 0 & 1 & 4 & 11 \\\\ \\hline\n",
      "-1 & 1 & 0 & 3 & 4 & 3, 31 \\\\ \\hline\n",
      "-1 & 1 & 1 & -5 & 4 & 11 \\\\ \\hline\n",
      "-1 & 1 & 1 & -3 & 4 &  \\\\ \\hline\n",
      "-1 & 1 & 1 & -2 & 3 &  \\\\ \\hline\n",
      "-1 & 1 & 1 & -1 & 4 & 3, 9, 27, 81 \\\\ \\hline\n",
      "-1 & 1 & 1 & 1 & 4 & 5, 25 \\\\ \\hline\n",
      "-1 & 1 & 2 & -3 & 4 & 3, 9 \\\\ \\hline\n",
      "-1 & 1 & 2 & -2 & 2 & 3 \\\\ \\hline\n",
      "-1 & 1 & 2 & -1 & 4 & 3, 9 \\\\ \\hline\n",
      "-1 & 1 & 3 & -5 & 4 &  \\\\ \\hline\n",
      "-1 & 1 & 3 & -3 & 4 & 3 \\\\ \\hline\n",
      "-1 & 1 & 4 & -6 & 2 & 7, 9, 47 \\\\ \\hline\n",
      "-1 & 1 & 4 & -5 & 4 &  \\\\ \\hline\n",
      "-1 & 2 & -5 & 4 & 3 &  \\\\ \\hline\n",
      "-1 & 2 & -5 & 6 & 3 & 3, 19 \\\\ \\hline\n",
      "-1 & 2 & -4 & 1 & 4 & 7, 21 \\\\ \\hline\n",
      "-1 & 2 & -4 & 2 & 1 &  \\\\ \\hline\n",
      "-1 & 2 & -4 & 3 & 4 & 3 \\\\ \\hline\n",
      "-1 & 2 & -4 & 5 & 4 &  \\\\ \\hline\n",
      "-1 & 2 & -4 & 7 & 4 &  \\\\ \\hline\n",
      "-1 & 2 & -3 & 1 & 4 &  \\\\ \\hline\n",
      "-1 & 2 & -3 & 2 & 3 & 3 \\\\ \\hline\n",
      "-1 & 2 & -3 & 4 & 3 &  \\\\ \\hline\n",
      "-1 & 2 & -3 & 5 & 4 & 3 \\\\ \\hline\n",
      "-1 & 2 & -3 & 8 & 3 & 3, 5 \\\\ \\hline\n",
      "-1 & 2 & -2 & 1 & 4 &  \\\\ \\hline\n",
      "-1 & 2 & -2 & 3 & 4 & 3, 7 \\\\ \\hline\n",
      "-1 & 2 & -2 & 4 & 1 &  \\\\ \\hline\n",
      "-1 & 2 & -2 & 5 & 4 & 3, 9, 11, 33 \\\\ \\hline\n",
      "-1 & 2 & -2 & 6 & 1 & 3 \\\\ \\hline\n",
      "-1 & 2 & -2 & 7 & 4 & 5 \\\\ \\hline\n",
      "-1 & 2 & -1 & 2 & 3 &  \\\\ \\hline\n",
      "-1 & 2 & -1 & 4 & 3 &  \\\\ \\hline\n",
      "-1 & 2 & 0 & -1 & 4 & 3 \\\\ \\hline\n",
      "-1 & 2 & 0 & 1 & 4 & 11 \\\\ \\hline\n",
      "-1 & 2 & 0 & 2 & 1 & 3, 5 \\\\ \\hline\n",
      "-1 & 2 & 0 & 3 & 4 & 3, 9 \\\\ \\hline\n",
      "-1 & 2 & 1 & 1 & 4 &  \\\\ \\hline\n",
      "-1 & 2 & 2 & -1 & 4 &  \\\\ \\hline\n",
      "-1 & 3 & -6 & 5 & 4 &  \\\\ \\hline\n",
      "-1 & 3 & -5 & 5 & 4 & 3, 7 \\\\ \\hline\n",
      "-1 & 3 & -5 & 6 & 3 & 5 \\\\ \\hline\n",
      "-1 & 3 & -5 & 7 & 4 & 3, 9 \\\\ \\hline\n",
      "-1 & 3 & -4 & 5 & 4 &  \\\\ \\hline\n",
      "-1 & 3 & -4 & 6 & 2 & 3 \\\\ \\hline\n",
      "-1 & 3 & -4 & 8 & 2 & 5 \\\\ \\hline\n",
      "-1 & 3 & -3 & 5 & 4 &  \\\\ \\hline\n",
      "-1 & 3 & -3 & 7 & 4 & 3, 5, 9, 27, 81 \\\\ \\hline\n",
      "-1 & 3 & -3 & 8 & 3 &  \\\\ \\hline\n",
      "-1 & 3 & -3 & 9 & 4 &  \\\\ \\hline\n",
      "-1 & 3 & -2 & 6 & 2 &  \\\\ \\hline\n",
      "-1 & 3 & -2 & 7 & 4 & 3, 9 \\\\ \\hline\n",
      "-1 & 3 & -1 & 3 & 4 & 3 \\\\ \\hline\n",
      "-1 & 3 & -1 & 5 & 4 & 35 \\\\ \\hline\n",
      "-1 & 3 & 1 & 3 & 4 & 5 \\\\ \\hline\n",
      "-1 & 4 & -6 & 9 & 4 & 3 \\\\ \\hline\n",
      "-1 & 4 & -5 & 10 & 3 &  \\\\ \\hline\n",
      "-1 & 4 & -4 & 9 & 4 & 3, 9 \\\\ \\hline\n",
      "-1 & 4 & -4 & 11 & 4 & 3, 9 \\\\ \\hline\n",
      "-1 & 4 & -2 & 9 & 4 & 11, 15, 19, 33, 55, 57, 61 \\\\ \\hline\n",
      "-1 & 5 & -5 & 13 & 4 &  \\\\ \\hline\n",
      "0 & -5 & 0 & 13 & 4 & 3, 5, 9, 11, 15, 25, 27, 31, 33, 45, 55, 59, 75, 93, 99 \\\\ \\hline\n",
      "0 & -4 & 0 & 9 & 4 & 3, 9, 11, 27, 97 \\\\ \\hline\n",
      "0 & -4 & 0 & 10 & 0 & 3, 7, 9, 47, 89 \\\\ \\hline\n",
