LMFDB - Group of Dirichlet characters of modulus 31200

Show commands: PariGP / SageMath

sage: H = DirichletGroup(31200)

pari: g = idealstar(,31200,2)

Character group

sage: G.order() pari: g.no
Order	=	7680
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{4}\times C_{120}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{31200}(1951,\cdot)$, $\chi_{31200}(27301,\cdot)$, $\chi_{31200}(20801,\cdot)$, $\chi_{31200}(14977,\cdot)$, $\chi_{31200}(12001,\cdot)$

First 32 of 7680 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	$-1$	$1$	$7$	$11$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{31200}(1,\cdot)$	31200.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{31200}(7,\cdot)$	31200.lg	12	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{12}\right)$	$-i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{31200}(11,\cdot)$	31200.bfl	120	yes	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{19}{24}\right)$
$\chi_{31200}(17,\cdot)$	31200.baj	60	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{31200}(19,\cdot)$	31200.bdq	120	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{5}{24}\right)$
$\chi_{31200}(23,\cdot)$	31200.bbh	60	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{31200}(29,\cdot)$	31200.beg	120	yes	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{1}{24}\right)$
$\chi_{31200}(31,\cdot)$	31200.rh	20	no	$1$	$1$	$-i$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{20}\right)$	$1$
$\chi_{31200}(37,\cdot)$	31200.bfa	120	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{13}{24}\right)$
$\chi_{31200}(41,\cdot)$	31200.bas	60	no	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{31200}(43,\cdot)$	31200.tn	24	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{24}\right)$	$1$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{24}\right)$
$\chi_{31200}(47,\cdot)$	31200.pj	20	no	$1$	$1$	$-1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{20}\right)$	$i$
$\chi_{31200}(49,\cdot)$	31200.fu	6	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{31200}(53,\cdot)$	31200.yy	40	no	$1$	$1$	$1$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{31200}(59,\cdot)$	31200.bea	120	yes	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{11}{24}\right)$
$\chi_{31200}(61,\cdot)$	31200.beh	120	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{5}{24}\right)$
$\chi_{31200}(67,\cdot)$	31200.bfb	120	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{7}{24}\right)$
$\chi_{31200}(71,\cdot)$	31200.bat	60	no	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{31200}(73,\cdot)$	31200.sz	20	no	$1$	$1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{19}{20}\right)$	$-1$
$\chi_{31200}(77,\cdot)$	31200.xf	40	yes	$1$	$1$	$-1$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{31200}(79,\cdot)$	31200.ka	10	no	$-1$	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$-1$
$\chi_{31200}(83,\cdot)$	31200.xz	40	yes	$1$	$1$	$i$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{31200}(89,\cdot)$	31200.bah	60	no	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{31200}(97,\cdot)$	31200.bcz	60	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{31200}(101,\cdot)$	31200.tu	24	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{24}\right)$	$-1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{24}\right)$
$\chi_{31200}(103,\cdot)$	31200.qw	20	no	$1$	$1$	$i$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{2}{5}\right)$	$1$
$\chi_{31200}(107,\cdot)$	31200.tl	24	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{24}\right)$	$-1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{24}\right)$
$\chi_{31200}(109,\cdot)$	31200.xg	40	no	$-1$	$1$	$-1$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{31200}(113,\cdot)$	31200.bci	60	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{31200}(119,\cdot)$	31200.bca	60	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{31200}(121,\cdot)$	31200.zx	60	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{31200}(127,\cdot)$	31200.bce	60	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{11}{12}\right)$

Click here to search among the remaining 7648 characters.

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	$31200$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{4}\times C_{120}\)
Order	$7680$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{31200}(1,\cdot)\)	31200.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{31200}(7,\cdot)\)	31200.lg	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{31200}(11,\cdot)\)	31200.bfl	120	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{19}{24}\right)\)
\(\chi_{31200}(17,\cdot)\)	31200.baj	60	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{31200}(19,\cdot)\)	31200.bdq	120	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{11}{120}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{5}{24}\right)\)
\(\chi_{31200}(23,\cdot)\)	31200.bbh	60	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{31200}(29,\cdot)\)	31200.beg	120	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{11}{120}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{1}{24}\right)\)
\(\chi_{31200}(31,\cdot)\)	31200.rh	20	no	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(1\)
\(\chi_{31200}(37,\cdot)\)	31200.bfa	120	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{13}{24}\right)\)
\(\chi_{31200}(41,\cdot)\)	31200.bas	60	no	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{31200}(43,\cdot)\)	31200.tn	24	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(1\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)
\(\chi_{31200}(47,\cdot)\)	31200.pj	20	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(i\)
\(\chi_{31200}(49,\cdot)\)	31200.fu	6	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{31200}(53,\cdot)\)	31200.yy	40	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{31200}(59,\cdot)\)	31200.bea	120	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{11}{24}\right)\)
\(\chi_{31200}(61,\cdot)\)	31200.beh	120	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{5}{24}\right)\)
\(\chi_{31200}(67,\cdot)\)	31200.bfb	120	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{7}{24}\right)\)
\(\chi_{31200}(71,\cdot)\)	31200.bat	60	no	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{31200}(73,\cdot)\)	31200.sz	20	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(-1\)
\(\chi_{31200}(77,\cdot)\)	31200.xf	40	yes	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{31200}(79,\cdot)\)	31200.ka	10	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(-1\)
\(\chi_{31200}(83,\cdot)\)	31200.xz	40	yes	\(1\)	\(1\)	\(i\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{31200}(89,\cdot)\)	31200.bah	60	no	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{31200}(97,\cdot)\)	31200.bcz	60	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{31200}(101,\cdot)\)	31200.tu	24	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(-1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{24}\right)\)
\(\chi_{31200}(103,\cdot)\)	31200.qw	20	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(1\)
\(\chi_{31200}(107,\cdot)\)	31200.tl	24	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(-1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{24}\right)\)
\(\chi_{31200}(109,\cdot)\)	31200.xg	40	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{31200}(113,\cdot)\)	31200.bci	60	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{31200}(119,\cdot)\)	31200.bca	60	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{31200}(121,\cdot)\)	31200.zx	60	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{31200}(127,\cdot)\)	31200.bce	60	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{11}{12}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 7680 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.