I am currently working on some tools to make contour integration in a proof assistant less painful and I'm looking for interesting examples of contours in the complex plane used in the literature. I am most interested in contours that add little epsilon detours in order to avoid singularities/branch cuts/etc.

One example of what I am looking for is the following contour that is used in the study of modular functions.

[An interesting integration contour from Apostol's "Modular Functions and Dirichlet Series in Number Theory"]