LMFDB - Group of Dirichlet characters of modulus 1625

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(1625)

gp:g = idealstar(,1625,2)

magma:G = FullDirichletGroup(1625);

Character group

Order	=	1200	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{4}\times C_{300}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{1625}(1002,\cdot)$, $\chi_{1625}(626,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 1200 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	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$14$
$\chi_{1625}(1,\cdot)$	1625.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1625}(2,\cdot)$	1625.cc	300	yes	$1$	$1$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{121}{300}\right)$	$e\left(\frac{14}{75}\right)$	$e\left(\frac{149}{300}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{121}{150}\right)$	$e\left(\frac{103}{300}\right)$	$e\left(\frac{59}{100}\right)$	$e\left(\frac{43}{50}\right)$
$\chi_{1625}(3,\cdot)$	1625.cd	300	yes	$-1$	$1$	$e\left(\frac{121}{300}\right)$	$e\left(\frac{247}{300}\right)$	$e\left(\frac{121}{150}\right)$	$e\left(\frac{17}{75}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{97}{150}\right)$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{63}{100}\right)$	$e\left(\frac{1}{50}\right)$
$\chi_{1625}(4,\cdot)$	1625.cb	150	yes	$1$	$1$	$e\left(\frac{14}{75}\right)$	$e\left(\frac{121}{150}\right)$	$e\left(\frac{28}{75}\right)$	$e\left(\frac{149}{150}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{46}{75}\right)$	$e\left(\frac{103}{150}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{18}{25}\right)$
$\chi_{1625}(6,\cdot)$	1625.ce	300	yes	$-1$	$1$	$e\left(\frac{149}{300}\right)$	$e\left(\frac{17}{75}\right)$	$e\left(\frac{149}{150}\right)$	$e\left(\frac{217}{300}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{49}{100}\right)$	$e\left(\frac{34}{75}\right)$	$e\left(\frac{299}{300}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{22}{25}\right)$
$\chi_{1625}(7,\cdot)$	1625.bm	60	no	$1$	$1$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{1625}(8,\cdot)$	1625.by	100	yes	$1$	$1$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{49}{100}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{3}{100}\right)$	$e\left(\frac{77}{100}\right)$	$e\left(\frac{29}{50}\right)$
$\chi_{1625}(9,\cdot)$	1625.ca	150	yes	$1$	$1$	$e\left(\frac{121}{150}\right)$	$e\left(\frac{97}{150}\right)$	$e\left(\frac{46}{75}\right)$	$e\left(\frac{34}{75}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{22}{75}\right)$	$e\left(\frac{23}{75}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{1}{25}\right)$
$\chi_{1625}(11,\cdot)$	1625.ce	300	yes	$-1$	$1$	$e\left(\frac{103}{300}\right)$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{103}{150}\right)$	$e\left(\frac{299}{300}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{3}{100}\right)$	$e\left(\frac{23}{75}\right)$	$e\left(\frac{253}{300}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{9}{25}\right)$
$\chi_{1625}(12,\cdot)$	1625.bu	100	yes	$-1$	$1$	$e\left(\frac{59}{100}\right)$	$e\left(\frac{63}{100}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{77}{100}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{37}{50}\right)$
$\chi_{1625}(14,\cdot)$	1625.bk	50	no	$1$	$1$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{24}{25}\right)$
$\chi_{1625}(16,\cdot)$	1625.bs	75	yes	$1$	$1$	$e\left(\frac{28}{75}\right)$	$e\left(\frac{46}{75}\right)$	$e\left(\frac{56}{75}\right)$	$e\left(\frac{74}{75}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{17}{75}\right)$	$e\left(\frac{28}{75}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{11}{25}\right)$
