LMFDB - Group of Dirichlet characters of modulus 966

Show commands: PariGP / SageMath

sage: H = DirichletGroup(966)

pari: g = idealstar(,966,2)

Character group

sage: G.order() pari: g.no
Order	=	264
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{66}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{966}(323,\cdot)$, $\chi_{966}(829,\cdot)$, $\chi_{966}(925,\cdot)$

First 32 of 264 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	$-1$	$1$	$5$	$11$	$13$	$17$	$19$	$25$	$29$	$31$	$37$	$41$
$\chi_{966}(1,\cdot)$	966.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{966}(5,\cdot)$	966.bc	66	no	$-1$	$1$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{966}(11,\cdot)$	966.bf	66	no	$1$	$1$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{966}(13,\cdot)$	966.v	22	no	$-1$	$1$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{3}{22}\right)$
$\chi_{966}(17,\cdot)$	966.bc	66	no	$-1$	$1$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{966}(19,\cdot)$	966.be	66	no	$1$	$1$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{966}(25,\cdot)$	966.y	33	no	$1$	$1$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{966}(29,\cdot)$	966.w	22	no	$-1$	$1$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{7}{22}\right)$
$\chi_{966}(31,\cdot)$	966.bb	66	no	$-1$	$1$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{17}{22}\right)$
$\chi_{966}(37,\cdot)$	966.z	66	no	$-1$	$1$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{966}(41,\cdot)$	966.t	22	no	$1$	$1$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{966}(43,\cdot)$	966.x	22	no	$-1$	$1$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{966}(47,\cdot)$	966.l	6	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$
$\chi_{966}(53,\cdot)$	966.bf	66	no	$1$	$1$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{19}{22}\right)$
$\chi_{966}(55,\cdot)$	966.v	22	no	$-1$	$1$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{21}{22}\right)$
$\chi_{966}(59,\cdot)$	966.bd	66	no	$1$	$1$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{966}(61,\cdot)$	966.be	66	no	$1$	$1$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{17}{22}\right)$
$\chi_{966}(65,\cdot)$	966.bf	66	no	$1$	$1$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{966}(67,\cdot)$	966.z	66	no	$-1$	$1$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{966}(71,\cdot)$	966.w	22	no	$-1$	$1$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{966}(73,\cdot)$	966.bb	66	no	$-1$	$1$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{966}(79,\cdot)$	966.z	66	no	$-1$	$1$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{966}(83,\cdot)$	966.u	22	no	$-1$	$1$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{966}(85,\cdot)$	966.q	11	no	$1$	$1$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{966}(89,\cdot)$	966.bc	66	no	$-1$	$1$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{966}(95,\cdot)$	966.ba	66	no	$-1$	$1$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{5}{22}\right)$
$\chi_{966}(97,\cdot)$	966.s	22	no	$1$	$1$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{1}{22}\right)$
$\chi_{966}(101,\cdot)$	966.bd	66	no	$1$	$1$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{966}(103,\cdot)$	966.be	66	no	$1$	$1$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{966}(107,\cdot)$	966.bf	66	no	$1$	$1$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{17}{22}\right)$
$\chi_{966}(109,\cdot)$	966.z	66	no	$-1$	$1$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{966}(113,\cdot)$	966.r	22	no	$1$	$1$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{13}{22}\right)$

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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	$966$
Structure	\(C_{2}\times C_{2}\times C_{66}\)
Order	$264$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(11\)	\(13\)	\(17\)	\(19\)	\(25\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{966}(1,\cdot)\)	966.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{966}(5,\cdot)\)	966.bc	66	no	\(-1\)	\(1\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{966}(11,\cdot)\)	966.bf	66	no	\(1\)	\(1\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{9}{22}\right)\)
\(\chi_{966}(13,\cdot)\)	966.v	22	no	\(-1\)	\(1\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)
\(\chi_{966}(17,\cdot)\)	966.bc	66	no	\(-1\)	\(1\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{966}(19,\cdot)\)	966.be	66	no	\(1\)	\(1\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{966}(25,\cdot)\)	966.y	33	no	\(1\)	\(1\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{966}(29,\cdot)\)	966.w	22	no	\(-1\)	\(1\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)
\(\chi_{966}(31,\cdot)\)	966.bb	66	no	\(-1\)	\(1\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{17}{22}\right)\)
\(\chi_{966}(37,\cdot)\)	966.z	66	no	\(-1\)	\(1\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{966}(41,\cdot)\)	966.t	22	no	\(1\)	\(1\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{966}(43,\cdot)\)	966.x	22	no	\(-1\)	\(1\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{966}(47,\cdot)\)	966.l	6	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)
\(\chi_{966}(53,\cdot)\)	966.bf	66	no	\(1\)	\(1\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{19}{22}\right)\)
\(\chi_{966}(55,\cdot)\)	966.v	22	no	\(-1\)	\(1\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)
\(\chi_{966}(59,\cdot)\)	966.bd	66	no	\(1\)	\(1\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{966}(61,\cdot)\)	966.be	66	no	\(1\)	\(1\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{17}{22}\right)\)
\(\chi_{966}(65,\cdot)\)	966.bf	66	no	\(1\)	\(1\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{966}(67,\cdot)\)	966.z	66	no	\(-1\)	\(1\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{966}(71,\cdot)\)	966.w	22	no	\(-1\)	\(1\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)
\(\chi_{966}(73,\cdot)\)	966.bb	66	no	\(-1\)	\(1\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{966}(79,\cdot)\)	966.z	66	no	\(-1\)	\(1\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{966}(83,\cdot)\)	966.u	22	no	\(-1\)	\(1\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{966}(85,\cdot)\)	966.q	11	no	\(1\)	\(1\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{966}(89,\cdot)\)	966.bc	66	no	\(-1\)	\(1\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{966}(95,\cdot)\)	966.ba	66	no	\(-1\)	\(1\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{5}{22}\right)\)
\(\chi_{966}(97,\cdot)\)	966.s	22	no	\(1\)	\(1\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)
\(\chi_{966}(101,\cdot)\)	966.bd	66	no	\(1\)	\(1\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{966}(103,\cdot)\)	966.be	66	no	\(1\)	\(1\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{9}{22}\right)\)
\(\chi_{966}(107,\cdot)\)	966.bf	66	no	\(1\)	\(1\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{17}{22}\right)\)
\(\chi_{966}(109,\cdot)\)	966.z	66	no	\(-1\)	\(1\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{966}(113,\cdot)\)	966.r	22	no	\(1\)	\(1\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)

Introduction

L-functions

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First 32 of 264 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.