sage: H = DirichletGroup(1287)
pari: g = idealstar(,1287,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 720 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{6}\times C_{60}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{1287}(1145,\cdot)$, $\chi_{1287}(937,\cdot)$, $\chi_{1287}(496,\cdot)$ |
First 32 of 720 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 | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(14\) | \(16\) | \(17\) | \(19\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{1287}(1,\cdot)\) | 1287.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{1287}(2,\cdot)\) | 1287.em | 60 | yes | \(-1\) | \(1\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{43}{60}\right)\) |
\(\chi_{1287}(4,\cdot)\) | 1287.dw | 30 | yes | \(1\) | \(1\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{13}{30}\right)\) |
\(\chi_{1287}(5,\cdot)\) | 1287.ea | 60 | yes | \(1\) | \(1\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(-1\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{19}{20}\right)\) |
\(\chi_{1287}(7,\cdot)\) | 1287.ee | 60 | yes | \(1\) | \(1\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{41}{60}\right)\) |
\(\chi_{1287}(8,\cdot)\) | 1287.cx | 20 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(1\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{3}{20}\right)\) |
\(\chi_{1287}(10,\cdot)\) | 1287.v | 6 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{1287}(14,\cdot)\) | 1287.df | 30 | no | \(-1\) | \(1\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(1\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) |
\(\chi_{1287}(16,\cdot)\) | 1287.cq | 15 | yes | \(1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{13}{15}\right)\) |
\(\chi_{1287}(17,\cdot)\) | 1287.dc | 30 | no | \(1\) | \(1\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{8}{15}\right)\) |
\(\chi_{1287}(19,\cdot)\) | 1287.ec | 60 | no | \(1\) | \(1\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{59}{60}\right)\) |
\(\chi_{1287}(20,\cdot)\) | 1287.eh | 60 | yes | \(1\) | \(1\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{23}{60}\right)\) |
\(\chi_{1287}(23,\cdot)\) | 1287.x | 6 | no | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{1287}(25,\cdot)\) | 1287.de | 30 | yes | \(1\) | \(1\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(1\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) |
\(\chi_{1287}(28,\cdot)\) | 1287.ec | 60 | no | \(1\) | \(1\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{7}{60}\right)\) |
\(\chi_{1287}(29,\cdot)\) | 1287.cy | 30 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{23}{30}\right)\) |
\(\chi_{1287}(31,\cdot)\) | 1287.eb | 60 | yes | \(-1\) | \(1\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(-1\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{11}{20}\right)\) |
\(\chi_{1287}(32,\cdot)\) | 1287.cb | 12 | yes | \(-1\) | \(1\) | \(-i\) | \(-1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(i\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{7}{12}\right)\) |
\(\chi_{1287}(34,\cdot)\) | 1287.ce | 12 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(-i\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(i\) |
\(\chi_{1287}(35,\cdot)\) | 1287.du | 30 | no | \(1\) | \(1\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{19}{30}\right)\) |
\(\chi_{1287}(37,\cdot)\) | 1287.eg | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{31}{60}\right)\) |
\(\chi_{1287}(38,\cdot)\) | 1287.ds | 30 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(1\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{7}{10}\right)\) |
\(\chi_{1287}(40,\cdot)\) | 1287.di | 30 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(-1\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) |
\(\chi_{1287}(41,\cdot)\) | 1287.ed | 60 | yes | \(-1\) | \(1\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{19}{60}\right)\) |
\(\chi_{1287}(43,\cdot)\) | 1287.bc | 6 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{1287}(46,\cdot)\) | 1287.ec | 60 | no | \(1\) | \(1\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{53}{60}\right)\) |
\(\chi_{1287}(47,\cdot)\) | 1287.ea | 60 | yes | \(1\) | \(1\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(-1\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{13}{20}\right)\) |
\(\chi_{1287}(49,\cdot)\) | 1287.dg | 30 | yes | \(1\) | \(1\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{11}{30}\right)\) |
\(\chi_{1287}(50,\cdot)\) | 1287.ed | 60 | yes | \(-1\) | \(1\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{37}{60}\right)\) |
\(\chi_{1287}(53,\cdot)\) | 1287.by | 10 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(1\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) |
\(\chi_{1287}(56,\cdot)\) | 1287.x | 6 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{1287}(58,\cdot)\) | 1287.ep | 60 | yes | \(-1\) | \(1\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{29}{60}\right)\) |