  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 $\mathrm{dim}(\mathcal C)$ are non-negative
integers, extending some results obtained by Zhou and Zhu (see \cite{zz}) in
the settings of semisimple quasitriangular Hopf algebras.
