LMFDB - Group of Dirichlet characters of modulus 6042

Show commands: PariGP / SageMath

sage: H = DirichletGroup(6042)

pari: g = idealstar(,6042,2)

Character group

sage: G.order() pari: g.no
Order	=	1872
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{468}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{6042}(2015,\cdot)$, $\chi_{6042}(4771,\cdot)$, $\chi_{6042}(2281,\cdot)$

First 32 of 1872 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	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$23$	$25$	$29$	$31$	$35$
$\chi_{6042}(1,\cdot)$	6042.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{6042}(5,\cdot)$	6042.ct	468	no	$1$	$1$	$e\left(\frac{95}{468}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{16}{117}\right)$	$e\left(\frac{50}{117}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{95}{234}\right)$	$e\left(\frac{22}{117}\right)$	$e\left(\frac{25}{156}\right)$	$e\left(\frac{89}{468}\right)$
$\chi_{6042}(7,\cdot)$	6042.by	78	no	$1$	$1$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{59}{78}\right)$
$\chi_{6042}(11,\cdot)$	6042.cd	78	no	$-1$	$1$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{8}{39}\right)$
$\chi_{6042}(13,\cdot)$	6042.co	234	no	$-1$	$1$	$e\left(\frac{16}{117}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{109}{234}\right)$	$e\left(\frac{46}{117}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{32}{117}\right)$	$e\left(\frac{223}{234}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{31}{117}\right)$
$\chi_{6042}(17,\cdot)$	6042.cj	234	no	$-1$	$1$	$e\left(\frac{50}{117}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{46}{117}\right)$	$e\left(\frac{229}{234}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{100}{117}\right)$	$e\left(\frac{185}{234}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{53}{117}\right)$
$\chi_{6042}(23,\cdot)$	6042.bo	36	no	$1$	$1$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{25}{36}\right)$
$\chi_{6042}(25,\cdot)$	6042.cn	234	no	$1$	$1$	$e\left(\frac{95}{234}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{32}{117}\right)$	$e\left(\frac{100}{117}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{95}{117}\right)$	$e\left(\frac{44}{117}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{89}{234}\right)$
$\chi_{6042}(29,\cdot)$	6042.cm	234	no	$1$	$1$	$e\left(\frac{22}{117}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{223}{234}\right)$	$e\left(\frac{185}{234}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{44}{117}\right)$	$e\left(\frac{29}{117}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{28}{117}\right)$
$\chi_{6042}(31,\cdot)$	6042.ch	156	no	$1$	$1$	$e\left(\frac{25}{156}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{7}{156}\right)$
$\chi_{6042}(35,\cdot)$	6042.ct	468	no	$1$	$1$	$e\left(\frac{89}{468}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{31}{117}\right)$	$e\left(\frac{53}{117}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{89}{234}\right)$	$e\left(\frac{28}{117}\right)$	$e\left(\frac{7}{156}\right)$	$e\left(\frac{443}{468}\right)$
$\chi_{6042}(37,\cdot)$	6042.bl	26	no	$-1$	$1$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{10}{13}\right)$	$-1$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{5}{26}\right)$
$\chi_{6042}(41,\cdot)$	6042.cs	468	no	$-1$	$1$	$e\left(\frac{341}{468}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{89}{234}\right)$	$e\left(\frac{44}{117}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{107}{234}\right)$	$e\left(\frac{137}{234}\right)$	$e\left(\frac{61}{156}\right)$	$e\left(\frac{83}{468}\right)$
$\chi_{6042}(43,\cdot)$	6042.cn	234	no	$1$	$1$	$e\left(\frac{25}{234}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{70}{117}\right)$	$e\left(\frac{14}{117}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{25}{117}\right)$	$e\left(\frac{67}{117}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{85}{234}\right)$
$\chi_{6042}(47,\cdot)$	6042.cl	234	no	$-1$	$1$	$e\left(\frac{89}{234}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{62}{117}\right)$	$e\left(\frac{95}{234}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{89}{117}\right)$	$e\left(\frac{229}{234}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{209}{234}\right)$
$\chi_{6042}(49,\cdot)$	6042.bs	39	no	$1$	$1$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{20}{39}\right)$
