sage: H = DirichletGroup(7)
pari: g = idealstar(,7,2)
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 | = | $\chi_{7}(3,\cdot)$ |
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 | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) |
|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{7}(1,\cdot)\) | 7.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(\chi_{7}(2,\cdot)\) | 7.c | 3 | yes | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
| \(\chi_{7}(3,\cdot)\) | 7.d | 6 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) |
| \(\chi_{7}(4,\cdot)\) | 7.c | 3 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
| \(\chi_{7}(5,\cdot)\) | 7.d | 6 | yes | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) |
| \(\chi_{7}(6,\cdot)\) | 7.b | 2 | yes | \(-1\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(-1\) |