LMFDB - Group of Dirichlet characters of modulus 625

Show commands: PariGP / SageMath

sage: H = DirichletGroup(625)

pari: g = idealstar(,625,2)

Character group

sage: G.order() pari: g.no
Order	=	500
sage: H.invariants() pari: g.cyc
Structure	=	$C_{500}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{625}(2,\cdot)$

First 32 of 500 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	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{625}(1,\cdot)$	625.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{625}(2,\cdot)$	625.l	500	yes	$-1$	$1$	$e\left(\frac{1}{500}\right)$	$e\left(\frac{107}{500}\right)$	$e\left(\frac{1}{250}\right)$	$e\left(\frac{27}{125}\right)$	$e\left(\frac{97}{100}\right)$	$e\left(\frac{3}{500}\right)$	$e\left(\frac{107}{250}\right)$	$e\left(\frac{119}{125}\right)$	$e\left(\frac{109}{500}\right)$	$e\left(\frac{139}{500}\right)$
$\chi_{625}(3,\cdot)$	625.l	500	yes	$-1$	$1$	$e\left(\frac{107}{500}\right)$	$e\left(\frac{449}{500}\right)$	$e\left(\frac{107}{250}\right)$	$e\left(\frac{14}{125}\right)$	$e\left(\frac{79}{100}\right)$	$e\left(\frac{321}{500}\right)$	$e\left(\frac{199}{250}\right)$	$e\left(\frac{108}{125}\right)$	$e\left(\frac{163}{500}\right)$	$e\left(\frac{373}{500}\right)$
$\chi_{625}(4,\cdot)$	625.k	250	yes	$1$	$1$	$e\left(\frac{1}{250}\right)$	$e\left(\frac{107}{250}\right)$	$e\left(\frac{1}{125}\right)$	$e\left(\frac{54}{125}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{3}{250}\right)$	$e\left(\frac{107}{125}\right)$	$e\left(\frac{113}{125}\right)$	$e\left(\frac{109}{250}\right)$	$e\left(\frac{139}{250}\right)$
$\chi_{625}(6,\cdot)$	625.j	125	yes	$1$	$1$	$e\left(\frac{27}{125}\right)$	$e\left(\frac{14}{125}\right)$	$e\left(\frac{54}{125}\right)$	$e\left(\frac{41}{125}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{81}{125}\right)$	$e\left(\frac{28}{125}\right)$	$e\left(\frac{102}{125}\right)$	$e\left(\frac{68}{125}\right)$	$e\left(\frac{3}{125}\right)$
$\chi_{625}(7,\cdot)$	625.i	100	no	$-1$	$1$	$e\left(\frac{97}{100}\right)$	$e\left(\frac{79}{100}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{73}{100}\right)$	$e\left(\frac{83}{100}\right)$
$\chi_{625}(8,\cdot)$	625.l	500	yes	$-1$	$1$	$e\left(\frac{3}{500}\right)$	$e\left(\frac{321}{500}\right)$	$e\left(\frac{3}{250}\right)$	$e\left(\frac{81}{125}\right)$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{9}{500}\right)$	$e\left(\frac{71}{250}\right)$	$e\left(\frac{107}{125}\right)$	$e\left(\frac{327}{500}\right)$	$e\left(\frac{417}{500}\right)$
$\chi_{625}(9,\cdot)$	625.k	250	yes	$1$	$1$	$e\left(\frac{107}{250}\right)$	$e\left(\frac{199}{250}\right)$	$e\left(\frac{107}{125}\right)$	$e\left(\frac{28}{125}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{71}{250}\right)$	$e\left(\frac{74}{125}\right)$	$e\left(\frac{91}{125}\right)$	$e\left(\frac{163}{250}\right)$	$e\left(\frac{123}{250}\right)$
$\chi_{625}(11,\cdot)$	625.j	125	yes	$1$	$1$	$e\left(\frac{119}{125}\right)$	$e\left(\frac{108}{125}\right)$	$e\left(\frac{113}{125}\right)$	$e\left(\frac{102}{125}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{107}{125}\right)$	$e\left(\frac{91}{125}\right)$	$e\left(\frac{19}{125}\right)$	$e\left(\frac{96}{125}\right)$	$e\left(\frac{41}{125}\right)$
