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^{12} - x^{11} + 7 x^{10} - 6 x^{9} + 41 x^{8} - 62 x^{7} + 266 x^{6} - 351 x^{5} + 1513 x^{4} + \cdots + 2401 $ x^12 - x^11 + 7*x^10 - 6*x^9 + 41*x^8 - 62*x^7 + 266*x^6 - 351*x^5 + 1513*x^4 - 1757*x^3 + 2107*x^2 - 2058*x + 2401

$\times$	$\chi_{ 95 } ( 1, ·)$	$\chi_{ 95 } ( 64, ·)$	$\chi_{ 95 } ( 68, ·)$	$\chi_{ 95 } ( 39, ·)$	$\chi_{ 95 } ( 11, ·)$	$\chi_{ 95 } ( 77, ·)$	$\chi_{ 95 } ( 49, ·)$	$\chi_{ 95 } ( 83, ·)$	$\chi_{ 95 } ( 87, ·)$	$\chi_{ 95 } ( 7, ·)$	$\chi_{ 95 } ( 26, ·)$	$\chi_{ 95 } ( 58, ·)$
$\chi_{ 95 }(1, ·)$	$\chi_{ 95 } ( 1, ·)$	$\chi_{ 95 } ( 64, ·)$	$\chi_{ 95 } ( 68, ·)$	$\chi_{ 95 } ( 39, ·)$	$\chi_{ 95 } ( 11, ·)$	$\chi_{ 95 } ( 77, ·)$	$\chi_{ 95 } ( 49, ·)$	$\chi_{ 95 } ( 83, ·)$	$\chi_{ 95 } ( 87, ·)$	$\chi_{ 95 } ( 7, ·)$	$\chi_{ 95 } ( 26, ·)$	$\chi_{ 95 } ( 58, ·)$
$\chi_{ 95 }(64, ·)$	$\chi_{ 95 } ( 64, ·)$	$\chi_{ 95 } ( 11, ·)$	$\chi_{ 95 } ( 77, ·)$	$\chi_{ 95 } ( 26, ·)$	$\chi_{ 95 } ( 39, ·)$	$\chi_{ 95 } ( 83, ·)$	$\chi_{ 95 } ( 1, ·)$	$\chi_{ 95 } ( 87, ·)$	$\chi_{ 95 } ( 58, ·)$	$\chi_{ 95 } ( 68, ·)$	$\chi_{ 95 } ( 49, ·)$	$\chi_{ 95 } ( 7, ·)$
$\chi_{ 95 }(68, ·)$	$\chi_{ 95 } ( 68, ·)$	$\chi_{ 95 } ( 77, ·)$	$\chi_{ 95 } ( 64, ·)$	$\chi_{ 95 } ( 87, ·)$	$\chi_{ 95 } ( 83, ·)$	$\chi_{ 95 } ( 11, ·)$	$\chi_{ 95 } ( 7, ·)$	$\chi_{ 95 } ( 39, ·)$	$\chi_{ 95 } ( 26, ·)$	$\chi_{ 95 } ( 1, ·)$	$\chi_{ 95 } ( 58, ·)$	$\chi_{ 95 } ( 49, ·)$
$\chi_{ 95 }(39, ·)$	$\chi_{ 95 } ( 39, ·)$	$\chi_{ 95 } ( 26, ·)$	$\chi_{ 95 } ( 87, ·)$	$\chi_{ 95 } ( 1, ·)$	$\chi_{ 95 } ( 49, ·)$	$\chi_{ 95 } ( 58, ·)$	$\chi_{ 95 } ( 11, ·)$	$\chi_{ 95 } ( 7, ·)$	$\chi_{ 95 } ( 68, ·)$	$\chi_{ 95 } ( 83, ·)$	$\chi_{ 95 } ( 64, ·)$	$\chi_{ 95 } ( 77, ·)$
$\chi_{ 95 }(11, ·)$	$\chi_{ 95 } ( 11, ·)$	$\chi_{ 95 } ( 39, ·)$	$\chi_{ 95 } ( 83, ·)$	$\chi_{ 95 } ( 49, ·)$	$\chi_{ 95 } ( 26, ·)$	$\chi_{ 95 } ( 87, ·)$	$\chi_{ 95 } ( 64, ·)$	$\chi_{ 95 } ( 58, ·)$	$\chi_{ 95 } ( 7, ·)$	$\chi_{ 95 } ( 77, ·)$	$\chi_{ 95 } ( 1, ·)$	$\chi_{ 95 } ( 68, ·)$
