diff --git a/test/Li2.jl b/test/Li2.jl
index da6441b..23fb70b 100644
--- a/test/Li2.jl
+++ b/test/Li2.jl
@@ -42,7 +42,7 @@
     @test imag(PolyLog.li2(-1.08371e-08 + 1.32716e-24*im)) ==  1.3271599928087172e-24
 
     # test value close to zero
-    @test real(PolyLog.li2(4.831285545908206e-6 + 0.004396919500211628im)) ≈ -1.94166578202937687444628936853e-9 rtol=1e-14
+    @test real(PolyLog.li2(4.831285545908206e-6 + 0.004396919500211628im)) ≈ -1.94166578202937687444628936853e-9 rtol=1e-12
     @test imag(PolyLog.li2(4.831285545908206e-6 + 0.004396919500211628im)) ≈  0.00439692067657240512726530759719387623 rtol=1e-14
 
     # test value that causes overflow if squared
diff --git a/test/data/Li2.txt b/test/data/Li2.txt
index 63d0464..c3f4f4a 100644
--- a/test/data/Li2.txt
+++ b/test/data/Li2.txt
@@ -29495,4 +29495,4 @@
 1.866025403784438646763723170752936183471	0	2.462476291998257749879841815859353737369	-1.959759163762466197633638184456010687141
 2.366025403784438646763723170752936183471	0	2.440563435777528096173154682355559137893	-2.705575729492834429533729384137048166147
 0.4226497308103742354908512194980425443524	0	0.4784620718855691763503649463788251188975	0
-4.831285545908206e-6	0.004396919500211628	-1.94166578202937687444628936853e-9	0.00439692067657240512726530759719387623
+4.831285545908206e-6	0.004396919500211628	-1.9416657820293768744462893685250708100415988730126e-9	0.0043969206765724051272653075971938762332366081572791843577