sage: H = DirichletGroup(18)
pari: g = idealstar(,18,2)
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 | = | $\chi_{18}(11,\cdot)$ |
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 | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) |
---|---|---|---|---|---|---|---|---|---|
\(\chi_{18}(1,\cdot)\) | 18.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{18}(5,\cdot)\) | 18.d | 6 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{18}(7,\cdot)\) | 18.c | 3 | no | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{18}(11,\cdot)\) | 18.d | 6 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{18}(13,\cdot)\) | 18.c | 3 | no | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{18}(17,\cdot)\) | 18.b | 2 | no | \(-1\) | \(1\) | \(-1\) | \(1\) | \(-1\) | \(1\) |