$\chi_{625}(12,\cdot)$	625.l	500	yes	$-1$	$1$	$e\left(\frac{109}{500}\right)$	$e\left(\frac{163}{500}\right)$	$e\left(\frac{109}{250}\right)$	$e\left(\frac{68}{125}\right)$	$e\left(\frac{73}{100}\right)$	$e\left(\frac{327}{500}\right)$	$e\left(\frac{163}{250}\right)$	$e\left(\frac{96}{125}\right)$	$e\left(\frac{381}{500}\right)$	$e\left(\frac{151}{500}\right)$
$\chi_{625}(13,\cdot)$	625.l	500	yes	$-1$	$1$	$e\left(\frac{139}{500}\right)$	$e\left(\frac{373}{500}\right)$	$e\left(\frac{139}{250}\right)$	$e\left(\frac{3}{125}\right)$	$e\left(\frac{83}{100}\right)$	$e\left(\frac{417}{500}\right)$	$e\left(\frac{123}{250}\right)$	$e\left(\frac{41}{125}\right)$	$e\left(\frac{151}{500}\right)$	$e\left(\frac{321}{500}\right)$
$\chi_{625}(14,\cdot)$	625.k	250	yes	$1$	$1$	$e\left(\frac{243}{250}\right)$	$e\left(\frac{1}{250}\right)$	$e\left(\frac{118}{125}\right)$	$e\left(\frac{122}{125}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{229}{250}\right)$	$e\left(\frac{1}{125}\right)$	$e\left(\frac{84}{125}\right)$	$e\left(\frac{237}{250}\right)$	$e\left(\frac{27}{250}\right)$
$\chi_{625}(16,\cdot)$	625.j	125	yes	$1$	$1$	$e\left(\frac{1}{125}\right)$	$e\left(\frac{107}{125}\right)$	$e\left(\frac{2}{125}\right)$	$e\left(\frac{108}{125}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{3}{125}\right)$	$e\left(\frac{89}{125}\right)$	$e\left(\frac{101}{125}\right)$	$e\left(\frac{109}{125}\right)$	$e\left(\frac{14}{125}\right)$
$\chi_{625}(17,\cdot)$	625.l	500	yes	$-1$	$1$	$e\left(\frac{173}{500}\right)$	$e\left(\frac{11}{500}\right)$	$e\left(\frac{173}{250}\right)$	$e\left(\frac{46}{125}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{19}{500}\right)$	$e\left(\frac{11}{250}\right)$	$e\left(\frac{87}{125}\right)$	$e\left(\frac{357}{500}\right)$	$e\left(\frac{47}{500}\right)$
$\chi_{625}(18,\cdot)$	625.i	100	no	$-1$	$1$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{1}{100}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{29}{100}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{87}{100}\right)$	$e\left(\frac{77}{100}\right)$
$\chi_{625}(19,\cdot)$	625.k	250	yes	$1$	$1$	$e\left(\frac{209}{250}\right)$	$e\left(\frac{113}{250}\right)$	$e\left(\frac{84}{125}\right)$	$e\left(\frac{36}{125}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{127}{250}\right)$	$e\left(\frac{113}{125}\right)$	$e\left(\frac{117}{125}\right)$	$e\left(\frac{31}{250}\right)$	$e\left(\frac{51}{250}\right)$
$\chi_{625}(21,\cdot)$	625.j	125	yes	$1$	$1$	$e\left(\frac{23}{125}\right)$	$e\left(\frac{86}{125}\right)$	$e\left(\frac{46}{125}\right)$	$e\left(\frac{109}{125}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{69}{125}\right)$	$e\left(\frac{47}{125}\right)$	$e\left(\frac{73}{125}\right)$	$e\left(\frac{7}{125}\right)$	$e\left(\frac{72}{125}\right)$
$\chi_{625}(22,\cdot)$	625.l	500	yes	$-1$	$1$	$e\left(\frac{477}{500}\right)$	$e\left(\frac{39}{500}\right)$	$e\left(\frac{227}{250}\right)$	$e\left(\frac{4}{125}\right)$	$e\left(\frac{69}{100}\right)$	$e\left(\frac{431}{500}\right)$	$e\left(\frac{39}{250}\right)$	$e\left(\frac{13}{125}\right)$	$e\left(\frac{493}{500}\right)$	$e\left(\frac{303}{500}\right)$