      "0 & -3 & -1 & 7 & 4 & 3 \\\\ \\hline\n",
      "0 & -3 & 0 & 6 & 2 & 3, 9, 27 \\\\ \\hline\n",
      "0 & -3 & 0 & 7 & 4 & 3, 5, 7, 9, 11, 15, 17, 21, 27, 33, 35, 39, 43, 45, 51, 61, 79, 85 \\\\ \\hline\n",
      "0 & -3 & 0 & 9 & 4 & 3, 5, 9, 11, 15, 27, 55, 59, 99 \\\\ \\hline\n",
      "0 & -3 & 1 & 7 & 4 & 3 \\\\ \\hline\n",
      "0 & -2 & -1 & 3 & 4 & 3 \\\\ \\hline\n",
      "0 & -2 & -1 & 5 & 4 & 3, 11 \\\\ \\hline\n",
      "0 & -2 & 0 & 1 & 4 & 3, 7, 9, 13, 21, 27, 47, 49, 63, 89, 91, 93 \\\\ \\hline\n",
      "0 & -2 & 0 & 2 & 0 & 3, 5, 9, 11, 15, 17, 29, 37, 45, 51, 53, 85, 87 \\\\ \\hline\n",
      "0 & -2 & 0 & 3 & 4 & 3, 5, 7, 9, 15, 25, 29, 35, 71 \\\\ \\hline\n",
      "0 & -2 & 0 & 4 & 0 & 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 25, 27, 31, 33, 35, 39, 41, 43, 45, 51, 55, 57, 61, 63, 65, 69, 71, 73, 75, 77, 85, 89, 91, 93, 99 \\\\ \\hline\n",
      "0 & -2 & 0 & 6 & 0 & 3, 9, 97 \\\\ \\hline\n",
      "0 & -2 & 0 & 7 & 4 & 3, 5, 7, 9, 17, 27, 51, 63, 85 \\\\ \\hline\n",
      "0 & -2 & 1 & 3 & 4 & 3 \\\\ \\hline\n",
      "0 & -2 & 1 & 5 & 4 & 3, 11 \\\\ \\hline\n",
      "0 & -1 & -2 & 2 & 2 &  \\\\ \\hline\n",
      "0 & -1 & -1 & -1 & 4 &  \\\\ \\hline\n",
      "0 & -1 & -1 & 0 & 3 & 3, 9, 15 \\\\ \\hline\n",
      "0 & -1 & -1 & 1 & 4 & 5, 53 \\\\ \\hline\n",
      "0 & -1 & -1 & 2 & 3 &  \\\\ \\hline\n",
      "0 & -1 & -1 & 3 & 4 & 3, 9 \\\\ \\hline\n",
      "0 & -1 & -1 & 4 & 3 &  \\\\ \\hline\n",
      "0 & -1 & -1 & 5 & 4 &  \\\\ \\hline\n",
      "0 & -1 & 0 & -3 & 4 & 3, 7, 9, 11, 17, 19, 21, 23, 27, 31, 47, 55, 57, 61, 69, 79, 93 \\\\ \\hline\n",
      "0 & -1 & 0 & -2 & 2 & 3, 5, 9, 15, 45, 59, 75, 99 \\\\ \\hline\n",
      "0 & -1 & 0 & -1 & 4 & 3, 7, 9, 11, 21, 41, 63, 83 \\\\ \\hline\n",
      "0 & -1 & 0 & 0 & 2 & 3, 9, 13, 27, 97 \\\\ \\hline\n",
      "0 & -1 & 0 & 1 & 4 & 3, 7, 9, 15, 45, 67, 83 \\\\ \\hline\n",
      "0 & -1 & 0 & 3 & 4 & 3, 5, 7, 9, 21, 27, 41, 59 \\\\ \\hline\n",
      "0 & -1 & 0 & 5 & 4 & 3, 9, 19 \\\\ \\hline\n",
      "0 & -1 & 0 & 7 & 4 & 3, 9, 15, 29, 41, 45 \\\\ \\hline\n",
      "0 & -1 & 1 & -1 & 4 &  \\\\ \\hline\n",
      "0 & -1 & 1 & 0 & 3 & 3, 9, 15 \\\\ \\hline\n",
      "0 & -1 & 1 & 1 & 4 & 5, 53 \\\\ \\hline\n",
      "0 & -1 & 1 & 2 & 3 &  \\\\ \\hline\n",
      "0 & -1 & 1 & 3 & 4 & 3, 9 \\\\ \\hline\n",
      "0 & -1 & 1 & 4 & 3 &  \\\\ \\hline\n",
      "0 & -1 & 1 & 5 & 4 &  \\\\ \\hline\n",
      "0 & -1 & 2 & 2 & 2 &  \\\\ \\hline\n",
      "0 & 0 & -3 & 1 & 4 & 3, 9, 27 \\\\ \\hline\n",
      "0 & 0 & -2 & -2 & 0 & 3 \\\\ \\hline\n",
      "0 & 0 & -2 & -1 & 4 & 11 \\\\ \\hline\n",
      "0 & 0 & -2 & 0 & 0 &  \\\\ \\hline\n",
      "0 & 0 & -2 & 2 & 0 &  \\\\ \\hline\n",
      "0 & 0 & -2 & 3 & 4 &  \\\\ \\hline\n",
      "0 & 0 & -1 & -5 & 4 & 3, 29 \\\\ \\hline\n",
      "0 & 0 & -1 & -4 & 3 &  \\\\ \\hline\n",
      "0 & 0 & -1 & -3 & 4 &  \\\\ \\hline\n",
      "0 & 0 & -1 & -1 & 4 &  \\\\ \\hline\n",
      "0 & 0 & -1 & 1 & 4 & 3 \\\\ \\hline\n",
      "0 & 0 & -1 & 2 & 3 &  \\\\ \\hline\n",
      "0 & 0 & -1 & 3 & 4 & 17 \\\\ \\hline\n",
      "0 & 0 & -1 & 5 & 4 &  \\\\ \\hline\n",
      "0 & 0 & 0 & -7 & 4 & 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 31, 33, 39, 47, 51, 53, 55, 57, 61, 63, 85, 93 \\\\ \\hline\n",
