LMFDB - Group of Dirichlet characters of modulus 1125

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1125)

pari: g = idealstar(,1125,2)

Character group

sage: G.order() pari: g.no
Order	=	600
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{300}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1125}(1001,\cdot)$, $\chi_{1125}(127,\cdot)$

First 32 of 600 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	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{1125}(1,\cdot)$	1125.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1125}(2,\cdot)$	1125.bj	300	yes	$1$	$1$	$e\left(\frac{53}{300}\right)$	$e\left(\frac{53}{150}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{53}{100}\right)$	$e\left(\frac{139}{150}\right)$	$e\left(\frac{217}{300}\right)$	$e\left(\frac{52}{75}\right)$	$e\left(\frac{53}{75}\right)$	$e\left(\frac{23}{100}\right)$	$e\left(\frac{9}{50}\right)$
$\chi_{1125}(4,\cdot)$	1125.bf	150	yes	$1$	$1$	$e\left(\frac{53}{150}\right)$	$e\left(\frac{53}{75}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{64}{75}\right)$	$e\left(\frac{67}{150}\right)$	$e\left(\frac{29}{75}\right)$	$e\left(\frac{31}{75}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{9}{25}\right)$
$\chi_{1125}(7,\cdot)$	1125.bb	60	no	$-1$	$1$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{1125}(8,\cdot)$	1125.be	100	no	$1$	$1$	$e\left(\frac{53}{100}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{59}{100}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{17}{100}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{69}{100}\right)$	$e\left(\frac{27}{50}\right)$
$\chi_{1125}(11,\cdot)$	1125.bh	150	yes	$-1$	$1$	$e\left(\frac{139}{150}\right)$	$e\left(\frac{64}{75}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{139}{150}\right)$	$e\left(\frac{73}{75}\right)$	$e\left(\frac{29}{150}\right)$	$e\left(\frac{53}{75}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{17}{25}\right)$
$\chi_{1125}(13,\cdot)$	1125.bi	300	yes	$-1$	$1$	$e\left(\frac{217}{300}\right)$	$e\left(\frac{67}{150}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{17}{100}\right)$	$e\left(\frac{73}{75}\right)$	$e\left(\frac{263}{300}\right)$	$e\left(\frac{31}{150}\right)$	$e\left(\frac{67}{75}\right)$	$e\left(\frac{47}{100}\right)$	$e\left(\frac{1}{50}\right)$
$\chi_{1125}(14,\cdot)$	1125.bg	150	yes	$-1$	$1$	$e\left(\frac{52}{75}\right)$	$e\left(\frac{29}{75}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{29}{150}\right)$	$e\left(\frac{31}{150}\right)$	$e\left(\frac{19}{150}\right)$	$e\left(\frac{58}{75}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{12}{25}\right)$
$\chi_{1125}(16,\cdot)$	1125.bc	75	yes	$1$	$1$	$e\left(\frac{53}{75}\right)$	$e\left(\frac{31}{75}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{53}{75}\right)$	$e\left(\frac{67}{75}\right)$	$e\left(\frac{58}{75}\right)$	$e\left(\frac{62}{75}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{18}{25}\right)$
$\chi_{1125}(17,\cdot)$	1125.be	100	no	$1$	$1$	$e\left(\frac{23}{100}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{69}{100}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{47}{100}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{79}{100}\right)$	$e\left(\frac{7}{50}\right)$
$\chi_{1125}(19,\cdot)$	1125.y	50	no	$1$	$1$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{6}{25}\right)$
$\chi_{1125}(22,\cdot)$	1125.bi	300	yes	$-1$	$1$	$e\left(\frac{31}{300}\right)$	$e\left(\frac{31}{150}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{64}{75}\right)$	$e\left(\frac{209}{300}\right)$	$e\left(\frac{133}{150}\right)$	$e\left(\frac{31}{75}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{43}{50}\right)$
$\chi_{1125}(23,\cdot)$	1125.bj	300	yes	$1$	$1$	$e\left(\frac{43}{300}\right)$	$e\left(\frac{43}{150}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{59}{150}\right)$	$e\left(\frac{227}{300}\right)$	$e\left(\frac{62}{75}\right)$	$e\left(\frac{43}{75}\right)$	$e\left(\frac{13}{100}\right)$	$e\left(\frac{29}{50}\right)$
$\chi_{1125}(26,\cdot)$	1125.n	10	no	$-1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{1125}(28,\cdot)$	1125.bd	100	no	$-1$	$1$	$e\left(\frac{87}{100}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{61}{100}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{93}{100}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{51}{100}\right)$	$e\left(\frac{33}{50}\right)$
$\chi_{1125}(29,\cdot)$	1125.bg	150	yes	$-1$	$1$	$e\left(\frac{59}{75}\right)$	$e\left(\frac{43}{75}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{43}{150}\right)$	$e\left(\frac{77}{150}\right)$	$e\left(\frac{23}{150}\right)$	$e\left(\frac{11}{75}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{4}{25}\right)$
$\chi_{1125}(31,\cdot)$	1125.bc	75	yes	$1$	$1$	$e\left(\frac{61}{75}\right)$	$e\left(\frac{47}{75}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{61}{75}\right)$	$e\left(\frac{29}{75}\right)$	$e\left(\frac{71}{75}\right)$	$e\left(\frac{19}{75}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{16}{25}\right)$
$\chi_{1125}(32,\cdot)$	1125.ba	60	no	$1$	$1$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{1125}(34,\cdot)$	1125.bf	150	yes	$1$	$1$	$e\left(\frac{61}{150}\right)$	$e\left(\frac{61}{75}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{29}{150}\right)$	$e\left(\frac{73}{75}\right)$	$e\left(\frac{47}{75}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{8}{25}\right)$
$\chi_{1125}(37,\cdot)$	1125.bd	100	no	$-1$	$1$	$e\left(\frac{29}{100}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{87}{100}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{17}{100}\right)$	$e\left(\frac{11}{50}\right)$
$\chi_{1125}(38,\cdot)$	1125.bj	300	yes	$1$	$1$	$e\left(\frac{107}{300}\right)$	$e\left(\frac{107}{150}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{91}{150}\right)$	$e\left(\frac{223}{300}\right)$	$e\left(\frac{13}{75}\right)$	$e\left(\frac{32}{75}\right)$	$e\left(\frac{37}{100}\right)$	$e\left(\frac{21}{50}\right)$
$\chi_{1125}(41,\cdot)$	1125.bh	150	yes	$-1$	$1$	$e\left(\frac{41}{150}\right)$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{41}{150}\right)$	$e\left(\frac{62}{75}\right)$	$e\left(\frac{1}{150}\right)$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{23}{25}\right)$
$\chi_{1125}(43,\cdot)$	1125.bb	60	no	$-1$	$1$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{1125}(44,\cdot)$	1125.z	50	no	$-1$	$1$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{1}{25}\right)$
$\chi_{1125}(46,\cdot)$	1125.t	25	no	$1$	$1$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{19}{25}\right)$
$\chi_{1125}(47,\cdot)$	1125.bj	300	yes	$1$	$1$	$e\left(\frac{41}{300}\right)$	$e\left(\frac{41}{150}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{41}{100}\right)$	$e\left(\frac{133}{150}\right)$	$e\left(\frac{49}{300}\right)$	$e\left(\frac{19}{75}\right)$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{23}{50}\right)$
