sage: H = DirichletGroup(2665)
pari: g = idealstar(,2665,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 1920 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{4}\times C_{4}\times C_{120}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{2665}(1067,\cdot)$, $\chi_{2665}(821,\cdot)$, $\chi_{2665}(1236,\cdot)$ |
First 32 of 1920 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 | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(14\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{2665}(1,\cdot)\) | 2665.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{2665}(2,\cdot)\) | 2665.gn | 60 | yes | \(1\) | \(1\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(-i\) |
\(\chi_{2665}(3,\cdot)\) | 2665.fi | 24 | yes | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(-1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) |
\(\chi_{2665}(4,\cdot)\) | 2665.fp | 30 | yes | \(1\) | \(1\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(-1\) |
\(\chi_{2665}(6,\cdot)\) | 2665.hw | 120 | no | \(1\) | \(1\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{13}{120}\right)\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{119}{120}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{5}{8}\right)\) |
\(\chi_{2665}(7,\cdot)\) | 2665.ho | 120 | yes | \(-1\) | \(1\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{43}{120}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{41}{120}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{7}{8}\right)\) |
\(\chi_{2665}(8,\cdot)\) | 2665.ep | 20 | yes | \(1\) | \(1\) | \(e\left(\frac{7}{10}\right)\) | \(-1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(i\) |
\(\chi_{2665}(9,\cdot)\) | 2665.cs | 12 | yes | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(-i\) | \(-i\) |
\(\chi_{2665}(11,\cdot)\) | 2665.hw | 120 | no | \(1\) | \(1\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{119}{120}\right)\) | \(e\left(\frac{41}{120}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{37}{120}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{7}{8}\right)\) |
\(\chi_{2665}(12,\cdot)\) | 2665.gf | 40 | yes | \(1\) | \(1\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(-i\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{3}{8}\right)\) |
\(\chi_{2665}(14,\cdot)\) | 2665.bz | 8 | no | \(-1\) | \(1\) | \(-i\) | \(e\left(\frac{7}{8}\right)\) | \(-1\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(i\) | \(-i\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) |
\(\chi_{2665}(16,\cdot)\) | 2665.ds | 15 | no | \(1\) | \(1\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(1\) |
\(\chi_{2665}(17,\cdot)\) | 2665.hx | 120 | yes | \(1\) | \(1\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{79}{120}\right)\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{77}{120}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{1}{8}\right)\) |
\(\chi_{2665}(18,\cdot)\) | 2665.eq | 20 | yes | \(1\) | \(1\) | \(e\left(\frac{9}{10}\right)\) | \(i\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(-1\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(-1\) |
\(\chi_{2665}(19,\cdot)\) | 2665.hk | 120 | yes | \(1\) | \(1\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{37}{120}\right)\) | \(e\left(\frac{103}{120}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{71}{120}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{5}{8}\right)\) |
\(\chi_{2665}(21,\cdot)\) | 2665.ed | 20 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{20}\right)\) | \(i\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(-1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(-i\) |
\(\chi_{2665}(22,\cdot)\) | 2665.hm | 120 | yes | \(1\) | \(1\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{7}{120}\right)\) | \(e\left(\frac{103}{120}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{101}{120}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{5}{8}\right)\) |
\(\chi_{2665}(23,\cdot)\) | 2665.gy | 60 | yes | \(-1\) | \(1\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(1\) |
\(\chi_{2665}(24,\cdot)\) | 2665.hz | 120 | yes | \(1\) | \(1\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{29}{120}\right)\) | \(e\left(\frac{71}{120}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{7}{120}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{1}{8}\right)\) |
\(\chi_{2665}(27,\cdot)\) | 2665.bu | 8 | no | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{5}{8}\right)\) | \(1\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(-1\) | \(i\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) |
\(\chi_{2665}(28,\cdot)\) | 2665.hr | 120 | yes | \(-1\) | \(1\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{83}{120}\right)\) | \(e\left(\frac{47}{120}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{49}{120}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{3}{8}\right)\) |
\(\chi_{2665}(29,\cdot)\) | 2665.hu | 120 | yes | \(-1\) | \(1\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{101}{120}\right)\) | \(e\left(\frac{119}{120}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{103}{120}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{3}{8}\right)\) |
\(\chi_{2665}(31,\cdot)\) | 2665.ea | 20 | no | \(-1\) | \(1\) | \(e\left(\frac{19}{20}\right)\) | \(-1\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(1\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(-1\) |
\(\chi_{2665}(32,\cdot)\) | 2665.dr | 12 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(-i\) |
\(\chi_{2665}(33,\cdot)\) | 2665.gi | 60 | yes | \(1\) | \(1\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(-i\) |
\(\chi_{2665}(34,\cdot)\) | 2665.ge | 40 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(i\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{7}{8}\right)\) |
\(\chi_{2665}(36,\cdot)\) | 2665.hg | 60 | no | \(1\) | \(1\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(i\) |
\(\chi_{2665}(37,\cdot)\) | 2665.gm | 60 | yes | \(1\) | \(1\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(-1\) |
\(\chi_{2665}(38,\cdot)\) | 2665.ch | 8 | yes | \(1\) | \(1\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(1\) | \(-i\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) |
\(\chi_{2665}(42,\cdot)\) | 2665.db | 12 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(-i\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(i\) | \(-1\) |
\(\chi_{2665}(43,\cdot)\) | 2665.gr | 60 | yes | \(-1\) | \(1\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(-i\) |
\(\chi_{2665}(44,\cdot)\) | 2665.cf | 8 | yes | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{8}\right)\) | \(1\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(1\) | \(i\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) |