LMFDB - Group of Dirichlet characters of modulus 288

Show commands: PariGP / SageMath

sage: H = DirichletGroup(288)

pari: g = idealstar(,288,2)

Character group

sage: G.order() pari: g.no
Order	=	96
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{24}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{288}(127,\cdot)$, $\chi_{288}(37,\cdot)$, $\chi_{288}(65,\cdot)$

First 32 of 96 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	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{288}(1,\cdot)$	288.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{288}(5,\cdot)$	288.be	24	yes	$-1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{13}{24}\right)$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{288}(7,\cdot)$	288.z	12	no	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$	$1$	$i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{288}(11,\cdot)$	288.bf	24	yes	$1$	$1$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{17}{24}\right)$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{288}(13,\cdot)$	288.bc	24	yes	$1$	$1$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{19}{24}\right)$	$-1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{288}(17,\cdot)$	288.h	2	no	$-1$	$1$	$1$	$1$	$1$	$-1$	$-1$	$-1$	$-1$	$1$	$1$	$1$
$\chi_{288}(19,\cdot)$	288.u	8	no	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$-i$	$-i$	$e\left(\frac{5}{8}\right)$	$-1$
$\chi_{288}(23,\cdot)$	288.y	12	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$-1$	$-i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{288}(25,\cdot)$	288.bb	12	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{12}\right)$	$1$	$-i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{288}(29,\cdot)$	288.be	24	yes	$-1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{23}{24}\right)$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{288}(31,\cdot)$	288.o	6	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{288}(35,\cdot)$	288.w	8	no	$1$	$1$	$e\left(\frac{7}{8}\right)$	$i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$1$	$e\left(\frac{1}{8}\right)$	$i$	$-i$	$e\left(\frac{5}{8}\right)$	$-1$
$\chi_{288}(37,\cdot)$	288.v	8	no	$1$	$1$	$e\left(\frac{1}{8}\right)$	$i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$-i$	$i$	$e\left(\frac{3}{8}\right)$	$1$
$\chi_{288}(41,\cdot)$	288.ba	12	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$-1$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{288}(43,\cdot)$	288.bd	24	yes	$-1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{17}{24}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{288}(47,\cdot)$	288.p	6	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{288}(49,\cdot)$	288.r	6	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{288}(53,\cdot)$	288.x	8	no	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$1$	$e\left(\frac{3}{8}\right)$	$i$	$i$	$e\left(\frac{3}{8}\right)$	$1$
$\chi_{288}(55,\cdot)$	288.m	4	no	$-1$	$1$	$-i$	$1$	$i$	$i$	$1$	$-i$	$1$	$-1$	$i$	$-1$
$\chi_{288}(59,\cdot)$	288.bf	24	yes	$1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{13}{24}\right)$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{288}(61,\cdot)$	288.bc	24	yes	$1$	$1$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{23}{24}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{288}(65,\cdot)$	288.q	6	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{288}(67,\cdot)$	288.bd	24	yes	$-1$	$1$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{7}{24}\right)$	$-1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{288}(71,\cdot)$	288.l	4	no	$1$	$1$	$-i$	$1$	$i$	$-i$	$-1$	$i$	$-1$	$-1$	$i$	$-1$
$\chi_{288}(73,\cdot)$	288.k	4	no	$1$	$1$	$-i$	$-1$	$-i$	$i$	$1$	$i$	$-1$	$-1$	$i$	$1$
$\chi_{288}(77,\cdot)$	288.be	24	yes	$-1$	$1$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{19}{24}\right)$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{288}(79,\cdot)$	288.t	6	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{288}(83,\cdot)$	288.bf	24	yes	$1$	$1$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{11}{24}\right)$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{288}(85,\cdot)$	288.bc	24	yes	$1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{24}\right)$	$-1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{288}(89,\cdot)$	288.j	4	no	$-1$	$1$	$-i$	$-1$	$-i$	$-i$	$-1$	$-i$	$1$	$-1$	$i$	$1$
$\chi_{288}(91,\cdot)$	288.u	8	no	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{3}{8}\right)$	$i$	$i$	$e\left(\frac{3}{8}\right)$	$-1$
$\chi_{288}(95,\cdot)$	288.s	6	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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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	$288$
Structure	\(C_{2}\times C_{2}\times C_{24}\)
Order	$96$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{288}(1,\cdot)\)	288.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{288}(5,\cdot)\)	288.be	24	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{288}(7,\cdot)\)	288.z	12	no	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(1\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{288}(11,\cdot)\)	288.bf	24	yes	\(1\)	\(1\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{288}(13,\cdot)\)	288.bc	24	yes	\(1\)	\(1\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{288}(17,\cdot)\)	288.h	2	no	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(1\)
\(\chi_{288}(19,\cdot)\)	288.u	8	no	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(-1\)
\(\chi_{288}(23,\cdot)\)	288.y	12	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{288}(25,\cdot)\)	288.bb	12	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{288}(29,\cdot)\)	288.be	24	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{288}(31,\cdot)\)	288.o	6	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{288}(35,\cdot)\)	288.w	8	no	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(-1\)
\(\chi_{288}(37,\cdot)\)	288.v	8	no	\(1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(1\)
\(\chi_{288}(41,\cdot)\)	288.ba	12	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{288}(43,\cdot)\)	288.bd	24	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{288}(47,\cdot)\)	288.p	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{288}(49,\cdot)\)	288.r	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{288}(53,\cdot)\)	288.x	8	no	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(1\)
\(\chi_{288}(55,\cdot)\)	288.m	4	no	\(-1\)	\(1\)	\(-i\)	\(1\)	\(i\)	\(i\)	\(1\)	\(-i\)	\(1\)	\(-1\)	\(i\)	\(-1\)
\(\chi_{288}(59,\cdot)\)	288.bf	24	yes	\(1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{288}(61,\cdot)\)	288.bc	24	yes	\(1\)	\(1\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{288}(65,\cdot)\)	288.q	6	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{288}(67,\cdot)\)	288.bd	24	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{288}(71,\cdot)\)	288.l	4	no	\(1\)	\(1\)	\(-i\)	\(1\)	\(i\)	\(-i\)	\(-1\)	\(i\)	\(-1\)	\(-1\)	\(i\)	\(-1\)
\(\chi_{288}(73,\cdot)\)	288.k	4	no	\(1\)	\(1\)	\(-i\)	\(-1\)	\(-i\)	\(i\)	\(1\)	\(i\)	\(-1\)	\(-1\)	\(i\)	\(1\)
\(\chi_{288}(77,\cdot)\)	288.be	24	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{288}(79,\cdot)\)	288.t	6	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{288}(83,\cdot)\)	288.bf	24	yes	\(1\)	\(1\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{288}(85,\cdot)\)	288.bc	24	yes	\(1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{288}(89,\cdot)\)	288.j	4	no	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(-i\)	\(-i\)	\(-1\)	\(-i\)	\(1\)	\(-1\)	\(i\)	\(1\)
\(\chi_{288}(91,\cdot)\)	288.u	8	no	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)
\(\chi_{288}(95,\cdot)\)	288.s	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

Properties

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Character group

First 32 of 96 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.