Preview for editing tables

In this editor you can enter or edit tables in YAML format, and you can get a preview of how numberdb would render it. You cannot save changes here. Once everything looks good, upload it to the git repository numberdb-data.
— preview —
Generalized Bernoulli numbers
edit on github
Numbers
$q$
$n$
$k$
$B_{k,\chi}$
INPUT{numbers.yaml} (not shown in preview)
Definition
Let $\chi$ be a Dirichlet character of modulus $q$. The generalized Bernoulli numbers $B_{k,\chi}$ attached to $\chi$ are defined as the Taylor coefficients of $\sum_{a=1}^q \chi(a) \frac{te^{at}}{e^{qt}-1} = \sum_{k=0}^\infty B_{k,\chi}\frac{t^k}{k!}$.
Parameters
$q$
—   modulus of $\chi$ ($q \geq 1$)
$n$
—   Conrey index of $\chi$ ($1 \leq n \leq \max(q-1,1)$)
$k$
—   integer ($k \geq 0$)
If $\chi(-1) \neq (-1)^k$, we have $B_{k,\chi}=0$ unless $(q,n)=(1,1)$ (that is, $\chi=1$). Thus we skip these trivial zero entries.
chi = DirichletGroup(3).an_element()