sage: H = DirichletGroup(280)
pari: g = idealstar(,280,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 96 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{2}\times C_{2}\times C_{12}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{280}(71,\cdot)$, $\chi_{280}(141,\cdot)$, $\chi_{280}(57,\cdot)$, $\chi_{280}(241,\cdot)$ |
First 32 of 96 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 | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{280}(1,\cdot)\) | 280.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{280}(3,\cdot)\) | 280.bp | 12 | yes | \(-1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(i\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(i\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{280}(9,\cdot)\) | 280.bg | 6 | no | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{280}(11,\cdot)\) | 280.z | 6 | no | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{280}(13,\cdot)\) | 280.s | 4 | yes | \(1\) | \(1\) | \(i\) | \(-1\) | \(-1\) | \(i\) | \(i\) | \(-1\) | \(i\) | \(-i\) | \(1\) | \(-1\) |
\(\chi_{280}(17,\cdot)\) | 280.bo | 12 | no | \(1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(i\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(-i\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{280}(19,\cdot)\) | 280.ba | 6 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{280}(23,\cdot)\) | 280.bs | 12 | no | \(1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(i\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(i\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{280}(27,\cdot)\) | 280.y | 4 | yes | \(-1\) | \(1\) | \(i\) | \(-1\) | \(1\) | \(-i\) | \(-i\) | \(1\) | \(i\) | \(-i\) | \(1\) | \(1\) |
\(\chi_{280}(29,\cdot)\) | 280.l | 2 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(-1\) | \(-1\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
\(\chi_{280}(31,\cdot)\) | 280.bc | 6 | no | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{280}(33,\cdot)\) | 280.bo | 12 | no | \(1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(-i\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(i\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{280}(37,\cdot)\) | 280.bt | 12 | yes | \(-1\) | \(1\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(i\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(-i\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{280}(39,\cdot)\) | 280.bd | 6 | no | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{280}(41,\cdot)\) | 280.f | 2 | no | \(-1\) | \(1\) | \(-1\) | \(1\) | \(1\) | \(-1\) | \(-1\) | \(-1\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
\(\chi_{280}(43,\cdot)\) | 280.w | 4 | no | \(1\) | \(1\) | \(i\) | \(-1\) | \(1\) | \(-i\) | \(-i\) | \(-1\) | \(-i\) | \(-i\) | \(1\) | \(-1\) |
\(\chi_{280}(47,\cdot)\) | 280.bu | 12 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(i\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(i\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{280}(51,\cdot)\) | 280.z | 6 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{280}(53,\cdot)\) | 280.bt | 12 | yes | \(-1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(-i\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(i\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{280}(57,\cdot)\) | 280.v | 4 | no | \(-1\) | \(1\) | \(-i\) | \(-1\) | \(1\) | \(-i\) | \(i\) | \(-1\) | \(-i\) | \(i\) | \(-1\) | \(1\) |
\(\chi_{280}(59,\cdot)\) | 280.ba | 6 | yes | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{280}(61,\cdot)\) | 280.be | 6 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{280}(67,\cdot)\) | 280.br | 12 | yes | \(1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(i\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(i\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{280}(69,\cdot)\) | 280.c | 2 | yes | \(-1\) | \(1\) | \(-1\) | \(1\) | \(-1\) | \(-1\) | \(1\) | \(1\) | \(-1\) | \(-1\) | \(-1\) | \(-1\) |
\(\chi_{280}(71,\cdot)\) | 280.d | 2 | no | \(-1\) | \(1\) | \(-1\) | \(1\) | \(-1\) | \(1\) | \(1\) | \(-1\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
\(\chi_{280}(73,\cdot)\) | 280.bo | 12 | no | \(1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(-i\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(i\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{280}(79,\cdot)\) | 280.bd | 6 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{280}(81,\cdot)\) | 280.q | 3 | no | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{280}(83,\cdot)\) | 280.y | 4 | yes | \(-1\) | \(1\) | \(-i\) | \(-1\) | \(1\) | \(i\) | \(i\) | \(1\) | \(-i\) | \(i\) | \(1\) | \(1\) |
\(\chi_{280}(87,\cdot)\) | 280.bu | 12 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(i\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(i\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{280}(89,\cdot)\) | 280.bb | 6 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{280}(93,\cdot)\) | 280.bt | 12 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(-i\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(i\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |