Riemann surface

This figure is piling squares which are prime numbers.


The pattern includes complex plane, so I think that I can describe Riemann surface.



θ=2nπ　(n=0,±1,±2........) and arg Z=θ+2nπ (-π＜θ≦π).
Therefore, arg Z change according to n.

n=0 →　-π＜arg Z≦π
n=1 →　π＜arg Z≦3π
n=5 →　9π＜arg Z≦11π
n=-5 → -11π＜arg Z≦-9π

∴(2n-1)π＜arg Z≦(2n+1)π

Complex planes Z depend on n, and these are piled infinitely.