      "0 & 0 & 0 & -6 & 0 & 3, 5, 9, 11, 15, 17, 23, 25, 27, 29, 33, 35, 37, 43, 45, 51, 53, 55, 65, 67, 69, 85, 87, 91, 99 \\\\ \\hline\n",
      "0 & 0 & 0 & -5 & 4 & 3, 5, 7, 9, 11, 15, 17, 21, 25, 27, 33, 35, 39, 41, 43, 45, 47, 51, 55, 61, 63, 79, 81, 85, 99 \\\\ \\hline\n",
      "0 & 0 & 0 & -3 & 4 & 3, 5, 7, 9, 13, 15, 17, 21, 27, 31, 35, 39, 41, 43, 49, 51, 63, 83, 89, 91, 93 \\\\ \\hline\n",
      "0 & 0 & 0 & -2 & 0 & 3, 5, 7, 9, 15, 17, 19, 21, 23, 25, 27, 31, 39, 45, 47, 51, 53, 57, 79, 83, 93 \\\\ \\hline\n",
      "0 & 0 & 0 & 0 & 0 & 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 51, 53, 55, 57, 63, 65, 69, 73, 75, 85, 87, 89, 91, 93, 95, 97, 99 \\\\ \\hline\n",
      "0 & 0 & 0 & 1 & 4 & 3, 5, 9, 11, 13, 15, 17, 23, 25, 27, 29, 31, 33, 35, 37, 39, 43, 45, 51, 53, 55, 57, 65, 75, 85, 87, 91, 95 \\\\ \\hline\n",
      "0 & 0 & 0 & 2 & 0 & 3, 5, 7, 9, 13, 15, 17, 19, 21, 23, 31, 39, 47, 51, 53, 57, 93 \\\\ \\hline\n",
      "0 & 0 & 0 & 3 & 4 & 3, 5, 7, 9, 13, 15, 17, 21, 25, 27, 31, 35, 39, 43, 49, 51, 59, 63, 71, 89, 91, 93, 95 \\\\ \\hline\n",
      "0 & 0 & 0 & 5 & 4 & 3, 5, 7, 9, 11, 15, 17, 21, 25, 27, 29, 33, 35, 41, 43, 45, 47, 51, 55, 59, 61, 63, 71, 81, 83, 85, 99 \\\\ \\hline\n",
      "0 & 0 & 0 & 6 & 0 & 3, 5, 7, 9, 11, 13, 15, 17, 23, 25, 27, 29, 33, 35, 37, 43, 45, 51, 53, 55, 65, 69, 71, 79, 85, 87, 91, 99 \\\\ \\hline\n",
      "0 & 0 & 1 & -5 & 4 & 3, 29 \\\\ \\hline\n",
      "0 & 0 & 1 & -4 & 3 &  \\\\ \\hline\n",
      "0 & 0 & 1 & -3 & 4 &  \\\\ \\hline\n",
      "0 & 0 & 1 & -1 & 4 &  \\\\ \\hline\n",
      "0 & 0 & 1 & 1 & 4 & 3 \\\\ \\hline\n",
      "0 & 0 & 1 & 2 & 3 &  \\\\ \\hline\n",
      "0 & 0 & 1 & 3 & 4 & 17 \\\\ \\hline\n",
      "0 & 0 & 1 & 5 & 4 &  \\\\ \\hline\n",
      "0 & 0 & 2 & -2 & 0 & 3 \\\\ \\hline\n",
      "0 & 0 & 2 & -1 & 4 & 11 \\\\ \\hline\n",
      "0 & 0 & 2 & 0 & 0 &  \\\\ \\hline\n",
      "0 & 0 & 2 & 2 & 0 &  \\\\ \\hline\n",
      "0 & 0 & 2 & 3 & 4 &  \\\\ \\hline\n",
      "0 & 0 & 3 & 1 & 4 & 3, 9, 27 \\\\ \\hline\n",
      "0 & 1 & -3 & -3 & 4 & 3, 9 \\\\ \\hline\n",
      "0 & 1 & -3 & -2 & 3 & 3, 9, 27 \\\\ \\hline\n",
      "0 & 1 & -3 & 0 & 3 & 3, 9 \\\\ \\hline\n",
      "0 & 1 & -3 & 1 & 4 & 3, 9, 27 \\\\ \\hline\n",
      "0 & 1 & -2 & -3 & 4 & 3 \\\\ \\hline\n",
      "0 & 1 & -2 & -1 & 4 & 3, 11, 17 \\\\ \\hline\n",
      "0 & 1 & -2 & 1 & 4 &  \\\\ \\hline\n",
      "0 & 1 & -2 & 2 & 2 & 3 \\\\ \\hline\n",
      "0 & 1 & -2 & 3 & 4 & 3 \\\\ \\hline\n",
      "0 & 1 & -1 & -3 & 4 & 3 \\\\ \\hline\n",
      "0 & 1 & -1 & -2 & 3 & 21 \\\\ \\hline\n",
      "0 & 1 & -1 & -1 & 4 & 3, 11, 39 \\\\ \\hline\n",
      "0 & 1 & -1 & 0 & 3 & 3 \\\\ \\hline\n",
      "0 & 1 & -1 & 2 & 3 & 3 \\\\ \\hline\n",
      "0 & 1 & -1 & 4 & 3 &  \\\\ \\hline\n",
      "0 & 1 & -1 & 5 & 4 & 3 \\\\ \\hline\n",
      "0 & 1 & 0 & -2 & 2 & 3, 5, 9, 15, 21, 27, 45, 59, 63, 75, 99 \\\\ \\hline\n",
      "0 & 1 & 0 & -1 & 4 & 3, 7, 9, 21, 41, 63, 83 \\\\ \\hline\n",
      "0 & 1 & 0 & 0 & 2 & 3, 9, 11, 13, 97 \\\\ \\hline\n",
      "0 & 1 & 0 & 1 & 4 & 3, 7, 9, 15, 27, 45, 67, 83 \\\\ \\hline\n",
      "0 & 1 & 0 & 3 & 4 & 3, 5, 7, 9, 41, 59 \\\\ \\hline\n",
      "0 & 1 & 0 & 4 & 2 & 3, 7, 9, 27, 47, 89 \\\\ \\hline\n",
