LMFDB - Group of Dirichlet characters of modulus 9240

Show commands: PariGP / SageMath

sage: H = DirichletGroup(9240)

pari: g = idealstar(,9240,2)

Character group

sage: G.order() pari: g.no
Order	=	1920
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{2}\times C_{2}\times C_{60}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{9240}(2311,\cdot)$, $\chi_{9240}(4621,\cdot)$, $\chi_{9240}(6161,\cdot)$, $\chi_{9240}(3697,\cdot)$, $\chi_{9240}(5281,\cdot)$, $\chi_{9240}(2521,\cdot)$

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	$-1$	$1$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$	$47$
$\chi_{9240}(1,\cdot)$	9240.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{9240}(13,\cdot)$	9240.kk	20	no	$-1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{4}{5}\right)$	$i$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{4}{5}\right)$	$i$	$e\left(\frac{1}{20}\right)$
$\chi_{9240}(17,\cdot)$	9240.ny	60	no	$1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{7}{10}\right)$	$i$	$e\left(\frac{47}{60}\right)$
$\chi_{9240}(19,\cdot)$	9240.lm	30	no	$-1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{2}{5}\right)$	$1$	$e\left(\frac{17}{30}\right)$
$\chi_{9240}(23,\cdot)$	9240.jd	12	no	$-1$	$1$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$-1$	$-i$	$e\left(\frac{5}{12}\right)$
$\chi_{9240}(29,\cdot)$	9240.ig	10	no	$1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$-1$	$e\left(\frac{3}{5}\right)$
$\chi_{9240}(31,\cdot)$	9240.mv	30	no	$1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{3}{10}\right)$	$-1$	$e\left(\frac{2}{15}\right)$
$\chi_{9240}(37,\cdot)$	9240.oj	60	no	$-1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{3}{5}\right)$	$i$	$e\left(\frac{31}{60}\right)$
$\chi_{9240}(41,\cdot)$	9240.gu	10	no	$-1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$-1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{10}\right)$	$-1$	$e\left(\frac{2}{5}\right)$
$\chi_{9240}(43,\cdot)$	9240.dd	4	no	$-1$	$1$	$i$	$i$	$1$	$-i$	$-1$	$-1$	$i$	$-1$	$-i$	$i$
$\chi_{9240}(47,\cdot)$	9240.nt	60	no	$1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{2}{5}\right)$	$i$	$e\left(\frac{49}{60}\right)$
$\chi_{9240}(53,\cdot)$	9240.os	60	yes	$1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{3}{10}\right)$	$-i$	$e\left(\frac{23}{60}\right)$
$\chi_{9240}(59,\cdot)$	9240.mn	30	yes	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{3}{5}\right)$	$-1$	$e\left(\frac{14}{15}\right)$
$\chi_{9240}(61,\cdot)$	9240.my	30	no	$1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{11}{30}\right)$
$\chi_{9240}(67,\cdot)$	9240.jv	12	no	$1$	$1$	$i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$1$	$-i$	$e\left(\frac{1}{12}\right)$
$\chi_{9240}(71,\cdot)$	9240.hi	10	no	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$-1$	$e\left(\frac{1}{5}\right)$
$\chi_{9240}(73,\cdot)$	9240.np	60	no	$-1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{3}{5}\right)$	$-i$	$e\left(\frac{11}{60}\right)$
$\chi_{9240}(79,\cdot)$	9240.mc	30	no	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{3}{10}\right)$	$-1$	$e\left(\frac{7}{15}\right)$
$\chi_{9240}(83,\cdot)$	9240.kq	20	yes	$-1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{10}\right)$	$i$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{10}\right)$	$-i$	$e\left(\frac{9}{20}\right)$
$\chi_{9240}(89,\cdot)$	9240.fy	6	no	$1$	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$
$\chi_{9240}(97,\cdot)$	9240.kl	20	no	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{4}{5}\right)$	$-i$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{10}\right)$	$-i$	$e\left(\frac{11}{20}\right)$
$\chi_{9240}(101,\cdot)$	9240.mo	30	no	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{3}{10}\right)$	$1$	$e\left(\frac{2}{15}\right)$
$\chi_{9240}(103,\cdot)$	9240.oc	60	no	$-1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{1}{10}\right)$	$-i$	$e\left(\frac{1}{60}\right)$
$\chi_{9240}(107,\cdot)$	9240.of	60	yes	$1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{2}{5}\right)$	$i$	$e\left(\frac{19}{60}\right)$
$\chi_{9240}(109,\cdot)$	9240.ea	6	no	$-1$	$1$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$
$\chi_{9240}(113,\cdot)$	9240.kp	20	no	$1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{10}\right)$	$-i$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{9}{10}\right)$	$i$	$e\left(\frac{13}{20}\right)$
$\chi_{9240}(127,\cdot)$	9240.kt	20	no	$-1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{10}\right)$	$i$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{10}\right)$	$-i$	$e\left(\frac{19}{20}\right)$
$\chi_{9240}(131,\cdot)$	9240.el	6	no	$1$	$1$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$
$\chi_{9240}(137,\cdot)$	9240.nv	60	no	$1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{7}{10}\right)$	$-i$	$e\left(\frac{17}{60}\right)$
$\chi_{9240}(139,\cdot)$	9240.gy	10	no	$-1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$1$	$e\left(\frac{1}{10}\right)$
$\chi_{9240}(149,\cdot)$	9240.mt	30	yes	$1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{5}\right)$	$-1$	$e\left(\frac{13}{15}\right)$
$\chi_{9240}(151,\cdot)$	9240.mx	30	no	$1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{9}{10}\right)$	$1$	$e\left(\frac{7}{30}\right)$

