sage: H = DirichletGroup(3920)
pari: g = idealstar(,3920,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 1344 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{2}\times C_{4}\times C_{84}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{3920}(1471,\cdot)$, $\chi_{3920}(981,\cdot)$, $\chi_{3920}(3137,\cdot)$, $\chi_{3920}(3041,\cdot)$ |
First 32 of 1344 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 | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{3920}(1,\cdot)\) | 3920.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{3920}(3,\cdot)\) | 3920.fg | 84 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{17}{84}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{3920}(9,\cdot)\) | 3920.fa | 42 | no | \(1\) | \(1\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{3920}(11,\cdot)\) | 3920.fv | 84 | no | \(-1\) | \(1\) | \(e\left(\frac{17}{84}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{71}{84}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{3920}(13,\cdot)\) | 3920.dt | 28 | yes | \(1\) | \(1\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(i\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(-1\) |
\(\chi_{3920}(17,\cdot)\) | 3920.fx | 84 | no | \(1\) | \(1\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{31}{84}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{3920}(19,\cdot)\) | 3920.cp | 12 | no | \(1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(i\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(i\) | \(i\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{3920}(23,\cdot)\) | 3920.fy | 84 | no | \(1\) | \(1\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{31}{84}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{3920}(27,\cdot)\) | 3920.eo | 28 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(i\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(1\) |
\(\chi_{3920}(29,\cdot)\) | 3920.eg | 28 | yes | \(1\) | \(1\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(i\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(1\) |
\(\chi_{3920}(31,\cdot)\) | 3920.bs | 6 | no | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{3920}(33,\cdot)\) | 3920.fx | 84 | no | \(1\) | \(1\) | \(e\left(\frac{19}{84}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{3920}(37,\cdot)\) | 3920.fi | 84 | yes | \(-1\) | \(1\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{25}{84}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{17}{84}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{3920}(39,\cdot)\) | 3920.ev | 42 | no | \(-1\) | \(1\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{3920}(41,\cdot)\) | 3920.dh | 14 | no | \(-1\) | \(1\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(1\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(-1\) |
\(\chi_{3920}(43,\cdot)\) | 3920.en | 28 | yes | \(1\) | \(1\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(-i\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(-1\) |
\(\chi_{3920}(47,\cdot)\) | 3920.fn | 84 | no | \(-1\) | \(1\) | \(e\left(\frac{31}{84}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{19}{84}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{65}{84}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{3920}(51,\cdot)\) | 3920.fv | 84 | no | \(-1\) | \(1\) | \(e\left(\frac{31}{84}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{1}{84}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{3920}(53,\cdot)\) | 3920.ga | 84 | yes | \(-1\) | \(1\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{65}{84}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{59}{84}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{67}{84}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{3920}(57,\cdot)\) | 3920.el | 28 | no | \(-1\) | \(1\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(1\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(1\) |
\(\chi_{3920}(59,\cdot)\) | 3920.ft | 84 | yes | \(1\) | \(1\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{3920}(61,\cdot)\) | 3920.fo | 84 | no | \(-1\) | \(1\) | \(e\left(\frac{43}{84}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{19}{84}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{3920}(67,\cdot)\) | 3920.dc | 12 | no | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(-1\) | \(-i\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{3920}(69,\cdot)\) | 3920.ec | 28 | yes | \(-1\) | \(1\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(i\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(-1\) |
\(\chi_{3920}(71,\cdot)\) | 3920.df | 14 | no | \(-1\) | \(1\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(1\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(-1\) |
\(\chi_{3920}(73,\cdot)\) | 3920.fm | 84 | no | \(1\) | \(1\) | \(e\left(\frac{53}{84}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{65}{84}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{3920}(79,\cdot)\) | 3920.bt | 6 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{3920}(81,\cdot)\) | 3920.ds | 21 | no | \(1\) | \(1\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{3920}(83,\cdot)\) | 3920.eo | 28 | yes | \(-1\) | \(1\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(-i\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(1\) |
\(\chi_{3920}(87,\cdot)\) | 3920.fw | 84 | no | \(-1\) | \(1\) | \(e\left(\frac{17}{84}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{47}{84}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{37}{84}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{3920}(89,\cdot)\) | 3920.et | 42 | no | \(-1\) | \(1\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{3920}(93,\cdot)\) | 3920.fi | 84 | yes | \(-1\) | \(1\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{31}{84}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{43}{84}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{1}{3}\right)\) |