  We generalize the Harary-Sachs theorem to $k$-uniform hypergraphs: the
codegree-$d$ coefficient of the characteristic polynomial of a uniform
hypergraph ${\cal H}$ can be expressed as a weighted sum of subgraph counts
over certain multi-hypergraphs with $d$ edges. We include a detailed
description of the aforementioned multi-hypergraphs and a formula for their
corresponding weights.
