LMFDB - Group of Dirichlet characters of modulus 875

sage:H = DirichletGroup(875)

pari:g = idealstar(,875,2)

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	=	$\chi_{875}(127,\cdot)$, $\chi_{875}(626,\cdot)$

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	$-1$	$1$	$2$	$3$	$4$	$6$	$8$	$9$	$11$	$12$	$13$	$16$
$\chi_{875}(1,\cdot)$	875.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{875}(2,\cdot)$	875.bi	300	yes	$-1$	$1$	$e\left(\frac{203}{300}\right)$	$e\left(\frac{121}{300}\right)$	$e\left(\frac{53}{150}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{3}{100}\right)$	$e\left(\frac{121}{150}\right)$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{227}{300}\right)$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{53}{75}\right)$
$\chi_{875}(3,\cdot)$	875.bj	300	yes	$1$	$1$	$e\left(\frac{121}{300}\right)$	$e\left(\frac{197}{300}\right)$	$e\left(\frac{121}{150}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{47}{150}\right)$	$e\left(\frac{74}{75}\right)$	$e\left(\frac{139}{300}\right)$	$e\left(\frac{23}{100}\right)$	$e\left(\frac{46}{75}\right)$
$\chi_{875}(4,\cdot)$	875.bg	150	yes	$1$	$1$	$e\left(\frac{53}{150}\right)$	$e\left(\frac{121}{150}\right)$	$e\left(\frac{53}{75}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{46}{75}\right)$	$e\left(\frac{14}{75}\right)$	$e\left(\frac{77}{150}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{31}{75}\right)$
$\chi_{875}(6,\cdot)$	875.x	50	yes	$-1$	$1$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{8}{25}\right)$
$\chi_{875}(8,\cdot)$	875.be	100	no	$-1$	$1$	$e\left(\frac{3}{100}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{9}{100}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{27}{100}\right)$	$e\left(\frac{17}{100}\right)$	$e\left(\frac{3}{25}\right)$
$\chi_{875}(9,\cdot)$	875.bg	150	yes	$1$	$1$	$e\left(\frac{121}{150}\right)$	$e\left(\frac{47}{150}\right)$	$e\left(\frac{46}{75}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{47}{75}\right)$	$e\left(\frac{73}{75}\right)$	$e\left(\frac{139}{150}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{17}{75}\right)$
$\chi_{875}(11,\cdot)$	875.bc	75	yes	$1$	$1$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{74}{75}\right)$	$e\left(\frac{14}{75}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{73}{75}\right)$	$e\left(\frac{32}{75}\right)$	$e\left(\frac{13}{75}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{28}{75}\right)$
$\chi_{875}(12,\cdot)$	875.bj	300	yes	$1$	$1$	$e\left(\frac{227}{300}\right)$	$e\left(\frac{139}{300}\right)$	$e\left(\frac{77}{150}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{27}{100}\right)$	$e\left(\frac{139}{150}\right)$	$e\left(\frac{13}{75}\right)$	$e\left(\frac{293}{300}\right)$	$e\left(\frac{1}{100}\right)$	$e\left(\frac{2}{75}\right)$
$\chi_{875}(13,\cdot)$	875.bd	100	yes	$1$	$1$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{23}{100}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{17}{100}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{1}{100}\right)$	$e\left(\frac{71}{100}\right)$	$e\left(\frac{14}{25}\right)$
$\chi_{875}(16,\cdot)$	875.bc	75	yes	$1$	$1$	$e\left(\frac{53}{75}\right)$	$e\left(\frac{46}{75}\right)$	$e\left(\frac{31}{75}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{17}{75}\right)$	$e\left(\frac{28}{75}\right)$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{62}{75}\right)$
$\chi_{875}(17,\cdot)$	875.bj	300	yes	$1$	$1$	$e\left(\frac{19}{300}\right)$	$e\left(\frac{83}{300}\right)$	$e\left(\frac{19}{150}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{19}{100}\right)$	$e\left(\frac{83}{150}\right)$	$e\left(\frac{11}{75}\right)$	$e\left(\frac{121}{300}\right)$	$e\left(\frac{97}{100}\right)$	$e\left(\frac{19}{75}\right)$
$\chi_{875}(18,\cdot)$	875.ba	60	no	$-1$	$1$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{875}(19,\cdot)$	875.bf	150	yes	$-1$	$1$	$e\left(\frac{127}{150}\right)$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{52}{75}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{14}{75}\right)$	$e\left(\frac{1}{75}\right)$	$e\left(\frac{59}{75}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{29}{75}\right)$
