LMFDB - Group of Dirichlet characters of modulus 476

sage:H = DirichletGroup(476)

pari:g = idealstar(,476,2)

Character group

sage:G.order() pari:g.no
Order	=	192
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{48}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{476}(239,\cdot)$, $\chi_{476}(409,\cdot)$, $\chi_{476}(309,\cdot)$

First 32 of 192 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	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$19$	$23$	$25$	$27$
$\chi_{476}(1,\cdot)$	476.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{476}(3,\cdot)$	476.bk	48	yes	$-1$	$1$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{29}{48}\right)$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{3}{16}\right)$
$\chi_{476}(5,\cdot)$	476.bl	48	no	$1$	$1$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{25}{48}\right)$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{476}(9,\cdot)$	476.bh	24	no	$1$	$1$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{24}\right)$	$-1$	$-i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{476}(11,\cdot)$	476.bm	48	yes	$1$	$1$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{11}{48}\right)$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{13}{16}\right)$
$\chi_{476}(13,\cdot)$	476.j	4	no	$-1$	$1$	$-i$	$-i$	$-1$	$-i$	$-1$	$-1$	$1$	$-i$	$-1$	$i$
$\chi_{476}(15,\cdot)$	476.v	8	no	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-i$	$e\left(\frac{1}{8}\right)$	$-1$	$-i$	$-i$	$e\left(\frac{1}{8}\right)$	$-i$	$e\left(\frac{5}{8}\right)$
$\chi_{476}(19,\cdot)$	476.bj	24	yes	$1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{23}{24}\right)$	$1$	$-i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{476}(23,\cdot)$	476.bm	48	yes	$1$	$1$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{19}{48}\right)$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{5}{16}\right)$
$\chi_{476}(25,\cdot)$	476.bh	24	no	$1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{24}\right)$	$-1$	$-i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{476}(27,\cdot)$	476.bf	16	yes	$-1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{16}\right)$	$i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{476}(29,\cdot)$	476.bc	16	no	$-1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{16}\right)$	$i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{476}(31,\cdot)$	476.bk	48	yes	$-1$	$1$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{5}{48}\right)$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{476}(33,\cdot)$	476.n	6	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$
$\chi_{476}(37,\cdot)$	476.bn	48	no	$-1$	$1$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{37}{48}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{3}{16}\right)$
$\chi_{476}(39,\cdot)$	476.bm	48	yes	$1$	$1$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{17}{48}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{476}(41,\cdot)$	476.be	16	no	$1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{16}\right)$	$i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{476}(43,\cdot)$	476.v	8	no	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{8}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$-1$	$i$	$i$	$e\left(\frac{3}{8}\right)$	$i$	$e\left(\frac{7}{8}\right)$
$\chi_{476}(45,\cdot)$	476.bl	48	no	$1$	$1$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{35}{48}\right)$	$i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{13}{16}\right)$
$\chi_{476}(47,\cdot)$	476.z	12	yes	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$-i$
$\chi_{476}(53,\cdot)$	476.bh	24	no	$1$	$1$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{19}{24}\right)$	$-1$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{476}(55,\cdot)$	476.k	4	yes	$1$	$1$	$-i$	$i$	$-1$	$-i$	$-1$	$1$	$-1$	$-i$	$-1$	$i$
$\chi_{476}(57,\cdot)$	476.bc	16	no	$-1$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{9}{16}\right)$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{16}\right)$
$\chi_{476}(59,\cdot)$	476.bj	24	yes	$1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{24}\right)$	$1$	$i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{476}(61,\cdot)$	476.bl	48	no	$1$	$1$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{31}{48}\right)$	$i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{16}\right)$
$\chi_{476}(65,\cdot)$	476.bn	48	no	$-1$	$1$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{13}{48}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{476}(67,\cdot)$	476.o	6	yes	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$
