sage: H = DirichletGroup(2205)
pari: g = idealstar(,2205,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 1008 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{6}\times C_{84}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{2205}(1226,\cdot)$, $\chi_{2205}(442,\cdot)$, $\chi_{2205}(1081,\cdot)$ |
First 32 of 1008 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 | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{2205}(1,\cdot)\) | 2205.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{2205}(2,\cdot)\) | 2205.el | 84 | yes | \(1\) | \(1\) | \(e\left(\frac{43}{84}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{43}{84}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{19}{84}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{37}{84}\right)\) | \(e\left(\frac{3}{28}\right)\) |
\(\chi_{2205}(4,\cdot)\) | 2205.db | 42 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{3}{14}\right)\) |
\(\chi_{2205}(8,\cdot)\) | 2205.cw | 28 | no | \(1\) | \(1\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(-1\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{9}{28}\right)\) |
\(\chi_{2205}(11,\cdot)\) | 2205.dx | 42 | no | \(-1\) | \(1\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{1}{42}\right)\) |
\(\chi_{2205}(13,\cdot)\) | 2205.ej | 84 | yes | \(1\) | \(1\) | \(e\left(\frac{43}{84}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{71}{84}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(1\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{65}{84}\right)\) |
\(\chi_{2205}(16,\cdot)\) | 2205.cr | 21 | no | \(1\) | \(1\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{3}{7}\right)\) |
\(\chi_{2205}(17,\cdot)\) | 2205.ed | 84 | no | \(-1\) | \(1\) | \(e\left(\frac{19}{84}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{53}{84}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{73}{84}\right)\) |
\(\chi_{2205}(19,\cdot)\) | 2205.bi | 6 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{2205}(22,\cdot)\) | 2205.eg | 84 | yes | \(-1\) | \(1\) | \(e\left(\frac{37}{84}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(-1\) | \(e\left(\frac{53}{84}\right)\) | \(e\left(\frac{11}{84}\right)\) |
\(\chi_{2205}(23,\cdot)\) | 2205.en | 84 | yes | \(1\) | \(1\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{65}{84}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{73}{84}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{67}{84}\right)\) |
\(\chi_{2205}(26,\cdot)\) | 2205.dg | 42 | no | \(1\) | \(1\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{37}{42}\right)\) |
\(\chi_{2205}(29,\cdot)\) | 2205.dp | 42 | yes | \(-1\) | \(1\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(1\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{13}{21}\right)\) |
\(\chi_{2205}(31,\cdot)\) | 2205.bc | 6 | no | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
\(\chi_{2205}(32,\cdot)\) | 2205.el | 84 | yes | \(1\) | \(1\) | \(e\left(\frac{47}{84}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{47}{84}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{17}{84}\right)\) | \(e\left(\frac{15}{28}\right)\) |
\(\chi_{2205}(34,\cdot)\) | 2205.dj | 42 | yes | \(-1\) | \(1\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(-1\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{41}{42}\right)\) |
\(\chi_{2205}(37,\cdot)\) | 2205.ei | 84 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{25}{84}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{59}{84}\right)\) |
\(\chi_{2205}(38,\cdot)\) | 2205.em | 84 | yes | \(-1\) | \(1\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{43}{84}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{47}{84}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{23}{84}\right)\) |
\(\chi_{2205}(41,\cdot)\) | 2205.de | 42 | no | \(1\) | \(1\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(-1\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{31}{42}\right)\) |
\(\chi_{2205}(43,\cdot)\) | 2205.eg | 84 | yes | \(-1\) | \(1\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{25}{84}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(-1\) | \(e\left(\frac{43}{84}\right)\) | \(e\left(\frac{1}{84}\right)\) |
\(\chi_{2205}(44,\cdot)\) | 2205.dr | 42 | no | \(-1\) | \(1\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{5}{21}\right)\) |
\(\chi_{2205}(46,\cdot)\) | 2205.cs | 21 | no | \(1\) | \(1\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{19}{21}\right)\) |
\(\chi_{2205}(47,\cdot)\) | 2205.ek | 84 | yes | \(-1\) | \(1\) | \(e\left(\frac{43}{84}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{1}{84}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{37}{84}\right)\) | \(e\left(\frac{3}{28}\right)\) |
\(\chi_{2205}(52,\cdot)\) | 2205.eo | 84 | yes | \(1\) | \(1\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{73}{84}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{71}{84}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{83}{84}\right)\) |
\(\chi_{2205}(53,\cdot)\) | 2205.ee | 84 | no | \(1\) | \(1\) | \(e\left(\frac{37}{84}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{17}{84}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{67}{84}\right)\) |
\(\chi_{2205}(58,\cdot)\) | 2205.ep | 84 | yes | \(-1\) | \(1\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{41}{84}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{47}{84}\right)\) | \(e\left(\frac{61}{84}\right)\) |
\(\chi_{2205}(59,\cdot)\) | 2205.dv | 42 | yes | \(1\) | \(1\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{3}{7}\right)\) |
\(\chi_{2205}(61,\cdot)\) | 2205.dn | 42 | no | \(-1\) | \(1\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{2}{7}\right)\) |
\(\chi_{2205}(62,\cdot)\) | 2205.cx | 28 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(1\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{3}{28}\right)\) |
\(\chi_{2205}(64,\cdot)\) | 2205.cn | 14 | no | \(1\) | \(1\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(1\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{9}{14}\right)\) |
\(\chi_{2205}(67,\cdot)\) | 2205.ci | 12 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(-i\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(-i\) |
\(\chi_{2205}(68,\cdot)\) | 2205.bv | 12 | no | \(-1\) | \(1\) | \(i\) | \(-1\) | \(-i\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) |