LMFDB - Group of Dirichlet characters

Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$

$K$ is the global number field defined by $x^{8} $ $\mathstrut -\mathstrut x^{7} $ $\mathstrut -\mathstrut 49 x^{6} $ $\mathstrut -\mathstrut 16 x^{5} $ $\mathstrut +\mathstrut 511 x^{4} $ $\mathstrut +\mathstrut 367 x^{3} $ $\mathstrut -\mathstrut 1499 x^{2} $ $\mathstrut -\mathstrut 798 x $ $\mathstrut +\mathstrut 1372 $

$\times$	$\chi_{ 113 } ( 1, ·)$	$\chi_{ 113 } ( 98, ·)$	$\chi_{ 113 } ( 69, ·)$	$\chi_{ 113 } ( 44, ·)$	$\chi_{ 113 } ( 15, ·)$	$\chi_{ 113 } ( 112, ·)$	$\chi_{ 113 } ( 18, ·)$	$\chi_{ 113 } ( 95, ·)$
$\chi_{ 113 }(1, ·)$	$\chi_{ 113 } ( 1, ·)$	$\chi_{ 113 } ( 98, ·)$	$\chi_{ 113 } ( 69, ·)$	$\chi_{ 113 } ( 44, ·)$	$\chi_{ 113 } ( 15, ·)$	$\chi_{ 113 } ( 112, ·)$	$\chi_{ 113 } ( 18, ·)$	$\chi_{ 113 } ( 95, ·)$
$\chi_{ 113 }(98, ·)$	$\chi_{ 113 } ( 98, ·)$	$\chi_{ 113 } ( 112, ·)$	$\chi_{ 113 } ( 95, ·)$	$\chi_{ 113 } ( 18, ·)$	$\chi_{ 113 } ( 1, ·)$	$\chi_{ 113 } ( 15, ·)$	$\chi_{ 113 } ( 69, ·)$	$\chi_{ 113 } ( 44, ·)$
$\chi_{ 113 }(69, ·)$	$\chi_{ 113 } ( 69, ·)$	$\chi_{ 113 } ( 95, ·)$	$\chi_{ 113 } ( 15, ·)$	$\chi_{ 113 } ( 98, ·)$	$\chi_{ 113 } ( 18, ·)$	$\chi_{ 113 } ( 44, ·)$	$\chi_{ 113 } ( 112, ·)$	$\chi_{ 113 } ( 1, ·)$
$\chi_{ 113 }(44, ·)$	$\chi_{ 113 } ( 44, ·)$	$\chi_{ 113 } ( 18, ·)$	$\chi_{ 113 } ( 98, ·)$	$\chi_{ 113 } ( 15, ·)$	$\chi_{ 113 } ( 95, ·)$	$\chi_{ 113 } ( 69, ·)$	$\chi_{ 113 } ( 1, ·)$	$\chi_{ 113 } ( 112, ·)$
$\chi_{ 113 }(15, ·)$	$\chi_{ 113 } ( 15, ·)$	$\chi_{ 113 } ( 1, ·)$	$\chi_{ 113 } ( 18, ·)$	$\chi_{ 113 } ( 95, ·)$	$\chi_{ 113 } ( 112, ·)$	$\chi_{ 113 } ( 98, ·)$	$\chi_{ 113 } ( 44, ·)$	$\chi_{ 113 } ( 69, ·)$
$\chi_{ 113 }(112, ·)$	$\chi_{ 113 } ( 112, ·)$	$\chi_{ 113 } ( 15, ·)$	$\chi_{ 113 } ( 44, ·)$	$\chi_{ 113 } ( 69, ·)$	$\chi_{ 113 } ( 98, ·)$	$\chi_{ 113 } ( 1, ·)$	$\chi_{ 113 } ( 95, ·)$	$\chi_{ 113 } ( 18, ·)$
$\chi_{ 113 }(18, ·)$	$\chi_{ 113 } ( 18, ·)$	$\chi_{ 113 } ( 69, ·)$	$\chi_{ 113 } ( 112, ·)$	$\chi_{ 113 } ( 1, ·)$	$\chi_{ 113 } ( 44, ·)$	$\chi_{ 113 } ( 95, ·)$	$\chi_{ 113 } ( 98, ·)$	$\chi_{ 113 } ( 15, ·)$
$\chi_{ 113 }(95, ·)$	$\chi_{ 113 } ( 95, ·)$	$\chi_{ 113 } ( 44, ·)$	$\chi_{ 113 } ( 1, ·)$	$\chi_{ 113 } ( 112, ·)$	$\chi_{ 113 } ( 69, ·)$	$\chi_{ 113 } ( 18, ·)$	$\chi_{ 113 } ( 15, ·)$	$\chi_{ 113 } ( 98, ·)$

