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 $x^{17} - x^{16} - 288 x^{15} + 265 x^{14} + 26034 x^{13} - 40228 x^{12} - 875968 x^{11} + 2022008 x^{10} + 8464009 x^{9} - 27681440 x^{8} - 8855367 x^{7} + 101412811 x^{6} - 87313302 x^{5} - 38624139 x^{4} + 67164168 x^{3} - 7149746 x^{2} - 7878215 x - 664471$

$\times$	$\chi_{ 613 } ( 1, ·)$	$\chi_{ 613 } ( 387, ·)$	$\chi_{ 613 } ( 197, ·)$	$\chi_{ 613 } ( 198, ·)$	$\chi_{ 613 } ( 583, ·)$	$\chi_{ 613 } ( 585, ·)$	$\chi_{ 613 } ( 586, ·)$	$\chi_{ 613 } ( 143, ·)$	$\chi_{ 613 } ( 220, ·)$	$\chi_{ 613 } ( 287, ·)$	$\chi_{ 613 } ( 546, ·)$	$\chi_{ 613 } ( 227, ·)$	$\chi_{ 613 } ( 37, ·)$	$\chi_{ 613 } ( 171, ·)$	$\chi_{ 613 } ( 430, ·)$	$\chi_{ 613 } ( 116, ·)$	$\chi_{ 613 } ( 190, ·)$
$\chi_{ 613 }(1, ·)$	$\chi_{ 613 } ( 1, ·)$	$\chi_{ 613 } ( 387, ·)$	$\chi_{ 613 } ( 197, ·)$	$\chi_{ 613 } ( 198, ·)$	$\chi_{ 613 } ( 583, ·)$	$\chi_{ 613 } ( 585, ·)$	$\chi_{ 613 } ( 586, ·)$	$\chi_{ 613 } ( 143, ·)$	$\chi_{ 613 } ( 220, ·)$	$\chi_{ 613 } ( 287, ·)$	$\chi_{ 613 } ( 546, ·)$	$\chi_{ 613 } ( 227, ·)$	$\chi_{ 613 } ( 37, ·)$	$\chi_{ 613 } ( 171, ·)$	$\chi_{ 613 } ( 430, ·)$	$\chi_{ 613 } ( 116, ·)$	$\chi_{ 613 } ( 190, ·)$
$\chi_{ 613 }(387, ·)$	$\chi_{ 613 } ( 387, ·)$	$\chi_{ 613 } ( 197, ·)$	$\chi_{ 613 } ( 227, ·)$	$\chi_{ 613 } ( 1, ·)$	$\chi_{ 613 } ( 37, ·)$	$\chi_{ 613 } ( 198, ·)$	$\chi_{ 613 } ( 585, ·)$	$\chi_{ 613 } ( 171, ·)$	$\chi_{ 613 } ( 546, ·)$	$\chi_{ 613 } ( 116, ·)$	$\chi_{ 613 } ( 430, ·)$	$\chi_{ 613 } ( 190, ·)$	$\chi_{ 613 } ( 220, ·)$	$\chi_{ 613 } ( 586, ·)$	$\chi_{ 613 } ( 287, ·)$	$\chi_{ 613 } ( 143, ·)$	$\chi_{ 613 } ( 583, ·)$
$\chi_{ 613 }(197, ·)$	$\chi_{ 613 } ( 197, ·)$	$\chi_{ 613 } ( 227, ·)$	$\chi_{ 613 } ( 190, ·)$	$\chi_{ 613 } ( 387, ·)$	$\chi_{ 613 } ( 220, ·)$	$\chi_{ 613 } ( 1, ·)$	$\chi_{ 613 } ( 198, ·)$	$\chi_{ 613 } ( 586, ·)$	$\chi_{ 613 } ( 430, ·)$	$\chi_{ 613 } ( 143, ·)$	$\chi_{ 613 } ( 287, ·)$	$\chi_{ 613 } ( 583, ·)$	$\chi_{ 613 } ( 546, ·)$	$\chi_{ 613 } ( 585, ·)$	$\chi_{ 613 } ( 116, ·)$	$\chi_{ 613 } ( 171, ·)$	$\chi_{ 613 } ( 37, ·)$
