sage: H = DirichletGroup(2790)
pari: g = idealstar(,2790,2)
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 | = | $\chi_{2790}(2171,\cdot)$, $\chi_{2790}(1117,\cdot)$, $\chi_{2790}(1801,\cdot)$ |
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 | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(37\) | \(41\) | \(43\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{2790}(1,\cdot)\) | 2790.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{2790}(7,\cdot)\) | 2790.ei | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{3}{20}\right)\) |
\(\chi_{2790}(11,\cdot)\) | 2790.dn | 30 | no | \(1\) | \(1\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{7}{30}\right)\) |
\(\chi_{2790}(13,\cdot)\) | 2790.ee | 60 | no | \(1\) | \(1\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{11}{20}\right)\) |
\(\chi_{2790}(17,\cdot)\) | 2790.ek | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{11}{60}\right)\) |
\(\chi_{2790}(19,\cdot)\) | 2790.dh | 30 | no | \(1\) | \(1\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{1}{30}\right)\) |
\(\chi_{2790}(23,\cdot)\) | 2790.em | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(i\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{41}{60}\right)\) |
\(\chi_{2790}(29,\cdot)\) | 2790.dk | 30 | no | \(1\) | \(1\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(1\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{13}{15}\right)\) |
\(\chi_{2790}(37,\cdot)\) | 2790.cm | 12 | no | \(1\) | \(1\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(i\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{12}\right)\) |
\(\chi_{2790}(41,\cdot)\) | 2790.cy | 30 | no | \(-1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) |
\(\chi_{2790}(43,\cdot)\) | 2790.ee | 60 | no | \(1\) | \(1\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{19}{20}\right)\) |
\(\chi_{2790}(47,\cdot)\) | 2790.eg | 60 | no | \(1\) | \(1\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(i\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{13}{60}\right)\) |
\(\chi_{2790}(49,\cdot)\) | 2790.dz | 30 | no | \(1\) | \(1\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{10}\right)\) |
\(\chi_{2790}(53,\cdot)\) | 2790.ek | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{1}{60}\right)\) |
\(\chi_{2790}(59,\cdot)\) | 2790.dl | 30 | no | \(-1\) | \(1\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{29}{30}\right)\) |
\(\chi_{2790}(61,\cdot)\) | 2790.bb | 6 | no | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{2790}(67,\cdot)\) | 2790.ch | 12 | no | \(-1\) | \(1\) | \(i\) | \(e\left(\frac{2}{3}\right)\) | \(-i\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(1\) | \(-i\) |
\(\chi_{2790}(71,\cdot)\) | 2790.dq | 30 | no | \(-1\) | \(1\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{4}{15}\right)\) |
\(\chi_{2790}(73,\cdot)\) | 2790.ed | 60 | no | \(1\) | \(1\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{49}{60}\right)\) |
\(\chi_{2790}(77,\cdot)\) | 2790.em | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(-i\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{23}{60}\right)\) |
\(\chi_{2790}(79,\cdot)\) | 2790.dw | 30 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) |
\(\chi_{2790}(83,\cdot)\) | 2790.ea | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{17}{60}\right)\) |
\(\chi_{2790}(89,\cdot)\) | 2790.bw | 10 | no | \(1\) | \(1\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(1\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) |
\(\chi_{2790}(91,\cdot)\) | 2790.bv | 10 | no | \(-1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(-1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) |
\(\chi_{2790}(97,\cdot)\) | 2790.en | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(i\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{49}{60}\right)\) |
\(\chi_{2790}(101,\cdot)\) | 2790.dr | 30 | no | \(-1\) | \(1\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(1\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{4}{15}\right)\) |
\(\chi_{2790}(103,\cdot)\) | 2790.ei | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{9}{20}\right)\) |
\(\chi_{2790}(107,\cdot)\) | 2790.ec | 60 | no | \(1\) | \(1\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{41}{60}\right)\) |
\(\chi_{2790}(109,\cdot)\) | 2790.bx | 10 | no | \(1\) | \(1\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(-1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{10}\right)\) |
\(\chi_{2790}(113,\cdot)\) | 2790.ef | 60 | no | \(1\) | \(1\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{13}{20}\right)\) |
\(\chi_{2790}(119,\cdot)\) | 2790.bo | 6 | no | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{2790}(121,\cdot)\) | 2790.cr | 15 | no | \(1\) | \(1\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{7}{15}\right)\) |