$\chi_{1625}(17,\cdot)$	1625.cg	300	yes	$-1$	$1$	$e\left(\frac{269}{300}\right)$	$e\left(\frac{233}{300}\right)$	$e\left(\frac{119}{150}\right)$	$e\left(\frac{101}{150}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{69}{100}\right)$	$e\left(\frac{83}{150}\right)$	$e\left(\frac{97}{150}\right)$	$e\left(\frac{57}{100}\right)$	$e\left(\frac{39}{50}\right)$
$\chi_{1625}(18,\cdot)$	1625.be	20	no	$1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{19}{20}\right)$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{1625}(19,\cdot)$	1625.cf	300	yes	$-1$	$1$	$e\left(\frac{179}{300}\right)$	$e\left(\frac{139}{150}\right)$	$e\left(\frac{29}{150}\right)$	$e\left(\frac{157}{300}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{79}{100}\right)$	$e\left(\frac{64}{75}\right)$	$e\left(\frac{179}{300}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{12}{25}\right)$
$\chi_{1625}(21,\cdot)$	1625.bw	100	yes	$-1$	$1$	$e\left(\frac{17}{100}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{61}{100}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{51}{100}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{67}{100}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{3}{25}\right)$
$\chi_{1625}(22,\cdot)$	1625.cd	300	yes	$-1$	$1$	$e\left(\frac{131}{300}\right)$	$e\left(\frac{17}{300}\right)$	$e\left(\frac{131}{150}\right)$	$e\left(\frac{37}{75}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{17}{150}\right)$	$e\left(\frac{14}{75}\right)$	$e\left(\frac{93}{100}\right)$	$e\left(\frac{11}{50}\right)$
$\chi_{1625}(23,\cdot)$	1625.cg	300	yes	$-1$	$1$	$e\left(\frac{43}{300}\right)$	$e\left(\frac{151}{300}\right)$	$e\left(\frac{43}{150}\right)$	$e\left(\frac{97}{150}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{1}{150}\right)$	$e\left(\frac{59}{150}\right)$	$e\left(\frac{79}{100}\right)$	$e\left(\frac{33}{50}\right)$
$\chi_{1625}(24,\cdot)$	1625.bn	60	no	$-1$	$1$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{1625}(27,\cdot)$	1625.bx	100	no	$-1$	$1$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{47}{100}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{63}{100}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{3}{50}\right)$
$\chi_{1625}(28,\cdot)$	1625.ch	300	yes	$1$	$1$	$e\left(\frac{143}{150}\right)$	$e\left(\frac{127}{300}\right)$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{113}{300}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{127}{150}\right)$	$e\left(\frac{211}{300}\right)$	$e\left(\frac{33}{100}\right)$	$e\left(\frac{41}{50}\right)$
$\chi_{1625}(29,\cdot)$	1625.ca	150	yes	$1$	$1$	$e\left(\frac{143}{150}\right)$	$e\left(\frac{101}{150}\right)$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{47}{75}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{26}{75}\right)$	$e\left(\frac{34}{75}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{8}{25}\right)$
$\chi_{1625}(31,\cdot)$	1625.bw	100	yes	$-1$	$1$	$e\left(\frac{23}{100}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{59}{100}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{69}{100}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{73}{100}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{7}{25}\right)$
$\chi_{1625}(32,\cdot)$	1625.br	60	no	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{1625}(33,\cdot)$	1625.cc	300	yes	$1$	$1$	$e\left(\frac{56}{75}\right)$	$e\left(\frac{143}{300}\right)$	$e\left(\frac{37}{75}\right)$	$e\left(\frac{67}{300}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{143}{150}\right)$	$e\left(\frac{149}{300}\right)$	$e\left(\frac{97}{100}\right)$	$e\left(\frac{19}{50}\right)$
$\chi_{1625}(34,\cdot)$	1625.bv	100	yes	$-1$	$1$	$e\left(\frac{99}{100}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{17}{100}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{97}{100}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{99}{100}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{16}{25}\right)$
