sage: H = DirichletGroup(740)
pari: g = idealstar(,740,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 288 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{4}\times C_{36}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{740}(371,\cdot)$, $\chi_{740}(297,\cdot)$, $\chi_{740}(261,\cdot)$ |
First 32 of 288 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 | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{740}(1,\cdot)\) | 740.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{740}(3,\cdot)\) | 740.ce | 36 | yes | \(1\) | \(1\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) |
\(\chi_{740}(7,\cdot)\) | 740.cf | 36 | yes | \(1\) | \(1\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) |
\(\chi_{740}(9,\cdot)\) | 740.br | 18 | no | \(1\) | \(1\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{740}(11,\cdot)\) | 740.z | 6 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(-1\) |
\(\chi_{740}(13,\cdot)\) | 740.ch | 36 | no | \(1\) | \(1\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{7}{12}\right)\) |
\(\chi_{740}(17,\cdot)\) | 740.cc | 36 | no | \(1\) | \(1\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{12}\right)\) |
\(\chi_{740}(19,\cdot)\) | 740.ca | 36 | yes | \(1\) | \(1\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{740}(21,\cdot)\) | 740.bq | 18 | no | \(1\) | \(1\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{740}(23,\cdot)\) | 740.bm | 12 | yes | \(-1\) | \(1\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-i\) |
\(\chi_{740}(27,\cdot)\) | 740.bh | 12 | yes | \(1\) | \(1\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(-i\) | \(-i\) |
\(\chi_{740}(29,\cdot)\) | 740.bd | 12 | no | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(i\) | \(1\) |
\(\chi_{740}(31,\cdot)\) | 740.u | 4 | no | \(1\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(1\) | \(-i\) | \(-i\) | \(i\) | \(-1\) | \(i\) | \(1\) |
\(\chi_{740}(33,\cdot)\) | 740.bz | 36 | no | \(-1\) | \(1\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) |
\(\chi_{740}(39,\cdot)\) | 740.ca | 36 | yes | \(1\) | \(1\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{740}(41,\cdot)\) | 740.bq | 18 | no | \(1\) | \(1\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{740}(43,\cdot)\) | 740.p | 4 | yes | \(-1\) | \(1\) | \(i\) | \(i\) | \(-1\) | \(1\) | \(-1\) | \(1\) | \(i\) | \(-1\) | \(1\) | \(-i\) |
\(\chi_{740}(47,\cdot)\) | 740.bg | 12 | yes | \(1\) | \(1\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(i\) | \(-i\) |
\(\chi_{740}(49,\cdot)\) | 740.br | 18 | no | \(1\) | \(1\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{740}(51,\cdot)\) | 740.be | 12 | no | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(i\) | \(1\) |
\(\chi_{740}(53,\cdot)\) | 740.bz | 36 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{36}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{12}\right)\) |
\(\chi_{740}(57,\cdot)\) | 740.ch | 36 | no | \(1\) | \(1\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{12}\right)\) |
\(\chi_{740}(59,\cdot)\) | 740.ca | 36 | yes | \(1\) | \(1\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{35}{36}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{740}(61,\cdot)\) | 740.cg | 36 | no | \(-1\) | \(1\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{740}(63,\cdot)\) | 740.bg | 12 | yes | \(1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(-i\) | \(i\) |
\(\chi_{740}(67,\cdot)\) | 740.ce | 36 | yes | \(1\) | \(1\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{35}{36}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) |
\(\chi_{740}(69,\cdot)\) | 740.cd | 36 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{740}(71,\cdot)\) | 740.bv | 18 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{740}(73,\cdot)\) | 740.r | 4 | no | \(-1\) | \(1\) | \(i\) | \(-i\) | \(-1\) | \(1\) | \(-i\) | \(i\) | \(1\) | \(1\) | \(-i\) | \(-i\) |
\(\chi_{740}(77,\cdot)\) | 740.by | 36 | no | \(-1\) | \(1\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) |
\(\chi_{740}(79,\cdot)\) | 740.ca | 36 | yes | \(1\) | \(1\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{35}{36}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{740}(81,\cdot)\) | 740.bc | 9 | no | \(1\) | \(1\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |