sage: H = DirichletGroup(110)
pari: g = idealstar(,110,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 40 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{20}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{110}(67,\cdot)$, $\chi_{110}(101,\cdot)$ |
First 32 of 40 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 | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{110}(1,\cdot)\) | 110.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{110}(3,\cdot)\) | 110.l | 20 | no | \(-1\) | \(1\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(1\) | \(i\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) |
\(\chi_{110}(7,\cdot)\) | 110.k | 20 | no | \(1\) | \(1\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(-1\) | \(-i\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{2}{5}\right)\) |
\(\chi_{110}(9,\cdot)\) | 110.j | 10 | no | \(1\) | \(1\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(1\) | \(-1\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) |
\(\chi_{110}(13,\cdot)\) | 110.k | 20 | no | \(1\) | \(1\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(-1\) | \(i\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{1}{5}\right)\) |
\(\chi_{110}(17,\cdot)\) | 110.k | 20 | no | \(1\) | \(1\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(-1\) | \(-i\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{4}{5}\right)\) |
\(\chi_{110}(19,\cdot)\) | 110.i | 10 | no | \(-1\) | \(1\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(-1\) | \(-1\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) |
\(\chi_{110}(21,\cdot)\) | 110.d | 2 | no | \(-1\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(-1\) | \(-1\) | \(-1\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
\(\chi_{110}(23,\cdot)\) | 110.e | 4 | no | \(-1\) | \(1\) | \(i\) | \(-i\) | \(-1\) | \(i\) | \(-i\) | \(-1\) | \(1\) | \(i\) | \(-i\) | \(-1\) |
\(\chi_{110}(27,\cdot)\) | 110.l | 20 | no | \(-1\) | \(1\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(1\) | \(-i\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{3}{10}\right)\) |
\(\chi_{110}(29,\cdot)\) | 110.i | 10 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(-1\) | \(-1\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{9}{10}\right)\) |
\(\chi_{110}(31,\cdot)\) | 110.g | 5 | no | \(1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) |
\(\chi_{110}(37,\cdot)\) | 110.l | 20 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(1\) | \(-i\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{9}{10}\right)\) |
\(\chi_{110}(39,\cdot)\) | 110.i | 10 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{3}{10}\right)\) |
\(\chi_{110}(41,\cdot)\) | 110.h | 10 | no | \(-1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{10}\right)\) |
\(\chi_{110}(43,\cdot)\) | 110.f | 4 | no | \(1\) | \(1\) | \(i\) | \(i\) | \(-1\) | \(-i\) | \(i\) | \(1\) | \(-1\) | \(i\) | \(-i\) | \(1\) |
\(\chi_{110}(47,\cdot)\) | 110.l | 20 | no | \(-1\) | \(1\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(1\) | \(-i\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) |
\(\chi_{110}(49,\cdot)\) | 110.j | 10 | no | \(1\) | \(1\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) |
\(\chi_{110}(51,\cdot)\) | 110.h | 10 | no | \(-1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(-1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) |
\(\chi_{110}(53,\cdot)\) | 110.l | 20 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(1\) | \(i\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{7}{10}\right)\) |
\(\chi_{110}(57,\cdot)\) | 110.k | 20 | no | \(1\) | \(1\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(-1\) | \(-i\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{1}{5}\right)\) |
\(\chi_{110}(59,\cdot)\) | 110.j | 10 | no | \(1\) | \(1\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(1\) | \(-1\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) |
\(\chi_{110}(61,\cdot)\) | 110.h | 10 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(-1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{3}{10}\right)\) |
\(\chi_{110}(63,\cdot)\) | 110.k | 20 | no | \(1\) | \(1\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(-1\) | \(i\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{3}{5}\right)\) |
\(\chi_{110}(67,\cdot)\) | 110.e | 4 | no | \(-1\) | \(1\) | \(-i\) | \(i\) | \(-1\) | \(-i\) | \(i\) | \(-1\) | \(1\) | \(-i\) | \(i\) | \(-1\) |
\(\chi_{110}(69,\cdot)\) | 110.j | 10 | no | \(1\) | \(1\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(1\) | \(-1\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) |
\(\chi_{110}(71,\cdot)\) | 110.g | 5 | no | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) |
\(\chi_{110}(73,\cdot)\) | 110.k | 20 | no | \(1\) | \(1\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(-1\) | \(i\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{2}{5}\right)\) |
\(\chi_{110}(79,\cdot)\) | 110.i | 10 | no | \(-1\) | \(1\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(-1\) | \(-1\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{7}{10}\right)\) |
\(\chi_{110}(81,\cdot)\) | 110.g | 5 | no | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) |
\(\chi_{110}(83,\cdot)\) | 110.k | 20 | no | \(1\) | \(1\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(-1\) | \(i\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{4}{5}\right)\) |
\(\chi_{110}(87,\cdot)\) | 110.f | 4 | no | \(1\) | \(1\) | \(-i\) | \(-i\) | \(-1\) | \(i\) | \(-i\) | \(1\) | \(-1\) | \(-i\) | \(i\) | \(1\) |