$\chi_{1125}(49,\cdot)$	1125.v	30	no	$1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{1125}(52,\cdot)$	1125.bi	300	yes	$-1$	$1$	$e\left(\frac{23}{300}\right)$	$e\left(\frac{23}{150}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{23}{100}\right)$	$e\left(\frac{62}{75}\right)$	$e\left(\frac{97}{300}\right)$	$e\left(\frac{89}{150}\right)$	$e\left(\frac{23}{75}\right)$	$e\left(\frac{93}{100}\right)$	$e\left(\frac{19}{50}\right)$
$\chi_{1125}(53,\cdot)$	1125.be	100	no	$1$	$1$	$e\left(\frac{17}{100}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{51}{100}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{13}{100}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{41}{100}\right)$	$e\left(\frac{3}{50}\right)$
$\chi_{1125}(56,\cdot)$	1125.bh	150	yes	$-1$	$1$	$e\left(\frac{7}{150}\right)$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{7}{150}\right)$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{77}{150}\right)$	$e\left(\frac{14}{75}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{21}{25}\right)$
$\chi_{1125}(58,\cdot)$	1125.bi	300	yes	$-1$	$1$	$e\left(\frac{289}{300}\right)$	$e\left(\frac{139}{150}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{16}{75}\right)$	$e\left(\frac{71}{300}\right)$	$e\left(\frac{127}{150}\right)$	$e\left(\frac{64}{75}\right)$	$e\left(\frac{99}{100}\right)$	$e\left(\frac{17}{50}\right)$
$\chi_{1125}(59,\cdot)$	1125.bg	150	yes	$-1$	$1$	$e\left(\frac{13}{75}\right)$	$e\left(\frac{26}{75}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{101}{150}\right)$	$e\left(\frac{139}{150}\right)$	$e\left(\frac{61}{150}\right)$	$e\left(\frac{52}{75}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{3}{25}\right)$

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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	$1125$
Structure	\(C_{2}\times C_{300}\)
Order	$600$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)
\(\chi_{1125}(1,\cdot)\)	1125.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1125}(2,\cdot)\)	1125.bj	300	yes	\(1\)	\(1\)	\(e\left(\frac{53}{300}\right)\)	\(e\left(\frac{53}{150}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{53}{100}\right)\)	\(e\left(\frac{139}{150}\right)\)	\(e\left(\frac{217}{300}\right)\)	\(e\left(\frac{52}{75}\right)\)	\(e\left(\frac{53}{75}\right)\)	\(e\left(\frac{23}{100}\right)\)	\(e\left(\frac{9}{50}\right)\)
\(\chi_{1125}(4,\cdot)\)	1125.bf	150	yes	\(1\)	\(1\)	\(e\left(\frac{53}{150}\right)\)	\(e\left(\frac{53}{75}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{64}{75}\right)\)	\(e\left(\frac{67}{150}\right)\)	\(e\left(\frac{29}{75}\right)\)	\(e\left(\frac{31}{75}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{9}{25}\right)\)
\(\chi_{1125}(7,\cdot)\)	1125.bb	60	no	\(-1\)	\(1\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{1125}(8,\cdot)\)	1125.be	100	no	\(1\)	\(1\)	\(e\left(\frac{53}{100}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{59}{100}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{17}{100}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{69}{100}\right)\)	\(e\left(\frac{27}{50}\right)\)
\(\chi_{1125}(11,\cdot)\)	1125.bh	150	yes	\(-1\)	\(1\)	\(e\left(\frac{139}{150}\right)\)	\(e\left(\frac{64}{75}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{139}{150}\right)\)	\(e\left(\frac{73}{75}\right)\)	\(e\left(\frac{29}{150}\right)\)	\(e\left(\frac{53}{75}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{17}{25}\right)\)
\(\chi_{1125}(13,\cdot)\)	1125.bi	300	yes	\(-1\)	\(1\)	\(e\left(\frac{217}{300}\right)\)	\(e\left(\frac{67}{150}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{17}{100}\right)\)	\(e\left(\frac{73}{75}\right)\)	\(e\left(\frac{263}{300}\right)\)	\(e\left(\frac{31}{150}\right)\)	\(e\left(\frac{67}{75}\right)\)	\(e\left(\frac{47}{100}\right)\)	\(e\left(\frac{1}{50}\right)\)