$\chi_{ 95 }(77, ·)$	$\chi_{ 95 } ( 77, ·)$	$\chi_{ 95 } ( 83, ·)$	$\chi_{ 95 } ( 11, ·)$	$\chi_{ 95 } ( 58, ·)$	$\chi_{ 95 } ( 87, ·)$	$\chi_{ 95 } ( 39, ·)$	$\chi_{ 95 } ( 68, ·)$	$\chi_{ 95 } ( 26, ·)$	$\chi_{ 95 } ( 49, ·)$	$\chi_{ 95 } ( 64, ·)$	$\chi_{ 95 } ( 7, ·)$	$\chi_{ 95 } ( 1, ·)$
$\chi_{ 95 }(49, ·)$	$\chi_{ 95 } ( 49, ·)$	$\chi_{ 95 } ( 1, ·)$	$\chi_{ 95 } ( 7, ·)$	$\chi_{ 95 } ( 11, ·)$	$\chi_{ 95 } ( 64, ·)$	$\chi_{ 95 } ( 68, ·)$	$\chi_{ 95 } ( 26, ·)$	$\chi_{ 95 } ( 77, ·)$	$\chi_{ 95 } ( 83, ·)$	$\chi_{ 95 } ( 58, ·)$	$\chi_{ 95 } ( 39, ·)$	$\chi_{ 95 } ( 87, ·)$
$\chi_{ 95 }(83, ·)$	$\chi_{ 95 } ( 83, ·)$	$\chi_{ 95 } ( 87, ·)$	$\chi_{ 95 } ( 39, ·)$	$\chi_{ 95 } ( 7, ·)$	$\chi_{ 95 } ( 58, ·)$	$\chi_{ 95 } ( 26, ·)$	$\chi_{ 95 } ( 77, ·)$	$\chi_{ 95 } ( 49, ·)$	$\chi_{ 95 } ( 1, ·)$	$\chi_{ 95 } ( 11, ·)$	$\chi_{ 95 } ( 68, ·)$	$\chi_{ 95 } ( 64, ·)$
$\chi_{ 95 }(87, ·)$	$\chi_{ 95 } ( 87, ·)$	$\chi_{ 95 } ( 58, ·)$	$\chi_{ 95 } ( 26, ·)$	$\chi_{ 95 } ( 68, ·)$	$\chi_{ 95 } ( 7, ·)$	$\chi_{ 95 } ( 49, ·)$	$\chi_{ 95 } ( 83, ·)$	$\chi_{ 95 } ( 1, ·)$	$\chi_{ 95 } ( 64, ·)$	$\chi_{ 95 } ( 39, ·)$	$\chi_{ 95 } ( 77, ·)$	$\chi_{ 95 } ( 11, ·)$
$\chi_{ 95 }(7, ·)$	$\chi_{ 95 } ( 7, ·)$	$\chi_{ 95 } ( 68, ·)$	$\chi_{ 95 } ( 1, ·)$	$\chi_{ 95 } ( 83, ·)$	$\chi_{ 95 } ( 77, ·)$	$\chi_{ 95 } ( 64, ·)$	$\chi_{ 95 } ( 58, ·)$	$\chi_{ 95 } ( 11, ·)$	$\chi_{ 95 } ( 39, ·)$	$\chi_{ 95 } ( 49, ·)$	$\chi_{ 95 } ( 87, ·)$	$\chi_{ 95 } ( 26, ·)$
$\chi_{ 95 }(26, ·)$	$\chi_{ 95 } ( 26, ·)$	$\chi_{ 95 } ( 49, ·)$	$\chi_{ 95 } ( 58, ·)$	$\chi_{ 95 } ( 64, ·)$	$\chi_{ 95 } ( 1, ·)$	$\chi_{ 95 } ( 7, ·)$	$\chi_{ 95 } ( 39, ·)$	$\chi_{ 95 } ( 68, ·)$	$\chi_{ 95 } ( 77, ·)$	$\chi_{ 95 } ( 87, ·)$	$\chi_{ 95 } ( 11, ·)$	$\chi_{ 95 } ( 83, ·)$
$\chi_{ 95 }(58, ·)$	$\chi_{ 95 } ( 58, ·)$	$\chi_{ 95 } ( 7, ·)$	$\chi_{ 95 } ( 49, ·)$	$\chi_{ 95 } ( 77, ·)$	$\chi_{ 95 } ( 68, ·)$	$\chi_{ 95 } ( 1, ·)$	$\chi_{ 95 } ( 87, ·)$	$\chi_{ 95 } ( 64, ·)$	$\chi_{ 95 } ( 11, ·)$	$\chi_{ 95 } ( 26, ·)$	$\chi_{ 95 } ( 83, ·)$	$\chi_{ 95 } ( 39, ·)$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

