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{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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