LMFDB - Group of Dirichlet characters of modulus 6084

Show commands: PariGP / SageMath

sage: H = DirichletGroup(6084)

pari: g = idealstar(,6084,2)

Character group

sage: G.order() pari: g.no
Order	=	1872
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{6}\times C_{156}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{6084}(3043,\cdot)$, $\chi_{6084}(677,\cdot)$, $\chi_{6084}(3889,\cdot)$

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	$-1$	$1$	$5$	$7$	$11$	$17$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{6084}(1,\cdot)$	6084.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{6084}(5,\cdot)$	6084.ea	156	no	$1$	$1$	$e\left(\frac{107}{156}\right)$	$e\left(\frac{79}{156}\right)$	$e\left(\frac{121}{156}\right)$	$e\left(\frac{12}{13}\right)$	$-i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{5}{26}\right)$
$\chi_{6084}(7,\cdot)$	6084.eh	156	yes	$1$	$1$	$e\left(\frac{79}{156}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{127}{156}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{1}{12}\right)$	$1$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{37}{156}\right)$	$e\left(\frac{5}{78}\right)$
$\chi_{6084}(11,\cdot)$	6084.el	156	yes	$-1$	$1$	$e\left(\frac{121}{156}\right)$	$e\left(\frac{127}{156}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{109}{156}\right)$	$e\left(\frac{23}{39}\right)$
$\chi_{6084}(17,\cdot)$	6084.cz	78	no	$-1$	$1$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{5}{78}\right)$
$\chi_{6084}(19,\cdot)$	6084.cb	12	no	$1$	$1$	$-i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$i$	$e\left(\frac{5}{6}\right)$
$\chi_{6084}(23,\cdot)$	6084.bc	6	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{6084}(25,\cdot)$	6084.de	78	no	$1$	$1$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{11}{13}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{5}{13}\right)$
$\chi_{6084}(29,\cdot)$	6084.dk	78	no	$-1$	$1$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{19}{78}\right)$
$\chi_{6084}(31,\cdot)$	6084.eo	156	yes	$1$	$1$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{37}{156}\right)$	$e\left(\frac{109}{156}\right)$	$e\left(\frac{17}{26}\right)$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{155}{156}\right)$	$e\left(\frac{3}{26}\right)$
$\chi_{6084}(35,\cdot)$	6084.dx	78	no	$1$	$1$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{10}{39}\right)$
$\chi_{6084}(37,\cdot)$	6084.eg	156	no	$-1$	$1$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{89}{156}\right)$	$e\left(\frac{109}{156}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{11}{39}\right)$
$\chi_{6084}(41,\cdot)$	6084.en	156	no	$1$	$1$	$e\left(\frac{11}{156}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{149}{156}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{55}{78}\right)$
$\chi_{6084}(43,\cdot)$	6084.dc	78	yes	$-1$	$1$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{17}{78}\right)$
$\chi_{6084}(47,\cdot)$	6084.eb	156	yes	$-1$	$1$	$e\left(\frac{73}{156}\right)$	$e\left(\frac{59}{156}\right)$	$e\left(\frac{41}{156}\right)$	$e\left(\frac{6}{13}\right)$	$-i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{49}{156}\right)$	$e\left(\frac{11}{13}\right)$
$\chi_{6084}(49,\cdot)$	6084.dl	78	no	$1$	$1$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{5}{39}\right)$
$\chi_{6084}(53,\cdot)$	6084.cn	26	no	$-1$	$1$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{21}{26}\right)$	$1$	$-1$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{19}{26}\right)$
$\chi_{6084}(55,\cdot)$	6084.cy	78	no	$-1$	$1$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{61}{78}\right)$
$\chi_{6084}(59,\cdot)$	6084.el	156	yes	$-1$	$1$	$e\left(\frac{29}{156}\right)$	$e\left(\frac{131}{156}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{1}{39}\right)$
$\chi_{6084}(61,\cdot)$	6084.cr	39	no	$1$	$1$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{4}{39}\right)$