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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	$9240$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{2}\times C_{2}\times C_{60}\)
Order	$1920$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)	\(47\)
\(\chi_{9240}(1,\cdot)\)	9240.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{9240}(13,\cdot)\)	9240.kk	20	no	\(-1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(i\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(i\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{9240}(17,\cdot)\)	9240.ny	60	no	\(1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(i\)	\(e\left(\frac{47}{60}\right)\)
\(\chi_{9240}(19,\cdot)\)	9240.lm	30	no	\(-1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(1\)	\(e\left(\frac{17}{30}\right)\)
\(\chi_{9240}(23,\cdot)\)	9240.jd	12	no	\(-1\)	\(1\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{9240}(29,\cdot)\)	9240.ig	10	no	\(1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(-1\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{9240}(31,\cdot)\)	9240.mv	30	no	\(1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(-1\)	\(e\left(\frac{2}{15}\right)\)
\(\chi_{9240}(37,\cdot)\)	9240.oj	60	no	\(-1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(i\)	\(e\left(\frac{31}{60}\right)\)
\(\chi_{9240}(41,\cdot)\)	9240.gu	10	no	\(-1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(-1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(-1\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{9240}(43,\cdot)\)	9240.dd	4	no	\(-1\)	\(1\)	\(i\)	\(i\)	\(1\)	\(-i\)	\(-1\)	\(-1\)	\(i\)	\(-1\)	\(-i\)	\(i\)
\(\chi_{9240}(47,\cdot)\)	9240.nt	60	no	\(1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(i\)	\(e\left(\frac{49}{60}\right)\)
\(\chi_{9240}(53,\cdot)\)	9240.os	60	yes	\(1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(-i\)	\(e\left(\frac{23}{60}\right)\)
\(\chi_{9240}(59,\cdot)\)	9240.mn	30	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(-1\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{9240}(61,\cdot)\)	9240.my	30	no	\(1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(1\)	\(e\left(\frac{11}{30}\right)\)
\(\chi_{9240}(67,\cdot)\)	9240.jv	12	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{9240}(71,\cdot)\)	9240.hi	10	no	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-1\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{9240}(73,\cdot)\)	9240.np	60	no	\(-1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(-i\)	\(e\left(\frac{11}{60}\right)\)
\(\chi_{9240}(79,\cdot)\)	9240.mc	30	no	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(-1\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{9240}(83,\cdot)\)	9240.kq	20	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(i\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-i\)	\(e\left(\frac{9}{20}\right)\)
\(\chi_{9240}(89,\cdot)\)	9240.fy	6	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{9240}(97,\cdot)\)	9240.kl	20	no	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-i\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(-i\)	\(e\left(\frac{11}{20}\right)\)
\(\chi_{9240}(101,\cdot)\)	9240.mo	30	no	\(-1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(1\)	\(e\left(\frac{2}{15}\right)\)
\(\chi_{9240}(103,\cdot)\)	9240.oc	60	no	\(-1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(-i\)	\(e\left(\frac{1}{60}\right)\)
\(\chi_{9240}(107,\cdot)\)	9240.of	60	yes	\(1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(i\)	\(e\left(\frac{19}{60}\right)\)
\(\chi_{9240}(109,\cdot)\)	9240.ea	6	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{9240}(113,\cdot)\)	9240.kp	20	no	\(1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(-i\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(i\)	\(e\left(\frac{13}{20}\right)\)
\(\chi_{9240}(127,\cdot)\)	9240.kt	20	no	\(-1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(i\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-i\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{9240}(131,\cdot)\)	9240.el	6	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{9240}(137,\cdot)\)	9240.nv	60	no	\(1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-i\)	\(e\left(\frac{17}{60}\right)\)
\(\chi_{9240}(139,\cdot)\)	9240.gy	10	no	\(-1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(1\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{9240}(149,\cdot)\)	9240.mt	30	yes	\(1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(-1\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{9240}(151,\cdot)\)	9240.mx	30	no	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(1\)	\(e\left(\frac{7}{30}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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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.