`DirichletCharacter(q, ell)`, rendered as $\chi_{q \, . \, \ell}$, represents the Dirichlet character with Conrey label $\left(q, \ell\right)$.

A character represents an object $\chi$
that can be called ( $\chi(n)$
) as a function from $\mathbb{Z}$
to $\mathbb{C}$.

`DirichletCharacter(q, ell, n)`, rendered as $\chi_{q \, . \, \ell}\!\left(n\right)$, represents the Dirichlet character with Conrey label $\left(q, \ell\right)$ evaluated at the integer $n$.

The Conrey label consists of integers $q \in \mathbb{Z}_{\ge 1}$
and $\ell \in \{1, 2, \ldots, \max\!\left(q, 2\right) - 1\}$
such that $\gcd\!\left(\ell, q\right) = 1$. In this scheme $\chi_{q \, . \, 1}$
always represents the trivial/principal character (taking only values 0 and 1) modulo $q$. Non-principal characters are defined by 4cf4e4 when $q$
is an odd prime power, by fc4f6a and 03fbe8 when $q$
is an even prime power, and in general by factoring $q$
into prime powers using 2a48bd.

References:

- http://www.lmfdb.org/Character/Labels

Definitions:

Fungrim symbol | Notation | Short description |
---|---|---|

DirichletCharacter | $\chi_{q \, . \, \ell}$ | Dirichlet character |

ZZ | $\mathbb{Z}$ | Integers |

CC | $\mathbb{C}$ | Complex numbers |

ZZGreaterEqual | $\mathbb{Z}_{\ge n}$ | Integers greater than or equal to n |

Range | $\{a, a + 1, \ldots, b\}$ | Integers between given endpoints |

GCD | $\gcd\!\left(a, b\right)$ | Greatest common divisor |

Source code for this entry:

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