\(\chi_{1125}(14,\cdot)\)	1125.bg	150	yes	\(-1\)	\(1\)	\(e\left(\frac{52}{75}\right)\)	\(e\left(\frac{29}{75}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{29}{150}\right)\)	\(e\left(\frac{31}{150}\right)\)	\(e\left(\frac{19}{150}\right)\)	\(e\left(\frac{58}{75}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{12}{25}\right)\)
\(\chi_{1125}(16,\cdot)\)	1125.bc	75	yes	\(1\)	\(1\)	\(e\left(\frac{53}{75}\right)\)	\(e\left(\frac{31}{75}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{53}{75}\right)\)	\(e\left(\frac{67}{75}\right)\)	\(e\left(\frac{58}{75}\right)\)	\(e\left(\frac{62}{75}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{18}{25}\right)\)
\(\chi_{1125}(17,\cdot)\)	1125.be	100	no	\(1\)	\(1\)	\(e\left(\frac{23}{100}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{69}{100}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{47}{100}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{79}{100}\right)\)	\(e\left(\frac{7}{50}\right)\)
\(\chi_{1125}(19,\cdot)\)	1125.y	50	no	\(1\)	\(1\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{6}{25}\right)\)
\(\chi_{1125}(22,\cdot)\)	1125.bi	300	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{300}\right)\)	\(e\left(\frac{31}{150}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{64}{75}\right)\)	\(e\left(\frac{209}{300}\right)\)	\(e\left(\frac{133}{150}\right)\)	\(e\left(\frac{31}{75}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{43}{50}\right)\)
\(\chi_{1125}(23,\cdot)\)	1125.bj	300	yes	\(1\)	\(1\)	\(e\left(\frac{43}{300}\right)\)	\(e\left(\frac{43}{150}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{59}{150}\right)\)	\(e\left(\frac{227}{300}\right)\)	\(e\left(\frac{62}{75}\right)\)	\(e\left(\frac{43}{75}\right)\)	\(e\left(\frac{13}{100}\right)\)	\(e\left(\frac{29}{50}\right)\)
\(\chi_{1125}(26,\cdot)\)	1125.n	10	no	\(-1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{1125}(28,\cdot)\)	1125.bd	100	no	\(-1\)	\(1\)	\(e\left(\frac{87}{100}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{61}{100}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{93}{100}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{51}{100}\right)\)	\(e\left(\frac{33}{50}\right)\)
\(\chi_{1125}(29,\cdot)\)	1125.bg	150	yes	\(-1\)	\(1\)	\(e\left(\frac{59}{75}\right)\)	\(e\left(\frac{43}{75}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{43}{150}\right)\)	\(e\left(\frac{77}{150}\right)\)	\(e\left(\frac{23}{150}\right)\)	\(e\left(\frac{11}{75}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{4}{25}\right)\)
\(\chi_{1125}(31,\cdot)\)	1125.bc	75	yes	\(1\)	\(1\)	\(e\left(\frac{61}{75}\right)\)	\(e\left(\frac{47}{75}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{61}{75}\right)\)	\(e\left(\frac{29}{75}\right)\)	\(e\left(\frac{71}{75}\right)\)	\(e\left(\frac{19}{75}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{16}{25}\right)\)
\(\chi_{1125}(32,\cdot)\)	1125.ba	60	no	\(1\)	\(1\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{1125}(34,\cdot)\)	1125.bf	150	yes	\(1\)	\(1\)	\(e\left(\frac{61}{150}\right)\)	\(e\left(\frac{61}{75}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{68}{75}\right)\)	\(e\left(\frac{29}{150}\right)\)	\(e\left(\frac{73}{75}\right)\)	\(e\left(\frac{47}{75}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{8}{25}\right)\)
\(\chi_{1125}(37,\cdot)\)	1125.bd	100	no	\(-1\)	\(1\)	\(e\left(\frac{29}{100}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{87}{100}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{17}{100}\right)\)	\(e\left(\frac{11}{50}\right)\)