$\chi_{ 613 }(198, ·)$	$\chi_{ 613 } ( 198, ·)$	$\chi_{ 613 } ( 1, ·)$	$\chi_{ 613 } ( 387, ·)$	$\chi_{ 613 } ( 585, ·)$	$\chi_{ 613 } ( 190, ·)$	$\chi_{ 613 } ( 586, ·)$	$\chi_{ 613 } ( 171, ·)$	$\chi_{ 613 } ( 116, ·)$	$\chi_{ 613 } ( 37, ·)$	$\chi_{ 613 } ( 430, ·)$	$\chi_{ 613 } ( 220, ·)$	$\chi_{ 613 } ( 197, ·)$	$\chi_{ 613 } ( 583, ·)$	$\chi_{ 613 } ( 143, ·)$	$\chi_{ 613 } ( 546, ·)$	$\chi_{ 613 } ( 287, ·)$	$\chi_{ 613 } ( 227, ·)$
$\chi_{ 613 }(583, ·)$	$\chi_{ 613 } ( 583, ·)$	$\chi_{ 613 } ( 37, ·)$	$\chi_{ 613 } ( 220, ·)$	$\chi_{ 613 } ( 190, ·)$	$\chi_{ 613 } ( 287, ·)$	$\chi_{ 613 } ( 227, ·)$	$\chi_{ 613 } ( 197, ·)$	$\chi_{ 613 } ( 1, ·)$	$\chi_{ 613 } ( 143, ·)$	$\chi_{ 613 } ( 585, ·)$	$\chi_{ 613 } ( 171, ·)$	$\chi_{ 613 } ( 546, ·)$	$\chi_{ 613 } ( 116, ·)$	$\chi_{ 613 } ( 387, ·)$	$\chi_{ 613 } ( 586, ·)$	$\chi_{ 613 } ( 198, ·)$	$\chi_{ 613 } ( 430, ·)$
$\chi_{ 613 }(585, ·)$	$\chi_{ 613 } ( 585, ·)$	$\chi_{ 613 } ( 198, ·)$	$\chi_{ 613 } ( 1, ·)$	$\chi_{ 613 } ( 586, ·)$	$\chi_{ 613 } ( 227, ·)$	$\chi_{ 613 } ( 171, ·)$	$\chi_{ 613 } ( 143, ·)$	$\chi_{ 613 } ( 287, ·)$	$\chi_{ 613 } ( 583, ·)$	$\chi_{ 613 } ( 546, ·)$	$\chi_{ 613 } ( 37, ·)$	$\chi_{ 613 } ( 387, ·)$	$\chi_{ 613 } ( 190, ·)$	$\chi_{ 613 } ( 116, ·)$	$\chi_{ 613 } ( 220, ·)$	$\chi_{ 613 } ( 430, ·)$	$\chi_{ 613 } ( 197, ·)$
$\chi_{ 613 }(586, ·)$	$\chi_{ 613 } ( 586, ·)$	$\chi_{ 613 } ( 585, ·)$	$\chi_{ 613 } ( 198, ·)$	$\chi_{ 613 } ( 171, ·)$	$\chi_{ 613 } ( 197, ·)$	$\chi_{ 613 } ( 143, ·)$	$\chi_{ 613 } ( 116, ·)$	$\chi_{ 613 } ( 430, ·)$	$\chi_{ 613 } ( 190, ·)$	$\chi_{ 613 } ( 220, ·)$	$\chi_{ 613 } ( 583, ·)$	$\chi_{ 613 } ( 1, ·)$	$\chi_{ 613 } ( 227, ·)$	$\chi_{ 613 } ( 287, ·)$	$\chi_{ 613 } ( 37, ·)$	$\chi_{ 613 } ( 546, ·)$	$\chi_{ 613 } ( 387, ·)$
$\chi_{ 613 }(143, ·)$	$\chi_{ 613 } ( 143, ·)$	$\chi_{ 613 } ( 171, ·)$	$\chi_{ 613 } ( 586, ·)$	$\chi_{ 613 } ( 116, ·)$	$\chi_{ 613 } ( 1, ·)$	$\chi_{ 613 } ( 287, ·)$	$\chi_{ 613 } ( 430, ·)$	$\chi_{ 613 } ( 220, ·)$	$\chi_{ 613 } ( 197, ·)$	$\chi_{ 613 } ( 583, ·)$	$\chi_{ 613 } ( 227, ·)$	$\chi_{ 613 } ( 585, ·)$	$\chi_{ 613 } ( 387, ·)$	$\chi_{ 613 } ( 546, ·)$	$\chi_{ 613 } ( 190, ·)$	$\chi_{ 613 } ( 37, ·)$	$\chi_{ 613 } ( 198, ·)$
