LMFDB - Group of Dirichlet characters of modulus 6762

Show commands: PariGP / SageMath

sage: H = DirichletGroup(6762)

pari: g = idealstar(,6762,2)

Character group

sage: G.order() pari: g.no
Order	=	1848
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{462}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{6762}(2255,\cdot)$, $\chi_{6762}(3727,\cdot)$, $\chi_{6762}(3823,\cdot)$

First 32 of 1848 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character	Orbit	Order	Primitive	$-1$	$1$	$5$	$11$	$13$	$17$	$19$	$25$	$29$	$31$	$37$	$41$
$\chi_{6762}(1,\cdot)$	6762.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{6762}(5,\cdot)$	6762.cj	462	no	$-1$	$1$	$e\left(\frac{263}{462}\right)$	$e\left(\frac{122}{231}\right)$	$e\left(\frac{65}{154}\right)$	$e\left(\frac{37}{462}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{32}{231}\right)$	$e\left(\frac{115}{154}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{23}{462}\right)$	$e\left(\frac{31}{77}\right)$
$\chi_{6762}(11,\cdot)$	6762.cf	462	no	$1$	$1$	$e\left(\frac{122}{231}\right)$	$e\left(\frac{64}{231}\right)$	$e\left(\frac{12}{77}\right)$	$e\left(\frac{40}{231}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{13}{231}\right)$	$e\left(\frac{1}{154}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{31}{462}\right)$	$e\left(\frac{107}{154}\right)$
$\chi_{6762}(13,\cdot)$	6762.ca	154	no	$-1$	$1$	$e\left(\frac{65}{154}\right)$	$e\left(\frac{12}{77}\right)$	$e\left(\frac{129}{154}\right)$	$e\left(\frac{15}{154}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{65}{77}\right)$	$e\left(\frac{46}{77}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{39}{77}\right)$	$e\left(\frac{65}{154}\right)$
$\chi_{6762}(17,\cdot)$	6762.cj	462	no	$-1$	$1$	$e\left(\frac{37}{462}\right)$	$e\left(\frac{40}{231}\right)$	$e\left(\frac{15}{154}\right)$	$e\left(\frac{281}{462}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{37}{231}\right)$	$e\left(\frac{145}{154}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{337}{462}\right)$	$e\left(\frac{19}{77}\right)$
$\chi_{6762}(19,\cdot)$	6762.bu	66	no	$1$	$1$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{6762}(25,\cdot)$	6762.ce	231	no	$1$	$1$	$e\left(\frac{32}{231}\right)$	$e\left(\frac{13}{231}\right)$	$e\left(\frac{65}{77}\right)$	$e\left(\frac{37}{231}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{64}{231}\right)$	$e\left(\frac{38}{77}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{23}{231}\right)$	$e\left(\frac{62}{77}\right)$
$\chi_{6762}(29,\cdot)$	6762.bx	154	no	$-1$	$1$	$e\left(\frac{115}{154}\right)$	$e\left(\frac{1}{154}\right)$	$e\left(\frac{46}{77}\right)$	$e\left(\frac{145}{154}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{38}{77}\right)$	$e\left(\frac{145}{154}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{69}{77}\right)$	$e\left(\frac{115}{154}\right)$
$\chi_{6762}(31,\cdot)$	6762.br	66	no	$-1$	$1$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{17}{22}\right)$
$\chi_{6762}(37,\cdot)$	6762.ck	462	no	$-1$	$1$	$e\left(\frac{23}{462}\right)$	$e\left(\frac{31}{462}\right)$	$e\left(\frac{39}{77}\right)$	$e\left(\frac{337}{462}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{23}{231}\right)$	$e\left(\frac{69}{77}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{197}{462}\right)$	$e\left(\frac{68}{77}\right)$