$\times$	\(\chi_{ 95 } ( 1, ·)\)	\(\chi_{ 95 } ( 64, ·)\)	\(\chi_{ 95 } ( 68, ·)\)	\(\chi_{ 95 } ( 39, ·)\)	\(\chi_{ 95 } ( 11, ·)\)	\(\chi_{ 95 } ( 77, ·)\)	\(\chi_{ 95 } ( 49, ·)\)	\(\chi_{ 95 } ( 83, ·)\)	\(\chi_{ 95 } ( 87, ·)\)	\(\chi_{ 95 } ( 7, ·)\)	\(\chi_{ 95 } ( 26, ·)\)	\(\chi_{ 95 } ( 58, ·)\)
\(\chi_{ 95 }(1, ·)\)	\(\chi_{ 95 } ( 1, ·)\)	\(\chi_{ 95 } ( 64, ·)\)	\(\chi_{ 95 } ( 68, ·)\)	\(\chi_{ 95 } ( 39, ·)\)	\(\chi_{ 95 } ( 11, ·)\)	\(\chi_{ 95 } ( 77, ·)\)	\(\chi_{ 95 } ( 49, ·)\)	\(\chi_{ 95 } ( 83, ·)\)	\(\chi_{ 95 } ( 87, ·)\)	\(\chi_{ 95 } ( 7, ·)\)	\(\chi_{ 95 } ( 26, ·)\)	\(\chi_{ 95 } ( 58, ·)\)
\(\chi_{ 95 }(64, ·)\)	\(\chi_{ 95 } ( 64, ·)\)	\(\chi_{ 95 } ( 11, ·)\)	\(\chi_{ 95 } ( 77, ·)\)	\(\chi_{ 95 } ( 26, ·)\)	\(\chi_{ 95 } ( 39, ·)\)	\(\chi_{ 95 } ( 83, ·)\)	\(\chi_{ 95 } ( 1, ·)\)	\(\chi_{ 95 } ( 87, ·)\)	\(\chi_{ 95 } ( 58, ·)\)	\(\chi_{ 95 } ( 68, ·)\)	\(\chi_{ 95 } ( 49, ·)\)	\(\chi_{ 95 } ( 7, ·)\)
\(\chi_{ 95 }(68, ·)\)	\(\chi_{ 95 } ( 68, ·)\)	\(\chi_{ 95 } ( 77, ·)\)	\(\chi_{ 95 } ( 64, ·)\)	\(\chi_{ 95 } ( 87, ·)\)	\(\chi_{ 95 } ( 83, ·)\)	\(\chi_{ 95 } ( 11, ·)\)	\(\chi_{ 95 } ( 7, ·)\)	\(\chi_{ 95 } ( 39, ·)\)	\(\chi_{ 95 } ( 26, ·)\)	\(\chi_{ 95 } ( 1, ·)\)	\(\chi_{ 95 } ( 58, ·)\)	\(\chi_{ 95 } ( 49, ·)\)
\(\chi_{ 95 }(39, ·)\)	\(\chi_{ 95 } ( 39, ·)\)	\(\chi_{ 95 } ( 26, ·)\)	\(\chi_{ 95 } ( 87, ·)\)	\(\chi_{ 95 } ( 1, ·)\)	\(\chi_{ 95 } ( 49, ·)\)	\(\chi_{ 95 } ( 58, ·)\)	\(\chi_{ 95 } ( 11, ·)\)	\(\chi_{ 95 } ( 7, ·)\)	\(\chi_{ 95 } ( 68, ·)\)	\(\chi_{ 95 } ( 83, ·)\)	\(\chi_{ 95 } ( 64, ·)\)	\(\chi_{ 95 } ( 77, ·)\)
\(\chi_{ 95 }(11, ·)\)	\(\chi_{ 95 } ( 11, ·)\)	\(\chi_{ 95 } ( 39, ·)\)	\(\chi_{ 95 } ( 83, ·)\)	\(\chi_{ 95 } ( 49, ·)\)	\(\chi_{ 95 } ( 26, ·)\)	\(\chi_{ 95 } ( 87, ·)\)	\(\chi_{ 95 } ( 64, ·)\)	\(\chi_{ 95 } ( 58, ·)\)	\(\chi_{ 95 } ( 7, ·)\)	\(\chi_{ 95 } ( 77, ·)\)	\(\chi_{ 95 } ( 1, ·)\)	\(\chi_{ 95 } ( 68, ·)\)
\(\chi_{ 95 }(77, ·)\)	\(\chi_{ 95 } ( 77, ·)\)	\(\chi_{ 95 } ( 83, ·)\)	\(\chi_{ 95 } ( 11, ·)\)	\(\chi_{ 95 } ( 58, ·)\)	\(\chi_{ 95 } ( 87, ·)\)	\(\chi_{ 95 } ( 39, ·)\)	\(\chi_{ 95 } ( 68, ·)\)	\(\chi_{ 95 } ( 26, ·)\)	\(\chi_{ 95 } ( 49, ·)\)	\(\chi_{ 95 } ( 64, ·)\)	\(\chi_{ 95 } ( 7, ·)\)	\(\chi_{ 95 } ( 1, ·)\)
