LMFDB - Group of Dirichlet characters of modulus 15125

Show commands: PariGP / SageMath

sage: H = DirichletGroup(15125)

pari: g = idealstar(,15125,2)

Character group

sage: G.order() pari: g.no
Order	=	11000
sage: H.invariants() pari: g.cyc
Structure	=	$C_{10}\times C_{1100}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{15125}(3752,\cdot)$, $\chi_{15125}(11376,\cdot)$

First 32 of 11000 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	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$12$	$13$	$14$
$\chi_{15125}(1,\cdot)$	15125.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{15125}(2,\cdot)$	15125.fl	1100	yes	$1$	$1$	$e\left(\frac{21}{1100}\right)$	$e\left(\frac{87}{100}\right)$	$e\left(\frac{21}{550}\right)$	$e\left(\frac{489}{550}\right)$	$e\left(\frac{201}{220}\right)$	$e\left(\frac{63}{1100}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{999}{1100}\right)$	$e\left(\frac{339}{1100}\right)$	$e\left(\frac{513}{550}\right)$
$\chi_{15125}(3,\cdot)$	15125.cw	100	no	$-1$	$1$	$e\left(\frac{87}{100}\right)$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{61}{100}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{63}{100}\right)$	$e\left(\frac{53}{100}\right)$	$e\left(\frac{21}{50}\right)$
$\chi_{15125}(4,\cdot)$	15125.et	550	yes	$1$	$1$	$e\left(\frac{21}{550}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{21}{275}\right)$	$e\left(\frac{214}{275}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{63}{550}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{449}{550}\right)$	$e\left(\frac{339}{550}\right)$	$e\left(\frac{238}{275}\right)$
$\chi_{15125}(6,\cdot)$	15125.ew	550	yes	$-1$	$1$	$e\left(\frac{489}{550}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{214}{275}\right)$	$e\left(\frac{357}{550}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{367}{550}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{148}{275}\right)$	$e\left(\frac{461}{550}\right)$	$e\left(\frac{97}{275}\right)$
$\chi_{15125}(7,\cdot)$	15125.eb	220	no	$1$	$1$	$e\left(\frac{201}{220}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{153}{220}\right)$	$e\left(\frac{163}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{83}{220}\right)$	$e\left(\frac{127}{220}\right)$	$e\left(\frac{67}{110}\right)$
$\chi_{15125}(8,\cdot)$	15125.fl	1100	yes	$1$	$1$	$e\left(\frac{63}{1100}\right)$	$e\left(\frac{61}{100}\right)$	$e\left(\frac{63}{550}\right)$	$e\left(\frac{367}{550}\right)$	$e\left(\frac{163}{220}\right)$	$e\left(\frac{189}{1100}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{797}{1100}\right)$	$e\left(\frac{1017}{1100}\right)$	$e\left(\frac{439}{550}\right)$
$\chi_{15125}(9,\cdot)$	15125.co	50	no	$1$	$1$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{21}{25}\right)$
$\chi_{15125}(12,\cdot)$	15125.fh	1100	yes	$-1$	$1$	$e\left(\frac{999}{1100}\right)$	$e\left(\frac{63}{100}\right)$	$e\left(\frac{449}{550}\right)$	$e\left(\frac{148}{275}\right)$	$e\left(\frac{83}{220}\right)$	$e\left(\frac{797}{1100}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{491}{1100}\right)$	$e\left(\frac{161}{1100}\right)$	$e\left(\frac{157}{550}\right)$
$\chi_{15125}(13,\cdot)$	15125.fe	1100	yes	$1$	$1$	$e\left(\frac{339}{1100}\right)$	$e\left(\frac{53}{100}\right)$	$e\left(\frac{339}{550}\right)$	$e\left(\frac{461}{550}\right)$	$e\left(\frac{127}{220}\right)$	$e\left(\frac{1017}{1100}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{161}{1100}\right)$	$e\left(\frac{1041}{1100}\right)$	$e\left(\frac{487}{550}\right)$
