sage: H = DirichletGroup(3330)
pari: g = idealstar(,3330,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 864 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{12}\times C_{36}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{3330}(371,\cdot)$, $\chi_{3330}(667,\cdot)$, $\chi_{3330}(631,\cdot)$ |
First 32 of 864 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 | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(41\) | \(43\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{3330}(1,\cdot)\) | 3330.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{3330}(7,\cdot)\) | 3330.fi | 36 | no | \(-1\) | \(1\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{5}{12}\right)\) |
\(\chi_{3330}(11,\cdot)\) | 3330.bg | 6 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{3330}(13,\cdot)\) | 3330.eu | 36 | no | \(1\) | \(1\) | \(e\left(\frac{31}{36}\right)\) | \(-1\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(-1\) | \(i\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{3330}(17,\cdot)\) | 3330.fl | 36 | no | \(-1\) | \(1\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(-i\) | \(e\left(\frac{8}{9}\right)\) | \(1\) |
\(\chi_{3330}(19,\cdot)\) | 3330.fs | 36 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(-i\) | \(e\left(\frac{17}{18}\right)\) | \(-i\) |
\(\chi_{3330}(23,\cdot)\) | 3330.cp | 12 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{3330}(29,\cdot)\) | 3330.dt | 12 | no | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(i\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(1\) | \(e\left(\frac{11}{12}\right)\) |
\(\chi_{3330}(31,\cdot)\) | 3330.cj | 12 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(-i\) | \(-i\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{12}\right)\) |
\(\chi_{3330}(41,\cdot)\) | 3330.ec | 18 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{9}\right)\) | \(-1\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{3330}(43,\cdot)\) | 3330.dl | 12 | no | \(1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-i\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{3330}(47,\cdot)\) | 3330.di | 12 | no | \(1\) | \(1\) | \(i\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{12}\right)\) |
\(\chi_{3330}(49,\cdot)\) | 3330.ef | 18 | no | \(1\) | \(1\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{3330}(53,\cdot)\) | 3330.fp | 36 | no | \(1\) | \(1\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{13}{18}\right)\) | \(i\) |
\(\chi_{3330}(59,\cdot)\) | 3330.fh | 36 | no | \(1\) | \(1\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{5}{36}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{1}{12}\right)\) |
\(\chi_{3330}(61,\cdot)\) | 3330.ft | 36 | no | \(-1\) | \(1\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{5}{12}\right)\) |
\(\chi_{3330}(67,\cdot)\) | 3330.gc | 36 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{36}\right)\) | \(1\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{35}{36}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(i\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{7}{12}\right)\) |
\(\chi_{3330}(71,\cdot)\) | 3330.eq | 18 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(e\left(\frac{17}{18}\right)\) | \(1\) |
\(\chi_{3330}(73,\cdot)\) | 3330.u | 4 | no | \(-1\) | \(1\) | \(-i\) | \(1\) | \(-i\) | \(i\) | \(1\) | \(-i\) | \(1\) | \(-1\) | \(1\) | \(-i\) |
\(\chi_{3330}(77,\cdot)\) | 3330.ev | 36 | no | \(1\) | \(1\) | \(e\left(\frac{25}{36}\right)\) | \(-1\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(-i\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{7}{12}\right)\) |
\(\chi_{3330}(79,\cdot)\) | 3330.fq | 36 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{35}{36}\right)\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{5}{12}\right)\) |
\(\chi_{3330}(83,\cdot)\) | 3330.ey | 36 | no | \(1\) | \(1\) | \(e\left(\frac{23}{36}\right)\) | \(-1\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(-i\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{11}{12}\right)\) |
\(\chi_{3330}(89,\cdot)\) | 3330.ff | 36 | no | \(1\) | \(1\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(i\) | \(e\left(\frac{2}{9}\right)\) | \(i\) |
\(\chi_{3330}(91,\cdot)\) | 3330.fr | 36 | no | \(-1\) | \(1\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{36}\right)\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(-i\) | \(e\left(\frac{7}{18}\right)\) | \(i\) |
\(\chi_{3330}(97,\cdot)\) | 3330.dd | 12 | no | \(1\) | \(1\) | \(i\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{3330}(101,\cdot)\) | 3330.bz | 6 | no | \(-1\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{3330}(103,\cdot)\) | 3330.dd | 12 | no | \(1\) | \(1\) | \(-i\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{3330}(107,\cdot)\) | 3330.fp | 36 | no | \(1\) | \(1\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{11}{18}\right)\) | \(-i\) |
\(\chi_{3330}(109,\cdot)\) | 3330.fs | 36 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(-i\) | \(e\left(\frac{1}{18}\right)\) | \(-i\) |
\(\chi_{3330}(113,\cdot)\) | 3330.fk | 36 | no | \(-1\) | \(1\) | \(e\left(\frac{35}{36}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{3330}(119,\cdot)\) | 3330.dt | 12 | no | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(-i\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(1\) | \(e\left(\frac{5}{12}\right)\) |
\(\chi_{3330}(121,\cdot)\) | 3330.j | 3 | no | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |