LMFDB - Group of Dirichlet characters of modulus 416

Show commands: PariGP / SageMath

sage: H = DirichletGroup(416)

pari: g = idealstar(,416,2)

Character group

sage: G.order() pari: g.no
Order	=	192
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{4}\times C_{24}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{416}(287,\cdot)$, $\chi_{416}(261,\cdot)$, $\chi_{416}(353,\cdot)$

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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$15$	$17$	$19$	$21$	$23$
$\chi_{416}(1,\cdot)$	416.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{416}(3,\cdot)$	416.by	24	yes	$-1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{416}(5,\cdot)$	416.bc	8	yes	$-1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-1$	$-i$	$e\left(\frac{7}{8}\right)$	$i$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$i$
$\chi_{416}(7,\cdot)$	416.bn	12	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$-1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$
$\chi_{416}(9,\cdot)$	416.br	12	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$-i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$e\left(\frac{1}{6}\right)$
$\chi_{416}(11,\cdot)$	416.cc	24	yes	$1$	$1$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{416}(15,\cdot)$	416.bk	12	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$-i$	$e\left(\frac{1}{3}\right)$
$\chi_{416}(17,\cdot)$	416.ba	6	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$
$\chi_{416}(19,\cdot)$	416.cc	24	yes	$1$	$1$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{416}(21,\cdot)$	416.bj	8	yes	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$1$	$-i$	$e\left(\frac{7}{8}\right)$	$-i$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$i$
$\chi_{416}(23,\cdot)$	416.bq	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$	$i$	$e\left(\frac{1}{3}\right)$
$\chi_{416}(25,\cdot)$	416.p	4	no	$1$	$1$	$-i$	$-i$	$1$	$-1$	$-i$	$-1$	$1$	$i$	$-i$	$-1$
$\chi_{416}(27,\cdot)$	416.bh	8	no	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-i$	$-i$	$e\left(\frac{1}{8}\right)$	$1$	$-1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$i$
$\chi_{416}(29,\cdot)$	416.ca	24	yes	$1$	$1$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{416}(31,\cdot)$	416.k	4	no	$1$	$1$	$-1$	$-i$	$-i$	$1$	$-i$	$i$	$-1$	$i$	$i$	$1$
$\chi_{416}(33,\cdot)$	416.bl	12	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$e\left(\frac{1}{6}\right)$
$\chi_{416}(35,\cdot)$	416.by	24	yes	$-1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{416}(37,\cdot)$	416.bw	24	yes	$-1$	$1$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{416}(41,\cdot)$	416.bm	12	no	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$-1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$
$\chi_{416}(43,\cdot)$	416.cb	24	yes	$-1$	$1$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{416}(45,\cdot)$	416.bw	24	yes	$-1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{416}(47,\cdot)$	416.u	4	no	$1$	$1$	$1$	$-i$	$i$	$1$	$-i$	$-i$	$-1$	$i$	$i$	$1$
$\chi_{416}(49,\cdot)$	416.ba	6	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$
$\chi_{416}(51,\cdot)$	416.be	8	yes	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$-i$	$i$	$e\left(\frac{3}{8}\right)$	$-1$	$-1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-i$
$\chi_{416}(53,\cdot)$	416.bf	8	no	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$i$	$-i$	$e\left(\frac{1}{8}\right)$	$-1$	$-1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-i$
$\chi_{416}(55,\cdot)$	416.bo	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$-i$	$e\left(\frac{1}{3}\right)$
$\chi_{416}(57,\cdot)$	416.r	4	no	$-1$	$1$	$-i$	$1$	$-i$	$-1$	$-1$	$-i$	$-1$	$-1$	$-1$	$1$
$\chi_{416}(59,\cdot)$	416.cc	24	yes	$1$	$1$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{416}(61,\cdot)$	416.ca	24	yes	$1$	$1$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{416}(63,\cdot)$	416.bu	12	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$-i$	$e\left(\frac{1}{3}\right)$
$\chi_{416}(67,\cdot)$	416.cc	24	yes	$1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{416}(69,\cdot)$	416.bz	24	yes	$1$	$1$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{12}\right)$

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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	$416$
Structure	\(C_{2}\times C_{4}\times C_{24}\)
Order	$192$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\(\chi_{416}(1,\cdot)\)	416.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{416}(3,\cdot)\)	416.by	24	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{416}(5,\cdot)\)	416.bc	8	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(i\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(i\)
\(\chi_{416}(7,\cdot)\)	416.bn	12	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{416}(9,\cdot)\)	416.br	12	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{416}(11,\cdot)\)	416.cc	24	yes	\(1\)	\(1\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{416}(15,\cdot)\)	416.bk	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{416}(17,\cdot)\)	416.ba	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{416}(19,\cdot)\)	416.cc	24	yes	\(1\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{416}(21,\cdot)\)	416.bj	8	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(i\)
\(\chi_{416}(23,\cdot)\)	416.bq	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{416}(25,\cdot)\)	416.p	4	no	\(1\)	\(1\)	\(-i\)	\(-i\)	\(1\)	\(-1\)	\(-i\)	\(-1\)	\(1\)	\(i\)	\(-i\)	\(-1\)
\(\chi_{416}(27,\cdot)\)	416.bh	8	no	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(i\)
\(\chi_{416}(29,\cdot)\)	416.ca	24	yes	\(1\)	\(1\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{416}(31,\cdot)\)	416.k	4	no	\(1\)	\(1\)	\(-1\)	\(-i\)	\(-i\)	\(1\)	\(-i\)	\(i\)	\(-1\)	\(i\)	\(i\)	\(1\)
\(\chi_{416}(33,\cdot)\)	416.bl	12	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{416}(35,\cdot)\)	416.by	24	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{416}(37,\cdot)\)	416.bw	24	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{416}(41,\cdot)\)	416.bm	12	no	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{416}(43,\cdot)\)	416.cb	24	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{416}(45,\cdot)\)	416.bw	24	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{416}(47,\cdot)\)	416.u	4	no	\(1\)	\(1\)	\(1\)	\(-i\)	\(i\)	\(1\)	\(-i\)	\(-i\)	\(-1\)	\(i\)	\(i\)	\(1\)
\(\chi_{416}(49,\cdot)\)	416.ba	6	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{416}(51,\cdot)\)	416.be	8	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)
\(\chi_{416}(53,\cdot)\)	416.bf	8	no	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)
\(\chi_{416}(55,\cdot)\)	416.bo	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{416}(57,\cdot)\)	416.r	4	no	\(-1\)	\(1\)	\(-i\)	\(1\)	\(-i\)	\(-1\)	\(-1\)	\(-i\)	\(-1\)	\(-1\)	\(-1\)	\(1\)
\(\chi_{416}(59,\cdot)\)	416.cc	24	yes	\(1\)	\(1\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{416}(61,\cdot)\)	416.ca	24	yes	\(1\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{416}(63,\cdot)\)	416.bu	12	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{416}(67,\cdot)\)	416.cc	24	yes	\(1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{416}(69,\cdot)\)	416.bz	24	yes	\(1\)	\(1\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{12}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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.