\(\chi_{1125}(38,\cdot)\)	1125.bj	300	yes	\(1\)	\(1\)	\(e\left(\frac{107}{300}\right)\)	\(e\left(\frac{107}{150}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{91}{150}\right)\)	\(e\left(\frac{223}{300}\right)\)	\(e\left(\frac{13}{75}\right)\)	\(e\left(\frac{32}{75}\right)\)	\(e\left(\frac{37}{100}\right)\)	\(e\left(\frac{21}{50}\right)\)
\(\chi_{1125}(41,\cdot)\)	1125.bh	150	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{150}\right)\)	\(e\left(\frac{41}{75}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{41}{150}\right)\)	\(e\left(\frac{62}{75}\right)\)	\(e\left(\frac{1}{150}\right)\)	\(e\left(\frac{7}{75}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{23}{25}\right)\)
\(\chi_{1125}(43,\cdot)\)	1125.bb	60	no	\(-1\)	\(1\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{1125}(44,\cdot)\)	1125.z	50	no	\(-1\)	\(1\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{1}{25}\right)\)
\(\chi_{1125}(46,\cdot)\)	1125.t	25	no	\(1\)	\(1\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{19}{25}\right)\)
\(\chi_{1125}(47,\cdot)\)	1125.bj	300	yes	\(1\)	\(1\)	\(e\left(\frac{41}{300}\right)\)	\(e\left(\frac{41}{150}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{41}{100}\right)\)	\(e\left(\frac{133}{150}\right)\)	\(e\left(\frac{49}{300}\right)\)	\(e\left(\frac{19}{75}\right)\)	\(e\left(\frac{41}{75}\right)\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{23}{50}\right)\)
\(\chi_{1125}(49,\cdot)\)	1125.v	30	no	\(1\)	\(1\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{1125}(52,\cdot)\)	1125.bi	300	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{300}\right)\)	\(e\left(\frac{23}{150}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{23}{100}\right)\)	\(e\left(\frac{62}{75}\right)\)	\(e\left(\frac{97}{300}\right)\)	\(e\left(\frac{89}{150}\right)\)	\(e\left(\frac{23}{75}\right)\)	\(e\left(\frac{93}{100}\right)\)	\(e\left(\frac{19}{50}\right)\)
\(\chi_{1125}(53,\cdot)\)	1125.be	100	no	\(1\)	\(1\)	\(e\left(\frac{17}{100}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{51}{100}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{13}{100}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{41}{100}\right)\)	\(e\left(\frac{3}{50}\right)\)
\(\chi_{1125}(56,\cdot)\)	1125.bh	150	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{150}\right)\)	\(e\left(\frac{7}{75}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{7}{150}\right)\)	\(e\left(\frac{49}{75}\right)\)	\(e\left(\frac{77}{150}\right)\)	\(e\left(\frac{14}{75}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{21}{25}\right)\)
\(\chi_{1125}(58,\cdot)\)	1125.bi	300	yes	\(-1\)	\(1\)	\(e\left(\frac{289}{300}\right)\)	\(e\left(\frac{139}{150}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{16}{75}\right)\)	\(e\left(\frac{71}{300}\right)\)	\(e\left(\frac{127}{150}\right)\)	\(e\left(\frac{64}{75}\right)\)	\(e\left(\frac{99}{100}\right)\)	\(e\left(\frac{17}{50}\right)\)
\(\chi_{1125}(59,\cdot)\)	1125.bg	150	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{75}\right)\)	\(e\left(\frac{26}{75}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{101}{150}\right)\)	\(e\left(\frac{139}{150}\right)\)	\(e\left(\frac{61}{150}\right)\)	\(e\left(\frac{52}{75}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{3}{25}\right)\)

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L-functions

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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.