$\chi_{ 613 }(220, ·)$	$\chi_{ 613 } ( 220, ·)$	$\chi_{ 613 } ( 546, ·)$	$\chi_{ 613 } ( 430, ·)$	$\chi_{ 613 } ( 37, ·)$	$\chi_{ 613 } ( 143, ·)$	$\chi_{ 613 } ( 583, ·)$	$\chi_{ 613 } ( 190, ·)$	$\chi_{ 613 } ( 197, ·)$	$\chi_{ 613 } ( 586, ·)$	$\chi_{ 613 } ( 1, ·)$	$\chi_{ 613 } ( 585, ·)$	$\chi_{ 613 } ( 287, ·)$	$\chi_{ 613 } ( 171, ·)$	$\chi_{ 613 } ( 227, ·)$	$\chi_{ 613 } ( 198, ·)$	$\chi_{ 613 } ( 387, ·)$	$\chi_{ 613 } ( 116, ·)$
$\chi_{ 613 }(287, ·)$	$\chi_{ 613 } ( 287, ·)$	$\chi_{ 613 } ( 116, ·)$	$\chi_{ 613 } ( 143, ·)$	$\chi_{ 613 } ( 430, ·)$	$\chi_{ 613 } ( 585, ·)$	$\chi_{ 613 } ( 546, ·)$	$\chi_{ 613 } ( 220, ·)$	$\chi_{ 613 } ( 583, ·)$	$\chi_{ 613 } ( 1, ·)$	$\chi_{ 613 } ( 227, ·)$	$\chi_{ 613 } ( 387, ·)$	$\chi_{ 613 } ( 171, ·)$	$\chi_{ 613 } ( 198, ·)$	$\chi_{ 613 } ( 37, ·)$	$\chi_{ 613 } ( 197, ·)$	$\chi_{ 613 } ( 190, ·)$	$\chi_{ 613 } ( 586, ·)$
$\chi_{ 613 }(546, ·)$	$\chi_{ 613 } ( 546, ·)$	$\chi_{ 613 } ( 430, ·)$	$\chi_{ 613 } ( 287, ·)$	$\chi_{ 613 } ( 220, ·)$	$\chi_{ 613 } ( 171, ·)$	$\chi_{ 613 } ( 37, ·)$	$\chi_{ 613 } ( 583, ·)$	$\chi_{ 613 } ( 227, ·)$	$\chi_{ 613 } ( 585, ·)$	$\chi_{ 613 } ( 387, ·)$	$\chi_{ 613 } ( 198, ·)$	$\chi_{ 613 } ( 116, ·)$	$\chi_{ 613 } ( 586, ·)$	$\chi_{ 613 } ( 190, ·)$	$\chi_{ 613 } ( 1, ·)$	$\chi_{ 613 } ( 197, ·)$	$\chi_{ 613 } ( 143, ·)$
$\chi_{ 613 }(227, ·)$	$\chi_{ 613 } ( 227, ·)$	$\chi_{ 613 } ( 190, ·)$	$\chi_{ 613 } ( 583, ·)$	$\chi_{ 613 } ( 197, ·)$	$\chi_{ 613 } ( 546, ·)$	$\chi_{ 613 } ( 387, ·)$	$\chi_{ 613 } ( 1, ·)$	$\chi_{ 613 } ( 585, ·)$	$\chi_{ 613 } ( 287, ·)$	$\chi_{ 613 } ( 171, ·)$	$\chi_{ 613 } ( 116, ·)$	$\chi_{ 613 } ( 37, ·)$	$\chi_{ 613 } ( 430, ·)$	$\chi_{ 613 } ( 198, ·)$	$\chi_{ 613 } ( 143, ·)$	$\chi_{ 613 } ( 586, ·)$	$\chi_{ 613 } ( 220, ·)$
$\chi_{ 613 }(37, ·)$	$\chi_{ 613 } ( 37, ·)$	$\chi_{ 613 } ( 220, ·)$	$\chi_{ 613 } ( 546, ·)$	$\chi_{ 613 } ( 583, ·)$	$\chi_{ 613 } ( 116, ·)$	$\chi_{ 613 } ( 190, ·)$	$\chi_{ 613 } ( 227, ·)$	$\chi_{ 613 } ( 387, ·)$	$\chi_{ 613 } ( 171, ·)$	$\chi_{ 613 } ( 198, ·)$	$\chi_{ 613 } ( 586, ·)$	$\chi_{ 613 } ( 430, ·)$	$\chi_{ 613 } ( 143, ·)$	$\chi_{ 613 } ( 197, ·)$	$\chi_{ 613 } ( 585, ·)$	$\chi_{ 613 } ( 1, ·)$	$\chi_{ 613 } ( 287, ·)$