$\chi_{6084}(67,\cdot)$	6084.eh	156	yes	$1$	$1$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{41}{156}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{11}{12}\right)$	$1$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{1}{78}\right)$
$\chi_{6084}(71,\cdot)$	6084.em	156	no	$-1$	$1$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{73}{156}\right)$	$e\left(\frac{71}{156}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{34}{39}\right)$
$\chi_{6084}(73,\cdot)$	6084.cw	52	no	$-1$	$1$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{19}{26}\right)$	$i$	$-1$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{6084}(77,\cdot)$	6084.dq	78	no	$-1$	$1$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{1}{26}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{17}{26}\right)$
$\chi_{6084}(79,\cdot)$	6084.dp	78	yes	$-1$	$1$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{6}{13}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{9}{26}\right)$
$\chi_{6084}(83,\cdot)$	6084.eb	156	yes	$-1$	$1$	$e\left(\frac{67}{156}\right)$	$e\left(\frac{5}{156}\right)$	$e\left(\frac{59}{156}\right)$	$e\left(\frac{8}{13}\right)$	$i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{139}{156}\right)$	$e\left(\frac{6}{13}\right)$
$\chi_{6084}(85,\cdot)$	6084.ef	156	no	$-1$	$1$	$e\left(\frac{95}{156}\right)$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{83}{156}\right)$	$e\left(\frac{10}{39}\right)$
$\chi_{6084}(89,\cdot)$	6084.bv	12	no	$1$	$1$	$-i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{1}{6}\right)$
$\chi_{6084}(95,\cdot)$	6084.dt	78	yes	$1$	$1$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{1}{39}\right)$
$\chi_{6084}(97,\cdot)$	6084.ec	156	no	$-1$	$1$	$e\left(\frac{49}{156}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{139}{156}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{1}{12}\right)$	$-1$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{97}{156}\right)$	$e\left(\frac{25}{39}\right)$
$\chi_{6084}(101,\cdot)$	6084.do	78	no	$-1$	$1$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{43}{78}\right)$
$\chi_{6084}(103,\cdot)$	6084.dj	78	yes	$-1$	$1$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{5}{13}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{1}{26}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$6084$
Structure	\(C_{2}\times C_{6}\times C_{156}\)
Order	$1872$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{6084}(1,\cdot)\)	6084.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{6084}(5,\cdot)\)	6084.ea	156	no	\(1\)	\(1\)	\(e\left(\frac{107}{156}\right)\)	\(e\left(\frac{79}{156}\right)\)	\(e\left(\frac{121}{156}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{5}{26}\right)\)
\(\chi_{6084}(7,\cdot)\)	6084.eh	156	yes	\(1\)	\(1\)	\(e\left(\frac{79}{156}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{127}{156}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(1\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{37}{156}\right)\)	\(e\left(\frac{5}{78}\right)\)
\(\chi_{6084}(11,\cdot)\)	6084.el	156	yes	\(-1\)	\(1\)	\(e\left(\frac{121}{156}\right)\)	\(e\left(\frac{127}{156}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{109}{156}\right)\)	\(e\left(\frac{23}{39}\right)\)
\(\chi_{6084}(17,\cdot)\)	6084.cz	78	no	\(-1\)	\(1\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{5}{78}\right)\)
\(\chi_{6084}(19,\cdot)\)	6084.cb	12	no	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{6084}(23,\cdot)\)	6084.bc	6	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{6084}(25,\cdot)\)	6084.de	78	no	\(1\)	\(1\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{5}{13}\right)\)
\(\chi_{6084}(29,\cdot)\)	6084.dk	78	no	\(-1\)	\(1\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{19}{78}\right)\)
\(\chi_{6084}(31,\cdot)\)	6084.eo	156	yes	\(1\)	\(1\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{37}{156}\right)\)	\(e\left(\frac{109}{156}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{155}{156}\right)\)	\(e\left(\frac{3}{26}\right)\)