$\chi_{625}(23,\cdot)$	625.l	500	yes	$-1$	$1$	$e\left(\frac{431}{500}\right)$	$e\left(\frac{117}{500}\right)$	$e\left(\frac{181}{250}\right)$	$e\left(\frac{12}{125}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{293}{500}\right)$	$e\left(\frac{117}{250}\right)$	$e\left(\frac{39}{125}\right)$	$e\left(\frac{479}{500}\right)$	$e\left(\frac{409}{500}\right)$
$\chi_{625}(24,\cdot)$	625.h	50	no	$1$	$1$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{29}{50}\right)$
$\chi_{625}(26,\cdot)$	625.g	25	no	$1$	$1$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{23}{25}\right)$
$\chi_{625}(27,\cdot)$	625.l	500	yes	$-1$	$1$	$e\left(\frac{321}{500}\right)$	$e\left(\frac{347}{500}\right)$	$e\left(\frac{71}{250}\right)$	$e\left(\frac{42}{125}\right)$	$e\left(\frac{37}{100}\right)$	$e\left(\frac{463}{500}\right)$	$e\left(\frac{97}{250}\right)$	$e\left(\frac{74}{125}\right)$	$e\left(\frac{489}{500}\right)$	$e\left(\frac{119}{500}\right)$
$\chi_{625}(28,\cdot)$	625.l	500	yes	$-1$	$1$	$e\left(\frac{487}{500}\right)$	$e\left(\frac{109}{500}\right)$	$e\left(\frac{237}{250}\right)$	$e\left(\frac{24}{125}\right)$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{461}{500}\right)$	$e\left(\frac{109}{250}\right)$	$e\left(\frac{78}{125}\right)$	$e\left(\frac{83}{500}\right)$	$e\left(\frac{193}{500}\right)$
$\chi_{625}(29,\cdot)$	625.k	250	yes	$1$	$1$	$e\left(\frac{81}{250}\right)$	$e\left(\frac{167}{250}\right)$	$e\left(\frac{81}{125}\right)$	$e\left(\frac{124}{125}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{243}{250}\right)$	$e\left(\frac{42}{125}\right)$	$e\left(\frac{28}{125}\right)$	$e\left(\frac{79}{250}\right)$	$e\left(\frac{9}{250}\right)$
$\chi_{625}(31,\cdot)$	625.j	125	yes	$1$	$1$	$e\left(\frac{12}{125}\right)$	$e\left(\frac{34}{125}\right)$	$e\left(\frac{24}{125}\right)$	$e\left(\frac{46}{125}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{36}{125}\right)$	$e\left(\frac{68}{125}\right)$	$e\left(\frac{87}{125}\right)$	$e\left(\frac{58}{125}\right)$	$e\left(\frac{43}{125}\right)$
$\chi_{625}(32,\cdot)$	625.i	100	no	$-1$	$1$	$e\left(\frac{1}{100}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{100}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{9}{100}\right)$	$e\left(\frac{39}{100}\right)$
$\chi_{625}(33,\cdot)$	625.l	500	yes	$-1$	$1$	$e\left(\frac{83}{500}\right)$	$e\left(\frac{381}{500}\right)$	$e\left(\frac{83}{250}\right)$	$e\left(\frac{116}{125}\right)$	$e\left(\frac{51}{100}\right)$	$e\left(\frac{249}{500}\right)$	$e\left(\frac{131}{250}\right)$	$e\left(\frac{2}{125}\right)$	$e\left(\frac{47}{500}\right)$	$e\left(\frac{37}{500}\right)$
$\chi_{625}(34,\cdot)$	625.k	250	yes	$1$	$1$	$e\left(\frac{87}{250}\right)$	$e\left(\frac{59}{250}\right)$	$e\left(\frac{87}{125}\right)$	$e\left(\frac{73}{125}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{11}{250}\right)$	$e\left(\frac{59}{125}\right)$	$e\left(\frac{81}{125}\right)$	$e\left(\frac{233}{250}\right)$	$e\left(\frac{93}{250}\right)$