$\chi_{15125}(14,\cdot)$	15125.ex	550	yes	$1$	$1$	$e\left(\frac{513}{550}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{238}{275}\right)$	$e\left(\frac{97}{275}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{439}{550}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{157}{550}\right)$	$e\left(\frac{487}{550}\right)$	$e\left(\frac{149}{275}\right)$
$\chi_{15125}(16,\cdot)$	15125.en	275	yes	$1$	$1$	$e\left(\frac{21}{275}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{42}{275}\right)$	$e\left(\frac{153}{275}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{63}{275}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{174}{275}\right)$	$e\left(\frac{64}{275}\right)$	$e\left(\frac{201}{275}\right)$
$\chi_{15125}(17,\cdot)$	15125.fj	1100	yes	$1$	$1$	$e\left(\frac{193}{1100}\right)$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{193}{550}\right)$	$e\left(\frac{267}{550}\right)$	$e\left(\frac{37}{220}\right)$	$e\left(\frac{579}{1100}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{727}{1100}\right)$	$e\left(\frac{507}{1100}\right)$	$e\left(\frac{189}{550}\right)$
$\chi_{15125}(18,\cdot)$	15125.eh	220	no	$1$	$1$	$e\left(\frac{167}{220}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{3}{220}\right)$	$e\left(\frac{61}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{37}{220}\right)$	$e\left(\frac{81}{220}\right)$	$e\left(\frac{17}{22}\right)$
$\chi_{15125}(19,\cdot)$	15125.fa	550	yes	$-1$	$1$	$e\left(\frac{257}{275}\right)$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{239}{275}\right)$	$e\left(\frac{327}{550}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{221}{275}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{291}{550}\right)$	$e\left(\frac{63}{275}\right)$	$e\left(\frac{142}{275}\right)$
$\chi_{15125}(21,\cdot)$	15125.er	550	yes	$-1$	$1$	$e\left(\frac{431}{550}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{156}{275}\right)$	$e\left(\frac{123}{550}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{193}{550}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{2}{275}\right)$	$e\left(\frac{59}{550}\right)$	$e\left(\frac{8}{275}\right)$
$\chi_{15125}(23,\cdot)$	15125.fh	1100	yes	$-1$	$1$	$e\left(\frac{1041}{1100}\right)$	$e\left(\frac{17}{100}\right)$	$e\left(\frac{491}{550}\right)$	$e\left(\frac{32}{275}\right)$	$e\left(\frac{177}{220}\right)$	$e\left(\frac{923}{1100}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{69}{1100}\right)$	$e\left(\frac{399}{1100}\right)$	$e\left(\frac{413}{550}\right)$
$\chi_{15125}(24,\cdot)$	15125.dr	110	no	$-1$	$1$	$e\left(\frac{51}{55}\right)$	$-1$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{43}{55}\right)$	$1$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{12}{55}\right)$
$\chi_{15125}(26,\cdot)$	15125.cr	55	no	$1$	$1$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{15125}(27,\cdot)$	15125.cw	100	no	$-1$	$1$	$e\left(\frac{61}{100}\right)$	$e\left(\frac{67}{100}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{83}{100}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{59}{100}\right)$	$e\left(\frac{13}{50}\right)$
$\chi_{15125}(28,\cdot)$	15125.fm	1100	yes	$1$	$1$	$e\left(\frac{1047}{1100}\right)$	$e\left(\frac{29}{100}\right)$	$e\left(\frac{497}{550}\right)$	$e\left(\frac{133}{550}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{941}{1100}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{213}{1100}\right)$	$e\left(\frac{213}{1100}\right)$	$e\left(\frac{261}{550}\right)$
$\chi_{15125}(29,\cdot)$	15125.fa	550	yes	$-1$	$1$	$e\left(\frac{213}{275}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{151}{275}\right)$	$e\left(\frac{393}{550}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{89}{275}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{269}{550}\right)$	$e\left(\frac{217}{275}\right)$	$e\left(\frac{153}{275}\right)$