      "0 & 1 & 0 & 7 & 4 & 3, 9, 15, 21, 27, 29, 41, 45, 63 \\\\ \\hline\n",
      "0 & 1 & 1 & -3 & 4 & 3 \\\\ \\hline\n",
      "0 & 1 & 1 & -2 & 3 & 21 \\\\ \\hline\n",
      "0 & 1 & 1 & -1 & 4 & 3, 11, 39 \\\\ \\hline\n",
      "0 & 1 & 1 & 0 & 3 & 3 \\\\ \\hline\n",
      "0 & 1 & 1 & 2 & 3 & 3 \\\\ \\hline\n",
      "0 & 1 & 1 & 4 & 3 &  \\\\ \\hline\n",
      "0 & 1 & 1 & 5 & 4 & 3 \\\\ \\hline\n",
      "0 & 1 & 2 & -3 & 4 & 3 \\\\ \\hline\n",
      "0 & 1 & 2 & -1 & 4 & 3, 11, 17 \\\\ \\hline\n",
      "0 & 1 & 2 & 1 & 4 &  \\\\ \\hline\n",
      "0 & 1 & 2 & 2 & 2 & 3 \\\\ \\hline\n",
      "0 & 1 & 2 & 3 & 4 & 3 \\\\ \\hline\n",
      "0 & 1 & 3 & -3 & 4 & 3, 9 \\\\ \\hline\n",
      "0 & 1 & 3 & -2 & 3 & 3, 9, 27 \\\\ \\hline\n",
      "0 & 1 & 3 & 0 & 3 & 3, 9 \\\\ \\hline\n",
      "0 & 1 & 3 & 1 & 4 & 3, 9, 27 \\\\ \\hline\n",
      "0 & 2 & -5 & -1 & 4 & 5, 11, 15, 55, 99 \\\\ \\hline\n",
      "0 & 2 & -4 & 2 & 0 & 89 \\\\ \\hline\n",
      "0 & 2 & -3 & 1 & 4 & 3, 9 \\\\ \\hline\n",
      "0 & 2 & -3 & 3 & 4 & 3, 7, 9, 27 \\\\ \\hline\n",
      "0 & 2 & -2 & 1 & 4 &  \\\\ \\hline\n",
      "0 & 2 & -2 & 2 & 0 &  \\\\ \\hline\n",
      "0 & 2 & -2 & 5 & 4 & 5 \\\\ \\hline\n",
      "0 & 2 & -1 & 1 & 4 &  \\\\ \\hline\n",
      "0 & 2 & -1 & 2 & 3 &  \\\\ \\hline\n",
      "0 & 2 & -1 & 3 & 4 & 3, 9 \\\\ \\hline\n",
      "0 & 2 & -1 & 5 & 4 & 5, 25, 65 \\\\ \\hline\n",
      "0 & 2 & -1 & 7 & 4 & 7 \\\\ \\hline\n",
      "0 & 2 & 0 & 2 & 0 & 3, 5, 9, 11, 15, 17, 29, 37, 45, 51, 53, 85, 87 \\\\ \\hline\n",
      "0 & 2 & 0 & 3 & 4 & 3, 5, 7, 9, 15, 25, 27, 29, 35, 71 \\\\ \\hline\n",
      "0 & 2 & 0 & 4 & 0 & 3, 5, 7, 9, 11, 13, 15, 17, 21, 23, 25, 31, 33, 35, 39, 41, 43, 45, 51, 55, 57, 61, 63, 65, 69, 71, 73, 75, 77, 85, 89, 91, 93, 99 \\\\ \\hline\n",
      "0 & 2 & 0 & 6 & 0 & 3, 9, 27, 97 \\\\ \\hline\n",
      "0 & 2 & 0 & 7 & 4 & 3, 5, 7, 9, 17, 51, 85 \\\\ \\hline\n",
      "0 & 2 & 1 & 1 & 4 &  \\\\ \\hline\n",
      "0 & 2 & 1 & 2 & 3 &  \\\\ \\hline\n",
      "0 & 2 & 1 & 3 & 4 & 3, 9 \\\\ \\hline\n",
      "0 & 2 & 1 & 5 & 4 & 5, 25, 65 \\\\ \\hline\n",
      "0 & 2 & 1 & 7 & 4 & 7 \\\\ \\hline\n",
      "0 & 2 & 2 & 1 & 4 &  \\\\ \\hline\n",
      "0 & 2 & 2 & 2 & 0 &  \\\\ \\hline\n",
      "0 & 2 & 2 & 5 & 4 & 5 \\\\ \\hline\n",
      "0 & 2 & 3 & 1 & 4 & 3, 9 \\\\ \\hline\n",
      "0 & 2 & 3 & 3 & 4 & 3, 9, 27 \\\\ \\hline\n",
      "0 & 2 & 4 & 2 & 0 & 89 \\\\ \\hline\n",
      "0 & 2 & 5 & -1 & 4 & 5, 11, 15, 55, 99 \\\\ \\hline\n",
      "0 & 3 & -2 & 5 & 4 &  \\\\ \\hline\n",
      "0 & 3 & -1 & 5 & 4 &  \\\\ \\hline\n",
      "0 & 3 & -1 & 8 & 3 &  \\\\ \\hline\n",
      "0 & 3 & 0 & 5 & 4 & 3, 7, 9, 11, 15, 17, 23, 27, 29, 33, 37, 39, 43, 45, 51, 53, 55, 63, 67, 79, 81, 87, 91, 99 \\\\ \\hline\n",
      "0 & 3 & 0 & 6 & 2 & 3, 9, 19, 27 \\\\ \\hline\n",
      "0 & 3 & 0 & 7 & 4 & 3, 5, 7, 9, 11, 15, 17, 21, 27, 33, 35, 39, 43, 45, 51, 61, 79, 85 \\\\ \\hline\n",
      "0 & 3 & 0 & 9 & 4 & 3, 5, 9, 11, 15, 27, 55, 59, 99 \\\\ \\hline\n",
      "0 & 3 & 1 & 5 & 4 &  \\\\ \\hline\n",
      "0 & 3 & 1 & 8 & 3 &  \\\\ \\hline\n",
      "0 & 3 & 2 & 5 & 4 &  \\\\ \\hline\n",
      "0 & 4 & -1 & 9 & 4 & 3 \\\\ \\hline\n",
      "0 & 4 & 0 & 9 & 4 & 3, 9, 97 \\\\ \\hline\n",
