sage: H = DirichletGroup(1520)
pari: g = idealstar(,1520,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 576 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{2}\times C_{4}\times C_{36}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{1520}(191,\cdot)$, $\chi_{1520}(1141,\cdot)$, $\chi_{1520}(1217,\cdot)$, $\chi_{1520}(401,\cdot)$ |
First 32 of 576 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 | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{1520}(1,\cdot)\) | 1520.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{1520}(3,\cdot)\) | 1520.ef | 36 | yes | \(-1\) | \(1\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{35}{36}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{36}\right)\) |
\(\chi_{1520}(7,\cdot)\) | 1520.cu | 12 | no | \(1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(-i\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(i\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{1520}(9,\cdot)\) | 1520.dp | 18 | no | \(1\) | \(1\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{18}\right)\) |
\(\chi_{1520}(11,\cdot)\) | 1520.cv | 12 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-i\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(-i\) | \(e\left(\frac{1}{12}\right)\) |
\(\chi_{1520}(13,\cdot)\) | 1520.ed | 36 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{17}{36}\right)\) |
\(\chi_{1520}(17,\cdot)\) | 1520.dw | 36 | no | \(-1\) | \(1\) | \(e\left(\frac{35}{36}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{17}{18}\right)\) |
\(\chi_{1520}(21,\cdot)\) | 1520.eo | 36 | no | \(-1\) | \(1\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{25}{36}\right)\) |
\(\chi_{1520}(23,\cdot)\) | 1520.dz | 36 | no | \(1\) | \(1\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{35}{36}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{8}{9}\right)\) |
\(\chi_{1520}(27,\cdot)\) | 1520.da | 12 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(i\) | \(e\left(\frac{1}{3}\right)\) | \(-i\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(-1\) | \(e\left(\frac{1}{12}\right)\) |
\(\chi_{1520}(29,\cdot)\) | 1520.du | 36 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{11}{36}\right)\) |
\(\chi_{1520}(31,\cdot)\) | 1520.bq | 6 | no | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{1520}(33,\cdot)\) | 1520.dy | 36 | no | \(1\) | \(1\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{9}\right)\) |
\(\chi_{1520}(37,\cdot)\) | 1520.bn | 4 | yes | \(1\) | \(1\) | \(1\) | \(-i\) | \(1\) | \(i\) | \(1\) | \(i\) | \(-i\) | \(i\) | \(1\) | \(-i\) |
\(\chi_{1520}(39,\cdot)\) | 1520.i | 2 | no | \(-1\) | \(1\) | \(-1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(-1\) | \(-1\) | \(1\) | \(-1\) | \(-1\) |
\(\chi_{1520}(41,\cdot)\) | 1520.dh | 18 | no | \(-1\) | \(1\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{9}\right)\) |
\(\chi_{1520}(43,\cdot)\) | 1520.eh | 36 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{5}{36}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{13}{36}\right)\) |
\(\chi_{1520}(47,\cdot)\) | 1520.el | 36 | no | \(1\) | \(1\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{35}{36}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{5}{36}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{18}\right)\) |
\(\chi_{1520}(49,\cdot)\) | 1520.bz | 6 | no | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{1520}(51,\cdot)\) | 1520.dt | 36 | no | \(1\) | \(1\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{35}{36}\right)\) |
\(\chi_{1520}(53,\cdot)\) | 1520.eg | 36 | yes | \(1\) | \(1\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{35}{36}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{23}{36}\right)\) |
\(\chi_{1520}(59,\cdot)\) | 1520.en | 36 | yes | \(1\) | \(1\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{25}{36}\right)\) |
\(\chi_{1520}(61,\cdot)\) | 1520.em | 36 | no | \(1\) | \(1\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{5}{36}\right)\) |
\(\chi_{1520}(63,\cdot)\) | 1520.el | 36 | no | \(1\) | \(1\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{36}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{13}{18}\right)\) |
\(\chi_{1520}(67,\cdot)\) | 1520.ea | 36 | yes | \(-1\) | \(1\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{29}{36}\right)\) |
\(\chi_{1520}(69,\cdot)\) | 1520.cx | 12 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(i\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(i\) | \(e\left(\frac{11}{12}\right)\) |
\(\chi_{1520}(71,\cdot)\) | 1520.dn | 18 | no | \(1\) | \(1\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{9}\right)\) |
\(\chi_{1520}(73,\cdot)\) | 1520.ei | 36 | no | \(-1\) | \(1\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{35}{36}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{7}{9}\right)\) |
\(\chi_{1520}(77,\cdot)\) | 1520.bo | 4 | no | \(-1\) | \(1\) | \(1\) | \(-i\) | \(1\) | \(-i\) | \(1\) | \(i\) | \(-i\) | \(i\) | \(1\) | \(-i\) |
\(\chi_{1520}(79,\cdot)\) | 1520.dj | 18 | no | \(1\) | \(1\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{18}\right)\) |
\(\chi_{1520}(81,\cdot)\) | 1520.ce | 9 | no | \(1\) | \(1\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{9}\right)\) |
\(\chi_{1520}(83,\cdot)\) | 1520.ch | 12 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(-i\) | \(e\left(\frac{2}{3}\right)\) | \(i\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(1\) | \(e\left(\frac{5}{12}\right)\) |