$\chi_{875}(22,\cdot)$	875.be	100	no	$-1$	$1$	$e\left(\frac{77}{100}\right)$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{93}{100}\right)$	$e\left(\frac{3}{100}\right)$	$e\left(\frac{2}{25}\right)$
$\chi_{875}(23,\cdot)$	875.bi	300	yes	$-1$	$1$	$e\left(\frac{293}{300}\right)$	$e\left(\frac{151}{300}\right)$	$e\left(\frac{143}{150}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{93}{100}\right)$	$e\left(\frac{1}{150}\right)$	$e\left(\frac{67}{75}\right)$	$e\left(\frac{137}{300}\right)$	$e\left(\frac{9}{100}\right)$	$e\left(\frac{68}{75}\right)$
$\chi_{875}(24,\cdot)$	875.v	30	no	$-1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{875}(26,\cdot)$	875.w	30	no	$-1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{15}\right)$
$\chi_{875}(27,\cdot)$	875.bd	100	yes	$1$	$1$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{97}{100}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{63}{100}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{69}{100}\right)$	$e\left(\frac{21}{25}\right)$
$\chi_{875}(29,\cdot)$	875.y	50	no	$1$	$1$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{12}{25}\right)$
$\chi_{875}(31,\cdot)$	875.bh	150	yes	$-1$	$1$	$e\left(\frac{61}{75}\right)$	$e\left(\frac{79}{150}\right)$	$e\left(\frac{47}{75}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{4}{75}\right)$	$e\left(\frac{11}{75}\right)$	$e\left(\frac{23}{150}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{19}{75}\right)$
$\chi_{875}(32,\cdot)$	875.ba	60	no	$-1$	$1$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{8}{15}\right)$
$\chi_{875}(33,\cdot)$	875.bj	300	yes	$1$	$1$	$e\left(\frac{149}{300}\right)$	$e\left(\frac{193}{300}\right)$	$e\left(\frac{149}{150}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{49}{100}\right)$	$e\left(\frac{43}{150}\right)$	$e\left(\frac{31}{75}\right)$	$e\left(\frac{191}{300}\right)$	$e\left(\frac{87}{100}\right)$	$e\left(\frac{74}{75}\right)$
$\chi_{875}(34,\cdot)$	875.z	50	yes	$-1$	$1$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{24}{25}\right)$
$\chi_{875}(36,\cdot)$	875.t	25	no	$1$	$1$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{16}{25}\right)$
$\chi_{875}(37,\cdot)$	875.bi	300	yes	$-1$	$1$	$e\left(\frac{287}{300}\right)$	$e\left(\frac{109}{300}\right)$	$e\left(\frac{137}{150}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{87}{100}\right)$	$e\left(\frac{109}{150}\right)$	$e\left(\frac{28}{75}\right)$	$e\left(\frac{83}{300}\right)$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{62}{75}\right)$
$\chi_{875}(38,\cdot)$	875.bj	300	yes	$1$	$1$	$e\left(\frac{157}{300}\right)$	$e\left(\frac{149}{300}\right)$	$e\left(\frac{7}{150}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{57}{100}\right)$	$e\left(\frac{149}{150}\right)$	$e\left(\frac{8}{75}\right)$	$e\left(\frac{163}{300}\right)$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{7}{75}\right)$
$\chi_{875}(39,\cdot)$	875.bg	150	yes	$1$	$1$	$e\left(\frac{119}{150}\right)$	$e\left(\frac{133}{150}\right)$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{58}{75}\right)$	$e\left(\frac{47}{75}\right)$	$e\left(\frac{71}{150}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{13}{75}\right)$
$\chi_{875}(41,\cdot)$	875.x	50	yes	$-1$	$1$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{19}{25}\right)$
$\chi_{875}(43,\cdot)$	875.r	20	no	$-1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{875}(44,\cdot)$	875.bg	150	yes	$1$	$1$	$e\left(\frac{67}{150}\right)$	$e\left(\frac{119}{150}\right)$	$e\left(\frac{67}{75}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{46}{75}\right)$	$e\left(\frac{103}{150}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{59}{75}\right)$
$\chi_{875}(46,\cdot)$	875.bc	75	yes	$1$	$1$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{23}{75}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{61}{75}\right)$	$e\left(\frac{74}{75}\right)$	$e\left(\frac{16}{75}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{46}{75}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$875$
Structure	\(C_{2}\times C_{300}\)
Order	$600$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)	\(16\)
