LMFDB - Group of Dirichlet characters of modulus 600

Show commands: PariGP / SageMath

sage: H = DirichletGroup(600)

pari: g = idealstar(,600,2)

Character group

sage: G.order() pari: g.no
Order	=	160
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{20}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{600}(151,\cdot)$, $\chi_{600}(301,\cdot)$, $\chi_{600}(401,\cdot)$, $\chi_{600}(577,\cdot)$

First 32 of 160 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	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{600}(1,\cdot)$	600.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{600}(7,\cdot)$	600.s	4	no	$1$	$1$	$-i$	$-1$	$-i$	$i$	$1$	$i$	$-1$	$-1$	$i$	$1$
$\chi_{600}(11,\cdot)$	600.bg	10	yes	$1$	$1$	$-1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{600}(13,\cdot)$	600.bs	20	no	$-1$	$1$	$-i$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{600}(17,\cdot)$	600.bu	20	no	$1$	$1$	$i$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{600}(19,\cdot)$	600.bh	10	no	$-1$	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{600}(23,\cdot)$	600.bo	20	no	$-1$	$1$	$i$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{600}(29,\cdot)$	600.z	10	yes	$-1$	$1$	$-1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{600}(31,\cdot)$	600.bd	10	no	$-1$	$1$	$-1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{600}(37,\cdot)$	600.bs	20	no	$-1$	$1$	$i$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{600}(41,\cdot)$	600.bl	10	no	$-1$	$1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{600}(43,\cdot)$	600.v	4	no	$1$	$1$	$i$	$1$	$-i$	$-i$	$-1$	$-i$	$1$	$-1$	$i$	$1$
$\chi_{600}(47,\cdot)$	600.bo	20	no	$-1$	$1$	$-i$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{600}(49,\cdot)$	600.f	2	no	$1$	$1$	$-1$	$1$	$-1$	$-1$	$1$	$-1$	$1$	$1$	$-1$	$1$
$\chi_{600}(53,\cdot)$	600.bp	20	yes	$1$	$1$	$-i$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{600}(59,\cdot)$	600.bk	10	yes	$1$	$1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{600}(61,\cdot)$	600.bm	10	no	$1$	$1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{600}(67,\cdot)$	600.bq	20	no	$1$	$1$	$-i$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{600}(71,\cdot)$	600.ba	10	no	$1$	$1$	$-1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{600}(73,\cdot)$	600.br	20	no	$-1$	$1$	$-i$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{600}(77,\cdot)$	600.bp	20	yes	$1$	$1$	$i$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{600}(79,\cdot)$	600.bn	10	no	$-1$	$1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{600}(83,\cdot)$	600.bv	20	yes	$-1$	$1$	$i$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{600}(89,\cdot)$	600.bf	10	no	$-1$	$1$	$-1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{600}(91,\cdot)$	600.bb	10	no	$-1$	$1$	$-1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{600}(97,\cdot)$	600.br	20	no	$-1$	$1$	$i$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{600}(101,\cdot)$	600.n	2	no	$-1$	$1$	$1$	$1$	$-1$	$-1$	$-1$	$-1$	$1$	$1$	$-1$	$-1$
$\chi_{600}(103,\cdot)$	600.bt	20	no	$1$	$1$	$i$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{600}(107,\cdot)$	600.q	4	no	$-1$	$1$	$-i$	$-1$	$i$	$-i$	$-1$	$-i$	$-1$	$-1$	$-i$	$-1$
$\chi_{600}(109,\cdot)$	600.be	10	no	$1$	$1$	$-1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{600}(113,\cdot)$	600.bu	20	no	$1$	$1$	$-i$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{600}(119,\cdot)$	600.bi	10	no	$1$	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{10}\right)$

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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	$600$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{20}\)
Order	$160$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{600}(1,\cdot)\)	600.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{600}(7,\cdot)\)	600.s	4	no	\(1\)	\(1\)	\(-i\)	\(-1\)	\(-i\)	\(i\)	\(1\)	\(i\)	\(-1\)	\(-1\)	\(i\)	\(1\)
\(\chi_{600}(11,\cdot)\)	600.bg	10	yes	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{600}(13,\cdot)\)	600.bs	20	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{600}(17,\cdot)\)	600.bu	20	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{600}(19,\cdot)\)	600.bh	10	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{600}(23,\cdot)\)	600.bo	20	no	\(-1\)	\(1\)	\(i\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{600}(29,\cdot)\)	600.z	10	yes	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{600}(31,\cdot)\)	600.bd	10	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{600}(37,\cdot)\)	600.bs	20	no	\(-1\)	\(1\)	\(i\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{600}(41,\cdot)\)	600.bl	10	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{600}(43,\cdot)\)	600.v	4	no	\(1\)	\(1\)	\(i\)	\(1\)	\(-i\)	\(-i\)	\(-1\)	\(-i\)	\(1\)	\(-1\)	\(i\)	\(1\)
\(\chi_{600}(47,\cdot)\)	600.bo	20	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{600}(49,\cdot)\)	600.f	2	no	\(1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(1\)
\(\chi_{600}(53,\cdot)\)	600.bp	20	yes	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{600}(59,\cdot)\)	600.bk	10	yes	\(1\)	\(1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{600}(61,\cdot)\)	600.bm	10	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{600}(67,\cdot)\)	600.bq	20	no	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{600}(71,\cdot)\)	600.ba	10	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{600}(73,\cdot)\)	600.br	20	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{600}(77,\cdot)\)	600.bp	20	yes	\(1\)	\(1\)	\(i\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{600}(79,\cdot)\)	600.bn	10	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{600}(83,\cdot)\)	600.bv	20	yes	\(-1\)	\(1\)	\(i\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{600}(89,\cdot)\)	600.bf	10	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{600}(91,\cdot)\)	600.bb	10	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{600}(97,\cdot)\)	600.br	20	no	\(-1\)	\(1\)	\(i\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{600}(101,\cdot)\)	600.n	2	no	\(-1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)
\(\chi_{600}(103,\cdot)\)	600.bt	20	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{600}(107,\cdot)\)	600.q	4	no	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(i\)	\(-i\)	\(-1\)	\(-i\)	\(-1\)	\(-1\)	\(-i\)	\(-1\)
\(\chi_{600}(109,\cdot)\)	600.be	10	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{600}(113,\cdot)\)	600.bu	20	no	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{600}(119,\cdot)\)	600.bi	10	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Character group

First 32 of 160 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.