LMFDB - Group of Dirichlet characters of modulus 9660

Show commands: PariGP / SageMath

sage: H = DirichletGroup(9660)

pari: g = idealstar(,9660,2)

Character group

sage: G.order() pari: g.no
Order	=	2112
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{2}\times C_{132}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{9660}(4831,\cdot)$, $\chi_{9660}(3221,\cdot)$, $\chi_{9660}(5797,\cdot)$, $\chi_{9660}(2761,\cdot)$, $\chi_{9660}(6721,\cdot)$

First 32 of 2112 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	$-1$	$1$	$11$	$13$	$17$	$19$	$29$	$31$	$37$	$41$	$43$	$47$
$\chi_{9660}(1,\cdot)$	9660.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{9660}(11,\cdot)$	9660.fw	66	no	$-1$	$1$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{9660}(13,\cdot)$	9660.fc	44	no	$1$	$1$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{19}{44}\right)$	$i$
$\chi_{9660}(17,\cdot)$	9660.hc	132	no	$1$	$1$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{19}{132}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{35}{132}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{9660}(19,\cdot)$	9660.gf	66	no	$-1$	$1$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{9660}(29,\cdot)$	9660.er	22	no	$-1$	$1$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{13}{22}\right)$	$1$
$\chi_{9660}(31,\cdot)$	9660.fz	66	no	$1$	$1$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{9660}(37,\cdot)$	9660.hb	132	no	$1$	$1$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{35}{132}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{127}{132}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{9660}(41,\cdot)$	9660.et	22	no	$1$	$1$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{8}{11}\right)$	$1$
$\chi_{9660}(43,\cdot)$	9660.fg	44	no	$-1$	$1$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{39}{44}\right)$	$i$
$\chi_{9660}(47,\cdot)$	9660.dj	12	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$1$	$i$	$e\left(\frac{5}{12}\right)$
$\chi_{9660}(53,\cdot)$	9660.hh	132	no	$-1$	$1$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{127}{132}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{29}{132}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{9660}(59,\cdot)$	9660.gi	66	yes	$-1$	$1$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{9660}(61,\cdot)$	9660.gd	66	no	$1$	$1$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{9660}(67,\cdot)$	9660.he	132	no	$-1$	$1$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{7}{132}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{131}{132}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{9660}(71,\cdot)$	9660.dz	22	no	$1$	$1$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{21}{22}\right)$	$1$
$\chi_{9660}(73,\cdot)$	9660.hi	132	no	$1$	$1$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{25}{132}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{119}{132}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{9660}(79,\cdot)$	9660.gs	66	no	$1$	$1$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{9660}(83,\cdot)$	9660.fh	44	yes	$-1$	$1$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{23}{44}\right)$	$i$
$\chi_{9660}(89,\cdot)$	9660.gl	66	no	$-1$	$1$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{9660}(97,\cdot)$	9660.fo	44	no	$-1$	$1$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{43}{44}\right)$	$-i$
$\chi_{9660}(101,\cdot)$	9660.gc	66	no	$1$	$1$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{9660}(103,\cdot)$	9660.hj	132	no	$1$	$1$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{59}{132}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{1}{132}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{9660}(107,\cdot)$	9660.gu	132	yes	$1$	$1$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{65}{132}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{19}{132}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{9660}(109,\cdot)$	9660.gb	66	no	$-1$	$1$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{9660}(113,\cdot)$	9660.ez	44	no	$-1$	$1$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{9}{44}\right)$	$i$
$\chi_{9660}(121,\cdot)$	9660.ey	33	no	$1$	$1$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{9660}(127,\cdot)$	9660.fk	44	no	$1$	$1$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{35}{44}\right)$	$-i$
$\chi_{9660}(131,\cdot)$	9660.gt	66	no	$-1$	$1$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{9660}(137,\cdot)$	9660.df	12	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$-i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$-1$	$i$	$e\left(\frac{1}{12}\right)$
$\chi_{9660}(139,\cdot)$	9660.q	2	no	$1$	$1$	$-1$	$1$	$1$	$1$	$1$	$1$	$-1$	$-1$	$1$	$-1$
$\chi_{9660}(143,\cdot)$	9660.gz	132	yes	$-1$	$1$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{97}{132}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{5}{132}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{7}{12}\right)$

