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