LMFDB - Group of Dirichlet characters of modulus 39600

Show commands: PariGP / SageMath

sage: H = DirichletGroup(39600)

pari: g = idealstar(,39600,2)

Character group

sage: G.order() pari: g.no
Order	=	9600
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{20}\times C_{60}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{39600}(24751,\cdot)$, $\chi_{39600}(29701,\cdot)$, $\chi_{39600}(35201,\cdot)$, $\chi_{39600}(22177,\cdot)$, $\chi_{39600}(14401,\cdot)$

First 32 of 9600 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	$-1$	$1$	$7$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{39600}(1,\cdot)$	39600.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{39600}(7,\cdot)$	39600.bkd	60	no	$-1$	$1$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{39600}(13,\cdot)$	39600.bof	60	yes	$1$	$1$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{1}{15}\right)$	$i$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{13}{15}\right)$	$-1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{39600}(17,\cdot)$	39600.sr	20	no	$-1$	$1$	$e\left(\frac{11}{20}\right)$	$i$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{4}{5}\right)$	$i$
$\chi_{39600}(19,\cdot)$	39600.oo	20	no	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{20}\right)$	$-1$	$e\left(\frac{9}{20}\right)$	$1$	$i$
$\chi_{39600}(23,\cdot)$	39600.blt	60	no	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{39600}(29,\cdot)$	39600.bhe	60	yes	$1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{39600}(31,\cdot)$	39600.bbd	30	no	$-1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{3}{5}\right)$	$-1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{39600}(37,\cdot)$	39600.pt	20	no	$-1$	$1$	$e\left(\frac{3}{20}\right)$	$-1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$	$1$
$\chi_{39600}(41,\cdot)$	39600.bbn	30	no	$1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{4}{5}\right)$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{39600}(43,\cdot)$	39600.ne	12	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{39600}(47,\cdot)$	39600.bky	60	no	$-1$	$1$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{17}{60}\right)$	$-i$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{13}{30}\right)$	$i$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{39600}(49,\cdot)$	39600.bao	30	no	$1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{39600}(53,\cdot)$	39600.ws	20	no	$1$	$1$	$e\left(\frac{9}{20}\right)$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$-1$
$\chi_{39600}(59,\cdot)$	39600.bgw	60	yes	$1$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{39600}(61,\cdot)$	39600.bph	60	yes	$-1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{41}{60}\right)$	$-1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{2}{15}\right)$	$-i$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{39600}(67,\cdot)$	39600.bns	60	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{39600}(71,\cdot)$	39600.kp	10	no	$1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{10}\right)$	$1$	$e\left(\frac{3}{5}\right)$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{10}\right)$	$1$
$\chi_{39600}(73,\cdot)$	39600.rn	20	no	$1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{20}\right)$	$-1$	$e\left(\frac{1}{20}\right)$	$-1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{10}\right)$	$i$
$\chi_{39600}(79,\cdot)$	39600.zm	30	no	$1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{39600}(83,\cdot)$	39600.bhy	60	yes	$1$	$1$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{39600}(89,\cdot)$	39600.eq	10	no	$-1$	$1$	$-1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$	$1$
$\chi_{39600}(91,\cdot)$	39600.om	20	no	$-1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{4}{5}\right)$	$i$	$e\left(\frac{1}{5}\right)$	$-i$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{10}\right)$	$-i$
$\chi_{39600}(97,\cdot)$	39600.bmc	60	no	$-1$	$1$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{39600}(101,\cdot)$	39600.bpl	60	no	$1$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{39600}(103,\cdot)$	39600.bna	60	no	$1$	$1$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{39600}(107,\cdot)$	39600.re	20	no	$1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{13}{20}\right)$	$i$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$1$
$\chi_{39600}(109,\cdot)$	39600.nu	20	no	$-1$	$1$	$-1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{4}{5}\right)$	$-i$
$\chi_{39600}(113,\cdot)$	39600.bju	60	no	$1$	$1$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{1}{20}\right)$	$-1$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{39600}(119,\cdot)$	39600.bem	30	no	$1$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{3}{5}\right)$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{39600}(127,\cdot)$	39600.tz	20	no	$-1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{17}{20}\right)$	$-i$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$i$	$e\left(\frac{9}{10}\right)$	$-i$
$\chi_{39600}(131,\cdot)$	39600.bqu	60	yes	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{12}\right)$

