generalized Bernoulli number

Let $\chi$ be a non-trivial primitive character mod $m$. The generalized Bernoulli numbers $B_{n,\chi }$ are given by

$$\sum _{a=1}^m\chi (a)\frac{t{e}^{at}}{e^{mt}-1}=\sum _{n=0}^{\mathrm{\infty }}{B}_{n,\chi }\frac{t^n}{n!}$$

They are members of the field $\mathbb{Q}(\chi )$ generated by the values of $\chi$.