$\chi_{1625}(36,\cdot)$	1625.bz	150	yes	$1$	$1$	$e\left(\frac{149}{150}\right)$	$e\left(\frac{34}{75}\right)$	$e\left(\frac{74}{75}\right)$	$e\left(\frac{67}{150}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{149}{150}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{19}{25}\right)$
$\chi_{1625}(37,\cdot)$	1625.ch	300	yes	$1$	$1$	$e\left(\frac{131}{150}\right)$	$e\left(\frac{109}{300}\right)$	$e\left(\frac{56}{75}\right)$	$e\left(\frac{71}{300}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{109}{150}\right)$	$e\left(\frac{37}{300}\right)$	$e\left(\frac{11}{100}\right)$	$e\left(\frac{47}{50}\right)$
$\chi_{1625}(38,\cdot)$	1625.bu	100	yes	$-1$	$1$	$e\left(\frac{69}{100}\right)$	$e\left(\frac{33}{100}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{71}{100}\right)$	$e\left(\frac{17}{50}\right)$
$\chi_{1625}(41,\cdot)$	1625.ce	300	yes	$-1$	$1$	$e\left(\frac{157}{300}\right)$	$e\left(\frac{31}{75}\right)$	$e\left(\frac{7}{150}\right)$	$e\left(\frac{281}{300}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{57}{100}\right)$	$e\left(\frac{62}{75}\right)$	$e\left(\frac{7}{300}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{21}{25}\right)$
$\chi_{1625}(42,\cdot)$	1625.cd	300	yes	$-1$	$1$	$e\left(\frac{79}{300}\right)$	$e\left(\frac{253}{300}\right)$	$e\left(\frac{79}{150}\right)$	$e\left(\frac{8}{75}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{79}{100}\right)$	$e\left(\frac{103}{150}\right)$	$e\left(\frac{1}{75}\right)$	$e\left(\frac{37}{100}\right)$	$e\left(\frac{49}{50}\right)$
$\chi_{1625}(43,\cdot)$	1625.bo	60	no	$-1$	$1$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{10}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$1625$
Structure	\(C_{4}\times C_{300}\)
Order	$1200$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(14\)
\(\chi_{1625}(1,\cdot)\)	1625.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1625}(2,\cdot)\)	1625.cc	300	yes	\(1\)	\(1\)	\(e\left(\frac{7}{75}\right)\)	\(e\left(\frac{121}{300}\right)\)	\(e\left(\frac{14}{75}\right)\)	\(e\left(\frac{149}{300}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{121}{150}\right)\)	\(e\left(\frac{103}{300}\right)\)	\(e\left(\frac{59}{100}\right)\)	\(e\left(\frac{43}{50}\right)\)
\(\chi_{1625}(3,\cdot)\)	1625.cd	300	yes	\(-1\)	\(1\)	\(e\left(\frac{121}{300}\right)\)	\(e\left(\frac{247}{300}\right)\)	\(e\left(\frac{121}{150}\right)\)	\(e\left(\frac{17}{75}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{97}{150}\right)\)	\(e\left(\frac{49}{75}\right)\)	\(e\left(\frac{63}{100}\right)\)	\(e\left(\frac{1}{50}\right)\)
\(\chi_{1625}(4,\cdot)\)	1625.cb	150	yes	\(1\)	\(1\)	\(e\left(\frac{14}{75}\right)\)	\(e\left(\frac{121}{150}\right)\)	\(e\left(\frac{28}{75}\right)\)	\(e\left(\frac{149}{150}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{46}{75}\right)\)	\(e\left(\frac{103}{150}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{18}{25}\right)\)
\(\chi_{1625}(6,\cdot)\)	1625.ce	300	yes	\(-1\)	\(1\)	\(e\left(\frac{149}{300}\right)\)	\(e\left(\frac{17}{75}\right)\)	\(e\left(\frac{149}{150}\right)\)	\(e\left(\frac{217}{300}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{49}{100}\right)\)	\(e\left(\frac{34}{75}\right)\)	\(e\left(\frac{299}{300}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{22}{25}\right)\)
\(\chi_{1625}(7,\cdot)\)	1625.bm	60	no	\(1\)	\(1\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{1625}(8,\cdot)\)	1625.by	100	yes	\(1\)	\(1\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{49}{100}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{3}{100}\right)\)	\(e\left(\frac{77}{100}\right)\)	\(e\left(\frac{29}{50}\right)\)
