Cyclotomic matrices and graphs over the ring of integers of some imaginary quadratic fields

We determine all Hermitian -matrices for which every eigenvalue is in the interval [−2,2], for each d∈{−2,−7,−11,−15}. To do so, we generalise charged signed graphs to L-graphs for appropriate finite sets L, and classify all 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 ±2.