LMFDB - Group of Dirichlet characters of modulus 1440

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1440)

pari: g = idealstar(,1440,2)

Character group

sage: G.order() pari: g.no
Order	=	384
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{24}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1440}(991,\cdot)$, $\chi_{1440}(901,\cdot)$, $\chi_{1440}(641,\cdot)$, $\chi_{1440}(577,\cdot)$

First 32 of 384 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	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{1440}(1,\cdot)$	1440.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1440}(7,\cdot)$	1440.dj	12	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$-i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{5}{6}\right)$
$\chi_{1440}(11,\cdot)$	1440.ec	24	no	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{17}{24}\right)$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{1440}(13,\cdot)$	1440.eg	24	yes	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{24}\right)$	$i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{1440}(17,\cdot)$	1440.bj	4	no	$1$	$1$	$i$	$1$	$i$	$-i$	$1$	$i$	$-1$	$1$	$-i$	$-1$
$\chi_{1440}(19,\cdot)$	1440.cm	8	no	$-1$	$1$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$1$	$e\left(\frac{5}{8}\right)$	$i$	$e\left(\frac{5}{8}\right)$	$-1$	$e\left(\frac{3}{8}\right)$	$i$
$\chi_{1440}(23,\cdot)$	1440.di	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$i$	$i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$
$\chi_{1440}(29,\cdot)$	1440.dx	24	yes	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{11}{24}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{1440}(31,\cdot)$	1440.cb	6	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{2}{3}\right)$
$\chi_{1440}(37,\cdot)$	1440.cf	8	no	$-1$	$1$	$-1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-i$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$1$	$e\left(\frac{3}{8}\right)$	$-i$
$\chi_{1440}(41,\cdot)$	1440.do	12	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$-1$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$-i$	$e\left(\frac{2}{3}\right)$
$\chi_{1440}(43,\cdot)$	1440.eh	24	yes	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{23}{24}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{1440}(47,\cdot)$	1440.dl	12	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$-1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{5}{6}\right)$
$\chi_{1440}(49,\cdot)$	1440.ca	6	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$
$\chi_{1440}(53,\cdot)$	1440.cr	8	no	$1$	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-i$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$1$	$e\left(\frac{3}{8}\right)$	$i$
$\chi_{1440}(59,\cdot)$	1440.dz	24	yes	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{1}{24}\right)$	$-1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{1440}(61,\cdot)$	1440.dw	24	no	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{23}{24}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{1440}(67,\cdot)$	1440.eh	24	yes	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{24}\right)$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{1440}(71,\cdot)$	1440.bl	4	no	$1$	$1$	$1$	$i$	$-i$	$-1$	$i$	$-1$	$i$	$-1$	$i$	$1$
$\chi_{1440}(73,\cdot)$	1440.bb	4	no	$-1$	$1$	$i$	$-i$	$-1$	$-i$	$-i$	$-i$	$-i$	$1$	$-1$	$-1$
$\chi_{1440}(77,\cdot)$	1440.du	24	yes	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{13}{24}\right)$	$i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{1440}(79,\cdot)$	1440.bp	6	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$
$\chi_{1440}(83,\cdot)$	1440.dv	24	yes	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{17}{24}\right)$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{1440}(89,\cdot)$	1440.bn	4	no	$-1$	$1$	$1$	$-i$	$i$	$1$	$-i$	$-1$	$i$	$1$	$-i$	$1$
$\chi_{1440}(91,\cdot)$	1440.cj	8	no	$-1$	$1$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{3}{8}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{1}{8}\right)$	$-i$
$\chi_{1440}(97,\cdot)$	1440.cz	12	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$i$	$-1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$i$	$e\left(\frac{1}{3}\right)$
$\chi_{1440}(101,\cdot)$	1440.ea	24	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{5}{24}\right)$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{1440}(103,\cdot)$	1440.df	12	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$-i$	$-i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$
$\chi_{1440}(107,\cdot)$	1440.cq	8	no	$-1$	$1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$i$
$\chi_{1440}(109,\cdot)$	1440.co	8	no	$1$	$1$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$1$	$e\left(\frac{1}{8}\right)$	$-i$	$e\left(\frac{5}{8}\right)$	$1$	$e\left(\frac{3}{8}\right)$	$i$
$\chi_{1440}(113,\cdot)$	1440.db	12	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$i$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$i$	$e\left(\frac{1}{6}\right)$
$\chi_{1440}(119,\cdot)$	1440.dq	12	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$	$1$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{1}{3}\right)$

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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	$1440$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{24}\)
Order	$384$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{1440}(1,\cdot)\)	1440.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1440}(7,\cdot)\)	1440.dj	12	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(-i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1440}(11,\cdot)\)	1440.ec	24	no	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{1440}(13,\cdot)\)	1440.eg	24	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{1440}(17,\cdot)\)	1440.bj	4	no	\(1\)	\(1\)	\(i\)	\(1\)	\(i\)	\(-i\)	\(1\)	\(i\)	\(-1\)	\(1\)	\(-i\)	\(-1\)
\(\chi_{1440}(19,\cdot)\)	1440.cm	8	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(i\)
\(\chi_{1440}(23,\cdot)\)	1440.di	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{1440}(29,\cdot)\)	1440.dx	24	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{1440}(31,\cdot)\)	1440.cb	6	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{1440}(37,\cdot)\)	1440.cf	8	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)
\(\chi_{1440}(41,\cdot)\)	1440.do	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{1440}(43,\cdot)\)	1440.eh	24	yes	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{1440}(47,\cdot)\)	1440.dl	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1440}(49,\cdot)\)	1440.ca	6	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{1440}(53,\cdot)\)	1440.cr	8	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(i\)
\(\chi_{1440}(59,\cdot)\)	1440.dz	24	yes	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{1440}(61,\cdot)\)	1440.dw	24	no	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{1440}(67,\cdot)\)	1440.eh	24	yes	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{1440}(71,\cdot)\)	1440.bl	4	no	\(1\)	\(1\)	\(1\)	\(i\)	\(-i\)	\(-1\)	\(i\)	\(-1\)	\(i\)	\(-1\)	\(i\)	\(1\)
\(\chi_{1440}(73,\cdot)\)	1440.bb	4	no	\(-1\)	\(1\)	\(i\)	\(-i\)	\(-1\)	\(-i\)	\(-i\)	\(-i\)	\(-i\)	\(1\)	\(-1\)	\(-1\)
\(\chi_{1440}(77,\cdot)\)	1440.du	24	yes	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{1440}(79,\cdot)\)	1440.bp	6	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{1440}(83,\cdot)\)	1440.dv	24	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{1440}(89,\cdot)\)	1440.bn	4	no	\(-1\)	\(1\)	\(1\)	\(-i\)	\(i\)	\(1\)	\(-i\)	\(-1\)	\(i\)	\(1\)	\(-i\)	\(1\)
\(\chi_{1440}(91,\cdot)\)	1440.cj	8	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)
\(\chi_{1440}(97,\cdot)\)	1440.cz	12	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{1440}(101,\cdot)\)	1440.ea	24	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{1440}(103,\cdot)\)	1440.df	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1440}(107,\cdot)\)	1440.cq	8	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(i\)
\(\chi_{1440}(109,\cdot)\)	1440.co	8	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(i\)
\(\chi_{1440}(113,\cdot)\)	1440.db	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(i\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1440}(119,\cdot)\)	1440.dq	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Character group

First 32 of 384 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.