\(\chi_{1625}(9,\cdot)\)	1625.ca	150	yes	\(1\)	\(1\)	\(e\left(\frac{121}{150}\right)\)	\(e\left(\frac{97}{150}\right)\)	\(e\left(\frac{46}{75}\right)\)	\(e\left(\frac{34}{75}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{22}{75}\right)\)	\(e\left(\frac{23}{75}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{1}{25}\right)\)
\(\chi_{1625}(11,\cdot)\)	1625.ce	300	yes	\(-1\)	\(1\)	\(e\left(\frac{103}{300}\right)\)	\(e\left(\frac{49}{75}\right)\)	\(e\left(\frac{103}{150}\right)\)	\(e\left(\frac{299}{300}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{3}{100}\right)\)	\(e\left(\frac{23}{75}\right)\)	\(e\left(\frac{253}{300}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{9}{25}\right)\)
\(\chi_{1625}(12,\cdot)\)	1625.bu	100	yes	\(-1\)	\(1\)	\(e\left(\frac{59}{100}\right)\)	\(e\left(\frac{63}{100}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{77}{100}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{37}{50}\right)\)
\(\chi_{1625}(14,\cdot)\)	1625.bk	50	no	\(1\)	\(1\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{24}{25}\right)\)
\(\chi_{1625}(16,\cdot)\)	1625.bs	75	yes	\(1\)	\(1\)	\(e\left(\frac{28}{75}\right)\)	\(e\left(\frac{46}{75}\right)\)	\(e\left(\frac{56}{75}\right)\)	\(e\left(\frac{74}{75}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{17}{75}\right)\)	\(e\left(\frac{28}{75}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{11}{25}\right)\)
\(\chi_{1625}(17,\cdot)\)	1625.cg	300	yes	\(-1\)	\(1\)	\(e\left(\frac{269}{300}\right)\)	\(e\left(\frac{233}{300}\right)\)	\(e\left(\frac{119}{150}\right)\)	\(e\left(\frac{101}{150}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{69}{100}\right)\)	\(e\left(\frac{83}{150}\right)\)	\(e\left(\frac{97}{150}\right)\)	\(e\left(\frac{57}{100}\right)\)	\(e\left(\frac{39}{50}\right)\)
\(\chi_{1625}(18,\cdot)\)	1625.be	20	no	\(1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{1625}(19,\cdot)\)	1625.cf	300	yes	\(-1\)	\(1\)	\(e\left(\frac{179}{300}\right)\)	\(e\left(\frac{139}{150}\right)\)	\(e\left(\frac{29}{150}\right)\)	\(e\left(\frac{157}{300}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{79}{100}\right)\)	\(e\left(\frac{64}{75}\right)\)	\(e\left(\frac{179}{300}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{12}{25}\right)\)
\(\chi_{1625}(21,\cdot)\)	1625.bw	100	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{100}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{61}{100}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{51}{100}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{67}{100}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{3}{25}\right)\)
\(\chi_{1625}(22,\cdot)\)	1625.cd	300	yes	\(-1\)	\(1\)	\(e\left(\frac{131}{300}\right)\)	\(e\left(\frac{17}{300}\right)\)	\(e\left(\frac{131}{150}\right)\)	\(e\left(\frac{37}{75}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{17}{150}\right)\)	\(e\left(\frac{14}{75}\right)\)	\(e\left(\frac{93}{100}\right)\)	\(e\left(\frac{11}{50}\right)\)
\(\chi_{1625}(23,\cdot)\)	1625.cg	300	yes	\(-1\)	\(1\)	\(e\left(\frac{43}{300}\right)\)	\(e\left(\frac{151}{300}\right)\)	\(e\left(\frac{43}{150}\right)\)	\(e\left(\frac{97}{150}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{1}{150}\right)\)	\(e\left(\frac{59}{150}\right)\)	\(e\left(\frac{79}{100}\right)\)	\(e\left(\frac{33}{50}\right)\)
\(\chi_{1625}(24,\cdot)\)	1625.bn	60	no	\(-1\)	\(1\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{1625}(27,\cdot)\)	1625.bx	100	no	\(-1\)	\(1\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{47}{100}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{63}{100}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{3}{50}\right)\)