$\chi_{6042}(55,\cdot)$	6042.cr	468	no	$-1$	$1$	$e\left(\frac{371}{468}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{28}{117}\right)$	$e\left(\frac{175}{234}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{137}{234}\right)$	$e\left(\frac{77}{234}\right)$	$e\left(\frac{151}{156}\right)$	$e\left(\frac{185}{468}\right)$
$\chi_{6042}(59,\cdot)$	6042.cm	234	no	$1$	$1$	$e\left(\frac{77}{117}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{137}{234}\right)$	$e\left(\frac{121}{234}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{37}{117}\right)$	$e\left(\frac{43}{117}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{98}{117}\right)$
$\chi_{6042}(61,\cdot)$	6042.cr	468	no	$-1$	$1$	$e\left(\frac{229}{468}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{110}{117}\right)$	$e\left(\frac{161}{234}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{229}{234}\right)$	$e\left(\frac{127}{234}\right)$	$e\left(\frac{89}{156}\right)$	$e\left(\frac{451}{468}\right)$
$\chi_{6042}(65,\cdot)$	6042.cf	156	no	$-1$	$1$	$e\left(\frac{53}{156}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{71}{156}\right)$
$\chi_{6042}(67,\cdot)$	6042.cq	468	no	$1$	$1$	$e\left(\frac{313}{468}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{151}{234}\right)$	$e\left(\frac{77}{234}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{79}{234}\right)$	$e\left(\frac{38}{117}\right)$	$e\left(\frac{107}{156}\right)$	$e\left(\frac{175}{468}\right)$
$\chi_{6042}(71,\cdot)$	6042.cs	468	no	$-1$	$1$	$e\left(\frac{167}{468}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{23}{234}\right)$	$e\left(\frac{14}{117}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{167}{234}\right)$	$e\left(\frac{17}{234}\right)$	$e\left(\frac{7}{156}\right)$	$e\left(\frac{53}{468}\right)$
$\chi_{6042}(73,\cdot)$	6042.cr	468	no	$-1$	$1$	$e\left(\frac{395}{468}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{85}{117}\right)$	$e\left(\frac{151}{234}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{161}{234}\right)$	$e\left(\frac{29}{234}\right)$	$e\left(\frac{67}{156}\right)$	$e\left(\frac{173}{468}\right)$
$\chi_{6042}(77,\cdot)$	6042.bm	26	no	$-1$	$1$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{9}{26}\right)$	$-1$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{25}{26}\right)$
$\chi_{6042}(79,\cdot)$	6042.cq	468	no	$1$	$1$	$e\left(\frac{71}{468}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{35}{234}\right)$	$e\left(\frac{7}{234}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{71}{234}\right)$	$e\left(\frac{46}{117}\right)$	$e\left(\frac{109}{156}\right)$	$e\left(\frac{101}{468}\right)$
$\chi_{6042}(83,\cdot)$	6042.x	12	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$i$	$e\left(\frac{1}{12}\right)$
$\chi_{6042}(85,\cdot)$	6042.cr	468	no	$-1$	$1$	$e\left(\frac{295}{468}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{62}{117}\right)$	$e\left(\frac{95}{234}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{61}{234}\right)$	$e\left(\frac{229}{234}\right)$	$e\left(\frac{131}{156}\right)$	$e\left(\frac{301}{468}\right)$
$\chi_{6042}(89,\cdot)$	6042.ck	234	no	$1$	$1$	$e\left(\frac{113}{234}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{1}{234}\right)$	$e\left(\frac{47}{234}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{113}{117}\right)$	$e\left(\frac{8}{117}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{197}{234}\right)$
$\chi_{6042}(91,\cdot)$	6042.cp	234	no	$-1$	$1$	$e\left(\frac{29}{234}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{139}{234}\right)$	$e\left(\frac{49}{117}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{29}{117}\right)$	$e\left(\frac{1}{234}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{5}{234}\right)$
$\chi_{6042}(97,\cdot)$	6042.co	234	no	$-1$	$1$	$e\left(\frac{14}{117}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{227}{234}\right)$	$e\left(\frac{11}{117}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{28}{117}\right)$	$e\left(\frac{5}{234}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{71}{117}\right)$
$\chi_{6042}(101,\cdot)$	6042.ct	468	no	$1$	$1$	$e\left(\frac{433}{468}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{68}{117}\right)$	$e\left(\frac{37}{117}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{199}{234}\right)$	$e\left(\frac{35}{117}\right)$	$e\left(\frac{155}{156}\right)$	$e\left(\frac{115}{468}\right)$
$\chi_{6042}(103,\cdot)$	6042.ch	156	no	$1$	$1$	$e\left(\frac{83}{156}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{17}{156}\right)$