$\chi_{6762}(41,\cdot)$	6762.cc	154	no	$1$	$1$	$e\left(\frac{31}{77}\right)$	$e\left(\frac{107}{154}\right)$	$e\left(\frac{65}{154}\right)$	$e\left(\frac{19}{77}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{62}{77}\right)$	$e\left(\frac{115}{154}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{68}{77}\right)$	$e\left(\frac{31}{77}\right)$
$\chi_{6762}(43,\cdot)$	6762.by	154	no	$-1$	$1$	$e\left(\frac{57}{154}\right)$	$e\left(\frac{117}{154}\right)$	$e\left(\frac{69}{77}\right)$	$e\left(\frac{25}{154}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{57}{77}\right)$	$e\left(\frac{51}{77}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{53}{154}\right)$	$e\left(\frac{67}{77}\right)$
$\chi_{6762}(47,\cdot)$	6762.bn	42	no	$1$	$1$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{6762}(53,\cdot)$	6762.cf	462	no	$1$	$1$	$e\left(\frac{62}{231}\right)$	$e\left(\frac{184}{231}\right)$	$e\left(\frac{73}{77}\right)$	$e\left(\frac{115}{231}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{124}{231}\right)$	$e\left(\frac{51}{154}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{349}{462}\right)$	$e\left(\frac{67}{154}\right)$
$\chi_{6762}(55,\cdot)$	6762.ca	154	no	$-1$	$1$	$e\left(\frac{15}{154}\right)$	$e\left(\frac{62}{77}\right)$	$e\left(\frac{89}{154}\right)$	$e\left(\frac{39}{154}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{15}{77}\right)$	$e\left(\frac{58}{77}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{9}{77}\right)$	$e\left(\frac{15}{154}\right)$
$\chi_{6762}(59,\cdot)$	6762.cg	462	no	$1$	$1$	$e\left(\frac{26}{231}\right)$	$e\left(\frac{281}{462}\right)$	$e\left(\frac{19}{154}\right)$	$e\left(\frac{160}{231}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{52}{231}\right)$	$e\left(\frac{81}{154}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{62}{231}\right)$	$e\left(\frac{60}{77}\right)$
$\chi_{6762}(61,\cdot)$	6762.ch	462	no	$1$	$1$	$e\left(\frac{85}{231}\right)$	$e\left(\frac{199}{462}\right)$	$e\left(\frac{71}{154}\right)$	$e\left(\frac{221}{231}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{170}{231}\right)$	$e\left(\frac{48}{77}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{281}{462}\right)$	$e\left(\frac{31}{154}\right)$
$\chi_{6762}(65,\cdot)$	6762.cf	462	no	$1$	$1$	$e\left(\frac{229}{231}\right)$	$e\left(\frac{158}{231}\right)$	$e\left(\frac{20}{77}\right)$	$e\left(\frac{41}{231}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{227}{231}\right)$	$e\left(\frac{53}{154}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{257}{462}\right)$	$e\left(\frac{127}{154}\right)$
$\chi_{6762}(67,\cdot)$	6762.bp	66	no	$-1$	$1$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{6762}(71,\cdot)$	6762.bx	154	no	$-1$	$1$	$e\left(\frac{25}{154}\right)$	$e\left(\frac{27}{154}\right)$	$e\left(\frac{10}{77}\right)$	$e\left(\frac{65}{154}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{25}{77}\right)$	$e\left(\frac{65}{154}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{15}{77}\right)$	$e\left(\frac{25}{154}\right)$
$\chi_{6762}(73,\cdot)$	6762.ci	462	no	$-1$	$1$	$e\left(\frac{337}{462}\right)$	$e\left(\frac{202}{231}\right)$	$e\left(\frac{95}{154}\right)$	$e\left(\frac{137}{462}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{106}{231}\right)$	$e\left(\frac{10}{77}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{2}{231}\right)$	$e\left(\frac{61}{154}\right)$
