How to speed up the plot of a function related to the incomplete Gamma functions? – mathematica.stackexchange.com

I found a function $F(z,m)$ that is related to incomplete Gamma function via: $$\Xi(z,m):=\sum _{n=1}^m \left(\pi n^2 e^{-\frac{\pi n^2}{m}} \left(1+m^{i z}\right) m^{-\frac{5}{4}-\frac{i ...