Properties

Modulus 3997
Structure \(C_{570}\times C_{6}\)
Order 3420

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Show commands for: Pari/GP / SageMath

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(3997)
 
pari: g = idealstar(,3997,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 3420
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{570}\times C_{6}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{3997}(1716,\cdot)$, $\chi_{3997}(2285,\cdot)$

First 32 of 3420 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.

orbit label order primitive -1 1 2 3 4 5 6 8 9 10 11 12
\(\chi_{3997}(1,\cdot)\) 3997.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{3997}(2,\cdot)\) 3997.ci 114 yes \(-1\) \(1\) \(e\left(\frac{29}{38}\right)\) \(e\left(\frac{11}{38}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{11}{38}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{35}{38}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{31}{38}\right)\)
\(\chi_{3997}(3,\cdot)\) 3997.db 570 yes \(1\) \(1\) \(e\left(\frac{11}{38}\right)\) \(e\left(\frac{16}{95}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{109}{190}\right)\) \(e\left(\frac{87}{190}\right)\) \(e\left(\frac{33}{38}\right)\) \(e\left(\frac{32}{95}\right)\) \(e\left(\frac{82}{95}\right)\) \(e\left(\frac{13}{95}\right)\) \(e\left(\frac{71}{95}\right)\)
\(\chi_{3997}(4,\cdot)\) 3997.bs 57 yes \(1\) \(1\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{12}{19}\right)\)
\(\chi_{3997}(5,\cdot)\) 3997.cq 570 yes \(-1\) \(1\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{109}{190}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{113}{190}\right)\) \(e\left(\frac{139}{190}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{14}{95}\right)\) \(e\left(\frac{143}{190}\right)\) \(e\left(\frac{71}{95}\right)\) \(e\left(\frac{169}{190}\right)\)
\(\chi_{3997}(6,\cdot)\) 3997.cj 190 yes \(-1\) \(1\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{87}{190}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{139}{190}\right)\) \(e\left(\frac{97}{190}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{87}{95}\right)\) \(e\left(\frac{149}{190}\right)\) \(e\left(\frac{68}{95}\right)\) \(e\left(\frac{107}{190}\right)\)
\(\chi_{3997}(8,\cdot)\) 3997.br 38 no \(-1\) \(1\) \(e\left(\frac{11}{38}\right)\) \(e\left(\frac{33}{38}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{33}{38}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{29}{38}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{17}{38}\right)\)
\(\chi_{3997}(9,\cdot)\) 3997.cm 285 yes \(1\) \(1\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{32}{95}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{14}{95}\right)\) \(e\left(\frac{87}{95}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{64}{95}\right)\) \(e\left(\frac{69}{95}\right)\) \(e\left(\frac{26}{95}\right)\) \(e\left(\frac{47}{95}\right)\)
\(\chi_{3997}(10,\cdot)\) 3997.db 570 yes \(1\) \(1\) \(e\left(\frac{35}{38}\right)\) \(e\left(\frac{82}{95}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{143}{190}\right)\) \(e\left(\frac{149}{190}\right)\) \(e\left(\frac{29}{38}\right)\) \(e\left(\frac{69}{95}\right)\) \(e\left(\frac{64}{95}\right)\) \(e\left(\frac{31}{95}\right)\) \(e\left(\frac{67}{95}\right)\)
\(\chi_{3997}(11,\cdot)\) 3997.cm 285 yes \(1\) \(1\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{13}{95}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{71}{95}\right)\) \(e\left(\frac{68}{95}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{26}{95}\right)\) \(e\left(\frac{31}{95}\right)\) \(e\left(\frac{64}{95}\right)\) \(e\left(\frac{28}{95}\right)\)
\(\chi_{3997}(12,\cdot)\) 3997.db 570 yes \(1\) \(1\) \(e\left(\frac{31}{38}\right)\) \(e\left(\frac{71}{95}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{169}{190}\right)\) \(e\left(\frac{107}{190}\right)\) \(e\left(\frac{17}{38}\right)\) \(e\left(\frac{47}{95}\right)\) \(e\left(\frac{67}{95}\right)\) \(e\left(\frac{28}{95}\right)\) \(e\left(\frac{36}{95}\right)\)
