coclasses in a galois cohomology group $h^1(k, t)$ parametrize extensions of a number field with certain galois group. it is natural to want to count these coclasses with general local conditions and with respect to a discriminant-like invariant. in joint work with brandon alberts, i present a novel tool for studying this: harmonic analysis on adelic cohomology, modeled after the celebrated use of harmonic analysis on the adeles in tate's thesis. this leads to a more illuminating explanation of a fact previously noticed by alberts, namely that the dirichlet series counting such coclasses is a finite sum of euler products; and we nail down the asymptotic count of coclasses in satisfying generality.