      "0 & 4 & 0 & 10 & 0 & 3, 7, 9, 27, 47, 89 \\\\ \\hline\n",
      "0 & 4 & 1 & 9 & 4 & 3 \\\\ \\hline\n",
      "1 & -3 & -2 & 5 & 4 &  \\\\ \\hline\n",
      "1 & -3 & -1 & 7 & 4 & 3, 9 \\\\ \\hline\n",
      "1 & -2 & -2 & 1 & 4 & 3 \\\\ \\hline\n",
      "1 & -2 & -2 & 2 & 1 & 3, 5, 9, 15, 17, 45 \\\\ \\hline\n",
      "1 & -2 & -2 & 3 & 4 & 3, 9, 13, 39 \\\\ \\hline\n",
      "1 & -2 & -1 & 3 & 4 & 5, 7, 9, 11, 15, 33, 45, 55, 59, 99 \\\\ \\hline\n",
      "1 & -2 & -1 & 4 & 3 &  \\\\ \\hline\n",
      "1 & -2 & 0 & 6 & 1 & 3, 5, 11 \\\\ \\hline\n",
      "1 & -2 & 0 & 7 & 4 &  \\\\ \\hline\n",
      "1 & -1 & -3 & -1 & 4 & 3, 11, 15, 23, 25, 29, 31, 33, 37, 45, 55, 71, 75, 77, 79, 89, 93, 99 \\\\ \\hline\n",
      "1 & -1 & -2 & -3 & 4 & 3 \\\\ \\hline\n",
      "1 & -1 & -2 & -1 & 4 &  \\\\ \\hline\n",
      "1 & -1 & -2 & 1 & 4 & 5 \\\\ \\hline\n",
      "1 & -1 & -1 & -1 & 4 & 3, 9, 83 \\\\ \\hline\n",
      "1 & -1 & -1 & 0 & 3 & 3 \\\\ \\hline\n",
      "1 & -1 & -1 & 1 & 4 &  \\\\ \\hline\n",
      "1 & -1 & -1 & 3 & 4 & 3 \\\\ \\hline\n",
      "1 & -1 & 0 & 2 & 2 & 3 \\\\ \\hline\n",
      "1 & -1 & 0 & 3 & 4 & 3, 9, 93 \\\\ \\hline\n",
      "1 & -1 & 0 & 5 & 4 & 3 \\\\ \\hline\n",
      "1 & -1 & 1 & 5 & 4 & 17 \\\\ \\hline\n",
      "1 & -1 & 1 & 7 & 4 &  \\\\ \\hline\n",
      "1 & 0 & -3 & -5 & 4 & 3, 9, 27, 81 \\\\ \\hline\n",
      "1 & 0 & -3 & -4 & 3 & 11 \\\\ \\hline\n",
      "1 & 0 & -2 & -7 & 4 & 29 \\\\ \\hline\n",
      "1 & 0 & -2 & -6 & 1 & 3 \\\\ \\hline\n",
      "1 & 0 & -2 & -5 & 4 & 3, 9 \\\\ \\hline\n",
      "1 & 0 & -2 & -4 & 1 &  \\\\ \\hline\n",
      "1 & 0 & -2 & -3 & 4 & 3 \\\\ \\hline\n",
      "1 & 0 & -2 & -2 & 1 & 3, 9 \\\\ \\hline\n",
      "1 & 0 & -2 & -1 & 4 & 7 \\\\ \\hline\n",
      "1 & 0 & -1 & -5 & 4 & 3, 9 \\\\ \\hline\n",
      "1 & 0 & -1 & -4 & 3 & 3 \\\\ \\hline\n",
      "1 & 0 & -1 & -3 & 4 & 5 \\\\ \\hline\n",
      "1 & 0 & -1 & -2 & 3 & 3, 9, 17 \\\\ \\hline\n",
      "1 & 0 & -1 & 0 & 3 &  \\\\ \\hline\n",
      "1 & 0 & -1 & 1 & 4 & 3, 9 \\\\ \\hline\n",
      "1 & 0 & 0 & -2 & 1 & 3, 9 \\\\ \\hline\n",
      "1 & 0 & 0 & -1 & 4 & 7, 35, 49 \\\\ \\hline\n",
      "1 & 0 & 0 & 1 & 4 & 3, 9 \\\\ \\hline\n",
      "1 & 0 & 0 & 2 & 1 & 5, 25 \\\\ \\hline\n",
      "1 & 0 & 0 & 3 & 4 & 11, 33 \\\\ \\hline\n",
      "1 & 0 & 1 & 1 & 4 & 3, 9 \\\\ \\hline\n",
      "1 & 0 & 1 & 2 & 3 &  \\\\ \\hline\n",
      "1 & 0 & 1 & 4 & 3 & 3, 9 \\\\ \\hline\n",
      "1 & 0 & 1 & 5 & 4 &  \\\\ \\hline\n",
      "1 & 0 & 2 & 4 & 1 & 3, 7, 9, 45 \\\\ \\hline\n",
      "1 & 0 & 2 & 5 & 4 & 3 \\\\ \\hline\n",
      "1 & 0 & 2 & 6 & 1 &  \\\\ \\hline\n",
      "1 & 0 & 2 & 7 & 4 & 3, 9 \\\\ \\hline\n",
      "1 & 1 & -4 & -6 & 2 & 7, 9, 47 \\\\ \\hline\n",
      "1 & 1 & -4 & -5 & 4 &  \\\\ \\hline\n",
      "1 & 1 & -3 & -5 & 4 &  \\\\ \\hline\n",
      "1 & 1 & -3 & -3 & 4 & 3 \\\\ \\hline\n",
      "1 & 1 & -2 & -3 & 4 & 3, 9 \\\\ \\hline\n",
      "1 & 1 & -2 & -2 & 2 & 3 \\\\ \\hline\n",
      "1 & 1 & -2 & -1 & 4 & 3, 9 \\\\ \\hline\n",
      "1 & 1 & -1 & -5 & 4 & 11 \\\\ \\hline\n",
      "1 & 1 & -1 & -3 & 4 &  \\\\ \\hline\n",
      "1 & 1 & -1 & -2 & 3 &  \\\\ \\hline\n",
      "1 & 1 & -1 & -1 & 4 & 3, 9, 27, 81 \\\\ \\hline\n",
      "1 & 1 & -1 & 1 & 4 & 5, 25 \\\\ \\hline\n",