$\chi_{ 613 }(171, ·)$	$\chi_{ 613 } ( 171, ·)$	$\chi_{ 613 } ( 586, ·)$	$\chi_{ 613 } ( 585, ·)$	$\chi_{ 613 } ( 143, ·)$	$\chi_{ 613 } ( 387, ·)$	$\chi_{ 613 } ( 116, ·)$	$\chi_{ 613 } ( 287, ·)$	$\chi_{ 613 } ( 546, ·)$	$\chi_{ 613 } ( 227, ·)$	$\chi_{ 613 } ( 37, ·)$	$\chi_{ 613 } ( 190, ·)$	$\chi_{ 613 } ( 198, ·)$	$\chi_{ 613 } ( 197, ·)$	$\chi_{ 613 } ( 430, ·)$	$\chi_{ 613 } ( 583, ·)$	$\chi_{ 613 } ( 220, ·)$	$\chi_{ 613 } ( 1, ·)$
$\chi_{ 613 }(430, ·)$	$\chi_{ 613 } ( 430, ·)$	$\chi_{ 613 } ( 287, ·)$	$\chi_{ 613 } ( 116, ·)$	$\chi_{ 613 } ( 546, ·)$	$\chi_{ 613 } ( 586, ·)$	$\chi_{ 613 } ( 220, ·)$	$\chi_{ 613 } ( 37, ·)$	$\chi_{ 613 } ( 190, ·)$	$\chi_{ 613 } ( 198, ·)$	$\chi_{ 613 } ( 197, ·)$	$\chi_{ 613 } ( 1, ·)$	$\chi_{ 613 } ( 143, ·)$	$\chi_{ 613 } ( 585, ·)$	$\chi_{ 613 } ( 583, ·)$	$\chi_{ 613 } ( 387, ·)$	$\chi_{ 613 } ( 227, ·)$	$\chi_{ 613 } ( 171, ·)$
$\chi_{ 613 }(116, ·)$	$\chi_{ 613 } ( 116, ·)$	$\chi_{ 613 } ( 143, ·)$	$\chi_{ 613 } ( 171, ·)$	$\chi_{ 613 } ( 287, ·)$	$\chi_{ 613 } ( 198, ·)$	$\chi_{ 613 } ( 430, ·)$	$\chi_{ 613 } ( 546, ·)$	$\chi_{ 613 } ( 37, ·)$	$\chi_{ 613 } ( 387, ·)$	$\chi_{ 613 } ( 190, ·)$	$\chi_{ 613 } ( 197, ·)$	$\chi_{ 613 } ( 586, ·)$	$\chi_{ 613 } ( 1, ·)$	$\chi_{ 613 } ( 220, ·)$	$\chi_{ 613 } ( 227, ·)$	$\chi_{ 613 } ( 583, ·)$	$\chi_{ 613 } ( 585, ·)$
$\chi_{ 613 }(190, ·)$	$\chi_{ 613 } ( 190, ·)$	$\chi_{ 613 } ( 583, ·)$	$\chi_{ 613 } ( 37, ·)$	$\chi_{ 613 } ( 227, ·)$	$\chi_{ 613 } ( 430, ·)$	$\chi_{ 613 } ( 197, ·)$	$\chi_{ 613 } ( 387, ·)$	$\chi_{ 613 } ( 198, ·)$	$\chi_{ 613 } ( 116, ·)$	$\chi_{ 613 } ( 586, ·)$	$\chi_{ 613 } ( 143, ·)$	$\chi_{ 613 } ( 220, ·)$	$\chi_{ 613 } ( 287, ·)$	$\chi_{ 613 } ( 1, ·)$	$\chi_{ 613 } ( 171, ·)$	$\chi_{ 613 } ( 585, ·)$	$\chi_{ 613 } ( 546, ·)$

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 $\F_{q}$

