sage: H = DirichletGroup(129)
pari: g = idealstar(,129,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 84 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{42}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{129}(44,\cdot)$, $\chi_{129}(46,\cdot)$ |
First 32 of 84 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 | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{129}(1,\cdot)\) | 129.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{129}(2,\cdot)\) | 129.j | 14 | yes | \(1\) | \(1\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(-1\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{3}{7}\right)\) |
\(\chi_{129}(4,\cdot)\) | 129.i | 7 | no | \(1\) | \(1\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(1\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{6}{7}\right)\) |
\(\chi_{129}(5,\cdot)\) | 129.n | 42 | yes | \(1\) | \(1\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{2}{7}\right)\) |
\(\chi_{129}(7,\cdot)\) | 129.g | 6 | no | \(-1\) | \(1\) | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
\(\chi_{129}(8,\cdot)\) | 129.j | 14 | yes | \(1\) | \(1\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(-1\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{2}{7}\right)\) |
\(\chi_{129}(10,\cdot)\) | 129.m | 21 | no | \(1\) | \(1\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{5}{7}\right)\) |
\(\chi_{129}(11,\cdot)\) | 129.l | 14 | yes | \(-1\) | \(1\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(1\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{1}{7}\right)\) |
\(\chi_{129}(13,\cdot)\) | 129.m | 21 | no | \(1\) | \(1\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{2}{7}\right)\) |
\(\chi_{129}(14,\cdot)\) | 129.o | 42 | yes | \(-1\) | \(1\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{3}{7}\right)\) |
\(\chi_{129}(16,\cdot)\) | 129.i | 7 | no | \(1\) | \(1\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(1\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{5}{7}\right)\) |
\(\chi_{129}(17,\cdot)\) | 129.o | 42 | yes | \(-1\) | \(1\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{5}{7}\right)\) |
\(\chi_{129}(19,\cdot)\) | 129.p | 42 | no | \(-1\) | \(1\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{6}{7}\right)\) |
\(\chi_{129}(20,\cdot)\) | 129.n | 42 | yes | \(1\) | \(1\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{1}{7}\right)\) |
\(\chi_{129}(22,\cdot)\) | 129.k | 14 | no | \(-1\) | \(1\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(-1\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{4}{7}\right)\) |
\(\chi_{129}(23,\cdot)\) | 129.o | 42 | yes | \(-1\) | \(1\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{1}{7}\right)\) |
\(\chi_{129}(25,\cdot)\) | 129.m | 21 | no | \(1\) | \(1\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{4}{7}\right)\) |
\(\chi_{129}(26,\cdot)\) | 129.n | 42 | yes | \(1\) | \(1\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{5}{7}\right)\) |
\(\chi_{129}(28,\cdot)\) | 129.p | 42 | no | \(-1\) | \(1\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{6}{7}\right)\) |
\(\chi_{129}(29,\cdot)\) | 129.n | 42 | yes | \(1\) | \(1\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{3}{7}\right)\) |
\(\chi_{129}(31,\cdot)\) | 129.m | 21 | no | \(1\) | \(1\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{3}{7}\right)\) |
\(\chi_{129}(32,\cdot)\) | 129.j | 14 | yes | \(1\) | \(1\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(-1\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{1}{7}\right)\) |
\(\chi_{129}(34,\cdot)\) | 129.p | 42 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{1}{7}\right)\) |
\(\chi_{129}(35,\cdot)\) | 129.l | 14 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(1\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{2}{7}\right)\) |
\(\chi_{129}(37,\cdot)\) | 129.g | 6 | no | \(-1\) | \(1\) | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
\(\chi_{129}(38,\cdot)\) | 129.o | 42 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{2}{7}\right)\) |
\(\chi_{129}(40,\cdot)\) | 129.m | 21 | no | \(1\) | \(1\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{4}{7}\right)\) |
\(\chi_{129}(41,\cdot)\) | 129.l | 14 | yes | \(-1\) | \(1\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(1\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{3}{7}\right)\) |
\(\chi_{129}(44,\cdot)\) | 129.c | 2 | no | \(-1\) | \(1\) | \(-1\) | \(1\) | \(-1\) | \(1\) | \(-1\) | \(1\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
\(\chi_{129}(46,\cdot)\) | 129.p | 42 | no | \(-1\) | \(1\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{4}{7}\right)\) |
\(\chi_{129}(47,\cdot)\) | 129.l | 14 | yes | \(-1\) | \(1\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(1\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{6}{7}\right)\) |
\(\chi_{129}(49,\cdot)\) | 129.e | 3 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |