sage: H = DirichletGroup(2736)
pari: g = idealstar(,2736,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 864 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{2}\times C_{6}\times C_{36}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{2736}(1711,\cdot)$, $\chi_{2736}(2053,\cdot)$, $\chi_{2736}(1217,\cdot)$, $\chi_{2736}(1009,\cdot)$ |
First 32 of 864 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 | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{2736}(1,\cdot)\) | 2736.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{2736}(5,\cdot)\) | 2736.he | 36 | yes | \(-1\) | \(1\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(-i\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(1\) | \(e\left(\frac{29}{36}\right)\) |
\(\chi_{2736}(7,\cdot)\) | 2736.cr | 6 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{2736}(11,\cdot)\) | 2736.ea | 12 | yes | \(1\) | \(1\) | \(-i\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(i\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{12}\right)\) |
\(\chi_{2736}(13,\cdot)\) | 2736.gp | 36 | yes | \(-1\) | \(1\) | \(e\left(\frac{31}{36}\right)\) | \(-1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{13}{36}\right)\) |
\(\chi_{2736}(17,\cdot)\) | 2736.fj | 18 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{13}{18}\right)\) |
\(\chi_{2736}(23,\cdot)\) | 2736.ez | 18 | no | \(1\) | \(1\) | \(e\left(\frac{4}{9}\right)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{17}{18}\right)\) |
\(\chi_{2736}(25,\cdot)\) | 2736.fd | 18 | no | \(1\) | \(1\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(1\) | \(e\left(\frac{11}{18}\right)\) |
\(\chi_{2736}(29,\cdot)\) | 2736.gz | 36 | yes | \(1\) | \(1\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(i\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(-1\) | \(e\left(\frac{19}{36}\right)\) |
\(\chi_{2736}(31,\cdot)\) | 2736.di | 6 | no | \(1\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{2736}(35,\cdot)\) | 2736.gv | 36 | no | \(1\) | \(1\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{36}\right)\) |
\(\chi_{2736}(37,\cdot)\) | 2736.w | 4 | no | \(-1\) | \(1\) | \(i\) | \(-1\) | \(i\) | \(i\) | \(1\) | \(-1\) | \(-1\) | \(i\) | \(-1\) | \(-i\) |
\(\chi_{2736}(41,\cdot)\) | 2736.fn | 18 | no | \(1\) | \(1\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(-1\) | \(e\left(\frac{8}{9}\right)\) |
\(\chi_{2736}(43,\cdot)\) | 2736.hi | 36 | yes | \(-1\) | \(1\) | \(e\left(\frac{29}{36}\right)\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{29}{36}\right)\) |
\(\chi_{2736}(47,\cdot)\) | 2736.gc | 18 | no | \(1\) | \(1\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(-1\) | \(e\left(\frac{7}{9}\right)\) |
\(\chi_{2736}(49,\cdot)\) | 2736.r | 3 | no | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{2736}(53,\cdot)\) | 2736.hc | 36 | no | \(1\) | \(1\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{25}{36}\right)\) |
\(\chi_{2736}(55,\cdot)\) | 2736.fv | 18 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{9}\right)\) |
\(\chi_{2736}(59,\cdot)\) | 2736.gx | 36 | yes | \(-1\) | \(1\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(i\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(1\) | \(e\left(\frac{35}{36}\right)\) |
\(\chi_{2736}(61,\cdot)\) | 2736.hf | 36 | yes | \(1\) | \(1\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(-i\) | \(e\left(\frac{5}{36}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{29}{36}\right)\) | \(1\) | \(e\left(\frac{25}{36}\right)\) |
\(\chi_{2736}(65,\cdot)\) | 2736.bf | 6 | no | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{2736}(67,\cdot)\) | 2736.hh | 36 | yes | \(1\) | \(1\) | \(e\left(\frac{19}{36}\right)\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{19}{36}\right)\) |
\(\chi_{2736}(71,\cdot)\) | 2736.fy | 18 | no | \(-1\) | \(1\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{18}\right)\) |
\(\chi_{2736}(73,\cdot)\) | 2736.fi | 18 | no | \(1\) | \(1\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{7}{18}\right)\) |
\(\chi_{2736}(77,\cdot)\) | 2736.ed | 12 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(-i\) |
\(\chi_{2736}(79,\cdot)\) | 2736.ex | 18 | no | \(1\) | \(1\) | \(e\left(\frac{8}{9}\right)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{18}\right)\) |
\(\chi_{2736}(83,\cdot)\) | 2736.dy | 12 | yes | \(1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(i\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{7}{12}\right)\) |
\(\chi_{2736}(85,\cdot)\) | 2736.gm | 36 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{36}\right)\) | \(-1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{19}{36}\right)\) |
\(\chi_{2736}(89,\cdot)\) | 2736.fh | 18 | no | \(1\) | \(1\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{9}\right)\) |
\(\chi_{2736}(91,\cdot)\) | 2736.gt | 36 | no | \(1\) | \(1\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{5}{36}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{25}{36}\right)\) |
\(\chi_{2736}(97,\cdot)\) | 2736.gg | 18 | no | \(-1\) | \(1\) | \(e\left(\frac{2}{9}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{9}\right)\) |
\(\chi_{2736}(101,\cdot)\) | 2736.he | 36 | yes | \(-1\) | \(1\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(-i\) | \(e\left(\frac{35}{36}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{5}{36}\right)\) | \(1\) | \(e\left(\frac{13}{36}\right)\) |