$\chi_{6762}(79,\cdot)$	6762.bp	66	no	$-1$	$1$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{6762}(83,\cdot)$	6762.bz	154	no	$-1$	$1$	$e\left(\frac{103}{154}\right)$	$e\left(\frac{51}{77}\right)$	$e\left(\frac{67}{154}\right)$	$e\left(\frac{83}{154}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{26}{77}\right)$	$e\left(\frac{83}{154}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{139}{154}\right)$	$e\left(\frac{13}{77}\right)$
$\chi_{6762}(85,\cdot)$	6762.bw	77	no	$1$	$1$	$e\left(\frac{50}{77}\right)$	$e\left(\frac{54}{77}\right)$	$e\left(\frac{40}{77}\right)$	$e\left(\frac{53}{77}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{23}{77}\right)$	$e\left(\frac{53}{77}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{60}{77}\right)$	$e\left(\frac{50}{77}\right)$
$\chi_{6762}(89,\cdot)$	6762.cj	462	no	$-1$	$1$	$e\left(\frac{281}{462}\right)$	$e\left(\frac{104}{231}\right)$	$e\left(\frac{39}{154}\right)$	$e\left(\frac{361}{462}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{50}{231}\right)$	$e\left(\frac{69}{154}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{137}{462}\right)$	$e\left(\frac{34}{77}\right)$
$\chi_{6762}(95,\cdot)$	6762.cl	462	no	$-1$	$1$	$e\left(\frac{193}{462}\right)$	$e\left(\frac{461}{462}\right)$	$e\left(\frac{36}{77}\right)$	$e\left(\frac{317}{462}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{193}{231}\right)$	$e\left(\frac{3}{154}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{8}{231}\right)$	$e\left(\frac{13}{154}\right)$
$\chi_{6762}(97,\cdot)$	6762.bb	22	no	$1$	$1$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{1}{22}\right)$
$\chi_{6762}(101,\cdot)$	6762.cg	462	no	$1$	$1$	$e\left(\frac{149}{231}\right)$	$e\left(\frac{251}{462}\right)$	$e\left(\frac{23}{154}\right)$	$e\left(\frac{64}{231}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{67}{231}\right)$	$e\left(\frac{17}{154}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{71}{231}\right)$	$e\left(\frac{24}{77}\right)$
$\chi_{6762}(103,\cdot)$	6762.ch	462	no	$1$	$1$	$e\left(\frac{100}{231}\right)$	$e\left(\frac{139}{462}\right)$	$e\left(\frac{79}{154}\right)$	$e\left(\frac{29}{231}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{200}{231}\right)$	$e\left(\frac{61}{77}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{317}{462}\right)$	$e\left(\frac{41}{154}\right)$
$\chi_{6762}(107,\cdot)$	6762.cf	462	no	$1$	$1$	$e\left(\frac{151}{231}\right)$	$e\left(\frac{83}{231}\right)$	$e\left(\frac{30}{77}\right)$	$e\left(\frac{23}{231}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{71}{231}\right)$	$e\left(\frac{41}{154}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{347}{462}\right)$	$e\left(\frac{75}{154}\right)$
$\chi_{6762}(109,\cdot)$	6762.ck	462	no	$-1$	$1$	$e\left(\frac{433}{462}\right)$	$e\left(\frac{443}{462}\right)$	$e\left(\frac{68}{77}\right)$	$e\left(\frac{17}{462}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{202}{231}\right)$	$e\left(\frac{67}{77}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{73}{462}\right)$	$e\left(\frac{8}{77}\right)$
$\chi_{6762}(113,\cdot)$	6762.cd	154	no	$1$	$1$	$e\left(\frac{62}{77}\right)$	$e\left(\frac{30}{77}\right)$	$e\left(\frac{65}{77}\right)$	$e\left(\frac{38}{77}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{47}{77}\right)$	$e\left(\frac{153}{154}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{41}{154}\right)$	$e\left(\frac{47}{154}\right)$

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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 $\F_{q}$

Modulus	$6762$
Structure	\(C_{2}\times C_{2}\times C_{462}\)