      "1 & 1 & 0 & -5 & 4 &  \\\\ \\hline\n",
      "1 & 1 & 0 & -2 & 2 &  \\\\ \\hline\n",
      "1 & 1 & 0 & -1 & 4 &  \\\\ \\hline\n",
      "1 & 1 & 0 & 0 & 2 & 3 \\\\ \\hline\n",
      "1 & 1 & 0 & 1 & 4 & 11 \\\\ \\hline\n",
      "1 & 1 & 0 & 3 & 4 & 3, 31 \\\\ \\hline\n",
      "1 & 1 & 1 & -3 & 4 & 3, 9, 13, 39 \\\\ \\hline\n",
      "1 & 1 & 1 & -1 & 4 & 3, 9 \\\\ \\hline\n",
      "1 & 1 & 1 & 0 & 3 & 3, 7, 9 \\\\ \\hline\n",
      "1 & 1 & 1 & 1 & 4 & 3 \\\\ \\hline\n",
      "1 & 1 & 1 & 2 & 3 & 3, 9, 11 \\\\ \\hline\n",
      "1 & 1 & 1 & 3 & 4 & 3, 9 \\\\ \\hline\n",
      "1 & 1 & 1 & 4 & 3 & 3 \\\\ \\hline\n",
      "1 & 1 & 1 & 5 & 4 & 3, 9, 13 \\\\ \\hline\n",
      "1 & 1 & 2 & 0 & 2 &  \\\\ \\hline\n",
      "1 & 1 & 2 & 1 & 4 &  \\\\ \\hline\n",
      "1 & 1 & 2 & 3 & 4 &  \\\\ \\hline\n",
      "1 & 1 & 2 & 4 & 2 &  \\\\ \\hline\n",
      "1 & 1 & 2 & 6 & 2 &  \\\\ \\hline\n",
      "1 & 1 & 2 & 7 & 4 &  \\\\ \\hline\n",
      "1 & 1 & 3 & 3 & 4 & 3, 63 \\\\ \\hline\n",
      "1 & 1 & 3 & 5 & 4 & 15 \\\\ \\hline\n",
      "1 & 1 & 3 & 7 & 4 &  \\\\ \\hline\n",
      "1 & 1 & 4 & 5 & 4 & 3, 9, 15 \\\\ \\hline\n",
      "1 & 2 & -2 & -1 & 4 &  \\\\ \\hline\n",
      "1 & 2 & -1 & 1 & 4 &  \\\\ \\hline\n",
      "1 & 2 & 0 & -1 & 4 & 3 \\\\ \\hline\n",
      "1 & 2 & 0 & 1 & 4 & 11 \\\\ \\hline\n",
      "1 & 2 & 0 & 2 & 1 & 3, 5 \\\\ \\hline\n",
      "1 & 2 & 0 & 3 & 4 & 3, 9 \\\\ \\hline\n",
      "1 & 2 & 1 & 2 & 3 &  \\\\ \\hline\n",
      "1 & 2 & 1 & 4 & 3 &  \\\\ \\hline\n",
      "1 & 2 & 2 & 1 & 4 &  \\\\ \\hline\n",
      "1 & 2 & 2 & 3 & 4 & 3 \\\\ \\hline\n",
      "1 & 2 & 2 & 4 & 1 &  \\\\ \\hline\n",
      "1 & 2 & 2 & 5 & 4 & 3, 9, 11, 33 \\\\ \\hline\n",
      "1 & 2 & 2 & 6 & 1 & 3 \\\\ \\hline\n",
      "1 & 2 & 2 & 7 & 4 & 5 \\\\ \\hline\n",
      "1 & 2 & 3 & 1 & 4 &  \\\\ \\hline\n",
      "1 & 2 & 3 & 2 & 3 & 3 \\\\ \\hline\n",
      "1 & 2 & 3 & 4 & 3 &  \\\\ \\hline\n",
      "1 & 2 & 3 & 5 & 4 & 3 \\\\ \\hline\n",
      "1 & 2 & 3 & 8 & 3 & 3, 5 \\\\ \\hline\n",
      "1 & 2 & 4 & 1 & 4 & 7, 21 \\\\ \\hline\n",
      "1 & 2 & 4 & 2 & 1 &  \\\\ \\hline\n",
      "1 & 2 & 4 & 3 & 4 & 3 \\\\ \\hline\n",
      "1 & 2 & 4 & 5 & 4 &  \\\\ \\hline\n",
      "1 & 2 & 4 & 7 & 4 &  \\\\ \\hline\n",
      "1 & 2 & 5 & 4 & 3 &  \\\\ \\hline\n",
      "1 & 2 & 5 & 6 & 3 & 3, 19 \\\\ \\hline\n",
      "1 & 3 & -1 & 3 & 4 & 5 \\\\ \\hline\n",
      "1 & 3 & 1 & 3 & 4 & 3 \\\\ \\hline\n",
      "1 & 3 & 1 & 5 & 4 & 35 \\\\ \\hline\n",
      "1 & 3 & 2 & 6 & 2 &  \\\\ \\hline\n",
      "1 & 3 & 2 & 7 & 4 & 3, 9 \\\\ \\hline\n",
      "1 & 3 & 3 & 5 & 4 &  \\\\ \\hline\n",
      "1 & 3 & 3 & 7 & 4 & 3, 5, 9, 27, 81 \\\\ \\hline\n",
      "1 & 3 & 3 & 8 & 3 &  \\\\ \\hline\n",
      "1 & 3 & 3 & 9 & 4 &  \\\\ \\hline\n",
      "1 & 3 & 4 & 5 & 4 &  \\\\ \\hline\n",
      "1 & 3 & 4 & 6 & 2 & 3 \\\\ \\hline\n",
      "1 & 3 & 4 & 8 & 2 & 5 \\\\ \\hline\n",
      "1 & 3 & 5 & 5 & 4 & 3 \\\\ \\hline\n",
      "1 & 3 & 5 & 6 & 3 & 5 \\\\ \\hline\n",
      "1 & 3 & 5 & 7 & 4 & 3, 9 \\\\ \\hline\n",
      "1 & 3 & 6 & 5 & 4 &  \\\\ \\hline\n",
      "1 & 4 & 2 & 9 & 4 & 11, 15, 19, 33, 55, 57, 61 \\\\ \\hline\n",
      "1 & 4 & 4 & 9 & 4 & 3, 9 \\\\ \\hline\n",
