sage: H = DirichletGroup(22)
pari: g = idealstar(,22,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 10 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{10}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{22}(13,\cdot)$ |
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 | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{22}(1,\cdot)\) | 22.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{22}(3,\cdot)\) | 22.c | 5 | no | \(1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) |
\(\chi_{22}(5,\cdot)\) | 22.c | 5 | no | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) |
\(\chi_{22}(7,\cdot)\) | 22.d | 10 | no | \(-1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) |
\(\chi_{22}(9,\cdot)\) | 22.c | 5 | no | \(1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) |
\(\chi_{22}(13,\cdot)\) | 22.d | 10 | no | \(-1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{3}{10}\right)\) |
\(\chi_{22}(15,\cdot)\) | 22.c | 5 | no | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) |
\(\chi_{22}(17,\cdot)\) | 22.d | 10 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{7}{10}\right)\) |
\(\chi_{22}(19,\cdot)\) | 22.d | 10 | no | \(-1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{9}{10}\right)\) |
\(\chi_{22}(21,\cdot)\) | 22.b | 2 | no | \(-1\) | \(1\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(-1\) | \(1\) | \(-1\) | \(-1\) |