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

$\times$	\(\chi_{ 113 } ( 1, ·)\)	\(\chi_{ 113 } ( 98, ·)\)	\(\chi_{ 113 } ( 69, ·)\)	\(\chi_{ 113 } ( 44, ·)\)	\(\chi_{ 113 } ( 15, ·)\)	\(\chi_{ 113 } ( 112, ·)\)	\(\chi_{ 113 } ( 18, ·)\)	\(\chi_{ 113 } ( 95, ·)\)
\(\chi_{ 113 }(1, ·)\)	\(\chi_{ 113 } ( 1, ·)\)	\(\chi_{ 113 } ( 98, ·)\)	\(\chi_{ 113 } ( 69, ·)\)	\(\chi_{ 113 } ( 44, ·)\)	\(\chi_{ 113 } ( 15, ·)\)	\(\chi_{ 113 } ( 112, ·)\)	\(\chi_{ 113 } ( 18, ·)\)	\(\chi_{ 113 } ( 95, ·)\)
\(\chi_{ 113 }(98, ·)\)	\(\chi_{ 113 } ( 98, ·)\)	\(\chi_{ 113 } ( 112, ·)\)	\(\chi_{ 113 } ( 95, ·)\)	\(\chi_{ 113 } ( 18, ·)\)	\(\chi_{ 113 } ( 1, ·)\)	\(\chi_{ 113 } ( 15, ·)\)	\(\chi_{ 113 } ( 69, ·)\)	\(\chi_{ 113 } ( 44, ·)\)
\(\chi_{ 113 }(69, ·)\)	\(\chi_{ 113 } ( 69, ·)\)	\(\chi_{ 113 } ( 95, ·)\)	\(\chi_{ 113 } ( 15, ·)\)	\(\chi_{ 113 } ( 98, ·)\)	\(\chi_{ 113 } ( 18, ·)\)	\(\chi_{ 113 } ( 44, ·)\)	\(\chi_{ 113 } ( 112, ·)\)	\(\chi_{ 113 } ( 1, ·)\)
\(\chi_{ 113 }(44, ·)\)	\(\chi_{ 113 } ( 44, ·)\)	\(\chi_{ 113 } ( 18, ·)\)	\(\chi_{ 113 } ( 98, ·)\)	\(\chi_{ 113 } ( 15, ·)\)	\(\chi_{ 113 } ( 95, ·)\)	\(\chi_{ 113 } ( 69, ·)\)	\(\chi_{ 113 } ( 1, ·)\)	\(\chi_{ 113 } ( 112, ·)\)
\(\chi_{ 113 }(15, ·)\)	\(\chi_{ 113 } ( 15, ·)\)	\(\chi_{ 113 } ( 1, ·)\)	\(\chi_{ 113 } ( 18, ·)\)	\(\chi_{ 113 } ( 95, ·)\)	\(\chi_{ 113 } ( 112, ·)\)	\(\chi_{ 113 } ( 98, ·)\)	\(\chi_{ 113 } ( 44, ·)\)	\(\chi_{ 113 } ( 69, ·)\)
\(\chi_{ 113 }(112, ·)\)	\(\chi_{ 113 } ( 112, ·)\)	\(\chi_{ 113 } ( 15, ·)\)	\(\chi_{ 113 } ( 44, ·)\)	\(\chi_{ 113 } ( 69, ·)\)	\(\chi_{ 113 } ( 98, ·)\)	\(\chi_{ 113 } ( 1, ·)\)	\(\chi_{ 113 } ( 95, ·)\)	\(\chi_{ 113 } ( 18, ·)\)
\(\chi_{ 113 }(18, ·)\)	\(\chi_{ 113 } ( 18, ·)\)	\(\chi_{ 113 } ( 69, ·)\)	\(\chi_{ 113 } ( 112, ·)\)	\(\chi_{ 113 } ( 1, ·)\)	\(\chi_{ 113 } ( 44, ·)\)	\(\chi_{ 113 } ( 95, ·)\)	\(\chi_{ 113 } ( 98, ·)\)	\(\chi_{ 113 } ( 15, ·)\)
\(\chi_{ 113 }(95, ·)\)	\(\chi_{ 113 } ( 95, ·)\)	\(\chi_{ 113 } ( 44, ·)\)	\(\chi_{ 113 } ( 1, ·)\)	\(\chi_{ 113 } ( 112, ·)\)	\(\chi_{ 113 } ( 69, ·)\)	\(\chi_{ 113 } ( 18, ·)\)	\(\chi_{ 113 } ( 15, ·)\)	\(\chi_{ 113 } ( 98, ·)\)

Introduction

L-functions

Modular forms

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Representations

Groups

Database

Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.