Click here to search among the remaining 9568 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	$39600$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{20}\times C_{60}\)
Order	$9600$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{39600}(1,\cdot)\)	39600.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{39600}(7,\cdot)\)	39600.bkd	60	no	\(-1\)	\(1\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{39600}(13,\cdot)\)	39600.bof	60	yes	\(1\)	\(1\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(i\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(-1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{39600}(17,\cdot)\)	39600.sr	20	no	\(-1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(i\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(i\)
\(\chi_{39600}(19,\cdot)\)	39600.oo	20	no	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(-1\)	\(e\left(\frac{9}{20}\right)\)	\(1\)	\(i\)
\(\chi_{39600}(23,\cdot)\)	39600.blt	60	no	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{39600}(29,\cdot)\)	39600.bhe	60	yes	\(1\)	\(1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{39600}(31,\cdot)\)	39600.bbd	30	no	\(-1\)	\(1\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(-1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{39600}(37,\cdot)\)	39600.pt	20	no	\(-1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(-1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(1\)
\(\chi_{39600}(41,\cdot)\)	39600.bbn	30	no	\(1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{39600}(43,\cdot)\)	39600.ne	12	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{39600}(47,\cdot)\)	39600.bky	60	no	\(-1\)	\(1\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(-i\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(i\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{39600}(49,\cdot)\)	39600.bao	30	no	\(1\)	\(1\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{39600}(53,\cdot)\)	39600.ws	20	no	\(1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(-1\)
\(\chi_{39600}(59,\cdot)\)	39600.bgw	60	yes	\(1\)	\(1\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{39600}(61,\cdot)\)	39600.bph	60	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(-1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(-i\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{39600}(67,\cdot)\)	39600.bns	60	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{39600}(71,\cdot)\)	39600.kp	10	no	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(1\)
\(\chi_{39600}(73,\cdot)\)	39600.rn	20	no	\(1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(-1\)	\(e\left(\frac{1}{20}\right)\)	\(-1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(i\)
\(\chi_{39600}(79,\cdot)\)	39600.zm	30	no	\(1\)	\(1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{39600}(83,\cdot)\)	39600.bhy	60	yes	\(1\)	\(1\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{39600}(89,\cdot)\)	39600.eq	10	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(1\)
\(\chi_{39600}(91,\cdot)\)	39600.om	20	no	\(-1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(i\)	\(e\left(\frac{1}{5}\right)\)	\(-i\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-i\)
\(\chi_{39600}(97,\cdot)\)	39600.bmc	60	no	\(-1\)	\(1\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{39600}(101,\cdot)\)	39600.bpl	60	no	\(1\)	\(1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{39600}(103,\cdot)\)	39600.bna	60	no	\(1\)	\(1\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{39600}(107,\cdot)\)	39600.re	20	no	\(1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(i\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(1\)
\(\chi_{39600}(109,\cdot)\)	39600.nu	20	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-i\)
\(\chi_{39600}(113,\cdot)\)	39600.bju	60	no	\(1\)	\(1\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(-1\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{39600}(119,\cdot)\)	39600.bem	30	no	\(1\)	\(1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(1\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{39600}(127,\cdot)\)	39600.tz	20	no	\(-1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(-i\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(i\)	\(e\left(\frac{9}{10}\right)\)	\(-i\)
\(\chi_{39600}(131,\cdot)\)	39600.bqu	60	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{12}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 9600 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.