$\times$	\(\chi_{ 613 } ( 1, ·)\)	\(\chi_{ 613 } ( 387, ·)\)	\(\chi_{ 613 } ( 197, ·)\)	\(\chi_{ 613 } ( 198, ·)\)	\(\chi_{ 613 } ( 583, ·)\)	\(\chi_{ 613 } ( 585, ·)\)	\(\chi_{ 613 } ( 586, ·)\)	\(\chi_{ 613 } ( 143, ·)\)	\(\chi_{ 613 } ( 220, ·)\)	\(\chi_{ 613 } ( 287, ·)\)	\(\chi_{ 613 } ( 546, ·)\)	\(\chi_{ 613 } ( 227, ·)\)	\(\chi_{ 613 } ( 37, ·)\)	\(\chi_{ 613 } ( 171, ·)\)	\(\chi_{ 613 } ( 430, ·)\)	\(\chi_{ 613 } ( 116, ·)\)	\(\chi_{ 613 } ( 190, ·)\)
\(\chi_{ 613 }(1, ·)\)	\(\chi_{ 613 } ( 1, ·)\)	\(\chi_{ 613 } ( 387, ·)\)	\(\chi_{ 613 } ( 197, ·)\)	\(\chi_{ 613 } ( 198, ·)\)	\(\chi_{ 613 } ( 583, ·)\)	\(\chi_{ 613 } ( 585, ·)\)	\(\chi_{ 613 } ( 586, ·)\)	\(\chi_{ 613 } ( 143, ·)\)	\(\chi_{ 613 } ( 220, ·)\)	\(\chi_{ 613 } ( 287, ·)\)	\(\chi_{ 613 } ( 546, ·)\)	\(\chi_{ 613 } ( 227, ·)\)	\(\chi_{ 613 } ( 37, ·)\)	\(\chi_{ 613 } ( 171, ·)\)	\(\chi_{ 613 } ( 430, ·)\)	\(\chi_{ 613 } ( 116, ·)\)	\(\chi_{ 613 } ( 190, ·)\)
\(\chi_{ 613 }(387, ·)\)	\(\chi_{ 613 } ( 387, ·)\)	\(\chi_{ 613 } ( 197, ·)\)	\(\chi_{ 613 } ( 227, ·)\)	\(\chi_{ 613 } ( 1, ·)\)	\(\chi_{ 613 } ( 37, ·)\)	\(\chi_{ 613 } ( 198, ·)\)	\(\chi_{ 613 } ( 585, ·)\)	\(\chi_{ 613 } ( 171, ·)\)	\(\chi_{ 613 } ( 546, ·)\)	\(\chi_{ 613 } ( 116, ·)\)	\(\chi_{ 613 } ( 430, ·)\)	\(\chi_{ 613 } ( 190, ·)\)	\(\chi_{ 613 } ( 220, ·)\)	\(\chi_{ 613 } ( 586, ·)\)	\(\chi_{ 613 } ( 287, ·)\)	\(\chi_{ 613 } ( 143, ·)\)	\(\chi_{ 613 } ( 583, ·)\)
\(\chi_{ 613 }(197, ·)\)	\(\chi_{ 613 } ( 197, ·)\)	\(\chi_{ 613 } ( 227, ·)\)	\(\chi_{ 613 } ( 190, ·)\)	\(\chi_{ 613 } ( 387, ·)\)	\(\chi_{ 613 } ( 220, ·)\)	\(\chi_{ 613 } ( 1, ·)\)	\(\chi_{ 613 } ( 198, ·)\)	\(\chi_{ 613 } ( 586, ·)\)	\(\chi_{ 613 } ( 430, ·)\)	\(\chi_{ 613 } ( 143, ·)\)	\(\chi_{ 613 } ( 287, ·)\)	\(\chi_{ 613 } ( 583, ·)\)	\(\chi_{ 613 } ( 546, ·)\)	\(\chi_{ 613 } ( 585, ·)\)	\(\chi_{ 613 } ( 116, ·)\)	\(\chi_{ 613 } ( 171, ·)\)	\(\chi_{ 613 } ( 37, ·)\)
\(\chi_{ 613 }(198, ·)\)	\(\chi_{ 613 } ( 198, ·)\)	\(\chi_{ 613 } ( 1, ·)\)	\(\chi_{ 613 } ( 387, ·)\)	\(\chi_{ 613 } ( 585, ·)\)	\(\chi_{ 613 } ( 190, ·)\)	\(\chi_{ 613 } ( 586, ·)\)	\(\chi_{ 613 } ( 171, ·)\)	\(\chi_{ 613 } ( 116, ·)\)	\(\chi_{ 613 } ( 37, ·)\)	\(\chi_{ 613 } ( 430, ·)\)	\(\chi_{ 613 } ( 220, ·)\)	\(\chi_{ 613 } ( 197, ·)\)	\(\chi_{ 613 } ( 583, ·)\)	\(\chi_{ 613 } ( 143, ·)\)	\(\chi_{ 613 } ( 546, ·)\)	\(\chi_{ 613 } ( 287, ·)\)	\(\chi_{ 613 } ( 227, ·)\)