$\chi_{15125}(31,\cdot)$	15125.ek	275	yes	$1$	$1$	$e\left(\frac{72}{275}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{144}{275}\right)$	$e\left(\frac{116}{275}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{216}{275}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{188}{275}\right)$	$e\left(\frac{188}{275}\right)$	$e\left(\frac{147}{275}\right)$
$\chi_{15125}(32,\cdot)$	15125.ea	220	no	$1$	$1$	$e\left(\frac{21}{220}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{63}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{119}{220}\right)$	$e\left(\frac{119}{220}\right)$	$e\left(\frac{73}{110}\right)$
$\chi_{15125}(34,\cdot)$	15125.eu	550	yes	$1$	$1$	$e\left(\frac{107}{550}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{107}{275}\right)$	$e\left(\frac{103}{275}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{321}{550}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{313}{550}\right)$	$e\left(\frac{423}{550}\right)$	$e\left(\frac{76}{275}\right)$
$\chi_{15125}(36,\cdot)$	15125.el	275	yes	$1$	$1$	$e\left(\frac{214}{275}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{153}{275}\right)$	$e\left(\frac{82}{275}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{92}{275}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{21}{275}\right)$	$e\left(\frac{186}{275}\right)$	$e\left(\frac{194}{275}\right)$
$\chi_{15125}(37,\cdot)$	15125.ff	1100	yes	$-1$	$1$	$e\left(\frac{739}{1100}\right)$	$e\left(\frac{63}{100}\right)$	$e\left(\frac{189}{550}\right)$	$e\left(\frac{83}{275}\right)$	$e\left(\frac{71}{220}\right)$	$e\left(\frac{17}{1100}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{1071}{1100}\right)$	$e\left(\frac{961}{1100}\right)$	$e\left(\frac{547}{550}\right)$
$\chi_{15125}(38,\cdot)$	15125.fg	1100	yes	$-1$	$1$	$e\left(\frac{1049}{1100}\right)$	$e\left(\frac{53}{100}\right)$	$e\left(\frac{499}{550}\right)$	$e\left(\frac{133}{275}\right)$	$e\left(\frac{109}{220}\right)$	$e\left(\frac{947}{1100}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{481}{1100}\right)$	$e\left(\frac{591}{1100}\right)$	$e\left(\frac{247}{550}\right)$
$\chi_{15125}(39,\cdot)$	15125.fb	550	yes	$-1$	$1$	$e\left(\frac{49}{275}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{98}{275}\right)$	$e\left(\frac{329}{550}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{147}{275}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{427}{550}\right)$	$e\left(\frac{131}{275}\right)$	$e\left(\frac{84}{275}\right)$
$\chi_{15125}(41,\cdot)$	15125.fc	550	yes	$-1$	$1$	$e\left(\frac{357}{550}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{82}{275}\right)$	$e\left(\frac{71}{550}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{521}{550}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{214}{275}\right)$	$e\left(\frac{153}{550}\right)$	$e\left(\frac{141}{275}\right)$
$\chi_{15125}(42,\cdot)$	15125.fi	1100	yes	$-1$	$1$	$e\left(\frac{883}{1100}\right)$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{333}{550}\right)$	$e\left(\frac{31}{275}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{449}{1100}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{1007}{1100}\right)$	$e\left(\frac{457}{1100}\right)$	$e\left(\frac{529}{550}\right)$
$\chi_{15125}(43,\cdot)$	15125.ea	220	no	$1$	$1$	$e\left(\frac{39}{220}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{117}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{220}\right)$	$e\left(\frac{1}{220}\right)$	$e\left(\frac{57}{110}\right)$

Click here to search among the remaining 10968 characters.