$\chi_{476}(69,\cdot)$	476.c	2	no	$-1$	$1$	$-1$	$-1$	$1$	$1$	$-1$	$1$	$-1$	$1$	$1$	$-1$
$\chi_{476}(71,\cdot)$	476.bd	16	no	$1$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{15}{16}\right)$	$i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{476}(73,\cdot)$	476.bl	48	no	$1$	$1$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{41}{48}\right)$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{476}(75,\cdot)$	476.bk	48	yes	$-1$	$1$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{31}{48}\right)$	$i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{16}\right)$
$\chi_{476}(79,\cdot)$	476.bm	48	yes	$1$	$1$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{43}{48}\right)$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{13}{16}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$476$
Structure	\(C_{2}\times C_{2}\times C_{48}\)
Order	$192$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(19\)	\(23\)	\(25\)	\(27\)
\(\chi_{476}(1,\cdot)\)	476.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{476}(3,\cdot)\)	476.bk	48	yes	\(-1\)	\(1\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{3}{16}\right)\)
\(\chi_{476}(5,\cdot)\)	476.bl	48	no	\(1\)	\(1\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{476}(9,\cdot)\)	476.bh	24	no	\(1\)	\(1\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{476}(11,\cdot)\)	476.bm	48	yes	\(1\)	\(1\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{13}{16}\right)\)
\(\chi_{476}(13,\cdot)\)	476.j	4	no	\(-1\)	\(1\)	\(-i\)	\(-i\)	\(-1\)	\(-i\)	\(-1\)	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(i\)
\(\chi_{476}(15,\cdot)\)	476.v	8	no	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(-i\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{476}(19,\cdot)\)	476.bj	24	yes	\(1\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{476}(23,\cdot)\)	476.bm	48	yes	\(1\)	\(1\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{5}{16}\right)\)
\(\chi_{476}(25,\cdot)\)	476.bh	24	no	\(1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{476}(27,\cdot)\)	476.bf	16	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{476}(29,\cdot)\)	476.bc	16	no	\(-1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{476}(31,\cdot)\)	476.bk	48	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{476}(33,\cdot)\)	476.n	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)
\(\chi_{476}(37,\cdot)\)	476.bn	48	no	\(-1\)	\(1\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{3}{16}\right)\)
\(\chi_{476}(39,\cdot)\)	476.bm	48	yes	\(1\)	\(1\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{476}(41,\cdot)\)	476.be	16	no	\(1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{476}(43,\cdot)\)	476.v	8	no	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(i\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{476}(45,\cdot)\)	476.bl	48	no	\(1\)	\(1\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{13}{16}\right)\)
\(\chi_{476}(47,\cdot)\)	476.z	12	yes	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)
\(\chi_{476}(53,\cdot)\)	476.bh	24	no	\(1\)	\(1\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{476}(55,\cdot)\)	476.k	4	yes	\(1\)	\(1\)	\(-i\)	\(i\)	\(-1\)	\(-i\)	\(-1\)	\(1\)	\(-1\)	\(-i\)	\(-1\)	\(i\)
\(\chi_{476}(57,\cdot)\)	476.bc	16	no	\(-1\)	\(1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)
\(\chi_{476}(59,\cdot)\)	476.bj	24	yes	\(1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(1\)	\(i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{476}(61,\cdot)\)	476.bl	48	no	\(1\)	\(1\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{16}\right)\)
\(\chi_{476}(65,\cdot)\)	476.bn	48	no	\(-1\)	\(1\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{476}(67,\cdot)\)	476.o	6	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)
\(\chi_{476}(69,\cdot)\)	476.c	2	no	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(-1\)
\(\chi_{476}(71,\cdot)\)	476.bd	16	no	\(1\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{476}(73,\cdot)\)	476.bl	48	no	\(1\)	\(1\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{476}(75,\cdot)\)	476.bk	48	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{16}\right)\)
\(\chi_{476}(79,\cdot)\)	476.bm	48	yes	\(1\)	\(1\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{13}{16}\right)\)

Introduction

L-functions

Modular forms

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Fields

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Properties

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Character group

First 32 of 192 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.