      "1 & 4 & 4 & 11 & 4 & 3, 9 \\\\ \\hline\n",
      "1 & 4 & 5 & 10 & 3 &  \\\\ \\hline\n",
      "1 & 4 & 6 & 9 & 4 & 3 \\\\ \\hline\n",
      "1 & 5 & 5 & 13 & 4 &  \\\\ \\hline\n",
      "2 & -1 & -3 & -1 & 4 & 3 \\\\ \\hline\n",
      "2 & 0 & -4 & -7 & 4 &  \\\\ \\hline\n",
      "2 & 0 & -4 & -6 & 0 & 3 \\\\ \\hline\n",
      "2 & 0 & -3 & -5 & 4 & 3, 9 \\\\ \\hline\n",
      "2 & 0 & -3 & -4 & 3 &  \\\\ \\hline\n",
      "2 & 0 & -2 & -2 & 0 & 3, 9, 45 \\\\ \\hline\n",
      "2 & 0 & -1 & 1 & 4 & 3, 9, 39 \\\\ \\hline\n",
      "2 & 0 & 2 & 9 & 4 & 3 \\\\ \\hline\n",
      "2 & 1 & -4 & -11 & 4 & 3, 7 \\\\ \\hline\n",
      "2 & 1 & -4 & -10 & 2 & 3, 9 \\\\ \\hline\n",
      "2 & 1 & -3 & -9 & 4 & 3 \\\\ \\hline\n",
      "2 & 1 & -3 & -8 & 3 & 23 \\\\ \\hline\n",
      "2 & 1 & -3 & -7 & 4 & 9, 11, 33, 99 \\\\ \\hline\n",
      "2 & 1 & -2 & -6 & 2 & 7 \\\\ \\hline\n",
      "2 & 1 & -2 & -5 & 4 & 5, 25 \\\\ \\hline\n",
      "2 & 1 & -2 & -3 & 4 & 9, 13, 47, 91, 93 \\\\ \\hline\n",
      "2 & 1 & -1 & -3 & 4 & 3, 9, 11, 33 \\\\ \\hline\n",
      "2 & 1 & -1 & -1 & 4 & 3, 9, 15 \\\\ \\hline\n",
      "2 & 1 & 0 & 1 & 4 & 15 \\\\ \\hline\n",
      "2 & 1 & 1 & 3 & 4 & 15 \\\\ \\hline\n",
      "2 & 1 & 1 & 4 & 3 &  \\\\ \\hline\n",
      "2 & 1 & 2 & 5 & 4 & 3, 9 \\\\ \\hline\n",
      "2 & 1 & 3 & 8 & 3 &  \\\\ \\hline\n",
      "2 & 2 & -3 & -7 & 4 & 3 \\\\ \\hline\n",
      "2 & 2 & -2 & -6 & 0 & 3, 11 \\\\ \\hline\n",
      "2 & 2 & -2 & -5 & 4 &  \\\\ \\hline\n",
      "2 & 2 & -1 & -5 & 4 &  \\\\ \\hline\n",
      "2 & 2 & -1 & -3 & 4 & 3 \\\\ \\hline\n",
      "2 & 2 & 0 & -4 & 0 & 3, 5, 11, 13, 15, 17, 21, 25, 29, 31, 33, 35, 37, 39, 41, 45, 51, 55, 61, 63, 65, 75, 77, 85, 91, 93, 99 \\\\ \\hline\n",
      "2 & 2 & 0 & -3 & 4 & 3, 9 \\\\ \\hline\n",
      "2 & 2 & 0 & -2 & 0 &  \\\\ \\hline\n",
      "2 & 2 & 0 & -1 & 4 & 3, 11 \\\\ \\hline\n",
      "2 & 2 & 1 & -1 & 4 & 3, 9, 15 \\\\ \\hline\n",
      "2 & 2 & 1 & 1 & 4 & 11 \\\\ \\hline\n",
      "2 & 2 & 2 & 1 & 4 & 5, 13, 97 \\\\ \\hline\n",
      "2 & 2 & 2 & 2 & 0 &  \\\\ \\hline\n",
      "2 & 2 & 2 & 3 & 4 & 3 \\\\ \\hline\n",
      "2 & 2 & 3 & 4 & 3 &  \\\\ \\hline\n",
      "2 & 2 & 3 & 5 & 4 & 3 \\\\ \\hline\n",
      "2 & 2 & 3 & 7 & 4 &  \\\\ \\hline\n",
      "2 & 2 & 4 & 7 & 4 &  \\\\ \\hline\n",
      "2 & 2 & 4 & 9 & 4 & 3 \\\\ \\hline\n",
      "2 & 2 & 5 & 11 & 4 & 5, 11, 15, 25, 31, 33, 45, 55 \\\\ \\hline\n",
      "2 & 3 & 0 & -1 & 4 &  \\\\ \\hline\n",
      "2 & 3 & 1 & 0 & 3 & 11, 55 \\\\ \\hline\n",
      "2 & 3 & 1 & 1 & 4 & 3, 9 \\\\ \\hline\n",
      "2 & 3 & 2 & 2 & 2 &  \\\\ \\hline\n",
      "2 & 3 & 2 & 3 & 4 & 3, 39 \\\\ \\hline\n",
      "2 & 3 & 3 & 2 & 3 &  \\\\ \\hline\n",
      "2 & 3 & 3 & 3 & 4 &  \\\\ \\hline\n",
      "2 & 3 & 3 & 5 & 4 & 5, 7, 25 \\\\ \\hline\n",
      "2 & 3 & 4 & 3 & 4 &  \\\\ \\hline\n",
      "2 & 3 & 4 & 5 & 4 & 3 \\\\ \\hline\n",
      "2 & 3 & 4 & 6 & 2 & 17 \\\\ \\hline\n",
      "2 & 3 & 4 & 7 & 4 & 3, 9, 17 \\\\ \\hline\n",
      "2 & 3 & 5 & 7 & 4 & 3, 9 \\\\ \\hline\n",
      "2 & 3 & 5 & 8 & 3 &  \\\\ \\hline\n",
      "2 & 3 & 5 & 9 & 4 & 3 \\\\ \\hline\n",
      "2 & 3 & 6 & 11 & 4 &  \\\\ \\hline\n",
      "2 & 4 & 3 & 5 & 4 & 9 \\\\ \\hline\n",
      "2 & 4 & 4 & 6 & 0 &  \\\\ \\hline\n",