\(\chi_{875}(1,\cdot)\)	875.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{875}(2,\cdot)\)	875.bi	300	yes	\(-1\)	\(1\)	\(e\left(\frac{203}{300}\right)\)	\(e\left(\frac{121}{300}\right)\)	\(e\left(\frac{53}{150}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{3}{100}\right)\)	\(e\left(\frac{121}{150}\right)\)	\(e\left(\frac{7}{75}\right)\)	\(e\left(\frac{227}{300}\right)\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{53}{75}\right)\)
\(\chi_{875}(3,\cdot)\)	875.bj	300	yes	\(1\)	\(1\)	\(e\left(\frac{121}{300}\right)\)	\(e\left(\frac{197}{300}\right)\)	\(e\left(\frac{121}{150}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{47}{150}\right)\)	\(e\left(\frac{74}{75}\right)\)	\(e\left(\frac{139}{300}\right)\)	\(e\left(\frac{23}{100}\right)\)	\(e\left(\frac{46}{75}\right)\)
\(\chi_{875}(4,\cdot)\)	875.bg	150	yes	\(1\)	\(1\)	\(e\left(\frac{53}{150}\right)\)	\(e\left(\frac{121}{150}\right)\)	\(e\left(\frac{53}{75}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{46}{75}\right)\)	\(e\left(\frac{14}{75}\right)\)	\(e\left(\frac{77}{150}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{31}{75}\right)\)
\(\chi_{875}(6,\cdot)\)	875.x	50	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{8}{25}\right)\)
\(\chi_{875}(8,\cdot)\)	875.be	100	no	\(-1\)	\(1\)	\(e\left(\frac{3}{100}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{9}{100}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{27}{100}\right)\)	\(e\left(\frac{17}{100}\right)\)	\(e\left(\frac{3}{25}\right)\)
\(\chi_{875}(9,\cdot)\)	875.bg	150	yes	\(1\)	\(1\)	\(e\left(\frac{121}{150}\right)\)	\(e\left(\frac{47}{150}\right)\)	\(e\left(\frac{46}{75}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{47}{75}\right)\)	\(e\left(\frac{73}{75}\right)\)	\(e\left(\frac{139}{150}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{17}{75}\right)\)
\(\chi_{875}(11,\cdot)\)	875.bc	75	yes	\(1\)	\(1\)	\(e\left(\frac{7}{75}\right)\)	\(e\left(\frac{74}{75}\right)\)	\(e\left(\frac{14}{75}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{73}{75}\right)\)	\(e\left(\frac{32}{75}\right)\)	\(e\left(\frac{13}{75}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{28}{75}\right)\)
\(\chi_{875}(12,\cdot)\)	875.bj	300	yes	\(1\)	\(1\)	\(e\left(\frac{227}{300}\right)\)	\(e\left(\frac{139}{300}\right)\)	\(e\left(\frac{77}{150}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{27}{100}\right)\)	\(e\left(\frac{139}{150}\right)\)	\(e\left(\frac{13}{75}\right)\)	\(e\left(\frac{293}{300}\right)\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{2}{75}\right)\)
\(\chi_{875}(13,\cdot)\)	875.bd	100	yes	\(1\)	\(1\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{23}{100}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{17}{100}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{71}{100}\right)\)	\(e\left(\frac{14}{25}\right)\)
\(\chi_{875}(16,\cdot)\)	875.bc	75	yes	\(1\)	\(1\)	\(e\left(\frac{53}{75}\right)\)	\(e\left(\frac{46}{75}\right)\)	\(e\left(\frac{31}{75}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{17}{75}\right)\)	\(e\left(\frac{28}{75}\right)\)	\(e\left(\frac{2}{75}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{62}{75}\right)\)
\(\chi_{875}(17,\cdot)\)	875.bj	300	yes	\(1\)	\(1\)	\(e\left(\frac{19}{300}\right)\)	\(e\left(\frac{83}{300}\right)\)	\(e\left(\frac{19}{150}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{19}{100}\right)\)	\(e\left(\frac{83}{150}\right)\)	\(e\left(\frac{11}{75}\right)\)	\(e\left(\frac{121}{300}\right)\)	\(e\left(\frac{97}{100}\right)\)	\(e\left(\frac{19}{75}\right)\)
\(\chi_{875}(18,\cdot)\)	875.ba	60	no	\(-1\)	\(1\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{875}(19,\cdot)\)	875.bf	150	yes	\(-1\)	\(1\)	\(e\left(\frac{127}{150}\right)\)	\(e\left(\frac{7}{75}\right)\)	\(e\left(\frac{52}{75}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{14}{75}\right)\)	\(e\left(\frac{1}{75}\right)\)	\(e\left(\frac{59}{75}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{29}{75}\right)\)
\(\chi_{875}(22,\cdot)\)	875.be	100	no	\(-1\)	\(1\)	\(e\left(\frac{77}{100}\right)\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{93}{100}\right)\)	\(e\left(\frac{3}{100}\right)\)	\(e\left(\frac{2}{25}\right)\)
