We investigate spectra of Cayley graphs for the Heisenberg group over finite rings $\mathbb(Z)$/$p^n\mathbb(Z)$, where $p$ is a prime. Emphasis is on graphs of degree four. We show that for odd $p$ there is only one such connected graph up to isomorphism. When $p = 2$, there are at most two isomorphism classes. We study the spectra using representations of the Heisenberg group. This allows us to produce histograms and butterfly diagrams of the spectra.
Mathematics Subject Classification: Primary: 11T99; Secondary: 20C33, 05C50.