      "2 & 4 & 4 & 7 & 4 &  \\\\ \\hline\n",
      "2 & 4 & 5 & 7 & 4 & 3, 11 \\\\ \\hline\n",
      "2 & 4 & 5 & 9 & 4 & 3, 9, 13, 39 \\\\ \\hline\n",
      "2 & 4 & 6 & 9 & 4 & 3 \\\\ \\hline\n",
      "2 & 4 & 6 & 10 & 0 &  \\\\ \\hline\n",
      "2 & 4 & 7 & 9 & 4 &  \\\\ \\hline\n",
      "2 & 4 & 7 & 10 & 3 & 11 \\\\ \\hline\n",
      "2 & 4 & 7 & 11 & 4 & 3, 9, 11, 33 \\\\ \\hline\n",
      "2 & 4 & 7 & 13 & 4 &  \\\\ \\hline\n",
      "2 & 4 & 8 & 10 & 0 & 3 \\\\ \\hline\n",
      "2 & 4 & 8 & 11 & 4 & 3, 9 \\\\ \\hline\n",
      "2 & 5 & 6 & 11 & 4 & 3, 73 \\\\ \\hline\n",
      "2 & 5 & 7 & 13 & 4 &  \\\\ \\hline\n",
      "2 & 5 & 8 & 13 & 4 & 13, 97 \\\\ \\hline\n",
      "2 & 5 & 9 & 14 & 3 & 3 \\\\ \\hline\n",
      "2 & 5 & 10 & 13 & 4 & 17 \\\\ \\hline\n",
      "2 & 6 & 9 & 17 & 4 & 11 \\\\ \\hline\n",
      "3 & 2 & -6 & -15 & 4 & 3, 7, 9, 27 \\\\ \\hline\n",
      "3 & 2 & -5 & -13 & 4 &  \\\\ \\hline\n",
      "3 & 2 & -4 & -10 & 1 &  \\\\ \\hline\n",
      "3 & 2 & 0 & 1 & 4 & 3, 5, 7, 9, 11, 15, 25, 31, 33, 45, 55, 75, 93, 99 \\\\ \\hline\n",
      "3 & 3 & -3 & -11 & 4 & 3, 5, 9, 27 \\\\ \\hline\n",
      "3 & 3 & -2 & -7 & 4 &  \\\\ \\hline\n",
      "3 & 3 & -1 & -5 & 4 & 3, 15, 17, 45 \\\\ \\hline\n",
      "3 & 3 & 0 & -3 & 4 & 3, 9, 27 \\\\ \\hline\n",
      "3 & 3 & 1 & 0 & 3 &  \\\\ \\hline\n",
      "3 & 3 & 2 & 3 & 4 &  \\\\ \\hline\n",
      "3 & 4 & 2 & -1 & 4 & 3 \\\\ \\hline\n",
      "3 & 4 & 4 & 5 & 4 & 3 \\\\ \\hline\n",
      "3 & 4 & 6 & 10 & 1 & 3, 9, 27 \\\\ \\hline\n",
      "3 & 5 & 5 & 5 & 4 &  \\\\ \\hline\n",
      "3 & 5 & 6 & 6 & 2 & 3, 9, 13, 27, 97 \\\\ \\hline\n",
      "3 & 5 & 6 & 7 & 4 & 3, 9 \\\\ \\hline\n",
      "3 & 5 & 7 & 9 & 4 & 3, 9 \\\\ \\hline\n",
      "3 & 5 & 7 & 11 & 4 & 17 \\\\ \\hline\n",
      "3 & 5 & 8 & 13 & 4 &  \\\\ \\hline\n",
      "3 & 5 & 9 & 15 & 4 & 3, 9, 27 \\\\ \\hline\n",
      "3 & 6 & 8 & 11 & 4 &  \\\\ \\hline\n",
      "3 & 6 & 9 & 12 & 3 & 3, 9, 27 \\\\ \\hline\n",
      "3 & 6 & 10 & 14 & 1 &  \\\\ \\hline\n",
      "3 & 6 & 10 & 15 & 4 &  \\\\ \\hline\n",
      "3 & 6 & 11 & 17 & 4 &  \\\\ \\hline\n",
      "3 & 6 & 12 & 19 & 4 & 3, 9, 27 \\\\ \\hline\n",
      "3 & 7 & 11 & 17 & 4 & 3 \\\\ \\hline\n",
      "3 & 7 & 12 & 19 & 4 & 3, 9, 27 \\\\ \\hline\n",
      "3 & 7 & 13 & 19 & 4 & 5 \\\\ \\hline\n",
      "3 & 7 & 13 & 21 & 4 & 3, 5 \\\\ \\hline\n",
      "3 & 8 & 14 & 23 & 4 & 11, 99 \\\\ \\hline\n",
      "4 & 4 & -7 & -21 & 4 & 11, 15, 19, 31, 33, 55, 57, 61, 93 \\\\ \\hline\n",
      "4 & 5 & -2 & -11 & 4 & 13, 97 \\\\ \\hline\n",
      "4 & 6 & 4 & 2 & 0 & 7, 89 \\\\ \\hline\n",
      "4 & 8 & 12 & 17 & 4 & 3, 5, 47, 89, 91, 93 \\\\ \\hline\n",
      "4 & 9 & 17 & 27 & 4 &  \\\\ \\hline\n",
      "4 & 10 & 19 & 29 & 4 & 3, 9 \\\\ \\hline\n",
      "5 & 12 & 20 & 29 & 4 & 5, 11, 15, 55, 99 \\\\ \\hline\n",
      "5 & 13 & 25 & 39 & 4 & 5, 11, 15, 19, 31, 33, 55, 57, 61, 85, 93 \\\\ \\hline\n"
     ]
    }
   ],
   "source": [
    "print(\"\\n\".join(List2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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    "name": "ipython",
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   "nbconvert_exporter": "python",
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