\(\chi_{ 613 }(583, ·)\)	\(\chi_{ 613 } ( 583, ·)\)	\(\chi_{ 613 } ( 37, ·)\)	\(\chi_{ 613 } ( 220, ·)\)	\(\chi_{ 613 } ( 190, ·)\)	\(\chi_{ 613 } ( 287, ·)\)	\(\chi_{ 613 } ( 227, ·)\)	\(\chi_{ 613 } ( 197, ·)\)	\(\chi_{ 613 } ( 1, ·)\)	\(\chi_{ 613 } ( 143, ·)\)	\(\chi_{ 613 } ( 585, ·)\)	\(\chi_{ 613 } ( 171, ·)\)	\(\chi_{ 613 } ( 546, ·)\)	\(\chi_{ 613 } ( 116, ·)\)	\(\chi_{ 613 } ( 387, ·)\)	\(\chi_{ 613 } ( 586, ·)\)	\(\chi_{ 613 } ( 198, ·)\)	\(\chi_{ 613 } ( 430, ·)\)
\(\chi_{ 613 }(585, ·)\)	\(\chi_{ 613 } ( 585, ·)\)	\(\chi_{ 613 } ( 198, ·)\)	\(\chi_{ 613 } ( 1, ·)\)	\(\chi_{ 613 } ( 586, ·)\)	\(\chi_{ 613 } ( 227, ·)\)	\(\chi_{ 613 } ( 171, ·)\)	\(\chi_{ 613 } ( 143, ·)\)	\(\chi_{ 613 } ( 287, ·)\)	\(\chi_{ 613 } ( 583, ·)\)	\(\chi_{ 613 } ( 546, ·)\)	\(\chi_{ 613 } ( 37, ·)\)	\(\chi_{ 613 } ( 387, ·)\)	\(\chi_{ 613 } ( 190, ·)\)	\(\chi_{ 613 } ( 116, ·)\)	\(\chi_{ 613 } ( 220, ·)\)	\(\chi_{ 613 } ( 430, ·)\)	\(\chi_{ 613 } ( 197, ·)\)
\(\chi_{ 613 }(586, ·)\)	\(\chi_{ 613 } ( 586, ·)\)	\(\chi_{ 613 } ( 585, ·)\)	\(\chi_{ 613 } ( 198, ·)\)	\(\chi_{ 613 } ( 171, ·)\)	\(\chi_{ 613 } ( 197, ·)\)	\(\chi_{ 613 } ( 143, ·)\)	\(\chi_{ 613 } ( 116, ·)\)	\(\chi_{ 613 } ( 430, ·)\)	\(\chi_{ 613 } ( 190, ·)\)	\(\chi_{ 613 } ( 220, ·)\)	\(\chi_{ 613 } ( 583, ·)\)	\(\chi_{ 613 } ( 1, ·)\)	\(\chi_{ 613 } ( 227, ·)\)	\(\chi_{ 613 } ( 287, ·)\)	\(\chi_{ 613 } ( 37, ·)\)	\(\chi_{ 613 } ( 546, ·)\)	\(\chi_{ 613 } ( 387, ·)\)
\(\chi_{ 613 }(143, ·)\)	\(\chi_{ 613 } ( 143, ·)\)	\(\chi_{ 613 } ( 171, ·)\)	\(\chi_{ 613 } ( 586, ·)\)	\(\chi_{ 613 } ( 116, ·)\)	\(\chi_{ 613 } ( 1, ·)\)	\(\chi_{ 613 } ( 287, ·)\)	\(\chi_{ 613 } ( 430, ·)\)	\(\chi_{ 613 } ( 220, ·)\)	\(\chi_{ 613 } ( 197, ·)\)	\(\chi_{ 613 } ( 583, ·)\)	\(\chi_{ 613 } ( 227, ·)\)	\(\chi_{ 613 } ( 585, ·)\)	\(\chi_{ 613 } ( 387, ·)\)	\(\chi_{ 613 } ( 546, ·)\)	\(\chi_{ 613 } ( 190, ·)\)	\(\chi_{ 613 } ( 37, ·)\)	\(\chi_{ 613 } ( 198, ·)\)