Order	$1848$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(11\)	\(13\)	\(17\)	\(19\)	\(25\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{6762}(1,\cdot)\)	6762.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{6762}(5,\cdot)\)	6762.cj	462	no	\(-1\)	\(1\)	\(e\left(\frac{263}{462}\right)\)	\(e\left(\frac{122}{231}\right)\)	\(e\left(\frac{65}{154}\right)\)	\(e\left(\frac{37}{462}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{32}{231}\right)\)	\(e\left(\frac{115}{154}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{23}{462}\right)\)	\(e\left(\frac{31}{77}\right)\)
\(\chi_{6762}(11,\cdot)\)	6762.cf	462	no	\(1\)	\(1\)	\(e\left(\frac{122}{231}\right)\)	\(e\left(\frac{64}{231}\right)\)	\(e\left(\frac{12}{77}\right)\)	\(e\left(\frac{40}{231}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{13}{231}\right)\)	\(e\left(\frac{1}{154}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{31}{462}\right)\)	\(e\left(\frac{107}{154}\right)\)
\(\chi_{6762}(13,\cdot)\)	6762.ca	154	no	\(-1\)	\(1\)	\(e\left(\frac{65}{154}\right)\)	\(e\left(\frac{12}{77}\right)\)	\(e\left(\frac{129}{154}\right)\)	\(e\left(\frac{15}{154}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{65}{77}\right)\)	\(e\left(\frac{46}{77}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{39}{77}\right)\)	\(e\left(\frac{65}{154}\right)\)
\(\chi_{6762}(17,\cdot)\)	6762.cj	462	no	\(-1\)	\(1\)	\(e\left(\frac{37}{462}\right)\)	\(e\left(\frac{40}{231}\right)\)	\(e\left(\frac{15}{154}\right)\)	\(e\left(\frac{281}{462}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{37}{231}\right)\)	\(e\left(\frac{145}{154}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{337}{462}\right)\)	\(e\left(\frac{19}{77}\right)\)
\(\chi_{6762}(19,\cdot)\)	6762.bu	66	no	\(1\)	\(1\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{6762}(25,\cdot)\)	6762.ce	231	no	\(1\)	\(1\)	\(e\left(\frac{32}{231}\right)\)	\(e\left(\frac{13}{231}\right)\)	\(e\left(\frac{65}{77}\right)\)	\(e\left(\frac{37}{231}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{64}{231}\right)\)	\(e\left(\frac{38}{77}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{23}{231}\right)\)	\(e\left(\frac{62}{77}\right)\)
\(\chi_{6762}(29,\cdot)\)	6762.bx	154	no	\(-1\)	\(1\)	\(e\left(\frac{115}{154}\right)\)	\(e\left(\frac{1}{154}\right)\)	\(e\left(\frac{46}{77}\right)\)	\(e\left(\frac{145}{154}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{38}{77}\right)\)	\(e\left(\frac{145}{154}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{69}{77}\right)\)	\(e\left(\frac{115}{154}\right)\)
\(\chi_{6762}(31,\cdot)\)	6762.br	66	no	\(-1\)	\(1\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{17}{22}\right)\)
\(\chi_{6762}(37,\cdot)\)	6762.ck	462	no	\(-1\)	\(1\)	\(e\left(\frac{23}{462}\right)\)	\(e\left(\frac{31}{462}\right)\)	\(e\left(\frac{39}{77}\right)\)	\(e\left(\frac{337}{462}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{23}{231}\right)\)	\(e\left(\frac{69}{77}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{197}{462}\right)\)	\(e\left(\frac{68}{77}\right)\)
\(\chi_{6762}(41,\cdot)\)	6762.cc	154	no	\(1\)	\(1\)	\(e\left(\frac{31}{77}\right)\)	\(e\left(\frac{107}{154}\right)\)	\(e\left(\frac{65}{154}\right)\)	\(e\left(\frac{19}{77}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{62}{77}\right)\)	\(e\left(\frac{115}{154}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{68}{77}\right)\)	\(e\left(\frac{31}{77}\right)\)
