LMFDB - Group of Dirichlet characters of modulus 676

Show commands: PariGP / SageMath

sage: H = DirichletGroup(676)

pari: g = idealstar(,676,2)

Character group

sage: G.order() pari: g.no
Order	=	312
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{156}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{676}(339,\cdot)$, $\chi_{676}(509,\cdot)$

First 32 of 312 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$15$	$17$	$19$	$21$	$23$
$\chi_{676}(1,\cdot)$	676.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{676}(3,\cdot)$	676.t	78	yes	$-1$	$1$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{676}(5,\cdot)$	676.r	52	no	$-1$	$1$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{11}{26}\right)$	$-i$	$e\left(\frac{17}{52}\right)$	$-1$
$\chi_{676}(7,\cdot)$	676.w	156	yes	$1$	$1$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{139}{156}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{113}{156}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{676}(9,\cdot)$	676.q	39	no	$1$	$1$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{676}(11,\cdot)$	676.w	156	yes	$1$	$1$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{79}{156}\right)$	$e\left(\frac{49}{156}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{676}(15,\cdot)$	676.w	156	yes	$1$	$1$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{113}{156}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{49}{156}\right)$	$e\left(\frac{139}{156}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{676}(17,\cdot)$	676.v	78	no	$1$	$1$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{676}(19,\cdot)$	676.l	12	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$-i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$i$	$e\left(\frac{2}{3}\right)$
$\chi_{676}(21,\cdot)$	676.r	52	no	$-1$	$1$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{5}{26}\right)$	$i$	$e\left(\frac{3}{52}\right)$	$-1$
$\chi_{676}(23,\cdot)$	676.i	6	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$
$\chi_{676}(25,\cdot)$	676.n	26	no	$1$	$1$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{11}{13}\right)$	$-1$	$e\left(\frac{17}{26}\right)$	$1$
$\chi_{676}(27,\cdot)$	676.o	26	yes	$-1$	$1$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{2}{13}\right)$	$-1$	$e\left(\frac{11}{13}\right)$	$-1$
$\chi_{676}(29,\cdot)$	676.q	39	no	$1$	$1$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{676}(31,\cdot)$	676.s	52	yes	$1$	$1$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{17}{26}\right)$	$i$	$e\left(\frac{5}{52}\right)$	$1$
$\chi_{676}(33,\cdot)$	676.x	156	no	$-1$	$1$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{109}{156}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{83}{156}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{676}(35,\cdot)$	676.t	78	yes	$-1$	$1$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{676}(37,\cdot)$	676.x	156	no	$-1$	$1$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{89}{156}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{109}{156}\right)$	$e\left(\frac{115}{156}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{676}(41,\cdot)$	676.x	156	no	$-1$	$1$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{47}{156}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{19}{156}\right)$	$e\left(\frac{73}{156}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{676}(43,\cdot)$	676.u	78	yes	$-1$	$1$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{676}(45,\cdot)$	676.x	156	no	$-1$	$1$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{43}{156}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{107}{156}\right)$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{676}(47,\cdot)$	676.s	52	yes	$1$	$1$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{25}{26}\right)$	$-i$	$e\left(\frac{15}{52}\right)$	$1$
$\chi_{676}(49,\cdot)$	676.v	78	no	$1$	$1$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{676}(51,\cdot)$	676.p	26	yes	$-1$	$1$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{9}{13}\right)$	$1$	$e\left(\frac{21}{26}\right)$	$-1$
$\chi_{676}(53,\cdot)$	676.m	13	no	$1$	$1$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{4}{13}\right)$	$1$	$e\left(\frac{9}{13}\right)$	$1$
$\chi_{676}(55,\cdot)$	676.t	78	yes	$-1$	$1$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{676}(57,\cdot)$	676.r	52	no	$-1$	$1$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{23}{26}\right)$	$-i$	$e\left(\frac{45}{52}\right)$	$-1$
$\chi_{676}(59,\cdot)$	676.w	156	yes	$1$	$1$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{79}{156}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{95}{156}\right)$	$e\left(\frac{53}{156}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{676}(61,\cdot)$	676.q	39	no	$1$	$1$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{676}(63,\cdot)$	676.w	156	yes	$1$	$1$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{155}{156}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{139}{156}\right)$	$e\left(\frac{25}{156}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{676}(67,\cdot)$	676.w	156	yes	$1$	$1$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{145}{156}\right)$	$e\left(\frac{7}{156}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{676}(69,\cdot)$	676.v	78	no	$1$	$1$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{2}{3}\right)$

