Zeros of the Selberg zeta-function for $\Gamma_0(4)$

I'll discuss an example of interplay between experimental and
theoretical Mathematics, in joint work with M.Fraczek and D.Mayer.
Markus Fraczek has done precise computations of zeros of the Selberg
zeta-function for $\Gamma_0(4)$ and a 1-parameter-group of
characters. I'll show a few observations in these computations and
will indicate how the spectral theory of automorphic forms allows us
to prove some of these observations.