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.