LMFDB - Group of Dirichlet characters of modulus 750

Show commands: PariGP / SageMath

sage: H = DirichletGroup(750)

pari: g = idealstar(,750,2)

Character group

sage: G.order() pari: g.no
Order	=	200
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{100}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{750}(251,\cdot)$, $\chi_{750}(127,\cdot)$

First 32 of 200 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	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{750}(1,\cdot)$	750.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{750}(7,\cdot)$	750.k	20	no	$-1$	$1$	$i$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{750}(11,\cdot)$	750.n	50	no	$-1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{47}{50}\right)$
$\chi_{750}(13,\cdot)$	750.q	100	no	$-1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{47}{100}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{9}{100}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{4}{25}\right)$
$\chi_{750}(17,\cdot)$	750.r	100	no	$1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{47}{100}\right)$	$e\left(\frac{79}{100}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{13}{100}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{17}{100}\right)$	$e\left(\frac{31}{50}\right)$
$\chi_{750}(19,\cdot)$	750.o	50	no	$1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{23}{25}\right)$
$\chi_{750}(23,\cdot)$	750.r	100	no	$1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{9}{100}\right)$	$e\left(\frac{13}{100}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{11}{100}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{99}{100}\right)$	$e\left(\frac{7}{50}\right)$
$\chi_{750}(29,\cdot)$	750.p	50	no	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{39}{50}\right)$
$\chi_{750}(31,\cdot)$	750.m	25	no	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{3}{25}\right)$
$\chi_{750}(37,\cdot)$	750.q	100	no	$-1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{17}{100}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{99}{100}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{41}{100}\right)$	$e\left(\frac{19}{25}\right)$
$\chi_{750}(41,\cdot)$	750.n	50	no	$-1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{43}{50}\right)$
$\chi_{750}(43,\cdot)$	750.k	20	no	$-1$	$1$	$-i$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{750}(47,\cdot)$	750.r	100	no	$1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{83}{100}\right)$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{57}{100}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{13}{100}\right)$	$e\left(\frac{9}{50}\right)$
$\chi_{750}(49,\cdot)$	750.h	10	no	$1$	$1$	$-1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{750}(53,\cdot)$	750.r	100	no	$1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{13}{100}\right)$	$e\left(\frac{41}{100}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{27}{100}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{49}{50}\right)$
$\chi_{750}(59,\cdot)$	750.p	50	no	$-1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{23}{50}\right)$
$\chi_{750}(61,\cdot)$	750.m	25	no	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{16}{25}\right)$
$\chi_{750}(67,\cdot)$	750.q	100	no	$-1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{49}{100}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{3}{100}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{77}{100}\right)$	$e\left(\frac{18}{25}\right)$
$\chi_{750}(71,\cdot)$	750.n	50	no	$-1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{9}{50}\right)$
$\chi_{750}(73,\cdot)$	750.q	100	no	$-1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{49}{100}\right)$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{1}{25}\right)$
$\chi_{750}(77,\cdot)$	750.r	100	no	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{79}{100}\right)$	$e\left(\frac{3}{100}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{41}{100}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{69}{100}\right)$	$e\left(\frac{17}{50}\right)$
$\chi_{750}(79,\cdot)$	750.o	50	no	$1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{2}{25}\right)$
$\chi_{750}(83,\cdot)$	750.r	100	no	$1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{77}{100}\right)$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{83}{100}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{47}{100}\right)$	$e\left(\frac{21}{50}\right)$
$\chi_{750}(89,\cdot)$	750.p	50	no	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{27}{50}\right)$
$\chi_{750}(91,\cdot)$	750.m	25	no	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{14}{25}\right)$
$\chi_{750}(97,\cdot)$	750.q	100	no	$-1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{1}{100}\right)$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{47}{100}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{73}{100}\right)$	$e\left(\frac{7}{25}\right)$
$\chi_{750}(101,\cdot)$	750.j	10	no	$-1$	$1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{750}(103,\cdot)$	750.q	100	no	$-1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{53}{100}\right)$	$e\left(\frac{71}{100}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{37}{100}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{83}{100}\right)$	$e\left(\frac{22}{25}\right)$
$\chi_{750}(107,\cdot)$	750.l	20	no	$1$	$1$	$i$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{750}(109,\cdot)$	750.o	50	no	$1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{19}{25}\right)$
$\chi_{750}(113,\cdot)$	750.r	100	no	$1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{1}{100}\right)$	$e\left(\frac{57}{100}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{79}{100}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{11}{100}\right)$	$e\left(\frac{23}{50}\right)$
$\chi_{750}(119,\cdot)$	750.p	50	no	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{1}{50}\right)$

