sage: H = DirichletGroup(9)
pari: g = idealstar(,9,2)
Character group
| sage: G.order()
pari: g.no
| ||
| Order | = | 6 |
| sage: H.invariants()
pari: g.cyc
| ||
| Structure | = | \(C_{6}\) |
| sage: H.gens()
pari: g.gen
| ||
| Generators | = | $\chi_{9}(2,\cdot)$ |
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 | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) |
|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{9}(1,\cdot)\) | 9.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(\chi_{9}(2,\cdot)\) | 9.d | 6 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) |
| \(\chi_{9}(4,\cdot)\) | 9.c | 3 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
| \(\chi_{9}(5,\cdot)\) | 9.d | 6 | yes | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) |
| \(\chi_{9}(7,\cdot)\) | 9.c | 3 | yes | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
| \(\chi_{9}(8,\cdot)\) | 9.b | 2 | no | \(-1\) | \(1\) | \(-1\) | \(1\) | \(-1\) | \(1\) |