sage: H = DirichletGroup(7440)
pari: g = idealstar(,7440,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 1920 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{60}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{7440}(6511,\cdot)$, $\chi_{7440}(1861,\cdot)$, $\chi_{7440}(4961,\cdot)$, $\chi_{7440}(2977,\cdot)$, $\chi_{7440}(5521,\cdot)$ |
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 | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(37\) | \(41\) | \(43\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{7440}(1,\cdot)\) | 7440.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{7440}(7,\cdot)\) | 7440.lt | 60 | no | \(1\) | \(1\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{29}{60}\right)\) |
\(\chi_{7440}(11,\cdot)\) | 7440.mf | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{19}{60}\right)\) |
\(\chi_{7440}(13,\cdot)\) | 7440.lk | 60 | no | \(1\) | \(1\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{29}{30}\right)\) |
\(\chi_{7440}(17,\cdot)\) | 7440.lu | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{11}{60}\right)\) |
\(\chi_{7440}(19,\cdot)\) | 7440.ko | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{17}{60}\right)\) |
\(\chi_{7440}(23,\cdot)\) | 7440.hy | 20 | no | \(1\) | \(1\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(-i\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{7}{20}\right)\) |
\(\chi_{7440}(29,\cdot)\) | 7440.hp | 20 | yes | \(1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(-i\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{19}{20}\right)\) |
\(\chi_{7440}(37,\cdot)\) | 7440.gk | 12 | no | \(1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(-i\) | \(-i\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{7440}(41,\cdot)\) | 7440.kf | 30 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{11}{30}\right)\) |
\(\chi_{7440}(43,\cdot)\) | 7440.lc | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{1}{30}\right)\) |
\(\chi_{7440}(47,\cdot)\) | 7440.hu | 20 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(i\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{20}\right)\) |
\(\chi_{7440}(49,\cdot)\) | 7440.jq | 30 | no | \(1\) | \(1\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{29}{30}\right)\) |
\(\chi_{7440}(53,\cdot)\) | 7440.lj | 60 | yes | \(-1\) | \(1\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{4}{15}\right)\) |
\(\chi_{7440}(59,\cdot)\) | 7440.kr | 60 | yes | \(1\) | \(1\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{23}{60}\right)\) |
\(\chi_{7440}(61,\cdot)\) | 7440.bj | 4 | no | \(-1\) | \(1\) | \(-1\) | \(i\) | \(-i\) | \(-1\) | \(i\) | \(1\) | \(-i\) | \(i\) | \(-1\) | \(i\) |
\(\chi_{7440}(67,\cdot)\) | 7440.gi | 12 | no | \(1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(-i\) | \(-i\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{7440}(71,\cdot)\) | 7440.ji | 30 | no | \(1\) | \(1\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{4}{15}\right)\) |
\(\chi_{7440}(73,\cdot)\) | 7440.lz | 60 | no | \(1\) | \(1\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{19}{60}\right)\) |
\(\chi_{7440}(77,\cdot)\) | 7440.ij | 20 | yes | \(-1\) | \(1\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(-1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) |
\(\chi_{7440}(79,\cdot)\) | 7440.kl | 30 | no | \(1\) | \(1\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{13}{30}\right)\) |
\(\chi_{7440}(83,\cdot)\) | 7440.lr | 60 | yes | \(1\) | \(1\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{13}{15}\right)\) |
\(\chi_{7440}(89,\cdot)\) | 7440.fn | 10 | no | \(1\) | \(1\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(-1\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{9}{10}\right)\) |
\(\chi_{7440}(91,\cdot)\) | 7440.hs | 20 | no | \(1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(-i\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{9}{20}\right)\) |
\(\chi_{7440}(97,\cdot)\) | 7440.hz | 20 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(i\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{3}{20}\right)\) |
\(\chi_{7440}(101,\cdot)\) | 7440.jd | 20 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(i\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{17}{20}\right)\) |
\(\chi_{7440}(103,\cdot)\) | 7440.lt | 60 | no | \(1\) | \(1\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{7}{60}\right)\) |
\(\chi_{7440}(107,\cdot)\) | 7440.lh | 60 | yes | \(-1\) | \(1\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{13}{30}\right)\) |
\(\chi_{7440}(109,\cdot)\) | 7440.hq | 20 | no | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(i\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{20}\right)\) |
\(\chi_{7440}(113,\cdot)\) | 7440.ku | 60 | no | \(1\) | \(1\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{19}{60}\right)\) |
\(\chi_{7440}(119,\cdot)\) | 7440.dj | 6 | no | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{7440}(121,\cdot)\) | 7440.jz | 30 | no | \(1\) | \(1\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{19}{30}\right)\) |