Cyclotomic Matrices and Graphs over the ring of integers of some imaginary quadratic fields

We determine all Hermitian ${\mathcal{O}}_{\text{Q}(\sqrt{d})}$-matrices for which every eigenvalue is in the interval [-2,2], for each d in {-2,-7,-11,-15}. To do so, we generalise charged signed graphs to $\mathcal{L}$-graphs for appropriate finite sets $\mathcal{L}$, and classify all $\mathcal{L}$-graphs satisfying the same eigenvalue constraints. We find that, as in the integer case, any such matrix / graph is contained in a maximal example with all eigenvalues $\pm 2$.