Spectrum of the Hypereclectic Spin Chain and P\'olya Counting

In earlier work we proposed a generating function that encodes the Jordan block spectrum of integrable Hypereclectic spin chain, related to one-loop dilatation operator dynamical fishnet quantum field theory. We significantly improve expressions for these functions, rendering them much more explicit and elegant. particular, treat case full chain without imposing any cyclicity constraints on states, as well cyclic states. The latter involves P\'olya enumeration theorem in conjunction with q-binomial coefficients.