sage: H = DirichletGroup(7524)
pari: g = idealstar(,7524,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 2160 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{2}\times C_{6}\times C_{90}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{7524}(3763,\cdot)$, $\chi_{7524}(6689,\cdot)$, $\chi_{7524}(4105,\cdot)$, $\chi_{7524}(2377,\cdot)$ |
First 32 of 2160 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 | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) | \(37\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{7524}(1,\cdot)\) | 7524.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{7524}(5,\cdot)\) | 7524.ja | 90 | no | \(-1\) | \(1\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{67}{90}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{41}{90}\right)\) | \(e\left(\frac{4}{5}\right)\) |
\(\chi_{7524}(7,\cdot)\) | 7524.hm | 30 | yes | \(1\) | \(1\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(-1\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{2}{5}\right)\) |
\(\chi_{7524}(13,\cdot)\) | 7524.jq | 90 | no | \(1\) | \(1\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{61}{90}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{19}{90}\right)\) | \(e\left(\frac{7}{10}\right)\) |
\(\chi_{7524}(17,\cdot)\) | 7524.is | 90 | no | \(1\) | \(1\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{61}{90}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{11}{45}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{4}{5}\right)\) |
\(\chi_{7524}(23,\cdot)\) | 7524.eg | 18 | no | \(1\) | \(1\) | \(e\left(\frac{17}{18}\right)\) | \(-1\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(1\) |
\(\chi_{7524}(25,\cdot)\) | 7524.ib | 45 | no | \(1\) | \(1\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{22}{45}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{3}{5}\right)\) |
\(\chi_{7524}(29,\cdot)\) | 7524.iy | 90 | no | \(-1\) | \(1\) | \(e\left(\frac{67}{90}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{11}{45}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{22}{45}\right)\) | \(e\left(\frac{11}{90}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{9}{10}\right)\) |
\(\chi_{7524}(31,\cdot)\) | 7524.ft | 30 | yes | \(1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{7}{10}\right)\) |
\(\chi_{7524}(35,\cdot)\) | 7524.jd | 90 | no | \(-1\) | \(1\) | \(e\left(\frac{41}{90}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{19}{90}\right)\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{1}{5}\right)\) |
\(\chi_{7524}(37,\cdot)\) | 7524.dh | 10 | no | \(-1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) |
\(\chi_{7524}(41,\cdot)\) | 7524.iy | 90 | no | \(-1\) | \(1\) | \(e\left(\frac{83}{90}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{19}{90}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{1}{10}\right)\) |
\(\chi_{7524}(43,\cdot)\) | 7524.fr | 18 | yes | \(1\) | \(1\) | \(e\left(\frac{5}{9}\right)\) | \(1\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(1\) |
\(\chi_{7524}(47,\cdot)\) | 7524.iw | 90 | yes | \(1\) | \(1\) | \(e\left(\frac{13}{90}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{13}{90}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{13}{45}\right)\) | \(e\left(\frac{29}{90}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{3}{5}\right)\) |
\(\chi_{7524}(49,\cdot)\) | 7524.dx | 15 | no | \(1\) | \(1\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(1\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{4}{5}\right)\) |
\(\chi_{7524}(53,\cdot)\) | 7524.jf | 90 | no | \(1\) | \(1\) | \(e\left(\frac{61}{90}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{59}{90}\right)\) | \(e\left(\frac{1}{90}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{49}{90}\right)\) | \(e\left(\frac{7}{10}\right)\) |
\(\chi_{7524}(59,\cdot)\) | 7524.in | 90 | yes | \(-1\) | \(1\) | \(e\left(\frac{77}{90}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{13}{90}\right)\) | \(e\left(\frac{77}{90}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{9}{10}\right)\) |
\(\chi_{7524}(61,\cdot)\) | 7524.ik | 90 | no | \(-1\) | \(1\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{71}{90}\right)\) | \(e\left(\frac{19}{90}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{77}{90}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{31}{90}\right)\) | \(e\left(\frac{4}{5}\right)\) |
\(\chi_{7524}(65,\cdot)\) | 7524.z | 6 | no | \(-1\) | \(1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
\(\chi_{7524}(67,\cdot)\) | 7524.ea | 18 | no | \(1\) | \(1\) | \(e\left(\frac{7}{9}\right)\) | \(-1\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(-1\) |
\(\chi_{7524}(71,\cdot)\) | 7524.iu | 90 | no | \(-1\) | \(1\) | \(e\left(\frac{29}{90}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{31}{90}\right)\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{29}{45}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{3}{10}\right)\) |
\(\chi_{7524}(73,\cdot)\) | 7524.it | 90 | no | \(-1\) | \(1\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{73}{90}\right)\) | \(e\left(\frac{47}{90}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{61}{90}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{53}{90}\right)\) | \(e\left(\frac{2}{5}\right)\) |
\(\chi_{7524}(79,\cdot)\) | 7524.ii | 90 | yes | \(-1\) | \(1\) | \(e\left(\frac{13}{45}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{11}{90}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{29}{45}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{22}{45}\right)\) | \(e\left(\frac{7}{10}\right)\) |
\(\chi_{7524}(83,\cdot)\) | 7524.gs | 30 | yes | \(-1\) | \(1\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(1\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{4}{5}\right)\) |
\(\chi_{7524}(85,\cdot)\) | 7524.jt | 90 | no | \(-1\) | \(1\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{17}{90}\right)\) | \(e\left(\frac{13}{90}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{7}{90}\right)\) | \(e\left(\frac{3}{5}\right)\) |
\(\chi_{7524}(89,\cdot)\) | 7524.eo | 18 | no | \(1\) | \(1\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(-1\) |
\(\chi_{7524}(91,\cdot)\) | 7524.iv | 90 | no | \(1\) | \(1\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{77}{90}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{67}{90}\right)\) | \(e\left(\frac{1}{10}\right)\) |
\(\chi_{7524}(97,\cdot)\) | 7524.ig | 90 | no | \(-1\) | \(1\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{19}{90}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{11}{45}\right)\) | \(e\left(\frac{73}{90}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{7}{10}\right)\) |
\(\chi_{7524}(101,\cdot)\) | 7524.il | 90 | no | \(1\) | \(1\) | \(e\left(\frac{61}{90}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{29}{90}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{1}{5}\right)\) |
\(\chi_{7524}(103,\cdot)\) | 7524.hh | 30 | yes | \(1\) | \(1\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(-1\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{9}{10}\right)\) |
\(\chi_{7524}(107,\cdot)\) | 7524.gc | 30 | no | \(1\) | \(1\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{1}{10}\right)\) |
\(\chi_{7524}(109,\cdot)\) | 7524.fd | 18 | no | \(1\) | \(1\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(-1\) |