$\chi_{625}(36,\cdot)$	625.j	125	yes	$1$	$1$	$e\left(\frac{54}{125}\right)$	$e\left(\frac{28}{125}\right)$	$e\left(\frac{108}{125}\right)$	$e\left(\frac{82}{125}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{37}{125}\right)$	$e\left(\frac{56}{125}\right)$	$e\left(\frac{79}{125}\right)$	$e\left(\frac{11}{125}\right)$	$e\left(\frac{6}{125}\right)$
$\chi_{625}(37,\cdot)$	625.l	500	yes	$-1$	$1$	$e\left(\frac{329}{500}\right)$	$e\left(\frac{203}{500}\right)$	$e\left(\frac{79}{250}\right)$	$e\left(\frac{8}{125}\right)$	$e\left(\frac{13}{100}\right)$	$e\left(\frac{487}{500}\right)$	$e\left(\frac{203}{250}\right)$	$e\left(\frac{26}{125}\right)$	$e\left(\frac{361}{500}\right)$	$e\left(\frac{231}{500}\right)$
$\chi_{625}(38,\cdot)$	625.l	500	yes	$-1$	$1$	$e\left(\frac{419}{500}\right)$	$e\left(\frac{333}{500}\right)$	$e\left(\frac{169}{250}\right)$	$e\left(\frac{63}{125}\right)$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{257}{500}\right)$	$e\left(\frac{83}{250}\right)$	$e\left(\frac{111}{125}\right)$	$e\left(\frac{171}{500}\right)$	$e\left(\frac{241}{500}\right)$
$\chi_{625}(39,\cdot)$	625.k	250	yes	$1$	$1$	$e\left(\frac{123}{250}\right)$	$e\left(\frac{161}{250}\right)$	$e\left(\frac{123}{125}\right)$	$e\left(\frac{17}{125}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{119}{250}\right)$	$e\left(\frac{36}{125}\right)$	$e\left(\frac{24}{125}\right)$	$e\left(\frac{157}{250}\right)$	$e\left(\frac{97}{250}\right)$

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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	$625$
Structure	\(C_{500}\)
Order	$500$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)
\(\chi_{625}(1,\cdot)\)	625.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{625}(2,\cdot)\)	625.l	500	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{500}\right)\)	\(e\left(\frac{107}{500}\right)\)	\(e\left(\frac{1}{250}\right)\)	\(e\left(\frac{27}{125}\right)\)	\(e\left(\frac{97}{100}\right)\)	\(e\left(\frac{3}{500}\right)\)	\(e\left(\frac{107}{250}\right)\)	\(e\left(\frac{119}{125}\right)\)	\(e\left(\frac{109}{500}\right)\)	\(e\left(\frac{139}{500}\right)\)
\(\chi_{625}(3,\cdot)\)	625.l	500	yes	\(-1\)	\(1\)	\(e\left(\frac{107}{500}\right)\)	\(e\left(\frac{449}{500}\right)\)	\(e\left(\frac{107}{250}\right)\)	\(e\left(\frac{14}{125}\right)\)	\(e\left(\frac{79}{100}\right)\)	\(e\left(\frac{321}{500}\right)\)	\(e\left(\frac{199}{250}\right)\)	\(e\left(\frac{108}{125}\right)\)	\(e\left(\frac{163}{500}\right)\)	\(e\left(\frac{373}{500}\right)\)
\(\chi_{625}(4,\cdot)\)	625.k	250	yes	\(1\)	\(1\)	\(e\left(\frac{1}{250}\right)\)	\(e\left(\frac{107}{250}\right)\)	\(e\left(\frac{1}{125}\right)\)	\(e\left(\frac{54}{125}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{3}{250}\right)\)	\(e\left(\frac{107}{125}\right)\)	\(e\left(\frac{113}{125}\right)\)	\(e\left(\frac{109}{250}\right)\)	\(e\left(\frac{139}{250}\right)\)
\(\chi_{625}(6,\cdot)\)	625.j	125	yes	\(1\)	\(1\)	\(e\left(\frac{27}{125}\right)\)	\(e\left(\frac{14}{125}\right)\)	\(e\left(\frac{54}{125}\right)\)	\(e\left(\frac{41}{125}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{81}{125}\right)\)	\(e\left(\frac{28}{125}\right)\)	\(e\left(\frac{102}{125}\right)\)	\(e\left(\frac{68}{125}\right)\)	\(e\left(\frac{3}{125}\right)\)
