  The one-loop dilatation operator in the holomorphic 3-scalar sector of the
dynamical fishnet theory is studied. Due to the non-unitary nature of the
underlying field theory this operator, dubbed the eclectic spin chain
Hamiltonian, is non-diagonalisable. The corresponding spectrum of Jordan blocks
leads to logarithms in the two-point functions, which is characteristic of
logarithmic conformal field theories. It was previously conjectured that for
certain filling conditions and generic couplings the spectrum of the eclectic
model is equivalent to the spectrum of a simpler model, the hypereclectic spin
chain. We provide further evidence for this conjecture, and introduce a
generating function which fully characterises the Jordan block spectrum of the
simplified model. This function is found by purely combinatorial means and is
simply related to the q-binomial coefficient.
