sage: H = DirichletGroup(104)
pari: g = idealstar(,104,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 48 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{2}\times C_{12}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{104}(79,\cdot)$, $\chi_{104}(53,\cdot)$, $\chi_{104}(41,\cdot)$ |
First 32 of 48 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 | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{104}(1,\cdot)\) | 104.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{104}(3,\cdot)\) | 104.n | 6 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{104}(5,\cdot)\) | 104.j | 4 | yes | \(-1\) | \(1\) | \(-1\) | \(i\) | \(i\) | \(1\) | \(-i\) | \(-i\) | \(-1\) | \(i\) | \(-i\) | \(-1\) |
\(\chi_{104}(7,\cdot)\) | 104.w | 12 | no | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(i\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(-i\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{104}(9,\cdot)\) | 104.i | 3 | no | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{104}(11,\cdot)\) | 104.u | 12 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(-i\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(i\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{104}(15,\cdot)\) | 104.w | 12 | no | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-i\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(i\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{104}(17,\cdot)\) | 104.o | 6 | no | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{104}(19,\cdot)\) | 104.u | 12 | yes | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(i\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(-i\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{104}(21,\cdot)\) | 104.j | 4 | yes | \(-1\) | \(1\) | \(-1\) | \(-i\) | \(-i\) | \(1\) | \(i\) | \(i\) | \(-1\) | \(-i\) | \(i\) | \(-1\) |
\(\chi_{104}(23,\cdot)\) | 104.q | 6 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{104}(25,\cdot)\) | 104.f | 2 | no | \(1\) | \(1\) | \(1\) | \(-1\) | \(-1\) | \(1\) | \(-1\) | \(-1\) | \(1\) | \(-1\) | \(-1\) | \(1\) |
\(\chi_{104}(27,\cdot)\) | 104.g | 2 | no | \(-1\) | \(1\) | \(1\) | \(-1\) | \(-1\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
\(\chi_{104}(29,\cdot)\) | 104.r | 6 | yes | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{104}(31,\cdot)\) | 104.k | 4 | no | \(1\) | \(1\) | \(-1\) | \(-i\) | \(-i\) | \(1\) | \(-i\) | \(i\) | \(-1\) | \(i\) | \(i\) | \(1\) |
\(\chi_{104}(33,\cdot)\) | 104.v | 12 | no | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(i\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(-i\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{104}(35,\cdot)\) | 104.n | 6 | yes | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{104}(37,\cdot)\) | 104.x | 12 | yes | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-i\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(i\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{104}(41,\cdot)\) | 104.v | 12 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(-i\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(i\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{104}(43,\cdot)\) | 104.p | 6 | yes | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{104}(45,\cdot)\) | 104.x | 12 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(i\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(-i\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{104}(47,\cdot)\) | 104.k | 4 | no | \(1\) | \(1\) | \(-1\) | \(i\) | \(i\) | \(1\) | \(i\) | \(-i\) | \(-1\) | \(-i\) | \(-i\) | \(1\) |
\(\chi_{104}(49,\cdot)\) | 104.o | 6 | no | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{104}(51,\cdot)\) | 104.h | 2 | yes | \(-1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
\(\chi_{104}(53,\cdot)\) | 104.b | 2 | no | \(1\) | \(1\) | \(-1\) | \(-1\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(1\) | \(-1\) | \(-1\) | \(1\) |
\(\chi_{104}(55,\cdot)\) | 104.t | 6 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{104}(57,\cdot)\) | 104.l | 4 | no | \(-1\) | \(1\) | \(1\) | \(-i\) | \(i\) | \(1\) | \(i\) | \(-i\) | \(-1\) | \(-i\) | \(i\) | \(-1\) |
\(\chi_{104}(59,\cdot)\) | 104.u | 12 | yes | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(-i\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(i\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{104}(61,\cdot)\) | 104.r | 6 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{104}(63,\cdot)\) | 104.w | 12 | no | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(i\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(-i\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{104}(67,\cdot)\) | 104.u | 12 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(i\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(-i\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{104}(69,\cdot)\) | 104.s | 6 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |