But there is a pattern. It's just a simple sum over all non-trivial zeros of the Riemann Zeta function[1]. It will pop right out at you if you take a look at the proof for the Riemann hypothesis (an exercise left to the reader). Also, speaking of Riemann, division by zero is also spoken for[2]

[1] https://en.wikipedia.org/wiki/Explicit_formulae_(L-function)

[2] https://en.wikipedia.org/wiki/Riemann_sphere