sage: H = DirichletGroup(34)
pari: g = idealstar(,34,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 16 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{16}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{34}(3,\cdot)$ |
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 | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{34}(1,\cdot)\) | 34.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{34}(3,\cdot)\) | 34.e | 16 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(i\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(-i\) | \(e\left(\frac{15}{16}\right)\) |
\(\chi_{34}(5,\cdot)\) | 34.e | 16 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(i\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(-i\) | \(e\left(\frac{11}{16}\right)\) |
\(\chi_{34}(7,\cdot)\) | 34.e | 16 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(-i\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(i\) | \(e\left(\frac{5}{16}\right)\) |
\(\chi_{34}(9,\cdot)\) | 34.d | 8 | no | \(1\) | \(1\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(i\) | \(e\left(\frac{7}{8}\right)\) | \(-1\) | \(-i\) | \(-i\) | \(-1\) | \(e\left(\frac{7}{8}\right)\) |
\(\chi_{34}(11,\cdot)\) | 34.e | 16 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(-i\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(i\) | \(e\left(\frac{9}{16}\right)\) |
\(\chi_{34}(13,\cdot)\) | 34.c | 4 | no | \(1\) | \(1\) | \(i\) | \(i\) | \(-i\) | \(-1\) | \(-i\) | \(1\) | \(-1\) | \(-1\) | \(1\) | \(-i\) |
\(\chi_{34}(15,\cdot)\) | 34.d | 8 | no | \(1\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(-i\) | \(e\left(\frac{5}{8}\right)\) | \(-1\) | \(i\) | \(i\) | \(-1\) | \(e\left(\frac{5}{8}\right)\) |
\(\chi_{34}(19,\cdot)\) | 34.d | 8 | no | \(1\) | \(1\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(-i\) | \(e\left(\frac{1}{8}\right)\) | \(-1\) | \(i\) | \(i\) | \(-1\) | \(e\left(\frac{1}{8}\right)\) |
\(\chi_{34}(21,\cdot)\) | 34.c | 4 | no | \(1\) | \(1\) | \(-i\) | \(-i\) | \(i\) | \(-1\) | \(i\) | \(1\) | \(-1\) | \(-1\) | \(1\) | \(i\) |
\(\chi_{34}(23,\cdot)\) | 34.e | 16 | no | \(-1\) | \(1\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(-i\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(i\) | \(e\left(\frac{1}{16}\right)\) |
\(\chi_{34}(25,\cdot)\) | 34.d | 8 | no | \(1\) | \(1\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(i\) | \(e\left(\frac{3}{8}\right)\) | \(-1\) | \(-i\) | \(-i\) | \(-1\) | \(e\left(\frac{3}{8}\right)\) |
\(\chi_{34}(27,\cdot)\) | 34.e | 16 | no | \(-1\) | \(1\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(-i\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(i\) | \(e\left(\frac{13}{16}\right)\) |
\(\chi_{34}(29,\cdot)\) | 34.e | 16 | no | \(-1\) | \(1\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(i\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(-i\) | \(e\left(\frac{3}{16}\right)\) |
\(\chi_{34}(31,\cdot)\) | 34.e | 16 | no | \(-1\) | \(1\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(i\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(-i\) | \(e\left(\frac{7}{16}\right)\) |
\(\chi_{34}(33,\cdot)\) | 34.b | 2 | no | \(1\) | \(1\) | \(-1\) | \(-1\) | \(-1\) | \(1\) | \(-1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(-1\) |