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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	$6042$
Structure	\(C_{2}\times C_{2}\times C_{468}\)
Order	$1872$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{6042}(1,\cdot)\)	6042.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{6042}(5,\cdot)\)	6042.ct	468	no	\(1\)	\(1\)	\(e\left(\frac{95}{468}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{16}{117}\right)\)	\(e\left(\frac{50}{117}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{95}{234}\right)\)	\(e\left(\frac{22}{117}\right)\)	\(e\left(\frac{25}{156}\right)\)	\(e\left(\frac{89}{468}\right)\)
\(\chi_{6042}(7,\cdot)\)	6042.by	78	no	\(1\)	\(1\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{59}{78}\right)\)
\(\chi_{6042}(11,\cdot)\)	6042.cd	78	no	\(-1\)	\(1\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{8}{39}\right)\)
\(\chi_{6042}(13,\cdot)\)	6042.co	234	no	\(-1\)	\(1\)	\(e\left(\frac{16}{117}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{109}{234}\right)\)	\(e\left(\frac{46}{117}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{32}{117}\right)\)	\(e\left(\frac{223}{234}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{31}{117}\right)\)
\(\chi_{6042}(17,\cdot)\)	6042.cj	234	no	\(-1\)	\(1\)	\(e\left(\frac{50}{117}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{46}{117}\right)\)	\(e\left(\frac{229}{234}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{100}{117}\right)\)	\(e\left(\frac{185}{234}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{53}{117}\right)\)
\(\chi_{6042}(23,\cdot)\)	6042.bo	36	no	\(1\)	\(1\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{25}{36}\right)\)
\(\chi_{6042}(25,\cdot)\)	6042.cn	234	no	\(1\)	\(1\)	\(e\left(\frac{95}{234}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{32}{117}\right)\)	\(e\left(\frac{100}{117}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{95}{117}\right)\)	\(e\left(\frac{44}{117}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{89}{234}\right)\)
\(\chi_{6042}(29,\cdot)\)	6042.cm	234	no	\(1\)	\(1\)	\(e\left(\frac{22}{117}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{223}{234}\right)\)	\(e\left(\frac{185}{234}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{44}{117}\right)\)	\(e\left(\frac{29}{117}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{28}{117}\right)\)
\(\chi_{6042}(31,\cdot)\)	6042.ch	156	no	\(1\)	\(1\)	\(e\left(\frac{25}{156}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{7}{156}\right)\)
\(\chi_{6042}(35,\cdot)\)	6042.ct	468	no	\(1\)	\(1\)	\(e\left(\frac{89}{468}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{31}{117}\right)\)	\(e\left(\frac{53}{117}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{89}{234}\right)\)	\(e\left(\frac{28}{117}\right)\)	\(e\left(\frac{7}{156}\right)\)	\(e\left(\frac{443}{468}\right)\)
\(\chi_{6042}(37,\cdot)\)	6042.bl	26	no	\(-1\)	\(1\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(-1\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{5}{26}\right)\)
\(\chi_{6042}(41,\cdot)\)	6042.cs	468	no	\(-1\)	\(1\)	\(e\left(\frac{341}{468}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{89}{234}\right)\)	\(e\left(\frac{44}{117}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{107}{234}\right)\)	\(e\left(\frac{137}{234}\right)\)	\(e\left(\frac{61}{156}\right)\)	\(e\left(\frac{83}{468}\right)\)
\(\chi_{6042}(43,\cdot)\)	6042.cn	234	no	\(1\)	\(1\)	\(e\left(\frac{25}{234}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{70}{117}\right)\)	\(e\left(\frac{14}{117}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{25}{117}\right)\)	\(e\left(\frac{67}{117}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{85}{234}\right)\)
\(\chi_{6042}(47,\cdot)\)	6042.cl	234	no	\(-1\)	\(1\)	\(e\left(\frac{89}{234}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{62}{117}\right)\)	\(e\left(\frac{95}{234}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{89}{117}\right)\)	\(e\left(\frac{229}{234}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{209}{234}\right)\)
\(\chi_{6042}(49,\cdot)\)	6042.bs	39	no	\(1\)	\(1\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{20}{39}\right)\)
\(\chi_{6042}(55,\cdot)\)	6042.cr	468	no	\(-1\)	\(1\)	\(e\left(\frac{371}{468}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{28}{117}\right)\)	\(e\left(\frac{175}{234}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{137}{234}\right)\)	\(e\left(\frac{77}{234}\right)\)	\(e\left(\frac{151}{156}\right)\)	\(e\left(\frac{185}{468}\right)\)
\(\chi_{6042}(59,\cdot)\)	6042.cm	234	no	\(1\)	\(1\)	\(e\left(\frac{77}{117}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{137}{234}\right)\)	\(e\left(\frac{121}{234}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{37}{117}\right)\)	\(e\left(\frac{43}{117}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{98}{117}\right)\)
\(\chi_{6042}(61,\cdot)\)	6042.cr	468	no	\(-1\)	\(1\)	\(e\left(\frac{229}{468}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{110}{117}\right)\)	\(e\left(\frac{161}{234}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{229}{234}\right)\)	\(e\left(\frac{127}{234}\right)\)	\(e\left(\frac{89}{156}\right)\)	\(e\left(\frac{451}{468}\right)\)
\(\chi_{6042}(65,\cdot)\)	6042.cf	156	no	\(-1\)	\(1\)	\(e\left(\frac{53}{156}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{71}{156}\right)\)
\(\chi_{6042}(67,\cdot)\)	6042.cq	468	no	\(1\)	\(1\)	\(e\left(\frac{313}{468}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{151}{234}\right)\)	\(e\left(\frac{77}{234}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{79}{234}\right)\)	\(e\left(\frac{38}{117}\right)\)	\(e\left(\frac{107}{156}\right)\)	\(e\left(\frac{175}{468}\right)\)
\(\chi_{6042}(71,\cdot)\)	6042.cs	468	no	\(-1\)	\(1\)	\(e\left(\frac{167}{468}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{23}{234}\right)\)	\(e\left(\frac{14}{117}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{167}{234}\right)\)	\(e\left(\frac{17}{234}\right)\)	\(e\left(\frac{7}{156}\right)\)	\(e\left(\frac{53}{468}\right)\)
\(\chi_{6042}(73,\cdot)\)	6042.cr	468	no	\(-1\)	\(1\)	\(e\left(\frac{395}{468}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{85}{117}\right)\)	\(e\left(\frac{151}{234}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{161}{234}\right)\)	\(e\left(\frac{29}{234}\right)\)	\(e\left(\frac{67}{156}\right)\)	\(e\left(\frac{173}{468}\right)\)
\(\chi_{6042}(77,\cdot)\)	6042.bm	26	no	\(-1\)	\(1\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(-1\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{25}{26}\right)\)
\(\chi_{6042}(79,\cdot)\)	6042.cq	468	no	\(1\)	\(1\)	\(e\left(\frac{71}{468}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{35}{234}\right)\)	\(e\left(\frac{7}{234}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{71}{234}\right)\)	\(e\left(\frac{46}{117}\right)\)	\(e\left(\frac{109}{156}\right)\)	\(e\left(\frac{101}{468}\right)\)
\(\chi_{6042}(83,\cdot)\)	6042.x	12	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{6042}(85,\cdot)\)	6042.cr	468	no	\(-1\)	\(1\)	\(e\left(\frac{295}{468}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{62}{117}\right)\)	\(e\left(\frac{95}{234}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{61}{234}\right)\)	\(e\left(\frac{229}{234}\right)\)	\(e\left(\frac{131}{156}\right)\)	\(e\left(\frac{301}{468}\right)\)
\(\chi_{6042}(89,\cdot)\)	6042.ck	234	no	\(1\)	\(1\)	\(e\left(\frac{113}{234}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{1}{234}\right)\)	\(e\left(\frac{47}{234}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{113}{117}\right)\)	\(e\left(\frac{8}{117}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{197}{234}\right)\)
\(\chi_{6042}(91,\cdot)\)	6042.cp	234	no	\(-1\)	\(1\)	\(e\left(\frac{29}{234}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{139}{234}\right)\)	\(e\left(\frac{49}{117}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{29}{117}\right)\)	\(e\left(\frac{1}{234}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{5}{234}\right)\)
\(\chi_{6042}(97,\cdot)\)	6042.co	234	no	\(-1\)	\(1\)	\(e\left(\frac{14}{117}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{227}{234}\right)\)	\(e\left(\frac{11}{117}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{28}{117}\right)\)	\(e\left(\frac{5}{234}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{71}{117}\right)\)
\(\chi_{6042}(101,\cdot)\)	6042.ct	468	no	\(1\)	\(1\)	\(e\left(\frac{433}{468}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{68}{117}\right)\)	\(e\left(\frac{37}{117}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{199}{234}\right)\)	\(e\left(\frac{35}{117}\right)\)	\(e\left(\frac{155}{156}\right)\)	\(e\left(\frac{115}{468}\right)\)
\(\chi_{6042}(103,\cdot)\)	6042.ch	156	no	\(1\)	\(1\)	\(e\left(\frac{83}{156}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{17}{156}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Character group

First 32 of 1872 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.