\(\chi_{3997}(13,\cdot)\) 3997.cz 570 yes \(-1\) \(1\) \(e\left(\frac{32}{57}\right)\) \(e\left(\frac{67}{570}\right)\) \(e\left(\frac{7}{57}\right)\) \(e\left(\frac{59}{570}\right)\) \(e\left(\frac{129}{190}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{67}{285}\right)\) \(e\left(\frac{379}{570}\right)\) \(e\left(\frac{143}{285}\right)\) \(e\left(\frac{137}{570}\right)\)
\(\chi_{3997}(15,\cdot)\) 3997.ck 190 no \(-1\) \(1\) \(e\left(\frac{17}{38}\right)\) \(e\left(\frac{141}{190}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{16}{95}\right)\) \(e\left(\frac{18}{95}\right)\) \(e\left(\frac{13}{38}\right)\) \(e\left(\frac{46}{95}\right)\) \(e\left(\frac{117}{190}\right)\) \(e\left(\frac{84}{95}\right)\) \(e\left(\frac{121}{190}\right)\)
\(\chi_{3997}(16,\cdot)\) 3997.bs 57 yes \(1\) \(1\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{5}{19}\right)\)
\(\chi_{3997}(17,\cdot)\) 3997.ct 570 yes \(1\) \(1\) \(e\left(\frac{25}{114}\right)\) \(e\left(\frac{254}{285}\right)\) \(e\left(\frac{25}{57}\right)\) \(e\left(\frac{341}{570}\right)\) \(e\left(\frac{21}{190}\right)\) \(e\left(\frac{25}{38}\right)\) \(e\left(\frac{223}{285}\right)\) \(e\left(\frac{233}{285}\right)\) \(e\left(\frac{242}{285}\right)\) \(e\left(\frac{94}{285}\right)\)
\(\chi_{3997}(18,\cdot)\) 3997.da 570 yes \(-1\) \(1\) \(e\left(\frac{13}{38}\right)\) \(e\left(\frac{119}{190}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{29}{95}\right)\) \(e\left(\frac{92}{95}\right)\) \(e\left(\frac{1}{38}\right)\) \(e\left(\frac{24}{95}\right)\) \(e\left(\frac{123}{190}\right)\) \(e\left(\frac{81}{95}\right)\) \(e\left(\frac{59}{190}\right)\)
\(\chi_{3997}(19,\cdot)\) 3997.ct 570 yes \(1\) \(1\) \(e\left(\frac{71}{114}\right)\) \(e\left(\frac{181}{285}\right)\) \(e\left(\frac{14}{57}\right)\) \(e\left(\frac{289}{570}\right)\) \(e\left(\frac{49}{190}\right)\) \(e\left(\frac{33}{38}\right)\) \(e\left(\frac{77}{285}\right)\) \(e\left(\frac{37}{285}\right)\) \(e\left(\frac{58}{285}\right)\) \(e\left(\frac{251}{285}\right)\)
\(\chi_{3997}(20,\cdot)\) 3997.cj 190 yes \(-1\) \(1\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{29}{190}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{173}{190}\right)\) \(e\left(\frac{159}{190}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{29}{95}\right)\) \(e\left(\frac{113}{190}\right)\) \(e\left(\frac{86}{95}\right)\) \(e\left(\frac{99}{190}\right)\)
\(\chi_{3997}(22,\cdot)\) 3997.ck 190 no \(-1\) \(1\) \(e\left(\frac{13}{38}\right)\) \(e\left(\frac{81}{190}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{86}{95}\right)\) \(e\left(\frac{73}{95}\right)\) \(e\left(\frac{1}{38}\right)\) \(e\left(\frac{81}{95}\right)\) \(e\left(\frac{47}{190}\right)\) \(e\left(\frac{24}{95}\right)\) \(e\left(\frac{21}{190}\right)\)
\(\chi_{3997}(23,\cdot)\) 3997.cp 285 yes \(1\) \(1\) \(e\left(\frac{50}{57}\right)\) \(e\left(\frac{218}{285}\right)\) \(e\left(\frac{43}{57}\right)\) \(e\left(\frac{226}{285}\right)\) \(e\left(\frac{61}{95}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{151}{285}\right)\) \(e\left(\frac{191}{285}\right)\) \(e\left(\frac{284}{285}\right)\) \(e\left(\frac{148}{285}\right)\)
\(\chi_{3997}(24,\cdot)\) 3997.cq 570 yes \(-1\) \(1\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{7}{190}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{9}{190}\right)\) \(e\left(\frac{117}{190}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{7}{95}\right)\) \(e\left(\frac{119}{190}\right)\) \(e\left(\frac{83}{95}\right)\) \(e\left(\frac{37}{190}\right)\)