\(\chi_{ 613 }(220, ·)\)	\(\chi_{ 613 } ( 220, ·)\)	\(\chi_{ 613 } ( 546, ·)\)	\(\chi_{ 613 } ( 430, ·)\)	\(\chi_{ 613 } ( 37, ·)\)	\(\chi_{ 613 } ( 143, ·)\)	\(\chi_{ 613 } ( 583, ·)\)	\(\chi_{ 613 } ( 190, ·)\)	\(\chi_{ 613 } ( 197, ·)\)	\(\chi_{ 613 } ( 586, ·)\)	\(\chi_{ 613 } ( 1, ·)\)	\(\chi_{ 613 } ( 585, ·)\)	\(\chi_{ 613 } ( 287, ·)\)	\(\chi_{ 613 } ( 171, ·)\)	\(\chi_{ 613 } ( 227, ·)\)	\(\chi_{ 613 } ( 198, ·)\)	\(\chi_{ 613 } ( 387, ·)\)	\(\chi_{ 613 } ( 116, ·)\)
\(\chi_{ 613 }(287, ·)\)	\(\chi_{ 613 } ( 287, ·)\)	\(\chi_{ 613 } ( 116, ·)\)	\(\chi_{ 613 } ( 143, ·)\)	\(\chi_{ 613 } ( 430, ·)\)	\(\chi_{ 613 } ( 585, ·)\)	\(\chi_{ 613 } ( 546, ·)\)	\(\chi_{ 613 } ( 220, ·)\)	\(\chi_{ 613 } ( 583, ·)\)	\(\chi_{ 613 } ( 1, ·)\)	\(\chi_{ 613 } ( 227, ·)\)	\(\chi_{ 613 } ( 387, ·)\)	\(\chi_{ 613 } ( 171, ·)\)	\(\chi_{ 613 } ( 198, ·)\)	\(\chi_{ 613 } ( 37, ·)\)	\(\chi_{ 613 } ( 197, ·)\)	\(\chi_{ 613 } ( 190, ·)\)	\(\chi_{ 613 } ( 586, ·)\)
\(\chi_{ 613 }(546, ·)\)	\(\chi_{ 613 } ( 546, ·)\)	\(\chi_{ 613 } ( 430, ·)\)	\(\chi_{ 613 } ( 287, ·)\)	\(\chi_{ 613 } ( 220, ·)\)	\(\chi_{ 613 } ( 171, ·)\)	\(\chi_{ 613 } ( 37, ·)\)	\(\chi_{ 613 } ( 583, ·)\)	\(\chi_{ 613 } ( 227, ·)\)	\(\chi_{ 613 } ( 585, ·)\)	\(\chi_{ 613 } ( 387, ·)\)	\(\chi_{ 613 } ( 198, ·)\)	\(\chi_{ 613 } ( 116, ·)\)	\(\chi_{ 613 } ( 586, ·)\)	\(\chi_{ 613 } ( 190, ·)\)	\(\chi_{ 613 } ( 1, ·)\)	\(\chi_{ 613 } ( 197, ·)\)	\(\chi_{ 613 } ( 143, ·)\)
\(\chi_{ 613 }(227, ·)\)	\(\chi_{ 613 } ( 227, ·)\)	\(\chi_{ 613 } ( 190, ·)\)	\(\chi_{ 613 } ( 583, ·)\)	\(\chi_{ 613 } ( 197, ·)\)	\(\chi_{ 613 } ( 546, ·)\)	\(\chi_{ 613 } ( 387, ·)\)	\(\chi_{ 613 } ( 1, ·)\)	\(\chi_{ 613 } ( 585, ·)\)	\(\chi_{ 613 } ( 287, ·)\)	\(\chi_{ 613 } ( 171, ·)\)	\(\chi_{ 613 } ( 116, ·)\)	\(\chi_{ 613 } ( 37, ·)\)	\(\chi_{ 613 } ( 430, ·)\)	\(\chi_{ 613 } ( 198, ·)\)	\(\chi_{ 613 } ( 143, ·)\)	\(\chi_{ 613 } ( 586, ·)\)	\(\chi_{ 613 } ( 220, ·)\)
\(\chi_{ 613 }(37, ·)\)	\(\chi_{ 613 } ( 37, ·)\)	\(\chi_{ 613 } ( 220, ·)\)	\(\chi_{ 613 } ( 546, ·)\)	\(\chi_{ 613 } ( 583, ·)\)	\(\chi_{ 613 } ( 116, ·)\)	\(\chi_{ 613 } ( 190, ·)\)	\(\chi_{ 613 } ( 227, ·)\)	\(\chi_{ 613 } ( 387, ·)\)	\(\chi_{ 613 } ( 171, ·)\)	\(\chi_{ 613 } ( 198, ·)\)	\(\chi_{ 613 } ( 586, ·)\)	\(\chi_{ 613 } ( 430, ·)\)	\(\chi_{ 613 } ( 143, ·)\)	\(\chi_{ 613 } ( 197, ·)\)	\(\chi_{ 613 } ( 585, ·)\)	\(\chi_{ 613 } ( 1, ·)\)	\(\chi_{ 613 } ( 287, ·)\)