\(\chi_{625}(7,\cdot)\)	625.i	100	no	\(-1\)	\(1\)	\(e\left(\frac{97}{100}\right)\)	\(e\left(\frac{79}{100}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{73}{100}\right)\)	\(e\left(\frac{83}{100}\right)\)
\(\chi_{625}(8,\cdot)\)	625.l	500	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{500}\right)\)	\(e\left(\frac{321}{500}\right)\)	\(e\left(\frac{3}{250}\right)\)	\(e\left(\frac{81}{125}\right)\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{9}{500}\right)\)	\(e\left(\frac{71}{250}\right)\)	\(e\left(\frac{107}{125}\right)\)	\(e\left(\frac{327}{500}\right)\)	\(e\left(\frac{417}{500}\right)\)
\(\chi_{625}(9,\cdot)\)	625.k	250	yes	\(1\)	\(1\)	\(e\left(\frac{107}{250}\right)\)	\(e\left(\frac{199}{250}\right)\)	\(e\left(\frac{107}{125}\right)\)	\(e\left(\frac{28}{125}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{71}{250}\right)\)	\(e\left(\frac{74}{125}\right)\)	\(e\left(\frac{91}{125}\right)\)	\(e\left(\frac{163}{250}\right)\)	\(e\left(\frac{123}{250}\right)\)
\(\chi_{625}(11,\cdot)\)	625.j	125	yes	\(1\)	\(1\)	\(e\left(\frac{119}{125}\right)\)	\(e\left(\frac{108}{125}\right)\)	\(e\left(\frac{113}{125}\right)\)	\(e\left(\frac{102}{125}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{107}{125}\right)\)	\(e\left(\frac{91}{125}\right)\)	\(e\left(\frac{19}{125}\right)\)	\(e\left(\frac{96}{125}\right)\)	\(e\left(\frac{41}{125}\right)\)
\(\chi_{625}(12,\cdot)\)	625.l	500	yes	\(-1\)	\(1\)	\(e\left(\frac{109}{500}\right)\)	\(e\left(\frac{163}{500}\right)\)	\(e\left(\frac{109}{250}\right)\)	\(e\left(\frac{68}{125}\right)\)	\(e\left(\frac{73}{100}\right)\)	\(e\left(\frac{327}{500}\right)\)	\(e\left(\frac{163}{250}\right)\)	\(e\left(\frac{96}{125}\right)\)	\(e\left(\frac{381}{500}\right)\)	\(e\left(\frac{151}{500}\right)\)
\(\chi_{625}(13,\cdot)\)	625.l	500	yes	\(-1\)	\(1\)	\(e\left(\frac{139}{500}\right)\)	\(e\left(\frac{373}{500}\right)\)	\(e\left(\frac{139}{250}\right)\)	\(e\left(\frac{3}{125}\right)\)	\(e\left(\frac{83}{100}\right)\)	\(e\left(\frac{417}{500}\right)\)	\(e\left(\frac{123}{250}\right)\)	\(e\left(\frac{41}{125}\right)\)	\(e\left(\frac{151}{500}\right)\)	\(e\left(\frac{321}{500}\right)\)
\(\chi_{625}(14,\cdot)\)	625.k	250	yes	\(1\)	\(1\)	\(e\left(\frac{243}{250}\right)\)	\(e\left(\frac{1}{250}\right)\)	\(e\left(\frac{118}{125}\right)\)	\(e\left(\frac{122}{125}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{229}{250}\right)\)	\(e\left(\frac{1}{125}\right)\)	\(e\left(\frac{84}{125}\right)\)	\(e\left(\frac{237}{250}\right)\)	\(e\left(\frac{27}{250}\right)\)
\(\chi_{625}(16,\cdot)\)	625.j	125	yes	\(1\)	\(1\)	\(e\left(\frac{1}{125}\right)\)	\(e\left(\frac{107}{125}\right)\)	\(e\left(\frac{2}{125}\right)\)	\(e\left(\frac{108}{125}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{3}{125}\right)\)	\(e\left(\frac{89}{125}\right)\)	\(e\left(\frac{101}{125}\right)\)	\(e\left(\frac{109}{125}\right)\)	\(e\left(\frac{14}{125}\right)\)
\(\chi_{625}(17,\cdot)\)	625.l	500	yes	\(-1\)	\(1\)	\(e\left(\frac{173}{500}\right)\)	\(e\left(\frac{11}{500}\right)\)	\(e\left(\frac{173}{250}\right)\)	\(e\left(\frac{46}{125}\right)\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{19}{500}\right)\)	\(e\left(\frac{11}{250}\right)\)	\(e\left(\frac{87}{125}\right)\)	\(e\left(\frac{357}{500}\right)\)	\(e\left(\frac{47}{500}\right)\)