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	$15125$
Structure	\(C_{10}\times C_{1100}\)
Order	$11000$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(12\)	\(13\)	\(14\)
\(\chi_{15125}(1,\cdot)\)	15125.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{15125}(2,\cdot)\)	15125.fl	1100	yes	\(1\)	\(1\)	\(e\left(\frac{21}{1100}\right)\)	\(e\left(\frac{87}{100}\right)\)	\(e\left(\frac{21}{550}\right)\)	\(e\left(\frac{489}{550}\right)\)	\(e\left(\frac{201}{220}\right)\)	\(e\left(\frac{63}{1100}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{999}{1100}\right)\)	\(e\left(\frac{339}{1100}\right)\)	\(e\left(\frac{513}{550}\right)\)
\(\chi_{15125}(3,\cdot)\)	15125.cw	100	no	\(-1\)	\(1\)	\(e\left(\frac{87}{100}\right)\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{61}{100}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{63}{100}\right)\)	\(e\left(\frac{53}{100}\right)\)	\(e\left(\frac{21}{50}\right)\)
\(\chi_{15125}(4,\cdot)\)	15125.et	550	yes	\(1\)	\(1\)	\(e\left(\frac{21}{550}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{21}{275}\right)\)	\(e\left(\frac{214}{275}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{63}{550}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{449}{550}\right)\)	\(e\left(\frac{339}{550}\right)\)	\(e\left(\frac{238}{275}\right)\)
\(\chi_{15125}(6,\cdot)\)	15125.ew	550	yes	\(-1\)	\(1\)	\(e\left(\frac{489}{550}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{214}{275}\right)\)	\(e\left(\frac{357}{550}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{367}{550}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{148}{275}\right)\)	\(e\left(\frac{461}{550}\right)\)	\(e\left(\frac{97}{275}\right)\)
\(\chi_{15125}(7,\cdot)\)	15125.eb	220	no	\(1\)	\(1\)	\(e\left(\frac{201}{220}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{153}{220}\right)\)	\(e\left(\frac{163}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{83}{220}\right)\)	\(e\left(\frac{127}{220}\right)\)	\(e\left(\frac{67}{110}\right)\)
\(\chi_{15125}(8,\cdot)\)	15125.fl	1100	yes	\(1\)	\(1\)	\(e\left(\frac{63}{1100}\right)\)	\(e\left(\frac{61}{100}\right)\)	\(e\left(\frac{63}{550}\right)\)	\(e\left(\frac{367}{550}\right)\)	\(e\left(\frac{163}{220}\right)\)	\(e\left(\frac{189}{1100}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{797}{1100}\right)\)	\(e\left(\frac{1017}{1100}\right)\)	\(e\left(\frac{439}{550}\right)\)
\(\chi_{15125}(9,\cdot)\)	15125.co	50	no	\(1\)	\(1\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{21}{25}\right)\)
\(\chi_{15125}(12,\cdot)\)	15125.fh	1100	yes	\(-1\)	\(1\)	\(e\left(\frac{999}{1100}\right)\)	\(e\left(\frac{63}{100}\right)\)	\(e\left(\frac{449}{550}\right)\)	\(e\left(\frac{148}{275}\right)\)	\(e\left(\frac{83}{220}\right)\)	\(e\left(\frac{797}{1100}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{491}{1100}\right)\)	\(e\left(\frac{161}{1100}\right)\)	\(e\left(\frac{157}{550}\right)\)
\(\chi_{15125}(13,\cdot)\)	15125.fe	1100	yes	\(1\)	\(1\)	\(e\left(\frac{339}{1100}\right)\)	\(e\left(\frac{53}{100}\right)\)	\(e\left(\frac{339}{550}\right)\)	\(e\left(\frac{461}{550}\right)\)	\(e\left(\frac{127}{220}\right)\)	\(e\left(\frac{1017}{1100}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{161}{1100}\right)\)	\(e\left(\frac{1041}{1100}\right)\)	\(e\left(\frac{487}{550}\right)\)
\(\chi_{15125}(14,\cdot)\)	15125.ex	550	yes	\(1\)	\(1\)	\(e\left(\frac{513}{550}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{238}{275}\right)\)	\(e\left(\frac{97}{275}\right)\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{439}{550}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{157}{550}\right)\)	\(e\left(\frac{487}{550}\right)\)	\(e\left(\frac{149}{275}\right)\)
