sage: H = DirichletGroup(195)
pari: g = idealstar(,195,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 96 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{4}\times C_{12}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{195}(131,\cdot)$, $\chi_{195}(157,\cdot)$, $\chi_{195}(106,\cdot)$ |
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 | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{195}(1,\cdot)\) | 195.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{195}(2,\cdot)\) | 195.bn | 12 | yes | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(e\left(\frac{1}{12}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{11}{12}\right)\) |
\(\chi_{195}(4,\cdot)\) | 195.v | 6 | no | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{195}(7,\cdot)\) | 195.bm | 12 | no | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(e\left(\frac{5}{12}\right)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) |
\(\chi_{195}(8,\cdot)\) | 195.j | 4 | yes | \(-1\) | \(1\) | \(-1\) | \(1\) | \(-1\) | \(-1\) | \(i\) | \(1\) | \(1\) | \(-i\) | \(-i\) | \(-i\) |
\(\chi_{195}(11,\cdot)\) | 195.bg | 12 | no | \(1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(i\) | \(e\left(\frac{7}{12}\right)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{195}(14,\cdot)\) | 195.f | 2 | no | \(-1\) | \(1\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(-1\) | \(-1\) | \(1\) | \(1\) | \(1\) | \(-1\) |
\(\chi_{195}(16,\cdot)\) | 195.i | 3 | no | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{195}(17,\cdot)\) | 195.bf | 12 | yes | \(1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(-i\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{7}{12}\right)\) |
\(\chi_{195}(19,\cdot)\) | 195.bi | 12 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(-i\) | \(e\left(\frac{11}{12}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{195}(22,\cdot)\) | 195.be | 12 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(-i\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{7}{12}\right)\) |
\(\chi_{195}(23,\cdot)\) | 195.bf | 12 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(i\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{12}\right)\) |
\(\chi_{195}(28,\cdot)\) | 195.bm | 12 | no | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(e\left(\frac{7}{12}\right)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{12}\right)\) |
\(\chi_{195}(29,\cdot)\) | 195.x | 6 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{195}(31,\cdot)\) | 195.p | 4 | no | \(-1\) | \(1\) | \(-i\) | \(-1\) | \(i\) | \(i\) | \(i\) | \(1\) | \(1\) | \(-1\) | \(-i\) | \(1\) |
\(\chi_{195}(32,\cdot)\) | 195.bn | 12 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(e\left(\frac{5}{12}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) |
\(\chi_{195}(34,\cdot)\) | 195.q | 4 | no | \(-1\) | \(1\) | \(-i\) | \(-1\) | \(i\) | \(i\) | \(-i\) | \(1\) | \(1\) | \(1\) | \(i\) | \(-1\) |
\(\chi_{195}(37,\cdot)\) | 195.bm | 12 | no | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(e\left(\frac{1}{12}\right)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{11}{12}\right)\) |
\(\chi_{195}(38,\cdot)\) | 195.s | 4 | yes | \(1\) | \(1\) | \(-i\) | \(-1\) | \(i\) | \(i\) | \(1\) | \(1\) | \(1\) | \(i\) | \(1\) | \(-i\) |
\(\chi_{195}(41,\cdot)\) | 195.bg | 12 | no | \(1\) | \(1\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(-i\) | \(e\left(\frac{1}{12}\right)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{195}(43,\cdot)\) | 195.bk | 12 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(-i\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{12}\right)\) |
\(\chi_{195}(44,\cdot)\) | 195.n | 4 | yes | \(1\) | \(1\) | \(-i\) | \(-1\) | \(-i\) | \(i\) | \(-i\) | \(-1\) | \(1\) | \(-1\) | \(-i\) | \(-1\) |
\(\chi_{195}(46,\cdot)\) | 195.bj | 12 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(-i\) | \(e\left(\frac{5}{12}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{195}(47,\cdot)\) | 195.u | 4 | yes | \(-1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(i\) | \(1\) | \(1\) | \(i\) | \(-i\) | \(i\) |
\(\chi_{195}(49,\cdot)\) | 195.v | 6 | no | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{195}(53,\cdot)\) | 195.m | 4 | no | \(1\) | \(1\) | \(i\) | \(-1\) | \(-i\) | \(-i\) | \(-1\) | \(1\) | \(1\) | \(i\) | \(-1\) | \(-i\) |
\(\chi_{195}(56,\cdot)\) | 195.w | 6 | no | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{195}(58,\cdot)\) | 195.bm | 12 | no | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(e\left(\frac{11}{12}\right)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) |
\(\chi_{195}(59,\cdot)\) | 195.bh | 12 | yes | \(1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(-i\) | \(e\left(\frac{11}{12}\right)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{195}(61,\cdot)\) | 195.i | 3 | no | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{195}(62,\cdot)\) | 195.bf | 12 | yes | \(1\) | \(1\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(-i\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{11}{12}\right)\) |
\(\chi_{195}(64,\cdot)\) | 195.h | 2 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |