Properties

Modulus 4004
Structure \(C_{60}\times C_{6}\times C_{2}\times C_{2}\)
Order 1440

Learn more about

Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(4004)
pari: g = idealstar(,4004,2)

Character group

sage: G.order()
pari: g.no
Order = 1440
sage: H.invariants()
pari: g.cyc
Structure = \(C_{60}\times C_{6}\times C_{2}\times C_{2}\)
sage: H.gens()
pari: g.gen
Generators = $\chi_{4004}(2173,\cdot)$, $\chi_{4004}(2089,\cdot)$, $\chi_{4004}(3277,\cdot)$, $\chi_{4004}(2003,\cdot)$

First 32 of 1440 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 3 5 9 15 17 19 23 25 27 29
\(\chi_{4004}(1,\cdot)\) 4004.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{4004}(3,\cdot)\) 4004.ft 30 Yes \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{14}{15}\right)\)
\(\chi_{4004}(5,\cdot)\) 4004.im 60 No \(1\) \(1\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{4004}(9,\cdot)\) 4004.fg 15 No \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{13}{15}\right)\)
\(\chi_{4004}(15,\cdot)\) 4004.ih 60 No \(1\) \(1\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{11}{15}\right)\)
\(\chi_{4004}(17,\cdot)\) 4004.gm 30 No \(1\) \(1\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{11}{30}\right)\) \(1\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{29}{30}\right)\)
\(\chi_{4004}(19,\cdot)\) 4004.ia 60 Yes \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{23}{30}\right)\)
\(\chi_{4004}(23,\cdot)\) 4004.cu 6 No \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{4004}(25,\cdot)\) 4004.hg 30 No \(1\) \(1\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{4004}(27,\cdot)\) 4004.dq 10 No \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(-1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{4004}(29,\cdot)\) 4004.gx 30 No \(-1\) \(1\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{30}\right)\)
\(\chi_{4004}(31,\cdot)\) 4004.iw 60 Yes \(-1\) \(1\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{4004}(37,\cdot)\) 4004.ja 60 No \(-1\) \(1\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{11}{60}\right)\) \(-1\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{11}{15}\right)\)
\(\chi_{4004}(41,\cdot)\) 4004.ij 60 No \(-1\) \(1\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{13}{30}\right)\)
\(\chi_{4004}(43,\cdot)\) 4004.cj 6 No \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(-1\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{4004}(45,\cdot)\) 4004.fa 12 No \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(1\) \(e\left(\frac{11}{12}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{4004}(47,\cdot)\) 4004.iw 60 Yes \(-1\) \(1\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{4004}(51,\cdot)\) 4004.ge 30 Yes \(1\) \(1\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{4004}(53,\cdot)\) 4004.fi 15 No \(1\) \(1\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{4004}(57,\cdot)\) 4004.fk 20 No \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{20}\right)\) \(-1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{4004}(59,\cdot)\) 4004.ir 60 Yes \(-1\) \(1\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{31}{60}\right)\) \(1\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{15}\right)\)
\(\chi_{4004}(61,\cdot)\) 4004.hu 30 No \(1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{29}{30}\right)\)
\(\chi_{4004}(67,\cdot)\) 4004.ec 12 No \(1\) \(1\) \(-1\) \(e\left(\frac{1}{12}\right)\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{4004}(69,\cdot)\) 4004.fz 30 No \(-1\) \(1\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{4}{15}\right)\)
\(\chi_{4004}(71,\cdot)\) 4004.ih 60 No \(1\) \(1\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{15}\right)\)
\(\chi_{4004}(73,\cdot)\) 4004.ii 60 No \(-1\) \(1\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{4004}(75,\cdot)\) 4004.hm 30 Yes \(1\) \(1\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{19}{30}\right)\) \(-1\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{8}{15}\right)\)
\(\chi_{4004}(79,\cdot)\) 4004.gq 30 No \(1\) \(1\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{4004}(81,\cdot)\) 4004.fg 15 No \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{11}{15}\right)\)
\(\chi_{4004}(83,\cdot)\) 4004.fn 20 Yes \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{4004}(85,\cdot)\) 4004.iz 60 No \(1\) \(1\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{23}{30}\right)\)
\(\chi_{4004}(87,\cdot)\) 4004.cb 6 Yes \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\)