When I am trying to compute complex dilog's to high precision, sage gives 
the wrong by just filling up with zeros:

ComplexField(600)(1/2+sqrt(-3)/2).dilog()
0.274155677808037739629767534643711712760705268010497093200683593750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
 
+ 
1.01494160640965362502224633965050127985270614620051806369642217221943674062982124585777232717020979180233553051948547363281250000000000000000000000000000000000000000000000000000000*I

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