sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(14)
pari: g = idealstar(,14,2)
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 | = | $\chi_{14}(3,\cdot)$ |
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.
| orbit label | order | primitive | -1 | 1 | 3 | 5 | 9 | 11 | |
|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{14}(1,\cdot)\) | 14.a | 1 | No | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(\chi_{14}(3,\cdot)\) | 14.d | 6 | No | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
| \(\chi_{14}(5,\cdot)\) | 14.d | 6 | No | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
| \(\chi_{14}(9,\cdot)\) | 14.c | 3 | No | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
| \(\chi_{14}(11,\cdot)\) | 14.c | 3 | No | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
| \(\chi_{14}(13,\cdot)\) | 14.b | 2 | No | \(-1\) | \(1\) | \(-1\) | \(-1\) | \(1\) | \(1\) |