LMFDB - Group of Dirichlet characters of modulus 2665

Show commands: PariGP / SageMath

sage: H = DirichletGroup(2665)

pari: g = idealstar(,2665,2)

Character group

sage: G.order() pari: g.no
Order	=	1920
sage: H.invariants() pari: g.cyc
Structure	=	$C_{4}\times C_{4}\times C_{120}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{2665}(1067,\cdot)$, $\chi_{2665}(821,\cdot)$, $\chi_{2665}(1236,\cdot)$

First 32 of 1920 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	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$14$
$\chi_{2665}(1,\cdot)$	2665.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2665}(2,\cdot)$	2665.gn	60	yes	$1$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{3}{10}\right)$	$-i$
$\chi_{2665}(3,\cdot)$	2665.fi	24	yes	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{1}{24}\right)$	$-1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{2665}(4,\cdot)$	2665.fp	30	yes	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{3}{5}\right)$	$-1$
$\chi_{2665}(6,\cdot)$	2665.hw	120	no	$1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{2665}(7,\cdot)$	2665.ho	120	yes	$-1$	$1$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{2665}(8,\cdot)$	2665.ep	20	yes	$1$	$1$	$e\left(\frac{7}{10}\right)$	$-1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{10}\right)$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{10}\right)$	$i$
$\chi_{2665}(9,\cdot)$	2665.cs	12	yes	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{12}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$-i$	$-i$
$\chi_{2665}(11,\cdot)$	2665.hw	120	no	$1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{2665}(12,\cdot)$	2665.gf	40	yes	$1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{9}{10}\right)$	$-i$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{2665}(14,\cdot)$	2665.bz	8	no	$-1$	$1$	$-i$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$i$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{2665}(16,\cdot)$	2665.ds	15	no	$1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{5}\right)$	$1$
$\chi_{2665}(17,\cdot)$	2665.hx	120	yes	$1$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{2665}(18,\cdot)$	2665.eq	20	yes	$1$	$1$	$e\left(\frac{9}{10}\right)$	$i$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$-1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{20}\right)$	$-1$
$\chi_{2665}(19,\cdot)$	2665.hk	120	yes	$1$	$1$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{2665}(21,\cdot)$	2665.ed	20	no	$-1$	$1$	$e\left(\frac{7}{20}\right)$	$i$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{20}\right)$	$-1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{19}{20}\right)$	$-i$
$\chi_{2665}(22,\cdot)$	2665.hm	120	yes	$1$	$1$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{2665}(23,\cdot)$	2665.gy	60	yes	$-1$	$1$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{20}\right)$	$1$
$\chi_{2665}(24,\cdot)$	2665.hz	120	yes	$1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{2665}(27,\cdot)$	2665.bu	8	no	$1$	$1$	$-1$	$e\left(\frac{5}{8}\right)$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-1$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{2665}(28,\cdot)$	2665.hr	120	yes	$-1$	$1$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{2665}(29,\cdot)$	2665.hu	120	yes	$-1$	$1$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{2665}(31,\cdot)$	2665.ea	20	no	$-1$	$1$	$e\left(\frac{19}{20}\right)$	$-1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{17}{20}\right)$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{2}{5}\right)$	$-1$
$\chi_{2665}(32,\cdot)$	2665.dr	12	yes	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$-i$
$\chi_{2665}(33,\cdot)$	2665.gi	60	yes	$1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{2}{5}\right)$	$-i$
$\chi_{2665}(34,\cdot)$	2665.ge	40	yes	$1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{3}{10}\right)$	$i$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{2665}(36,\cdot)$	2665.hg	60	no	$1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{7}{20}\right)$	$i$
$\chi_{2665}(37,\cdot)$	2665.gm	60	yes	$1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{7}{20}\right)$	$-1$
$\chi_{2665}(38,\cdot)$	2665.ch	8	yes	$1$	$1$	$1$	$e\left(\frac{3}{8}\right)$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{8}\right)$	$1$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{2665}(42,\cdot)$	2665.db	12	no	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$	$-i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$i$	$-1$
$\chi_{2665}(43,\cdot)$	2665.gr	60	yes	$-1$	$1$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{3}{10}\right)$	$-i$
$\chi_{2665}(44,\cdot)$	2665.cf	8	yes	$1$	$1$	$1$	$e\left(\frac{1}{8}\right)$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$1$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$

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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	$2665$
Structure	\(C_{4}\times C_{4}\times C_{120}\)
Order	$1920$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(14\)
\(\chi_{2665}(1,\cdot)\)	2665.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2665}(2,\cdot)\)	2665.gn	60	yes	\(1\)	\(1\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(-i\)
\(\chi_{2665}(3,\cdot)\)	2665.fi	24	yes	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(-1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{2665}(4,\cdot)\)	2665.fp	30	yes	\(1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(-1\)
\(\chi_{2665}(6,\cdot)\)	2665.hw	120	no	\(1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{2665}(7,\cdot)\)	2665.ho	120	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{2665}(8,\cdot)\)	2665.ep	20	yes	\(1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(-1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(i\)
\(\chi_{2665}(9,\cdot)\)	2665.cs	12	yes	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(-i\)
\(\chi_{2665}(11,\cdot)\)	2665.hw	120	no	\(1\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{2665}(12,\cdot)\)	2665.gf	40	yes	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(-i\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{2665}(14,\cdot)\)	2665.bz	8	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(i\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{2665}(16,\cdot)\)	2665.ds	15	no	\(1\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(1\)
\(\chi_{2665}(17,\cdot)\)	2665.hx	120	yes	\(1\)	\(1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{2665}(18,\cdot)\)	2665.eq	20	yes	\(1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(i\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(-1\)
\(\chi_{2665}(19,\cdot)\)	2665.hk	120	yes	\(1\)	\(1\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{2665}(21,\cdot)\)	2665.ed	20	no	\(-1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(i\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(-1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(-i\)
\(\chi_{2665}(22,\cdot)\)	2665.hm	120	yes	\(1\)	\(1\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{2665}(23,\cdot)\)	2665.gy	60	yes	\(-1\)	\(1\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(1\)
\(\chi_{2665}(24,\cdot)\)	2665.hz	120	yes	\(1\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{2665}(27,\cdot)\)	2665.bu	8	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{2665}(28,\cdot)\)	2665.hr	120	yes	\(-1\)	\(1\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{2665}(29,\cdot)\)	2665.hu	120	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{2665}(31,\cdot)\)	2665.ea	20	no	\(-1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(-1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(-1\)
\(\chi_{2665}(32,\cdot)\)	2665.dr	12	yes	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(-i\)
\(\chi_{2665}(33,\cdot)\)	2665.gi	60	yes	\(1\)	\(1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(-i\)
\(\chi_{2665}(34,\cdot)\)	2665.ge	40	yes	\(1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(i\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{2665}(36,\cdot)\)	2665.hg	60	no	\(1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(i\)
\(\chi_{2665}(37,\cdot)\)	2665.gm	60	yes	\(1\)	\(1\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(-1\)
\(\chi_{2665}(38,\cdot)\)	2665.ch	8	yes	\(1\)	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{2665}(42,\cdot)\)	2665.db	12	no	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(-1\)
\(\chi_{2665}(43,\cdot)\)	2665.gr	60	yes	\(-1\)	\(1\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(-i\)
\(\chi_{2665}(44,\cdot)\)	2665.cf	8	yes	\(1\)	\(1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(1\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)

Introduction

L-functions

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Character group

First 32 of 1920 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.