\(\chi_{15125}(16,\cdot)\)	15125.en	275	yes	\(1\)	\(1\)	\(e\left(\frac{21}{275}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{42}{275}\right)\)	\(e\left(\frac{153}{275}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{63}{275}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{174}{275}\right)\)	\(e\left(\frac{64}{275}\right)\)	\(e\left(\frac{201}{275}\right)\)
\(\chi_{15125}(17,\cdot)\)	15125.fj	1100	yes	\(1\)	\(1\)	\(e\left(\frac{193}{1100}\right)\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{193}{550}\right)\)	\(e\left(\frac{267}{550}\right)\)	\(e\left(\frac{37}{220}\right)\)	\(e\left(\frac{579}{1100}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{727}{1100}\right)\)	\(e\left(\frac{507}{1100}\right)\)	\(e\left(\frac{189}{550}\right)\)
\(\chi_{15125}(18,\cdot)\)	15125.eh	220	no	\(1\)	\(1\)	\(e\left(\frac{167}{220}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{3}{220}\right)\)	\(e\left(\frac{61}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{37}{220}\right)\)	\(e\left(\frac{81}{220}\right)\)	\(e\left(\frac{17}{22}\right)\)
\(\chi_{15125}(19,\cdot)\)	15125.fa	550	yes	\(-1\)	\(1\)	\(e\left(\frac{257}{275}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{239}{275}\right)\)	\(e\left(\frac{327}{550}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{221}{275}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{291}{550}\right)\)	\(e\left(\frac{63}{275}\right)\)	\(e\left(\frac{142}{275}\right)\)
\(\chi_{15125}(21,\cdot)\)	15125.er	550	yes	\(-1\)	\(1\)	\(e\left(\frac{431}{550}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{156}{275}\right)\)	\(e\left(\frac{123}{550}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{193}{550}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{2}{275}\right)\)	\(e\left(\frac{59}{550}\right)\)	\(e\left(\frac{8}{275}\right)\)
\(\chi_{15125}(23,\cdot)\)	15125.fh	1100	yes	\(-1\)	\(1\)	\(e\left(\frac{1041}{1100}\right)\)	\(e\left(\frac{17}{100}\right)\)	\(e\left(\frac{491}{550}\right)\)	\(e\left(\frac{32}{275}\right)\)	\(e\left(\frac{177}{220}\right)\)	\(e\left(\frac{923}{1100}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{69}{1100}\right)\)	\(e\left(\frac{399}{1100}\right)\)	\(e\left(\frac{413}{550}\right)\)
\(\chi_{15125}(24,\cdot)\)	15125.dr	110	no	\(-1\)	\(1\)	\(e\left(\frac{51}{55}\right)\)	\(-1\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(1\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{12}{55}\right)\)
\(\chi_{15125}(26,\cdot)\)	15125.cr	55	no	\(1\)	\(1\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{15125}(27,\cdot)\)	15125.cw	100	no	\(-1\)	\(1\)	\(e\left(\frac{61}{100}\right)\)	\(e\left(\frac{67}{100}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{83}{100}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{59}{100}\right)\)	\(e\left(\frac{13}{50}\right)\)
\(\chi_{15125}(28,\cdot)\)	15125.fm	1100	yes	\(1\)	\(1\)	\(e\left(\frac{1047}{1100}\right)\)	\(e\left(\frac{29}{100}\right)\)	\(e\left(\frac{497}{550}\right)\)	\(e\left(\frac{133}{550}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{941}{1100}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{213}{1100}\right)\)	\(e\left(\frac{213}{1100}\right)\)	\(e\left(\frac{261}{550}\right)\)
\(\chi_{15125}(29,\cdot)\)	15125.fa	550	yes	\(-1\)	\(1\)	\(e\left(\frac{213}{275}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{151}{275}\right)\)	\(e\left(\frac{393}{550}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{89}{275}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{269}{550}\right)\)	\(e\left(\frac{217}{275}\right)\)	\(e\left(\frac{153}{275}\right)\)
\(\chi_{15125}(31,\cdot)\)	15125.ek	275	yes	\(1\)	\(1\)	\(e\left(\frac{72}{275}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{144}{275}\right)\)	\(e\left(\frac{116}{275}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{216}{275}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{188}{275}\right)\)	\(e\left(\frac{188}{275}\right)\)	\(e\left(\frac{147}{275}\right)\)
\(\chi_{15125}(32,\cdot)\)	15125.ea	220	no	\(1\)	\(1\)	\(e\left(\frac{21}{220}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{63}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{119}{220}\right)\)	\(e\left(\frac{119}{220}\right)\)	\(e\left(\frac{73}{110}\right)\)
\(\chi_{15125}(34,\cdot)\)	15125.eu	550	yes	\(1\)	\(1\)	\(e\left(\frac{107}{550}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{107}{275}\right)\)	\(e\left(\frac{103}{275}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{321}{550}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{313}{550}\right)\)	\(e\left(\frac{423}{550}\right)\)	\(e\left(\frac{76}{275}\right)\)
\(\chi_{15125}(36,\cdot)\)	15125.el	275	yes	\(1\)	\(1\)	\(e\left(\frac{214}{275}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{153}{275}\right)\)	\(e\left(\frac{82}{275}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{92}{275}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{21}{275}\right)\)	\(e\left(\frac{186}{275}\right)\)	\(e\left(\frac{194}{275}\right)\)
\(\chi_{15125}(37,\cdot)\)	15125.ff	1100	yes	\(-1\)	\(1\)	\(e\left(\frac{739}{1100}\right)\)	\(e\left(\frac{63}{100}\right)\)	\(e\left(\frac{189}{550}\right)\)	\(e\left(\frac{83}{275}\right)\)	\(e\left(\frac{71}{220}\right)\)	\(e\left(\frac{17}{1100}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{1071}{1100}\right)\)	\(e\left(\frac{961}{1100}\right)\)	\(e\left(\frac{547}{550}\right)\)
\(\chi_{15125}(38,\cdot)\)	15125.fg	1100	yes	\(-1\)	\(1\)	\(e\left(\frac{1049}{1100}\right)\)	\(e\left(\frac{53}{100}\right)\)	\(e\left(\frac{499}{550}\right)\)	\(e\left(\frac{133}{275}\right)\)	\(e\left(\frac{109}{220}\right)\)	\(e\left(\frac{947}{1100}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{481}{1100}\right)\)	\(e\left(\frac{591}{1100}\right)\)	\(e\left(\frac{247}{550}\right)\)
\(\chi_{15125}(39,\cdot)\)	15125.fb	550	yes	\(-1\)	\(1\)	\(e\left(\frac{49}{275}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{98}{275}\right)\)	\(e\left(\frac{329}{550}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{147}{275}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{427}{550}\right)\)	\(e\left(\frac{131}{275}\right)\)	\(e\left(\frac{84}{275}\right)\)
\(\chi_{15125}(41,\cdot)\)	15125.fc	550	yes	\(-1\)	\(1\)	\(e\left(\frac{357}{550}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{82}{275}\right)\)	\(e\left(\frac{71}{550}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{521}{550}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{214}{275}\right)\)	\(e\left(\frac{153}{550}\right)\)	\(e\left(\frac{141}{275}\right)\)
\(\chi_{15125}(42,\cdot)\)	15125.fi	1100	yes	\(-1\)	\(1\)	\(e\left(\frac{883}{1100}\right)\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{333}{550}\right)\)	\(e\left(\frac{31}{275}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{449}{1100}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{1007}{1100}\right)\)	\(e\left(\frac{457}{1100}\right)\)	\(e\left(\frac{529}{550}\right)\)
\(\chi_{15125}(43,\cdot)\)	15125.ea	220	no	\(1\)	\(1\)	\(e\left(\frac{39}{220}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{117}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{220}\right)\)	\(e\left(\frac{1}{220}\right)\)	\(e\left(\frac{57}{110}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 11000 characters

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