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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	$750$
Structure	\(C_{2}\times C_{100}\)
Order	$200$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{750}(1,\cdot)\)	750.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{750}(7,\cdot)\)	750.k	20	no	\(-1\)	\(1\)	\(i\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{750}(11,\cdot)\)	750.n	50	no	\(-1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{47}{50}\right)\)
\(\chi_{750}(13,\cdot)\)	750.q	100	no	\(-1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{47}{100}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{9}{100}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{4}{25}\right)\)
\(\chi_{750}(17,\cdot)\)	750.r	100	no	\(1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{47}{100}\right)\)	\(e\left(\frac{79}{100}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{13}{100}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{17}{100}\right)\)	\(e\left(\frac{31}{50}\right)\)
\(\chi_{750}(19,\cdot)\)	750.o	50	no	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{23}{25}\right)\)
\(\chi_{750}(23,\cdot)\)	750.r	100	no	\(1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{9}{100}\right)\)	\(e\left(\frac{13}{100}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{11}{100}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{99}{100}\right)\)	\(e\left(\frac{7}{50}\right)\)
\(\chi_{750}(29,\cdot)\)	750.p	50	no	\(-1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{39}{50}\right)\)
\(\chi_{750}(31,\cdot)\)	750.m	25	no	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{3}{25}\right)\)
\(\chi_{750}(37,\cdot)\)	750.q	100	no	\(-1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{17}{100}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{99}{100}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{41}{100}\right)\)	\(e\left(\frac{19}{25}\right)\)
\(\chi_{750}(41,\cdot)\)	750.n	50	no	\(-1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{43}{50}\right)\)
\(\chi_{750}(43,\cdot)\)	750.k	20	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{750}(47,\cdot)\)	750.r	100	no	\(1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{83}{100}\right)\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{57}{100}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{13}{100}\right)\)	\(e\left(\frac{9}{50}\right)\)
\(\chi_{750}(49,\cdot)\)	750.h	10	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{750}(53,\cdot)\)	750.r	100	no	\(1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{13}{100}\right)\)	\(e\left(\frac{41}{100}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{27}{100}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{49}{50}\right)\)
\(\chi_{750}(59,\cdot)\)	750.p	50	no	\(-1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{23}{50}\right)\)
\(\chi_{750}(61,\cdot)\)	750.m	25	no	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{16}{25}\right)\)
\(\chi_{750}(67,\cdot)\)	750.q	100	no	\(-1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{49}{100}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{3}{100}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{77}{100}\right)\)	\(e\left(\frac{18}{25}\right)\)
\(\chi_{750}(71,\cdot)\)	750.n	50	no	\(-1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{9}{50}\right)\)
\(\chi_{750}(73,\cdot)\)	750.q	100	no	\(-1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{49}{100}\right)\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{1}{25}\right)\)
\(\chi_{750}(77,\cdot)\)	750.r	100	no	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{79}{100}\right)\)	\(e\left(\frac{3}{100}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{41}{100}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{69}{100}\right)\)	\(e\left(\frac{17}{50}\right)\)
\(\chi_{750}(79,\cdot)\)	750.o	50	no	\(1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{2}{25}\right)\)
\(\chi_{750}(83,\cdot)\)	750.r	100	no	\(1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{77}{100}\right)\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{83}{100}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{47}{100}\right)\)	\(e\left(\frac{21}{50}\right)\)
\(\chi_{750}(89,\cdot)\)	750.p	50	no	\(-1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{27}{50}\right)\)
\(\chi_{750}(91,\cdot)\)	750.m	25	no	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{14}{25}\right)\)
\(\chi_{750}(97,\cdot)\)	750.q	100	no	\(-1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{47}{100}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{73}{100}\right)\)	\(e\left(\frac{7}{25}\right)\)
\(\chi_{750}(101,\cdot)\)	750.j	10	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{750}(103,\cdot)\)	750.q	100	no	\(-1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{53}{100}\right)\)	\(e\left(\frac{71}{100}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{37}{100}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{83}{100}\right)\)	\(e\left(\frac{22}{25}\right)\)
\(\chi_{750}(107,\cdot)\)	750.l	20	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{750}(109,\cdot)\)	750.o	50	no	\(1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{19}{25}\right)\)
\(\chi_{750}(113,\cdot)\)	750.r	100	no	\(1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{57}{100}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{79}{100}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{11}{100}\right)\)	\(e\left(\frac{23}{50}\right)\)
\(\chi_{750}(119,\cdot)\)	750.p	50	no	\(-1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{1}{50}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

Properties

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Character group

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.