\(\chi_{625}(18,\cdot)\)	625.i	100	no	\(-1\)	\(1\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{29}{100}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{87}{100}\right)\)	\(e\left(\frac{77}{100}\right)\)
\(\chi_{625}(19,\cdot)\)	625.k	250	yes	\(1\)	\(1\)	\(e\left(\frac{209}{250}\right)\)	\(e\left(\frac{113}{250}\right)\)	\(e\left(\frac{84}{125}\right)\)	\(e\left(\frac{36}{125}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{127}{250}\right)\)	\(e\left(\frac{113}{125}\right)\)	\(e\left(\frac{117}{125}\right)\)	\(e\left(\frac{31}{250}\right)\)	\(e\left(\frac{51}{250}\right)\)
\(\chi_{625}(21,\cdot)\)	625.j	125	yes	\(1\)	\(1\)	\(e\left(\frac{23}{125}\right)\)	\(e\left(\frac{86}{125}\right)\)	\(e\left(\frac{46}{125}\right)\)	\(e\left(\frac{109}{125}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{69}{125}\right)\)	\(e\left(\frac{47}{125}\right)\)	\(e\left(\frac{73}{125}\right)\)	\(e\left(\frac{7}{125}\right)\)	\(e\left(\frac{72}{125}\right)\)
\(\chi_{625}(22,\cdot)\)	625.l	500	yes	\(-1\)	\(1\)	\(e\left(\frac{477}{500}\right)\)	\(e\left(\frac{39}{500}\right)\)	\(e\left(\frac{227}{250}\right)\)	\(e\left(\frac{4}{125}\right)\)	\(e\left(\frac{69}{100}\right)\)	\(e\left(\frac{431}{500}\right)\)	\(e\left(\frac{39}{250}\right)\)	\(e\left(\frac{13}{125}\right)\)	\(e\left(\frac{493}{500}\right)\)	\(e\left(\frac{303}{500}\right)\)
\(\chi_{625}(23,\cdot)\)	625.l	500	yes	\(-1\)	\(1\)	\(e\left(\frac{431}{500}\right)\)	\(e\left(\frac{117}{500}\right)\)	\(e\left(\frac{181}{250}\right)\)	\(e\left(\frac{12}{125}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{293}{500}\right)\)	\(e\left(\frac{117}{250}\right)\)	\(e\left(\frac{39}{125}\right)\)	\(e\left(\frac{479}{500}\right)\)	\(e\left(\frac{409}{500}\right)\)
\(\chi_{625}(24,\cdot)\)	625.h	50	no	\(1\)	\(1\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{29}{50}\right)\)
\(\chi_{625}(26,\cdot)\)	625.g	25	no	\(1\)	\(1\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{23}{25}\right)\)
\(\chi_{625}(27,\cdot)\)	625.l	500	yes	\(-1\)	\(1\)	\(e\left(\frac{321}{500}\right)\)	\(e\left(\frac{347}{500}\right)\)	\(e\left(\frac{71}{250}\right)\)	\(e\left(\frac{42}{125}\right)\)	\(e\left(\frac{37}{100}\right)\)	\(e\left(\frac{463}{500}\right)\)	\(e\left(\frac{97}{250}\right)\)	\(e\left(\frac{74}{125}\right)\)	\(e\left(\frac{489}{500}\right)\)	\(e\left(\frac{119}{500}\right)\)
\(\chi_{625}(28,\cdot)\)	625.l	500	yes	\(-1\)	\(1\)	\(e\left(\frac{487}{500}\right)\)	\(e\left(\frac{109}{500}\right)\)	\(e\left(\frac{237}{250}\right)\)	\(e\left(\frac{24}{125}\right)\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{461}{500}\right)\)	\(e\left(\frac{109}{250}\right)\)	\(e\left(\frac{78}{125}\right)\)	\(e\left(\frac{83}{500}\right)\)	\(e\left(\frac{193}{500}\right)\)
\(\chi_{625}(29,\cdot)\)	625.k	250	yes	\(1\)	\(1\)	\(e\left(\frac{81}{250}\right)\)	\(e\left(\frac{167}{250}\right)\)	\(e\left(\frac{81}{125}\right)\)	\(e\left(\frac{124}{125}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{243}{250}\right)\)	\(e\left(\frac{42}{125}\right)\)	\(e\left(\frac{28}{125}\right)\)	\(e\left(\frac{79}{250}\right)\)	\(e\left(\frac{9}{250}\right)\)