\(\chi_{1625}(28,\cdot)\)	1625.ch	300	yes	\(1\)	\(1\)	\(e\left(\frac{143}{150}\right)\)	\(e\left(\frac{127}{300}\right)\)	\(e\left(\frac{68}{75}\right)\)	\(e\left(\frac{113}{300}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{127}{150}\right)\)	\(e\left(\frac{211}{300}\right)\)	\(e\left(\frac{33}{100}\right)\)	\(e\left(\frac{41}{50}\right)\)
\(\chi_{1625}(29,\cdot)\)	1625.ca	150	yes	\(1\)	\(1\)	\(e\left(\frac{143}{150}\right)\)	\(e\left(\frac{101}{150}\right)\)	\(e\left(\frac{68}{75}\right)\)	\(e\left(\frac{47}{75}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{26}{75}\right)\)	\(e\left(\frac{34}{75}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{8}{25}\right)\)
\(\chi_{1625}(31,\cdot)\)	1625.bw	100	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{100}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{59}{100}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{69}{100}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{73}{100}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{7}{25}\right)\)
\(\chi_{1625}(32,\cdot)\)	1625.br	60	no	\(1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{1625}(33,\cdot)\)	1625.cc	300	yes	\(1\)	\(1\)	\(e\left(\frac{56}{75}\right)\)	\(e\left(\frac{143}{300}\right)\)	\(e\left(\frac{37}{75}\right)\)	\(e\left(\frac{67}{300}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{143}{150}\right)\)	\(e\left(\frac{149}{300}\right)\)	\(e\left(\frac{97}{100}\right)\)	\(e\left(\frac{19}{50}\right)\)
\(\chi_{1625}(34,\cdot)\)	1625.bv	100	yes	\(-1\)	\(1\)	\(e\left(\frac{99}{100}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{17}{100}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{97}{100}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{99}{100}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{16}{25}\right)\)
\(\chi_{1625}(36,\cdot)\)	1625.bz	150	yes	\(1\)	\(1\)	\(e\left(\frac{149}{150}\right)\)	\(e\left(\frac{34}{75}\right)\)	\(e\left(\frac{74}{75}\right)\)	\(e\left(\frac{67}{150}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{68}{75}\right)\)	\(e\left(\frac{149}{150}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{19}{25}\right)\)
\(\chi_{1625}(37,\cdot)\)	1625.ch	300	yes	\(1\)	\(1\)	\(e\left(\frac{131}{150}\right)\)	\(e\left(\frac{109}{300}\right)\)	\(e\left(\frac{56}{75}\right)\)	\(e\left(\frac{71}{300}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{109}{150}\right)\)	\(e\left(\frac{37}{300}\right)\)	\(e\left(\frac{11}{100}\right)\)	\(e\left(\frac{47}{50}\right)\)
\(\chi_{1625}(38,\cdot)\)	1625.bu	100	yes	\(-1\)	\(1\)	\(e\left(\frac{69}{100}\right)\)	\(e\left(\frac{33}{100}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{71}{100}\right)\)	\(e\left(\frac{17}{50}\right)\)
\(\chi_{1625}(41,\cdot)\)	1625.ce	300	yes	\(-1\)	\(1\)	\(e\left(\frac{157}{300}\right)\)	\(e\left(\frac{31}{75}\right)\)	\(e\left(\frac{7}{150}\right)\)	\(e\left(\frac{281}{300}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{57}{100}\right)\)	\(e\left(\frac{62}{75}\right)\)	\(e\left(\frac{7}{300}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{21}{25}\right)\)
\(\chi_{1625}(42,\cdot)\)	1625.cd	300	yes	\(-1\)	\(1\)	\(e\left(\frac{79}{300}\right)\)	\(e\left(\frac{253}{300}\right)\)	\(e\left(\frac{79}{150}\right)\)	\(e\left(\frac{8}{75}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{79}{100}\right)\)	\(e\left(\frac{103}{150}\right)\)	\(e\left(\frac{1}{75}\right)\)	\(e\left(\frac{37}{100}\right)\)	\(e\left(\frac{49}{50}\right)\)
\(\chi_{1625}(43,\cdot)\)	1625.bo	60	no	\(-1\)	\(1\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)

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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.