Let $\chi$ be a non-trivial primitive character mod $m$ . The generalized Bernoulli numbers $B_{n,\chi}$ are given by$$ \sum_{a=1}^m \chi(a)\frac{te^{at}}{e^{mt}-1}=\sum_{n=0}^\infty B_{n,\chi}\frac{t^n}{n!}$$ They are members of the field$\mathbb{Q}(\chi)$generated by the values of $\chi$ .
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