# Graphing on the complex plane

I've seen many graphs of functions in the complex plane. For example the $\Psi_0(x)$. They look very nice and I wonder how may I graph them by hand. If and only if it is possible. Other ones I want to graph are $$\operatorname{Li}_s(z)$$. How do you know what colors to use in the graph?

Given a function $f:\mathbb{C}\rightarrow\mathbb{C}$, you can color the complex plane by associating to each point a color based on the angle $f(z)/|f(z)|$ makes with the real axis. You can also change the brightness depending on the value of $|f(z)|$.