LMFDB - Group of Dirichlet characters of modulus 4760

Show commands: PariGP / SageMath

sage: H = DirichletGroup(4760)

pari: g = idealstar(,4760,2)

Character group

sage: G.order() pari: g.no
Order	=	1536
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{48}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{4760}(1191,\cdot)$, $\chi_{4760}(2381,\cdot)$, $\chi_{4760}(2857,\cdot)$, $\chi_{4760}(1361,\cdot)$, $\chi_{4760}(3641,\cdot)$

First 32 of 1536 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	$-1$	$1$	$3$	$9$	$11$	$13$	$19$	$23$	$27$	$29$	$31$	$33$
$\chi_{4760}(1,\cdot)$	4760.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{4760}(3,\cdot)$	4760.jx	48	yes	$1$	$1$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{5}{48}\right)$	$-1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{4760}(9,\cdot)$	4760.jt	24	no	$1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{24}\right)$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{4760}(11,\cdot)$	4760.kq	48	no	$1$	$1$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{35}{48}\right)$	$i$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{4760}(13,\cdot)$	4760.bn	4	yes	$1$	$1$	$-1$	$1$	$i$	$i$	$1$	$1$	$-1$	$i$	$-i$	$-i$
$\chi_{4760}(19,\cdot)$	4760.jp	24	yes	$1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{24}\right)$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{4760}(23,\cdot)$	4760.kv	48	no	$-1$	$1$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{19}{48}\right)$	$1$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{4760}(27,\cdot)$	4760.ho	16	yes	$1$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{16}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{11}{16}\right)$	$-i$
$\chi_{4760}(29,\cdot)$	4760.ia	16	no	$-1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{16}\right)$	$i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{5}{16}\right)$	$1$
$\chi_{4760}(31,\cdot)$	4760.ke	48	no	$-1$	$1$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{5}{48}\right)$	$-i$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{4760}(33,\cdot)$	4760.gw	12	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$-i$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{4760}(37,\cdot)$	4760.kd	48	yes	$1$	$1$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{13}{48}\right)$	$-1$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{4760}(39,\cdot)$	4760.kl	48	no	$1$	$1$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{17}{48}\right)$	$-i$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{4760}(41,\cdot)$	4760.ib	16	no	$1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{16}\right)$	$i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{11}{16}\right)$	$1$
$\chi_{4760}(43,\cdot)$	4760.et	8	no	$1$	$1$	$e\left(\frac{3}{8}\right)$	$-i$	$e\left(\frac{7}{8}\right)$	$i$	$i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{8}\right)$	$i$
$\chi_{4760}(47,\cdot)$	4760.fp	12	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$-i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{4760}(53,\cdot)$	4760.jb	24	yes	$-1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{24}\right)$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{4760}(57,\cdot)$	4760.hp	16	no	$1$	$1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{9}{16}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{7}{16}\right)$	$i$
$\chi_{4760}(59,\cdot)$	4760.jp	24	yes	$1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{24}\right)$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{4760}(61,\cdot)$	4760.kg	48	no	$1$	$1$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{7}{48}\right)$	$-i$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{4760}(67,\cdot)$	4760.gz	12	yes	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{4760}(69,\cdot)$	4760.d	2	no	$-1$	$1$	$-1$	$1$	$-1$	$-1$	$1$	$-1$	$-1$	$-1$	$-1$	$1$
$\chi_{4760}(71,\cdot)$	4760.hz	16	no	$1$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{15}{16}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{16}\right)$	$-1$
$\chi_{4760}(73,\cdot)$	4760.lb	48	no	$-1$	$1$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{41}{48}\right)$	$1$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{4760}(79,\cdot)$	4760.kl	48	no	$1$	$1$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{43}{48}\right)$	$i$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{4760}(81,\cdot)$	4760.gq	12	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{4760}(83,\cdot)$	4760.fd	8	yes	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$i$	$e\left(\frac{5}{8}\right)$	$-i$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$-i$
$\chi_{4760}(87,\cdot)$	4760.jj	24	no	$-1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{24}\right)$	$-i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{4760}(89,\cdot)$	4760.gm	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$i$	$-i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{4760}(93,\cdot)$	4760.jm	24	yes	$-1$	$1$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{24}\right)$	$i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{4760}(97,\cdot)$	4760.hq	16	no	$-1$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{11}{16}\right)$	$-1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{13}{16}\right)$	$-i$
$\chi_{4760}(99,\cdot)$	4760.ie	16	no	$1$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{15}{16}\right)$	$i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{9}{16}\right)$	$1$

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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	$4760$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{48}\)
Order	$1536$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(9\)	\(11\)	\(13\)	\(19\)	\(23\)	\(27\)	\(29\)	\(31\)	\(33\)
\(\chi_{4760}(1,\cdot)\)	4760.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{4760}(3,\cdot)\)	4760.jx	48	yes	\(1\)	\(1\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(-1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{4760}(9,\cdot)\)	4760.jt	24	no	\(1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{4760}(11,\cdot)\)	4760.kq	48	no	\(1\)	\(1\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(i\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{4760}(13,\cdot)\)	4760.bn	4	yes	\(1\)	\(1\)	\(-1\)	\(1\)	\(i\)	\(i\)	\(1\)	\(1\)	\(-1\)	\(i\)	\(-i\)	\(-i\)
\(\chi_{4760}(19,\cdot)\)	4760.jp	24	yes	\(1\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{4760}(23,\cdot)\)	4760.kv	48	no	\(-1\)	\(1\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{4760}(27,\cdot)\)	4760.ho	16	yes	\(1\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(-i\)
\(\chi_{4760}(29,\cdot)\)	4760.ia	16	no	\(-1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(1\)
\(\chi_{4760}(31,\cdot)\)	4760.ke	48	no	\(-1\)	\(1\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(-i\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{4760}(33,\cdot)\)	4760.gw	12	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{4760}(37,\cdot)\)	4760.kd	48	yes	\(1\)	\(1\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(-1\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{4760}(39,\cdot)\)	4760.kl	48	no	\(1\)	\(1\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(-i\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{4760}(41,\cdot)\)	4760.ib	16	no	\(1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(1\)
\(\chi_{4760}(43,\cdot)\)	4760.et	8	no	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(i\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(i\)
\(\chi_{4760}(47,\cdot)\)	4760.fp	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{4760}(53,\cdot)\)	4760.jb	24	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{4760}(57,\cdot)\)	4760.hp	16	no	\(1\)	\(1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(i\)
\(\chi_{4760}(59,\cdot)\)	4760.jp	24	yes	\(1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{4760}(61,\cdot)\)	4760.kg	48	no	\(1\)	\(1\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(-i\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{4760}(67,\cdot)\)	4760.gz	12	yes	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{4760}(69,\cdot)\)	4760.d	2	no	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)
\(\chi_{4760}(71,\cdot)\)	4760.hz	16	no	\(1\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(-1\)
\(\chi_{4760}(73,\cdot)\)	4760.lb	48	no	\(-1\)	\(1\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(1\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{4760}(79,\cdot)\)	4760.kl	48	no	\(1\)	\(1\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(i\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{4760}(81,\cdot)\)	4760.gq	12	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{4760}(83,\cdot)\)	4760.fd	8	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)
\(\chi_{4760}(87,\cdot)\)	4760.jj	24	no	\(-1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(-i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{4760}(89,\cdot)\)	4760.gm	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(i\)	\(-i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{4760}(93,\cdot)\)	4760.jm	24	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{4760}(97,\cdot)\)	4760.hq	16	no	\(-1\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(-i\)
\(\chi_{4760}(99,\cdot)\)	4760.ie	16	no	\(1\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(1\)

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

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Properties

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Character group

First 32 of 1536 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.