\(\chi_{625}(31,\cdot)\)	625.j	125	yes	\(1\)	\(1\)	\(e\left(\frac{12}{125}\right)\)	\(e\left(\frac{34}{125}\right)\)	\(e\left(\frac{24}{125}\right)\)	\(e\left(\frac{46}{125}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{36}{125}\right)\)	\(e\left(\frac{68}{125}\right)\)	\(e\left(\frac{87}{125}\right)\)	\(e\left(\frac{58}{125}\right)\)	\(e\left(\frac{43}{125}\right)\)
\(\chi_{625}(32,\cdot)\)	625.i	100	no	\(-1\)	\(1\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{100}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{9}{100}\right)\)	\(e\left(\frac{39}{100}\right)\)
\(\chi_{625}(33,\cdot)\)	625.l	500	yes	\(-1\)	\(1\)	\(e\left(\frac{83}{500}\right)\)	\(e\left(\frac{381}{500}\right)\)	\(e\left(\frac{83}{250}\right)\)	\(e\left(\frac{116}{125}\right)\)	\(e\left(\frac{51}{100}\right)\)	\(e\left(\frac{249}{500}\right)\)	\(e\left(\frac{131}{250}\right)\)	\(e\left(\frac{2}{125}\right)\)	\(e\left(\frac{47}{500}\right)\)	\(e\left(\frac{37}{500}\right)\)
\(\chi_{625}(34,\cdot)\)	625.k	250	yes	\(1\)	\(1\)	\(e\left(\frac{87}{250}\right)\)	\(e\left(\frac{59}{250}\right)\)	\(e\left(\frac{87}{125}\right)\)	\(e\left(\frac{73}{125}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{11}{250}\right)\)	\(e\left(\frac{59}{125}\right)\)	\(e\left(\frac{81}{125}\right)\)	\(e\left(\frac{233}{250}\right)\)	\(e\left(\frac{93}{250}\right)\)
\(\chi_{625}(36,\cdot)\)	625.j	125	yes	\(1\)	\(1\)	\(e\left(\frac{54}{125}\right)\)	\(e\left(\frac{28}{125}\right)\)	\(e\left(\frac{108}{125}\right)\)	\(e\left(\frac{82}{125}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{37}{125}\right)\)	\(e\left(\frac{56}{125}\right)\)	\(e\left(\frac{79}{125}\right)\)	\(e\left(\frac{11}{125}\right)\)	\(e\left(\frac{6}{125}\right)\)
\(\chi_{625}(37,\cdot)\)	625.l	500	yes	\(-1\)	\(1\)	\(e\left(\frac{329}{500}\right)\)	\(e\left(\frac{203}{500}\right)\)	\(e\left(\frac{79}{250}\right)\)	\(e\left(\frac{8}{125}\right)\)	\(e\left(\frac{13}{100}\right)\)	\(e\left(\frac{487}{500}\right)\)	\(e\left(\frac{203}{250}\right)\)	\(e\left(\frac{26}{125}\right)\)	\(e\left(\frac{361}{500}\right)\)	\(e\left(\frac{231}{500}\right)\)
\(\chi_{625}(38,\cdot)\)	625.l	500	yes	\(-1\)	\(1\)	\(e\left(\frac{419}{500}\right)\)	\(e\left(\frac{333}{500}\right)\)	\(e\left(\frac{169}{250}\right)\)	\(e\left(\frac{63}{125}\right)\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{257}{500}\right)\)	\(e\left(\frac{83}{250}\right)\)	\(e\left(\frac{111}{125}\right)\)	\(e\left(\frac{171}{500}\right)\)	\(e\left(\frac{241}{500}\right)\)
\(\chi_{625}(39,\cdot)\)	625.k	250	yes	\(1\)	\(1\)	\(e\left(\frac{123}{250}\right)\)	\(e\left(\frac{161}{250}\right)\)	\(e\left(\frac{123}{125}\right)\)	\(e\left(\frac{17}{125}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{119}{250}\right)\)	\(e\left(\frac{36}{125}\right)\)	\(e\left(\frac{24}{125}\right)\)	\(e\left(\frac{157}{250}\right)\)	\(e\left(\frac{97}{250}\right)\)

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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.