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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	$676$
Structure	\(C_{2}\times C_{156}\)
Order	$312$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\(\chi_{676}(1,\cdot)\)	676.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{676}(3,\cdot)\)	676.t	78	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{676}(5,\cdot)\)	676.r	52	no	\(-1\)	\(1\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(-i\)	\(e\left(\frac{17}{52}\right)\)	\(-1\)
\(\chi_{676}(7,\cdot)\)	676.w	156	yes	\(1\)	\(1\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{139}{156}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{23}{156}\right)\)	\(e\left(\frac{113}{156}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{676}(9,\cdot)\)	676.q	39	no	\(1\)	\(1\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{676}(11,\cdot)\)	676.w	156	yes	\(1\)	\(1\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{23}{156}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{79}{156}\right)\)	\(e\left(\frac{49}{156}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{676}(15,\cdot)\)	676.w	156	yes	\(1\)	\(1\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{113}{156}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{49}{156}\right)\)	\(e\left(\frac{139}{156}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{676}(17,\cdot)\)	676.v	78	no	\(1\)	\(1\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{676}(19,\cdot)\)	676.l	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(i\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{676}(21,\cdot)\)	676.r	52	no	\(-1\)	\(1\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(i\)	\(e\left(\frac{3}{52}\right)\)	\(-1\)
\(\chi_{676}(23,\cdot)\)	676.i	6	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{676}(25,\cdot)\)	676.n	26	no	\(1\)	\(1\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(-1\)	\(e\left(\frac{17}{26}\right)\)	\(1\)
\(\chi_{676}(27,\cdot)\)	676.o	26	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(-1\)	\(e\left(\frac{11}{13}\right)\)	\(-1\)
\(\chi_{676}(29,\cdot)\)	676.q	39	no	\(1\)	\(1\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{676}(31,\cdot)\)	676.s	52	yes	\(1\)	\(1\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(i\)	\(e\left(\frac{5}{52}\right)\)	\(1\)
\(\chi_{676}(33,\cdot)\)	676.x	156	no	\(-1\)	\(1\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{109}{156}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{83}{156}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{676}(35,\cdot)\)	676.t	78	yes	\(-1\)	\(1\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{676}(37,\cdot)\)	676.x	156	no	\(-1\)	\(1\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{89}{156}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{109}{156}\right)\)	\(e\left(\frac{115}{156}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{676}(41,\cdot)\)	676.x	156	no	\(-1\)	\(1\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{47}{156}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{19}{156}\right)\)	\(e\left(\frac{73}{156}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{676}(43,\cdot)\)	676.u	78	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{676}(45,\cdot)\)	676.x	156	no	\(-1\)	\(1\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{43}{156}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{107}{156}\right)\)	\(e\left(\frac{17}{156}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{676}(47,\cdot)\)	676.s	52	yes	\(1\)	\(1\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(-i\)	\(e\left(\frac{15}{52}\right)\)	\(1\)
\(\chi_{676}(49,\cdot)\)	676.v	78	no	\(1\)	\(1\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{676}(51,\cdot)\)	676.p	26	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(1\)	\(e\left(\frac{21}{26}\right)\)	\(-1\)
\(\chi_{676}(53,\cdot)\)	676.m	13	no	\(1\)	\(1\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(1\)	\(e\left(\frac{9}{13}\right)\)	\(1\)
\(\chi_{676}(55,\cdot)\)	676.t	78	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{676}(57,\cdot)\)	676.r	52	no	\(-1\)	\(1\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(-i\)	\(e\left(\frac{45}{52}\right)\)	\(-1\)
\(\chi_{676}(59,\cdot)\)	676.w	156	yes	\(1\)	\(1\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{79}{156}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{95}{156}\right)\)	\(e\left(\frac{53}{156}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{676}(61,\cdot)\)	676.q	39	no	\(1\)	\(1\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{676}(63,\cdot)\)	676.w	156	yes	\(1\)	\(1\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{155}{156}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{139}{156}\right)\)	\(e\left(\frac{25}{156}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{676}(67,\cdot)\)	676.w	156	yes	\(1\)	\(1\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{145}{156}\right)\)	\(e\left(\frac{7}{156}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{676}(69,\cdot)\)	676.v	78	no	\(1\)	\(1\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{2}{3}\right)\)

Introduction

L-functions

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First 32 of 312 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.