sage: H = DirichletGroup(3420)
pari: g = idealstar(,3420,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 864 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{2}\times C_{6}\times C_{36}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{3420}(1711,\cdot)$, $\chi_{3420}(1901,\cdot)$, $\chi_{3420}(2737,\cdot)$, $\chi_{3420}(3061,\cdot)$ |
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 | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{3420}(1,\cdot)\) | 3420.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{3420}(7,\cdot)\) | 3420.ek | 12 | yes | \(1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(-i\) | \(e\left(\frac{7}{12}\right)\) | \(i\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(i\) | \(e\left(\frac{2}{3}\right)\) | \(i\) |
\(\chi_{3420}(11,\cdot)\) | 3420.cj | 6 | no | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{3420}(13,\cdot)\) | 3420.gu | 36 | no | \(1\) | \(1\) | \(-i\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(i\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{1}{36}\right)\) |
\(\chi_{3420}(17,\cdot)\) | 3420.ha | 36 | no | \(1\) | \(1\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(i\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{23}{36}\right)\) |
\(\chi_{3420}(23,\cdot)\) | 3420.gv | 36 | yes | \(-1\) | \(1\) | \(i\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{5}{36}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(-i\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{31}{36}\right)\) |
\(\chi_{3420}(29,\cdot)\) | 3420.fp | 18 | no | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{5}{18}\right)\) |
\(\chi_{3420}(31,\cdot)\) | 3420.cy | 6 | no | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{3420}(37,\cdot)\) | 3420.bb | 4 | no | \(1\) | \(1\) | \(i\) | \(1\) | \(i\) | \(i\) | \(-i\) | \(1\) | \(-1\) | \(-i\) | \(-1\) | \(-i\) |
\(\chi_{3420}(41,\cdot)\) | 3420.fc | 18 | no | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(-1\) | \(-1\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{8}{9}\right)\) |
\(\chi_{3420}(43,\cdot)\) | 3420.hc | 36 | yes | \(1\) | \(1\) | \(i\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(-i\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{23}{36}\right)\) |
\(\chi_{3420}(47,\cdot)\) | 3420.hh | 36 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(1\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{35}{36}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(-1\) | \(i\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{1}{36}\right)\) |
\(\chi_{3420}(49,\cdot)\) | 3420.cf | 6 | no | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
\(\chi_{3420}(53,\cdot)\) | 3420.hf | 36 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{35}{36}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(i\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{1}{36}\right)\) |
\(\chi_{3420}(59,\cdot)\) | 3420.fo | 18 | yes | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(1\) | \(1\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{2}{9}\right)\) |
\(\chi_{3420}(61,\cdot)\) | 3420.dl | 9 | no | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(1\) | \(1\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{4}{9}\right)\) |
\(\chi_{3420}(67,\cdot)\) | 3420.gz | 36 | yes | \(-1\) | \(1\) | \(-i\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{36}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(-i\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{25}{36}\right)\) |
\(\chi_{3420}(71,\cdot)\) | 3420.ft | 18 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{13}{18}\right)\) |
\(\chi_{3420}(73,\cdot)\) | 3420.gt | 36 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{35}{36}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(-i\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{29}{36}\right)\) |
\(\chi_{3420}(77,\cdot)\) | 3420.ef | 12 | no | \(1\) | \(1\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(-i\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(i\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{12}\right)\) |
\(\chi_{3420}(79,\cdot)\) | 3420.gj | 18 | yes | \(1\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{2}{9}\right)\) |
\(\chi_{3420}(83,\cdot)\) | 3420.dv | 12 | yes | \(-1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(i\) | \(e\left(\frac{7}{12}\right)\) | \(i\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(-i\) | \(e\left(\frac{1}{6}\right)\) | \(-i\) |
\(\chi_{3420}(89,\cdot)\) | 3420.fz | 18 | no | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{17}{18}\right)\) |
\(\chi_{3420}(91,\cdot)\) | 3420.fy | 18 | no | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{5}{18}\right)\) |
\(\chi_{3420}(97,\cdot)\) | 3420.gu | 36 | no | \(1\) | \(1\) | \(i\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(-i\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{11}{36}\right)\) |
\(\chi_{3420}(101,\cdot)\) | 3420.fe | 18 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(1\) | \(1\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{1}{9}\right)\) |
\(\chi_{3420}(103,\cdot)\) | 3420.eh | 12 | yes | \(-1\) | \(1\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(-i\) | \(e\left(\frac{5}{12}\right)\) | \(-i\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(i\) | \(e\left(\frac{5}{6}\right)\) | \(-i\) |
\(\chi_{3420}(107,\cdot)\) | 3420.er | 12 | no | \(1\) | \(1\) | \(-i\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-i\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{7}{12}\right)\) |
\(\chi_{3420}(109,\cdot)\) | 3420.fw | 18 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{13}{18}\right)\) |
\(\chi_{3420}(113,\cdot)\) | 3420.em | 12 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(i\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(i\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{12}\right)\) |
\(\chi_{3420}(119,\cdot)\) | 3420.gg | 18 | yes | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{8}{9}\right)\) |
\(\chi_{3420}(121,\cdot)\) | 3420.q | 3 | no | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |