sage: H = DirichletGroup(8)
pari: g = idealstar(,8,2)
Character group
| sage: G.order()
pari: g.no
| ||
| Order | = | 4 |
| sage: H.invariants()
pari: g.cyc
| ||
| Structure | = | \(C_{2}\times C_{2}\) |
| sage: H.gens()
pari: g.gen
| ||
| Generators | = | $\chi_{8}(7,\cdot)$, $\chi_{8}(5,\cdot)$ |
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 | \(-1\) | \(1\) | \(3\) | \(5\) |
|---|---|---|---|---|---|---|---|
| \(\chi_{8}(1,\cdot)\) | 8.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) |
| \(\chi_{8}(3,\cdot)\) | 8.d | 2 | yes | \(-1\) | \(1\) | \(1\) | \(-1\) |
| \(\chi_{8}(5,\cdot)\) | 8.b | 2 | yes | \(1\) | \(1\) | \(-1\) | \(-1\) |
| \(\chi_{8}(7,\cdot)\) | 8.c | 2 | no | \(-1\) | \(1\) | \(-1\) | \(1\) |