\(\chi_{6762}(43,\cdot)\)	6762.by	154	no	\(-1\)	\(1\)	\(e\left(\frac{57}{154}\right)\)	\(e\left(\frac{117}{154}\right)\)	\(e\left(\frac{69}{77}\right)\)	\(e\left(\frac{25}{154}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{57}{77}\right)\)	\(e\left(\frac{51}{77}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{53}{154}\right)\)	\(e\left(\frac{67}{77}\right)\)
\(\chi_{6762}(47,\cdot)\)	6762.bn	42	no	\(1\)	\(1\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{6762}(53,\cdot)\)	6762.cf	462	no	\(1\)	\(1\)	\(e\left(\frac{62}{231}\right)\)	\(e\left(\frac{184}{231}\right)\)	\(e\left(\frac{73}{77}\right)\)	\(e\left(\frac{115}{231}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{124}{231}\right)\)	\(e\left(\frac{51}{154}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{349}{462}\right)\)	\(e\left(\frac{67}{154}\right)\)
\(\chi_{6762}(55,\cdot)\)	6762.ca	154	no	\(-1\)	\(1\)	\(e\left(\frac{15}{154}\right)\)	\(e\left(\frac{62}{77}\right)\)	\(e\left(\frac{89}{154}\right)\)	\(e\left(\frac{39}{154}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{15}{77}\right)\)	\(e\left(\frac{58}{77}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{9}{77}\right)\)	\(e\left(\frac{15}{154}\right)\)
\(\chi_{6762}(59,\cdot)\)	6762.cg	462	no	\(1\)	\(1\)	\(e\left(\frac{26}{231}\right)\)	\(e\left(\frac{281}{462}\right)\)	\(e\left(\frac{19}{154}\right)\)	\(e\left(\frac{160}{231}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{52}{231}\right)\)	\(e\left(\frac{81}{154}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{62}{231}\right)\)	\(e\left(\frac{60}{77}\right)\)
\(\chi_{6762}(61,\cdot)\)	6762.ch	462	no	\(1\)	\(1\)	\(e\left(\frac{85}{231}\right)\)	\(e\left(\frac{199}{462}\right)\)	\(e\left(\frac{71}{154}\right)\)	\(e\left(\frac{221}{231}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{170}{231}\right)\)	\(e\left(\frac{48}{77}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{281}{462}\right)\)	\(e\left(\frac{31}{154}\right)\)
\(\chi_{6762}(65,\cdot)\)	6762.cf	462	no	\(1\)	\(1\)	\(e\left(\frac{229}{231}\right)\)	\(e\left(\frac{158}{231}\right)\)	\(e\left(\frac{20}{77}\right)\)	\(e\left(\frac{41}{231}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{227}{231}\right)\)	\(e\left(\frac{53}{154}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{257}{462}\right)\)	\(e\left(\frac{127}{154}\right)\)
\(\chi_{6762}(67,\cdot)\)	6762.bp	66	no	\(-1\)	\(1\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{6762}(71,\cdot)\)	6762.bx	154	no	\(-1\)	\(1\)	\(e\left(\frac{25}{154}\right)\)	\(e\left(\frac{27}{154}\right)\)	\(e\left(\frac{10}{77}\right)\)	\(e\left(\frac{65}{154}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{25}{77}\right)\)	\(e\left(\frac{65}{154}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{15}{77}\right)\)	\(e\left(\frac{25}{154}\right)\)
\(\chi_{6762}(73,\cdot)\)	6762.ci	462	no	\(-1\)	\(1\)	\(e\left(\frac{337}{462}\right)\)	\(e\left(\frac{202}{231}\right)\)	\(e\left(\frac{95}{154}\right)\)	\(e\left(\frac{137}{462}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{106}{231}\right)\)	\(e\left(\frac{10}{77}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{2}{231}\right)\)	\(e\left(\frac{61}{154}\right)\)
\(\chi_{6762}(79,\cdot)\)	6762.bp	66	no	\(-1\)	\(1\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{6762}(83,\cdot)\)	6762.bz	154	no	\(-1\)	\(1\)	\(e\left(\frac{103}{154}\right)\)	\(e\left(\frac{51}{77}\right)\)	\(e\left(\frac{67}{154}\right)\)	\(e\left(\frac{83}{154}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{26}{77}\right)\)	\(e\left(\frac{83}{154}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{139}{154}\right)\)	\(e\left(\frac{13}{77}\right)\)
