LMFDB - Group of Dirichlet characters of modulus 1932

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1932)

pari: g = idealstar(,1932,2)

Character group

sage: G.order() pari: g.no
Order	=	528
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{66}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1932}(967,\cdot)$, $\chi_{1932}(1289,\cdot)$, $\chi_{1932}(829,\cdot)$, $\chi_{1932}(925,\cdot)$

First 32 of 528 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	$-1$	$1$	$5$	$11$	$13$	$17$	$19$	$25$	$29$	$31$	$37$	$41$
$\chi_{1932}(1,\cdot)$	1932.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1932}(5,\cdot)$	1932.ce	66	no	$-1$	$1$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{1932}(11,\cdot)$	1932.cg	66	yes	$-1$	$1$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{1932}(13,\cdot)$	1932.br	22	no	$-1$	$1$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{3}{22}\right)$
$\chi_{1932}(17,\cdot)$	1932.ce	66	no	$-1$	$1$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{1932}(19,\cdot)$	1932.ck	66	no	$-1$	$1$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{1932}(25,\cdot)$	1932.bw	33	no	$1$	$1$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{1932}(29,\cdot)$	1932.bs	22	no	$-1$	$1$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{7}{22}\right)$
$\chi_{1932}(31,\cdot)$	1932.ca	66	no	$1$	$1$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{17}{22}\right)$
$\chi_{1932}(37,\cdot)$	1932.bx	66	no	$-1$	$1$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{1932}(41,\cdot)$	1932.bn	22	no	$1$	$1$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{1932}(43,\cdot)$	1932.bo	22	no	$1$	$1$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{1932}(47,\cdot)$	1932.r	6	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$
$\chi_{1932}(53,\cdot)$	1932.cj	66	no	$1$	$1$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{19}{22}\right)$
$\chi_{1932}(55,\cdot)$	1932.bu	22	no	$1$	$1$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{21}{22}\right)$
$\chi_{1932}(59,\cdot)$	1932.cl	66	yes	$-1$	$1$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{1932}(61,\cdot)$	1932.ci	66	no	$1$	$1$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{17}{22}\right)$
$\chi_{1932}(65,\cdot)$	1932.cj	66	no	$1$	$1$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{1932}(67,\cdot)$	1932.cc	66	no	$1$	$1$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{1932}(71,\cdot)$	1932.bp	22	no	$1$	$1$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{1932}(73,\cdot)$	1932.cd	66	no	$-1$	$1$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{1932}(79,\cdot)$	1932.cc	66	no	$1$	$1$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{1932}(83,\cdot)$	1932.bv	22	yes	$1$	$1$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{1932}(85,\cdot)$	1932.bg	11	no	$1$	$1$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{1932}(89,\cdot)$	1932.ce	66	no	$-1$	$1$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{1932}(95,\cdot)$	1932.cb	66	yes	$1$	$1$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{5}{22}\right)$
$\chi_{1932}(97,\cdot)$	1932.bm	22	no	$1$	$1$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{1}{22}\right)$
$\chi_{1932}(101,\cdot)$	1932.ch	66	no	$1$	$1$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{1932}(103,\cdot)$	1932.ck	66	no	$-1$	$1$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{1932}(107,\cdot)$	1932.cg	66	yes	$-1$	$1$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{17}{22}\right)$
$\chi_{1932}(109,\cdot)$	1932.bx	66	no	$-1$	$1$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{1932}(113,\cdot)$	1932.bh	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	$1932$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{66}\)
Order	$528$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(11\)	\(13\)	\(17\)	\(19\)	\(25\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{1932}(1,\cdot)\)	1932.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1932}(5,\cdot)\)	1932.ce	66	no	\(-1\)	\(1\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{1932}(11,\cdot)\)	1932.cg	66	yes	\(-1\)	\(1\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{9}{22}\right)\)
\(\chi_{1932}(13,\cdot)\)	1932.br	22	no	\(-1\)	\(1\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)
\(\chi_{1932}(17,\cdot)\)	1932.ce	66	no	\(-1\)	\(1\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{1932}(19,\cdot)\)	1932.ck	66	no	\(-1\)	\(1\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{1932}(25,\cdot)\)	1932.bw	33	no	\(1\)	\(1\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{1932}(29,\cdot)\)	1932.bs	22	no	\(-1\)	\(1\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)
\(\chi_{1932}(31,\cdot)\)	1932.ca	66	no	\(1\)	\(1\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{17}{22}\right)\)
\(\chi_{1932}(37,\cdot)\)	1932.bx	66	no	\(-1\)	\(1\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{1932}(41,\cdot)\)	1932.bn	22	no	\(1\)	\(1\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{1932}(43,\cdot)\)	1932.bo	22	no	\(1\)	\(1\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{1932}(47,\cdot)\)	1932.r	6	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)
\(\chi_{1932}(53,\cdot)\)	1932.cj	66	no	\(1\)	\(1\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{19}{22}\right)\)
\(\chi_{1932}(55,\cdot)\)	1932.bu	22	no	\(1\)	\(1\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)
\(\chi_{1932}(59,\cdot)\)	1932.cl	66	yes	\(-1\)	\(1\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{1932}(61,\cdot)\)	1932.ci	66	no	\(1\)	\(1\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{17}{22}\right)\)
\(\chi_{1932}(65,\cdot)\)	1932.cj	66	no	\(1\)	\(1\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{1932}(67,\cdot)\)	1932.cc	66	no	\(1\)	\(1\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{1932}(71,\cdot)\)	1932.bp	22	no	\(1\)	\(1\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)
\(\chi_{1932}(73,\cdot)\)	1932.cd	66	no	\(-1\)	\(1\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{1932}(79,\cdot)\)	1932.cc	66	no	\(1\)	\(1\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{1932}(83,\cdot)\)	1932.bv	22	yes	\(1\)	\(1\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{1932}(85,\cdot)\)	1932.bg	11	no	\(1\)	\(1\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{1932}(89,\cdot)\)	1932.ce	66	no	\(-1\)	\(1\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{1932}(95,\cdot)\)	1932.cb	66	yes	\(1\)	\(1\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{5}{22}\right)\)
\(\chi_{1932}(97,\cdot)\)	1932.bm	22	no	\(1\)	\(1\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)
\(\chi_{1932}(101,\cdot)\)	1932.ch	66	no	\(1\)	\(1\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{1932}(103,\cdot)\)	1932.ck	66	no	\(-1\)	\(1\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{9}{22}\right)\)
\(\chi_{1932}(107,\cdot)\)	1932.cg	66	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{17}{22}\right)\)
\(\chi_{1932}(109,\cdot)\)	1932.bx	66	no	\(-1\)	\(1\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{1932}(113,\cdot)\)	1932.bh	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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Character group

First 32 of 528 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.