\(\chi_{3997}(25,\cdot)\) 3997.cm 285 yes \(1\) \(1\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{14}{95}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{18}{95}\right)\) \(e\left(\frac{44}{95}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{28}{95}\right)\) \(e\left(\frac{48}{95}\right)\) \(e\left(\frac{47}{95}\right)\) \(e\left(\frac{74}{95}\right)\)
\(\chi_{3997}(26,\cdot)\) 3997.cr 570 yes \(1\) \(1\) \(e\left(\frac{37}{114}\right)\) \(e\left(\frac{116}{285}\right)\) \(e\left(\frac{37}{57}\right)\) \(e\left(\frac{149}{570}\right)\) \(e\left(\frac{139}{190}\right)\) \(e\left(\frac{37}{38}\right)\) \(e\left(\frac{232}{285}\right)\) \(e\left(\frac{167}{285}\right)\) \(e\left(\frac{23}{285}\right)\) \(e\left(\frac{16}{285}\right)\)
\(\chi_{3997}(27,\cdot)\) 3997.cl 190 yes \(1\) \(1\) \(e\left(\frac{33}{38}\right)\) \(e\left(\frac{48}{95}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{137}{190}\right)\) \(e\left(\frac{71}{190}\right)\) \(e\left(\frac{23}{38}\right)\) \(e\left(\frac{1}{95}\right)\) \(e\left(\frac{56}{95}\right)\) \(e\left(\frac{39}{95}\right)\) \(e\left(\frac{23}{95}\right)\)
\(\chi_{3997}(29,\cdot)\) 3997.bv 57 no \(1\) \(1\) \(e\left(\frac{13}{57}\right)\) \(e\left(\frac{20}{57}\right)\) \(e\left(\frac{26}{57}\right)\) \(e\left(\frac{4}{57}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{40}{57}\right)\) \(e\left(\frac{17}{57}\right)\) \(e\left(\frac{2}{57}\right)\) \(e\left(\frac{46}{57}\right)\)
\(\chi_{3997}(30,\cdot)\) 3997.cm 285 yes \(1\) \(1\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{3}{95}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{31}{95}\right)\) \(e\left(\frac{23}{95}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{6}{95}\right)\) \(e\left(\frac{51}{95}\right)\) \(e\left(\frac{44}{95}\right)\) \(e\left(\frac{43}{95}\right)\)
\(\chi_{3997}(31,\cdot)\) 3997.cg 114 yes \(-1\) \(1\) \(e\left(\frac{22}{57}\right)\) \(e\left(\frac{37}{114}\right)\) \(e\left(\frac{44}{57}\right)\) \(e\left(\frac{53}{114}\right)\) \(e\left(\frac{27}{38}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{37}{57}\right)\) \(e\left(\frac{97}{114}\right)\) \(e\left(\frac{56}{57}\right)\) \(e\left(\frac{11}{114}\right)\)
\(\chi_{3997}(32,\cdot)\) 3997.ci 114 yes \(-1\) \(1\) \(e\left(\frac{31}{38}\right)\) \(e\left(\frac{17}{38}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{17}{38}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{23}{38}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{3}{38}\right)\)
\(\chi_{3997}(33,\cdot)\) 3997.db 570 yes \(1\) \(1\) \(e\left(\frac{33}{38}\right)\) \(e\left(\frac{29}{95}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{61}{190}\right)\) \(e\left(\frac{33}{190}\right)\) \(e\left(\frac{23}{38}\right)\) \(e\left(\frac{58}{95}\right)\) \(e\left(\frac{18}{95}\right)\) \(e\left(\frac{77}{95}\right)\) \(e\left(\frac{4}{95}\right)\)
\(\chi_{3997}(34,\cdot)\) 3997.cz 570 yes \(-1\) \(1\) \(e\left(\frac{56}{57}\right)\) \(e\left(\frac{103}{570}\right)\) \(e\left(\frac{55}{57}\right)\) \(e\left(\frac{431}{570}\right)\) \(e\left(\frac{31}{190}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{103}{285}\right)\) \(e\left(\frac{421}{570}\right)\) \(e\left(\frac{122}{285}\right)\) \(e\left(\frac{83}{570}\right)\)
\(\chi_{3997}(36,\cdot)\) 3997.bw 95 no \(1\) \(1\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{87}{95}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{44}{95}\right)\) \(e\left(\frac{2}{95}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{79}{95}\right)\) \(e\left(\frac{54}{95}\right)\) \(e\left(\frac{41}{95}\right)\) \(e\left(\frac{12}{95}\right)\)
\(\chi_{3997}(37,\cdot)\) 3997.cm 285 yes \(1\) \(1\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{87}{95}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{44}{95}\right)\) \(e\left(\frac{2}{95}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{79}{95}\right)\) \(e\left(\frac{54}{95}\right)\) \(e\left(\frac{41}{95}\right)\) \(e\left(\frac{12}{95}\right)\)