import mpmath as mp
def check(s, z):
    pl1 = mp.polylog(s, z)
    print(pl1.real)
    with mp.workdps(32):
        pl2 = mp.polylog(s, z)
        print(pl2.real)
check(1+1e-15, -2) # bad
check(1, -2 + 1e-8j) # ok (s exactly an integer)
check(1+1e-15, -0.5 + 1e-8j) # ok (|z| < 1)