Below you can find a catalog of all topological zeta functions of matroids that I computed. For all computation I use as the -function, for the -function I use
where is the number of atoms less then or equal to , and is the rank of .
Since closed forms are known for the rank and cases these are not included. Obviously the zeta function is invariant under matroid simplification, so I only compute it for the simple matroids (note that then ). Also, since the zeta function is multiplicative under direct sums I only compute it for connected matroids. I use Yoshitake Matsumoto‘s databases of matroids to systematically compute zeta functions.
Every entry consists of 3 lines: the revlex representation of the matroid, the topological zeta function, represented as the pair (numerator, denominator), and the set of candidate poles.