Structure constants for pre-modular categories

In this paper we study conjugacy classes for pivotal fusion categories. In particular we prove a Burnside type formula for the structure constants concerning the product of two conjugacy class sums of a such fusion category. For a braided weakly integral fusion category $\mathcal{C}$ we show that these structure constants multiplied by $\mathrm{d}\mathrm{i}\mathrm{m}(\mathcal{C})$ are non-negative integers, extending some results obtained by Zhou and Zhu (see \cite{zz}) in the settings of semisimple quasitriangular Hopf algebras.