sage: H = DirichletGroup(15)
pari: g = idealstar(,15,2)
Character group
| sage: G.order()
pari: g.no
| ||
| Order | = | 8 |
| sage: H.invariants()
pari: g.cyc
| ||
| Structure | = | \(C_{2}\times C_{4}\) |
| sage: H.gens()
pari: g.gen
| ||
| Generators | = | $\chi_{15}(11,\cdot)$, $\chi_{15}(7,\cdot)$ |
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 | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{15}(1,\cdot)\) | 15.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(\chi_{15}(2,\cdot)\) | 15.e | 4 | yes | \(1\) | \(1\) | \(-i\) | \(-1\) | \(i\) | \(i\) | \(-1\) | \(-i\) |
| \(\chi_{15}(4,\cdot)\) | 15.b | 2 | no | \(1\) | \(1\) | \(-1\) | \(1\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
| \(\chi_{15}(7,\cdot)\) | 15.f | 4 | no | \(-1\) | \(1\) | \(i\) | \(-1\) | \(i\) | \(-i\) | \(1\) | \(-i\) |
| \(\chi_{15}(8,\cdot)\) | 15.e | 4 | yes | \(1\) | \(1\) | \(i\) | \(-1\) | \(-i\) | \(-i\) | \(-1\) | \(i\) |
| \(\chi_{15}(11,\cdot)\) | 15.c | 2 | no | \(-1\) | \(1\) | \(-1\) | \(1\) | \(1\) | \(-1\) | \(-1\) | \(1\) |
| \(\chi_{15}(13,\cdot)\) | 15.f | 4 | no | \(-1\) | \(1\) | \(-i\) | \(-1\) | \(-i\) | \(i\) | \(1\) | \(i\) |
| \(\chi_{15}(14,\cdot)\) | 15.d | 2 | yes | \(-1\) | \(1\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(-1\) | \(-1\) |