\(\chi_{6762}(85,\cdot)\)	6762.bw	77	no	\(1\)	\(1\)	\(e\left(\frac{50}{77}\right)\)	\(e\left(\frac{54}{77}\right)\)	\(e\left(\frac{40}{77}\right)\)	\(e\left(\frac{53}{77}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{23}{77}\right)\)	\(e\left(\frac{53}{77}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{60}{77}\right)\)	\(e\left(\frac{50}{77}\right)\)
\(\chi_{6762}(89,\cdot)\)	6762.cj	462	no	\(-1\)	\(1\)	\(e\left(\frac{281}{462}\right)\)	\(e\left(\frac{104}{231}\right)\)	\(e\left(\frac{39}{154}\right)\)	\(e\left(\frac{361}{462}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{50}{231}\right)\)	\(e\left(\frac{69}{154}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{137}{462}\right)\)	\(e\left(\frac{34}{77}\right)\)
\(\chi_{6762}(95,\cdot)\)	6762.cl	462	no	\(-1\)	\(1\)	\(e\left(\frac{193}{462}\right)\)	\(e\left(\frac{461}{462}\right)\)	\(e\left(\frac{36}{77}\right)\)	\(e\left(\frac{317}{462}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{193}{231}\right)\)	\(e\left(\frac{3}{154}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{8}{231}\right)\)	\(e\left(\frac{13}{154}\right)\)
\(\chi_{6762}(97,\cdot)\)	6762.bb	22	no	\(1\)	\(1\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)
\(\chi_{6762}(101,\cdot)\)	6762.cg	462	no	\(1\)	\(1\)	\(e\left(\frac{149}{231}\right)\)	\(e\left(\frac{251}{462}\right)\)	\(e\left(\frac{23}{154}\right)\)	\(e\left(\frac{64}{231}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{67}{231}\right)\)	\(e\left(\frac{17}{154}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{71}{231}\right)\)	\(e\left(\frac{24}{77}\right)\)
\(\chi_{6762}(103,\cdot)\)	6762.ch	462	no	\(1\)	\(1\)	\(e\left(\frac{100}{231}\right)\)	\(e\left(\frac{139}{462}\right)\)	\(e\left(\frac{79}{154}\right)\)	\(e\left(\frac{29}{231}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{200}{231}\right)\)	\(e\left(\frac{61}{77}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{317}{462}\right)\)	\(e\left(\frac{41}{154}\right)\)
\(\chi_{6762}(107,\cdot)\)	6762.cf	462	no	\(1\)	\(1\)	\(e\left(\frac{151}{231}\right)\)	\(e\left(\frac{83}{231}\right)\)	\(e\left(\frac{30}{77}\right)\)	\(e\left(\frac{23}{231}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{71}{231}\right)\)	\(e\left(\frac{41}{154}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{347}{462}\right)\)	\(e\left(\frac{75}{154}\right)\)
\(\chi_{6762}(109,\cdot)\)	6762.ck	462	no	\(-1\)	\(1\)	\(e\left(\frac{433}{462}\right)\)	\(e\left(\frac{443}{462}\right)\)	\(e\left(\frac{68}{77}\right)\)	\(e\left(\frac{17}{462}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{202}{231}\right)\)	\(e\left(\frac{67}{77}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{73}{462}\right)\)	\(e\left(\frac{8}{77}\right)\)
\(\chi_{6762}(113,\cdot)\)	6762.cd	154	no	\(1\)	\(1\)	\(e\left(\frac{62}{77}\right)\)	\(e\left(\frac{30}{77}\right)\)	\(e\left(\frac{65}{77}\right)\)	\(e\left(\frac{38}{77}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{47}{77}\right)\)	\(e\left(\frac{153}{154}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{41}{154}\right)\)	\(e\left(\frac{47}{154}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Character group

First 32 of 1848 characters

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