\(\chi_{ 613 }(171, ·)\)	\(\chi_{ 613 } ( 171, ·)\)	\(\chi_{ 613 } ( 586, ·)\)	\(\chi_{ 613 } ( 585, ·)\)	\(\chi_{ 613 } ( 143, ·)\)	\(\chi_{ 613 } ( 387, ·)\)	\(\chi_{ 613 } ( 116, ·)\)	\(\chi_{ 613 } ( 287, ·)\)	\(\chi_{ 613 } ( 546, ·)\)	\(\chi_{ 613 } ( 227, ·)\)	\(\chi_{ 613 } ( 37, ·)\)	\(\chi_{ 613 } ( 190, ·)\)	\(\chi_{ 613 } ( 198, ·)\)	\(\chi_{ 613 } ( 197, ·)\)	\(\chi_{ 613 } ( 430, ·)\)	\(\chi_{ 613 } ( 583, ·)\)	\(\chi_{ 613 } ( 220, ·)\)	\(\chi_{ 613 } ( 1, ·)\)
\(\chi_{ 613 }(430, ·)\)	\(\chi_{ 613 } ( 430, ·)\)	\(\chi_{ 613 } ( 287, ·)\)	\(\chi_{ 613 } ( 116, ·)\)	\(\chi_{ 613 } ( 546, ·)\)	\(\chi_{ 613 } ( 586, ·)\)	\(\chi_{ 613 } ( 220, ·)\)	\(\chi_{ 613 } ( 37, ·)\)	\(\chi_{ 613 } ( 190, ·)\)	\(\chi_{ 613 } ( 198, ·)\)	\(\chi_{ 613 } ( 197, ·)\)	\(\chi_{ 613 } ( 1, ·)\)	\(\chi_{ 613 } ( 143, ·)\)	\(\chi_{ 613 } ( 585, ·)\)	\(\chi_{ 613 } ( 583, ·)\)	\(\chi_{ 613 } ( 387, ·)\)	\(\chi_{ 613 } ( 227, ·)\)	\(\chi_{ 613 } ( 171, ·)\)
\(\chi_{ 613 }(116, ·)\)	\(\chi_{ 613 } ( 116, ·)\)	\(\chi_{ 613 } ( 143, ·)\)	\(\chi_{ 613 } ( 171, ·)\)	\(\chi_{ 613 } ( 287, ·)\)	\(\chi_{ 613 } ( 198, ·)\)	\(\chi_{ 613 } ( 430, ·)\)	\(\chi_{ 613 } ( 546, ·)\)	\(\chi_{ 613 } ( 37, ·)\)	\(\chi_{ 613 } ( 387, ·)\)	\(\chi_{ 613 } ( 190, ·)\)	\(\chi_{ 613 } ( 197, ·)\)	\(\chi_{ 613 } ( 586, ·)\)	\(\chi_{ 613 } ( 1, ·)\)	\(\chi_{ 613 } ( 220, ·)\)	\(\chi_{ 613 } ( 227, ·)\)	\(\chi_{ 613 } ( 583, ·)\)	\(\chi_{ 613 } ( 585, ·)\)
\(\chi_{ 613 }(190, ·)\)	\(\chi_{ 613 } ( 190, ·)\)	\(\chi_{ 613 } ( 583, ·)\)	\(\chi_{ 613 } ( 37, ·)\)	\(\chi_{ 613 } ( 227, ·)\)	\(\chi_{ 613 } ( 430, ·)\)	\(\chi_{ 613 } ( 197, ·)\)	\(\chi_{ 613 } ( 387, ·)\)	\(\chi_{ 613 } ( 198, ·)\)	\(\chi_{ 613 } ( 116, ·)\)	\(\chi_{ 613 } ( 586, ·)\)	\(\chi_{ 613 } ( 143, ·)\)	\(\chi_{ 613 } ( 220, ·)\)	\(\chi_{ 613 } ( 287, ·)\)	\(\chi_{ 613 } ( 1, ·)\)	\(\chi_{ 613 } ( 171, ·)\)	\(\chi_{ 613 } ( 585, ·)\)	\(\chi_{ 613 } ( 546, ·)\)

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.