sage: H = DirichletGroup(1421)
pari: g = idealstar(,1421,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 1176 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{14}\times C_{84}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{1421}(1277,\cdot)$, $\chi_{1421}(785,\cdot)$ |
First 32 of 1176 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 | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{1421}(1,\cdot)\) | 1421.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{1421}(2,\cdot)\) | 1421.dt | 84 | yes | \(-1\) | \(1\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{67}{84}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{73}{84}\right)\) | \(e\left(\frac{55}{84}\right)\) | \(e\left(\frac{5}{84}\right)\) |
\(\chi_{1421}(3,\cdot)\) | 1421.ea | 84 | yes | \(1\) | \(1\) | \(e\left(\frac{67}{84}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{43}{84}\right)\) |
\(\chi_{1421}(4,\cdot)\) | 1421.cv | 42 | yes | \(1\) | \(1\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{5}{42}\right)\) |
\(\chi_{1421}(5,\cdot)\) | 1421.db | 42 | yes | \(-1\) | \(1\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{2}{21}\right)\) |
\(\chi_{1421}(6,\cdot)\) | 1421.bi | 14 | yes | \(-1\) | \(1\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{4}{7}\right)\) |
\(\chi_{1421}(8,\cdot)\) | 1421.co | 28 | yes | \(-1\) | \(1\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{5}{28}\right)\) |
\(\chi_{1421}(9,\cdot)\) | 1421.de | 42 | yes | \(1\) | \(1\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{42}\right)\) |
\(\chi_{1421}(10,\cdot)\) | 1421.ea | 84 | yes | \(1\) | \(1\) | \(e\left(\frac{73}{84}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{13}{84}\right)\) |
\(\chi_{1421}(11,\cdot)\) | 1421.du | 84 | yes | \(-1\) | \(1\) | \(e\left(\frac{55}{84}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{61}{84}\right)\) |
\(\chi_{1421}(12,\cdot)\) | 1421.dz | 84 | yes | \(1\) | \(1\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{43}{84}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{53}{84}\right)\) |
\(\chi_{1421}(13,\cdot)\) | 1421.bq | 14 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{14}\right)\) | \(1\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{1}{7}\right)\) |
\(\chi_{1421}(15,\cdot)\) | 1421.co | 28 | yes | \(-1\) | \(1\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{17}{28}\right)\) |
\(\chi_{1421}(16,\cdot)\) | 1421.bz | 21 | yes | \(1\) | \(1\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{5}{21}\right)\) |
\(\chi_{1421}(17,\cdot)\) | 1421.dz | 84 | yes | \(1\) | \(1\) | \(e\left(\frac{19}{84}\right)\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{47}{84}\right)\) | \(e\left(\frac{67}{84}\right)\) |
\(\chi_{1421}(18,\cdot)\) | 1421.dr | 84 | no | \(-1\) | \(1\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{53}{84}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{59}{84}\right)\) | \(e\left(\frac{41}{84}\right)\) | \(e\left(\frac{1}{12}\right)\) |
\(\chi_{1421}(19,\cdot)\) | 1421.dy | 84 | no | \(1\) | \(1\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{37}{84}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{19}{84}\right)\) | \(e\left(\frac{31}{84}\right)\) | \(e\left(\frac{5}{12}\right)\) |
\(\chi_{1421}(20,\cdot)\) | 1421.br | 14 | yes | \(-1\) | \(1\) | \(1\) | \(e\left(\frac{3}{14}\right)\) | \(1\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(1\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{3}{14}\right)\) |
\(\chi_{1421}(22,\cdot)\) | 1421.bp | 14 | yes | \(1\) | \(1\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(1\) | \(1\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{11}{14}\right)\) |
\(\chi_{1421}(23,\cdot)\) | 1421.bx | 21 | yes | \(1\) | \(1\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{20}{21}\right)\) |
\(\chi_{1421}(24,\cdot)\) | 1421.dk | 42 | yes | \(-1\) | \(1\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{29}{42}\right)\) |
\(\chi_{1421}(25,\cdot)\) | 1421.by | 21 | yes | \(1\) | \(1\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{4}{21}\right)\) |
\(\chi_{1421}(26,\cdot)\) | 1421.do | 84 | yes | \(1\) | \(1\) | \(e\left(\frac{17}{84}\right)\) | \(e\left(\frac{67}{84}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{73}{84}\right)\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{17}{84}\right)\) |
\(\chi_{1421}(27,\cdot)\) | 1421.cd | 28 | yes | \(1\) | \(1\) | \(e\left(\frac{11}{28}\right)\) | \(-i\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(-1\) | \(i\) | \(i\) | \(e\left(\frac{15}{28}\right)\) |
\(\chi_{1421}(30,\cdot)\) | 1421.e | 3 | no | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{1421}(31,\cdot)\) | 1421.dy | 84 | no | \(1\) | \(1\) | \(e\left(\frac{31}{84}\right)\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{47}{84}\right)\) | \(e\left(\frac{1}{12}\right)\) |
\(\chi_{1421}(32,\cdot)\) | 1421.dt | 84 | yes | \(-1\) | \(1\) | \(e\left(\frac{55}{84}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{25}{84}\right)\) |
\(\chi_{1421}(33,\cdot)\) | 1421.cr | 42 | yes | \(-1\) | \(1\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{21}\right)\) |
\(\chi_{1421}(34,\cdot)\) | 1421.be | 14 | yes | \(-1\) | \(1\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{6}{7}\right)\) |
\(\chi_{1421}(36,\cdot)\) | 1421.l | 7 | yes | \(1\) | \(1\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{1}{7}\right)\) |
\(\chi_{1421}(37,\cdot)\) | 1421.ec | 84 | yes | \(-1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{25}{84}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(-i\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{31}{84}\right)\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{11}{84}\right)\) |
\(\chi_{1421}(38,\cdot)\) | 1421.da | 42 | yes | \(-1\) | \(1\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{10}{21}\right)\) |