\(\chi_{6084}(35,\cdot)\)	6084.dx	78	no	\(1\)	\(1\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{10}{39}\right)\)
\(\chi_{6084}(37,\cdot)\)	6084.eg	156	no	\(-1\)	\(1\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{89}{156}\right)\)	\(e\left(\frac{109}{156}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{11}{39}\right)\)
\(\chi_{6084}(41,\cdot)\)	6084.en	156	no	\(1\)	\(1\)	\(e\left(\frac{11}{156}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{149}{156}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{17}{156}\right)\)	\(e\left(\frac{55}{78}\right)\)
\(\chi_{6084}(43,\cdot)\)	6084.dc	78	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{17}{78}\right)\)
\(\chi_{6084}(47,\cdot)\)	6084.eb	156	yes	\(-1\)	\(1\)	\(e\left(\frac{73}{156}\right)\)	\(e\left(\frac{59}{156}\right)\)	\(e\left(\frac{41}{156}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{49}{156}\right)\)	\(e\left(\frac{11}{13}\right)\)
\(\chi_{6084}(49,\cdot)\)	6084.dl	78	no	\(1\)	\(1\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{5}{39}\right)\)
\(\chi_{6084}(53,\cdot)\)	6084.cn	26	no	\(-1\)	\(1\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{19}{26}\right)\)
\(\chi_{6084}(55,\cdot)\)	6084.cy	78	no	\(-1\)	\(1\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{61}{78}\right)\)
\(\chi_{6084}(59,\cdot)\)	6084.el	156	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{156}\right)\)	\(e\left(\frac{131}{156}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{1}{39}\right)\)
\(\chi_{6084}(61,\cdot)\)	6084.cr	39	no	\(1\)	\(1\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)
\(\chi_{6084}(67,\cdot)\)	6084.eh	156	yes	\(1\)	\(1\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{41}{156}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(1\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{23}{156}\right)\)	\(e\left(\frac{1}{78}\right)\)
\(\chi_{6084}(71,\cdot)\)	6084.em	156	no	\(-1\)	\(1\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{73}{156}\right)\)	\(e\left(\frac{71}{156}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{34}{39}\right)\)
\(\chi_{6084}(73,\cdot)\)	6084.cw	52	no	\(-1\)	\(1\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{6084}(77,\cdot)\)	6084.dq	78	no	\(-1\)	\(1\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{17}{26}\right)\)
\(\chi_{6084}(79,\cdot)\)	6084.dp	78	yes	\(-1\)	\(1\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{9}{26}\right)\)
\(\chi_{6084}(83,\cdot)\)	6084.eb	156	yes	\(-1\)	\(1\)	\(e\left(\frac{67}{156}\right)\)	\(e\left(\frac{5}{156}\right)\)	\(e\left(\frac{59}{156}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{139}{156}\right)\)	\(e\left(\frac{6}{13}\right)\)
\(\chi_{6084}(85,\cdot)\)	6084.ef	156	no	\(-1\)	\(1\)	\(e\left(\frac{95}{156}\right)\)	\(e\left(\frac{101}{156}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{83}{156}\right)\)	\(e\left(\frac{10}{39}\right)\)
\(\chi_{6084}(89,\cdot)\)	6084.bv	12	no	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{6084}(95,\cdot)\)	6084.dt	78	yes	\(1\)	\(1\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)
\(\chi_{6084}(97,\cdot)\)	6084.ec	156	no	\(-1\)	\(1\)	\(e\left(\frac{49}{156}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{139}{156}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-1\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{97}{156}\right)\)	\(e\left(\frac{25}{39}\right)\)
\(\chi_{6084}(101,\cdot)\)	6084.do	78	no	\(-1\)	\(1\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{43}{78}\right)\)
\(\chi_{6084}(103,\cdot)\)	6084.dj	78	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{1}{26}\right)\)

Introduction

L-functions

Modular forms

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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.