new fatou.gp program

[JmsNxn]

Then what was up with the spikes in the imaginary part with one precision, and then straight line at zero at a higher precision?
How do I use fatou.gp to show the non real valuedness of the analytic continuation of the Kneser method, with base the pith root of pi in a way that is not spikey?

You never use numerical approximation as a proof of anything. So, you can't. But the spikes are just noise in the program... nothing you can do about that--except write your own program that tries to reduce noise.