To any discrete subgroup of SU(2), or an affine ADE quiver, equipped with a certain data, there is an associated 4d N=2 gauge theory partition function, describing equivariant cohomology of the moduli space of self-dual connections on a four-manifold and defined combinatorially on the space of multi-colored partitions. For all such theories, the asymptotics of this partition function is found explicitly in terms of the periods of certain algebraic integrable system associated to the moduli of holomorphic ADE bundles on elliptic curves.