\(\chi_{875}(23,\cdot)\)	875.bi	300	yes	\(-1\)	\(1\)	\(e\left(\frac{293}{300}\right)\)	\(e\left(\frac{151}{300}\right)\)	\(e\left(\frac{143}{150}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{93}{100}\right)\)	\(e\left(\frac{1}{150}\right)\)	\(e\left(\frac{67}{75}\right)\)	\(e\left(\frac{137}{300}\right)\)	\(e\left(\frac{9}{100}\right)\)	\(e\left(\frac{68}{75}\right)\)
\(\chi_{875}(24,\cdot)\)	875.v	30	no	\(-1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{875}(26,\cdot)\)	875.w	30	no	\(-1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{15}\right)\)
\(\chi_{875}(27,\cdot)\)	875.bd	100	yes	\(1\)	\(1\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{97}{100}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{63}{100}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{69}{100}\right)\)	\(e\left(\frac{21}{25}\right)\)
\(\chi_{875}(29,\cdot)\)	875.y	50	no	\(1\)	\(1\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{12}{25}\right)\)
\(\chi_{875}(31,\cdot)\)	875.bh	150	yes	\(-1\)	\(1\)	\(e\left(\frac{61}{75}\right)\)	\(e\left(\frac{79}{150}\right)\)	\(e\left(\frac{47}{75}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{4}{75}\right)\)	\(e\left(\frac{11}{75}\right)\)	\(e\left(\frac{23}{150}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{19}{75}\right)\)
\(\chi_{875}(32,\cdot)\)	875.ba	60	no	\(-1\)	\(1\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{8}{15}\right)\)
\(\chi_{875}(33,\cdot)\)	875.bj	300	yes	\(1\)	\(1\)	\(e\left(\frac{149}{300}\right)\)	\(e\left(\frac{193}{300}\right)\)	\(e\left(\frac{149}{150}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{49}{100}\right)\)	\(e\left(\frac{43}{150}\right)\)	\(e\left(\frac{31}{75}\right)\)	\(e\left(\frac{191}{300}\right)\)	\(e\left(\frac{87}{100}\right)\)	\(e\left(\frac{74}{75}\right)\)
\(\chi_{875}(34,\cdot)\)	875.z	50	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{24}{25}\right)\)
\(\chi_{875}(36,\cdot)\)	875.t	25	no	\(1\)	\(1\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{16}{25}\right)\)
\(\chi_{875}(37,\cdot)\)	875.bi	300	yes	\(-1\)	\(1\)	\(e\left(\frac{287}{300}\right)\)	\(e\left(\frac{109}{300}\right)\)	\(e\left(\frac{137}{150}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{87}{100}\right)\)	\(e\left(\frac{109}{150}\right)\)	\(e\left(\frac{28}{75}\right)\)	\(e\left(\frac{83}{300}\right)\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{62}{75}\right)\)
\(\chi_{875}(38,\cdot)\)	875.bj	300	yes	\(1\)	\(1\)	\(e\left(\frac{157}{300}\right)\)	\(e\left(\frac{149}{300}\right)\)	\(e\left(\frac{7}{150}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{57}{100}\right)\)	\(e\left(\frac{149}{150}\right)\)	\(e\left(\frac{8}{75}\right)\)	\(e\left(\frac{163}{300}\right)\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{7}{75}\right)\)
\(\chi_{875}(39,\cdot)\)	875.bg	150	yes	\(1\)	\(1\)	\(e\left(\frac{119}{150}\right)\)	\(e\left(\frac{133}{150}\right)\)	\(e\left(\frac{44}{75}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{58}{75}\right)\)	\(e\left(\frac{47}{75}\right)\)	\(e\left(\frac{71}{150}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{13}{75}\right)\)
\(\chi_{875}(41,\cdot)\)	875.x	50	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{19}{25}\right)\)
\(\chi_{875}(43,\cdot)\)	875.r	20	no	\(-1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{875}(44,\cdot)\)	875.bg	150	yes	\(1\)	\(1\)	\(e\left(\frac{67}{150}\right)\)	\(e\left(\frac{119}{150}\right)\)	\(e\left(\frac{67}{75}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{44}{75}\right)\)	\(e\left(\frac{46}{75}\right)\)	\(e\left(\frac{103}{150}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{59}{75}\right)\)
\(\chi_{875}(46,\cdot)\)	875.bc	75	yes	\(1\)	\(1\)	\(e\left(\frac{49}{75}\right)\)	\(e\left(\frac{68}{75}\right)\)	\(e\left(\frac{23}{75}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{61}{75}\right)\)	\(e\left(\frac{74}{75}\right)\)	\(e\left(\frac{16}{75}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{46}{75}\right)\)

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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.