Dokchitser Project for Sage Days 11
Here's the version (closest to Dokchitser's original pari code) that still uses continued fraction approximation:
(needs gamma_series.py to run:
The version with Pade approximation (l5.py) has a negligible speedup but only really works for low precision. I'm not sure if Pade gives us a means of computing bounds (I think Mike Rubinstein said that continued fractions won't). Also, l4.py doesn't work for imaginary inputs yet - some coercion with SymbolicRing that I didn't try.