LMFDB - Group of Dirichlet characters of modulus 322

Show commands: PariGP / SageMath

sage: H = DirichletGroup(322)

pari: g = idealstar(,322,2)

Character group

sage: G.order() pari: g.no
Order	=	132
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{66}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{322}(185,\cdot)$, $\chi_{322}(281,\cdot)$

First 32 of 132 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	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$25$	$27$
$\chi_{322}(1,\cdot)$	322.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{322}(3,\cdot)$	322.n	66	no	$-1$	$1$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{322}(5,\cdot)$	322.o	66	no	$1$	$1$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{322}(9,\cdot)$	322.m	33	no	$1$	$1$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{322}(11,\cdot)$	322.p	66	no	$-1$	$1$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{322}(13,\cdot)$	322.l	22	no	$-1$	$1$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{1}{22}\right)$
$\chi_{322}(15,\cdot)$	322.j	22	no	$-1$	$1$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{322}(17,\cdot)$	322.o	66	no	$1$	$1$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{17}{22}\right)$
$\chi_{322}(19,\cdot)$	322.o	66	no	$1$	$1$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{5}{22}\right)$
$\chi_{322}(25,\cdot)$	322.m	33	no	$1$	$1$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{322}(27,\cdot)$	322.l	22	no	$-1$	$1$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{5}{22}\right)$
$\chi_{322}(29,\cdot)$	322.i	11	no	$1$	$1$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{322}(31,\cdot)$	322.n	66	no	$-1$	$1$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{322}(33,\cdot)$	322.o	66	no	$1$	$1$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{1}{22}\right)$
$\chi_{322}(37,\cdot)$	322.p	66	no	$-1$	$1$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{322}(39,\cdot)$	322.m	33	no	$1$	$1$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{322}(41,\cdot)$	322.l	22	no	$-1$	$1$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{322}(43,\cdot)$	322.j	22	no	$-1$	$1$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{10}{11}\right)$
$\chi_{322}(45,\cdot)$	322.g	6	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$
$\chi_{322}(47,\cdot)$	322.h	6	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$
$\chi_{322}(51,\cdot)$	322.p	66	no	$-1$	$1$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{2}{11}\right)$
$\chi_{322}(53,\cdot)$	322.p	66	no	$-1$	$1$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{322}(55,\cdot)$	322.l	22	no	$-1$	$1$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{22}\right)$
$\chi_{322}(57,\cdot)$	322.j	22	no	$-1$	$1$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{322}(59,\cdot)$	322.n	66	no	$-1$	$1$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{1}{22}\right)$
$\chi_{322}(61,\cdot)$	322.o	66	no	$1$	$1$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{322}(65,\cdot)$	322.p	66	no	$-1$	$1$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{322}(67,\cdot)$	322.p	66	no	$-1$	$1$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{322}(71,\cdot)$	322.i	11	no	$1$	$1$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{322}(73,\cdot)$	322.n	66	no	$-1$	$1$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{5}{22}\right)$
$\chi_{322}(75,\cdot)$	322.n	66	no	$-1$	$1$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{17}{22}\right)$
$\chi_{322}(79,\cdot)$	322.p	66	no	$-1$	$1$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{6}{11}\right)$

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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	$322$
Structure	\(C_{2}\times C_{66}\)
Order	$132$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(25\)	\(27\)
\(\chi_{322}(1,\cdot)\)	322.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{322}(3,\cdot)\)	322.n	66	no	\(-1\)	\(1\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{9}{22}\right)\)
\(\chi_{322}(5,\cdot)\)	322.o	66	no	\(1\)	\(1\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{322}(9,\cdot)\)	322.m	33	no	\(1\)	\(1\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{322}(11,\cdot)\)	322.p	66	no	\(-1\)	\(1\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{322}(13,\cdot)\)	322.l	22	no	\(-1\)	\(1\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)
\(\chi_{322}(15,\cdot)\)	322.j	22	no	\(-1\)	\(1\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{322}(17,\cdot)\)	322.o	66	no	\(1\)	\(1\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{17}{22}\right)\)
\(\chi_{322}(19,\cdot)\)	322.o	66	no	\(1\)	\(1\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{5}{22}\right)\)
\(\chi_{322}(25,\cdot)\)	322.m	33	no	\(1\)	\(1\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{322}(27,\cdot)\)	322.l	22	no	\(-1\)	\(1\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)
\(\chi_{322}(29,\cdot)\)	322.i	11	no	\(1\)	\(1\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{322}(31,\cdot)\)	322.n	66	no	\(-1\)	\(1\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{13}{22}\right)\)
\(\chi_{322}(33,\cdot)\)	322.o	66	no	\(1\)	\(1\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{1}{22}\right)\)
\(\chi_{322}(37,\cdot)\)	322.p	66	no	\(-1\)	\(1\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{322}(39,\cdot)\)	322.m	33	no	\(1\)	\(1\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{322}(41,\cdot)\)	322.l	22	no	\(-1\)	\(1\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{322}(43,\cdot)\)	322.j	22	no	\(-1\)	\(1\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)
\(\chi_{322}(45,\cdot)\)	322.g	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)
\(\chi_{322}(47,\cdot)\)	322.h	6	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)
\(\chi_{322}(51,\cdot)\)	322.p	66	no	\(-1\)	\(1\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{2}{11}\right)\)
\(\chi_{322}(53,\cdot)\)	322.p	66	no	\(-1\)	\(1\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{322}(55,\cdot)\)	322.l	22	no	\(-1\)	\(1\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)
\(\chi_{322}(57,\cdot)\)	322.j	22	no	\(-1\)	\(1\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{322}(59,\cdot)\)	322.n	66	no	\(-1\)	\(1\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{1}{22}\right)\)
\(\chi_{322}(61,\cdot)\)	322.o	66	no	\(1\)	\(1\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{13}{22}\right)\)
\(\chi_{322}(65,\cdot)\)	322.p	66	no	\(-1\)	\(1\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{322}(67,\cdot)\)	322.p	66	no	\(-1\)	\(1\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{322}(71,\cdot)\)	322.i	11	no	\(1\)	\(1\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{322}(73,\cdot)\)	322.n	66	no	\(-1\)	\(1\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{5}{22}\right)\)
\(\chi_{322}(75,\cdot)\)	322.n	66	no	\(-1\)	\(1\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{17}{22}\right)\)
\(\chi_{322}(79,\cdot)\)	322.p	66	no	\(-1\)	\(1\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{6}{11}\right)\)

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L-functions

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First 32 of 132 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.