\(\chi_{ 95 }(49, ·)\)	\(\chi_{ 95 } ( 49, ·)\)	\(\chi_{ 95 } ( 1, ·)\)	\(\chi_{ 95 } ( 7, ·)\)	\(\chi_{ 95 } ( 11, ·)\)	\(\chi_{ 95 } ( 64, ·)\)	\(\chi_{ 95 } ( 68, ·)\)	\(\chi_{ 95 } ( 26, ·)\)	\(\chi_{ 95 } ( 77, ·)\)	\(\chi_{ 95 } ( 83, ·)\)	\(\chi_{ 95 } ( 58, ·)\)	\(\chi_{ 95 } ( 39, ·)\)	\(\chi_{ 95 } ( 87, ·)\)
\(\chi_{ 95 }(83, ·)\)	\(\chi_{ 95 } ( 83, ·)\)	\(\chi_{ 95 } ( 87, ·)\)	\(\chi_{ 95 } ( 39, ·)\)	\(\chi_{ 95 } ( 7, ·)\)	\(\chi_{ 95 } ( 58, ·)\)	\(\chi_{ 95 } ( 26, ·)\)	\(\chi_{ 95 } ( 77, ·)\)	\(\chi_{ 95 } ( 49, ·)\)	\(\chi_{ 95 } ( 1, ·)\)	\(\chi_{ 95 } ( 11, ·)\)	\(\chi_{ 95 } ( 68, ·)\)	\(\chi_{ 95 } ( 64, ·)\)
\(\chi_{ 95 }(87, ·)\)	\(\chi_{ 95 } ( 87, ·)\)	\(\chi_{ 95 } ( 58, ·)\)	\(\chi_{ 95 } ( 26, ·)\)	\(\chi_{ 95 } ( 68, ·)\)	\(\chi_{ 95 } ( 7, ·)\)	\(\chi_{ 95 } ( 49, ·)\)	\(\chi_{ 95 } ( 83, ·)\)	\(\chi_{ 95 } ( 1, ·)\)	\(\chi_{ 95 } ( 64, ·)\)	\(\chi_{ 95 } ( 39, ·)\)	\(\chi_{ 95 } ( 77, ·)\)	\(\chi_{ 95 } ( 11, ·)\)
\(\chi_{ 95 }(7, ·)\)	\(\chi_{ 95 } ( 7, ·)\)	\(\chi_{ 95 } ( 68, ·)\)	\(\chi_{ 95 } ( 1, ·)\)	\(\chi_{ 95 } ( 83, ·)\)	\(\chi_{ 95 } ( 77, ·)\)	\(\chi_{ 95 } ( 64, ·)\)	\(\chi_{ 95 } ( 58, ·)\)	\(\chi_{ 95 } ( 11, ·)\)	\(\chi_{ 95 } ( 39, ·)\)	\(\chi_{ 95 } ( 49, ·)\)	\(\chi_{ 95 } ( 87, ·)\)	\(\chi_{ 95 } ( 26, ·)\)
\(\chi_{ 95 }(26, ·)\)	\(\chi_{ 95 } ( 26, ·)\)	\(\chi_{ 95 } ( 49, ·)\)	\(\chi_{ 95 } ( 58, ·)\)	\(\chi_{ 95 } ( 64, ·)\)	\(\chi_{ 95 } ( 1, ·)\)	\(\chi_{ 95 } ( 7, ·)\)	\(\chi_{ 95 } ( 39, ·)\)	\(\chi_{ 95 } ( 68, ·)\)	\(\chi_{ 95 } ( 77, ·)\)	\(\chi_{ 95 } ( 87, ·)\)	\(\chi_{ 95 } ( 11, ·)\)	\(\chi_{ 95 } ( 83, ·)\)
\(\chi_{ 95 }(58, ·)\)	\(\chi_{ 95 } ( 58, ·)\)	\(\chi_{ 95 } ( 7, ·)\)	\(\chi_{ 95 } ( 49, ·)\)	\(\chi_{ 95 } ( 77, ·)\)	\(\chi_{ 95 } ( 68, ·)\)	\(\chi_{ 95 } ( 1, ·)\)	\(\chi_{ 95 } ( 87, ·)\)	\(\chi_{ 95 } ( 64, ·)\)	\(\chi_{ 95 } ( 11, ·)\)	\(\chi_{ 95 } ( 26, ·)\)	\(\chi_{ 95 } ( 83, ·)\)	\(\chi_{ 95 } ( 39, ·)\)

Introduction

L-functions

Modular forms

Varieties

Fields

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.