sage: H = DirichletGroup(95)
pari: g = idealstar(,95,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 72 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{36}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{95}(77,\cdot)$, $\chi_{95}(21,\cdot)$ |
First 32 of 72 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 | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{95}(1,\cdot)\) | 95.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{95}(2,\cdot)\) | 95.r | 36 | yes | \(1\) | \(1\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{36}\right)\) |
\(\chi_{95}(3,\cdot)\) | 95.r | 36 | yes | \(1\) | \(1\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{31}{36}\right)\) |
\(\chi_{95}(4,\cdot)\) | 95.p | 18 | yes | \(1\) | \(1\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{18}\right)\) |
\(\chi_{95}(6,\cdot)\) | 95.k | 9 | no | \(1\) | \(1\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{8}{9}\right)\) |
\(\chi_{95}(7,\cdot)\) | 95.m | 12 | yes | \(-1\) | \(1\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(i\) | \(-i\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(i\) | \(e\left(\frac{5}{12}\right)\) |
\(\chi_{95}(8,\cdot)\) | 95.l | 12 | yes | \(1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(-i\) | \(-i\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(i\) | \(e\left(\frac{1}{12}\right)\) |
\(\chi_{95}(9,\cdot)\) | 95.p | 18 | yes | \(1\) | \(1\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{13}{18}\right)\) |
\(\chi_{95}(11,\cdot)\) | 95.e | 3 | no | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{95}(12,\cdot)\) | 95.l | 12 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(i\) | \(i\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-i\) | \(e\left(\frac{11}{12}\right)\) |
\(\chi_{95}(13,\cdot)\) | 95.r | 36 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{23}{36}\right)\) |
\(\chi_{95}(14,\cdot)\) | 95.o | 18 | yes | \(-1\) | \(1\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{4}{9}\right)\) |
\(\chi_{95}(16,\cdot)\) | 95.k | 9 | no | \(1\) | \(1\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{9}\right)\) |
\(\chi_{95}(17,\cdot)\) | 95.q | 36 | yes | \(-1\) | \(1\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{35}{36}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{19}{36}\right)\) |
\(\chi_{95}(18,\cdot)\) | 95.g | 4 | yes | \(1\) | \(1\) | \(i\) | \(-i\) | \(-1\) | \(1\) | \(-i\) | \(-i\) | \(-1\) | \(1\) | \(i\) | \(-i\) |
\(\chi_{95}(21,\cdot)\) | 95.n | 18 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{18}\right)\) |
\(\chi_{95}(22,\cdot)\) | 95.r | 36 | yes | \(1\) | \(1\) | \(e\left(\frac{35}{36}\right)\) | \(e\left(\frac{5}{36}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{13}{36}\right)\) |
\(\chi_{95}(23,\cdot)\) | 95.q | 36 | yes | \(-1\) | \(1\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{29}{36}\right)\) |
\(\chi_{95}(24,\cdot)\) | 95.p | 18 | yes | \(1\) | \(1\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{17}{18}\right)\) |
\(\chi_{95}(26,\cdot)\) | 95.e | 3 | no | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{95}(27,\cdot)\) | 95.l | 12 | yes | \(1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(i\) | \(i\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-i\) | \(e\left(\frac{7}{12}\right)\) |
\(\chi_{95}(28,\cdot)\) | 95.q | 36 | yes | \(-1\) | \(1\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{17}{36}\right)\) |
\(\chi_{95}(29,\cdot)\) | 95.o | 18 | yes | \(-1\) | \(1\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{9}\right)\) |
\(\chi_{95}(31,\cdot)\) | 95.j | 6 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{95}(32,\cdot)\) | 95.r | 36 | yes | \(1\) | \(1\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{36}\right)\) |
\(\chi_{95}(33,\cdot)\) | 95.r | 36 | yes | \(1\) | \(1\) | \(e\left(\frac{5}{36}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{7}{36}\right)\) |
\(\chi_{95}(34,\cdot)\) | 95.o | 18 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{9}\right)\) |
\(\chi_{95}(36,\cdot)\) | 95.k | 9 | no | \(1\) | \(1\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{7}{9}\right)\) |
\(\chi_{95}(37,\cdot)\) | 95.g | 4 | yes | \(1\) | \(1\) | \(-i\) | \(i\) | \(-1\) | \(1\) | \(i\) | \(i\) | \(-1\) | \(1\) | \(-i\) | \(i\) |
\(\chi_{95}(39,\cdot)\) | 95.b | 2 | no | \(1\) | \(1\) | \(-1\) | \(-1\) | \(1\) | \(1\) | \(-1\) | \(-1\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
\(\chi_{95}(41,\cdot)\) | 95.n | 18 | no | \(-1\) | \(1\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{11}{18}\right)\) |
\(\chi_{95}(42,\cdot)\) | 95.q | 36 | yes | \(-1\) | \(1\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{11}{36}\right)\) |