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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	$9660$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{2}\times C_{132}\)
Order	$2112$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(11\)	\(13\)	\(17\)	\(19\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)	\(47\)
\(\chi_{9660}(1,\cdot)\)	9660.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{9660}(11,\cdot)\)	9660.fw	66	no	\(-1\)	\(1\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{9660}(13,\cdot)\)	9660.fc	44	no	\(1\)	\(1\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(i\)
\(\chi_{9660}(17,\cdot)\)	9660.hc	132	no	\(1\)	\(1\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{19}{132}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{35}{132}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{9660}(19,\cdot)\)	9660.gf	66	no	\(-1\)	\(1\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{9660}(29,\cdot)\)	9660.er	22	no	\(-1\)	\(1\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(1\)
\(\chi_{9660}(31,\cdot)\)	9660.fz	66	no	\(1\)	\(1\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{9660}(37,\cdot)\)	9660.hb	132	no	\(1\)	\(1\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{35}{132}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{127}{132}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{9660}(41,\cdot)\)	9660.et	22	no	\(1\)	\(1\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(1\)
\(\chi_{9660}(43,\cdot)\)	9660.fg	44	no	\(-1\)	\(1\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(i\)
\(\chi_{9660}(47,\cdot)\)	9660.dj	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(1\)	\(i\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{9660}(53,\cdot)\)	9660.hh	132	no	\(-1\)	\(1\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{127}{132}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{29}{132}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{9660}(59,\cdot)\)	9660.gi	66	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{9660}(61,\cdot)\)	9660.gd	66	no	\(1\)	\(1\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{9660}(67,\cdot)\)	9660.he	132	no	\(-1\)	\(1\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{7}{132}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{131}{132}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{9660}(71,\cdot)\)	9660.dz	22	no	\(1\)	\(1\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(1\)
\(\chi_{9660}(73,\cdot)\)	9660.hi	132	no	\(1\)	\(1\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{25}{132}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{119}{132}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{9660}(79,\cdot)\)	9660.gs	66	no	\(1\)	\(1\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{9660}(83,\cdot)\)	9660.fh	44	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(i\)
\(\chi_{9660}(89,\cdot)\)	9660.gl	66	no	\(-1\)	\(1\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{9660}(97,\cdot)\)	9660.fo	44	no	\(-1\)	\(1\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(-i\)
\(\chi_{9660}(101,\cdot)\)	9660.gc	66	no	\(1\)	\(1\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{9660}(103,\cdot)\)	9660.hj	132	no	\(1\)	\(1\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{59}{132}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{1}{132}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{9660}(107,\cdot)\)	9660.gu	132	yes	\(1\)	\(1\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{65}{132}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{19}{132}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{9660}(109,\cdot)\)	9660.gb	66	no	\(-1\)	\(1\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{9660}(113,\cdot)\)	9660.ez	44	no	\(-1\)	\(1\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(i\)
\(\chi_{9660}(121,\cdot)\)	9660.ey	33	no	\(1\)	\(1\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{9660}(127,\cdot)\)	9660.fk	44	no	\(1\)	\(1\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(-i\)
\(\chi_{9660}(131,\cdot)\)	9660.gt	66	no	\(-1\)	\(1\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{9660}(137,\cdot)\)	9660.df	12	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(-i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{9660}(139,\cdot)\)	9660.q	2	no	\(1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(-1\)
\(\chi_{9660}(143,\cdot)\)	9660.gz	132	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{97}{132}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{5}{132}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{7}{12}\right)\)

Introduction

L-functions

Modular forms

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Properties

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Character group

First 32 of 2112 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.