sage: H = DirichletGroup(7920)
pari: g = idealstar(,7920,2)
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 | = | $\chi_{7920}(991,\cdot)$, $\chi_{7920}(5941,\cdot)$, $\chi_{7920}(3521,\cdot)$, $\chi_{7920}(6337,\cdot)$, $\chi_{7920}(6481,\cdot)$ |
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 | \(-1\) | \(1\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{7920}(1,\cdot)\) | 7920.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{7920}(7,\cdot)\) | 7920.lc | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{11}{12}\right)\) |
\(\chi_{7920}(13,\cdot)\) | 7920.lz | 60 | yes | \(1\) | \(1\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{7920}(17,\cdot)\) | 7920.if | 20 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(i\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(i\) |
\(\chi_{7920}(19,\cdot)\) | 7920.hm | 20 | no | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(-1\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(i\) |
\(\chi_{7920}(23,\cdot)\) | 7920.gl | 12 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(i\) | \(-1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(i\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{12}\right)\) |
\(\chi_{7920}(29,\cdot)\) | 7920.kt | 60 | yes | \(1\) | \(1\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{5}{12}\right)\) |
\(\chi_{7920}(31,\cdot)\) | 7920.js | 30 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{7920}(37,\cdot)\) | 7920.iu | 20 | no | \(-1\) | \(1\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(i\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(1\) |
\(\chi_{7920}(41,\cdot)\) | 7920.jq | 30 | no | \(1\) | \(1\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{7920}(43,\cdot)\) | 7920.ha | 12 | yes | \(-1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(i\) | \(i\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{7920}(47,\cdot)\) | 7920.lg | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{11}{12}\right)\) |
\(\chi_{7920}(49,\cdot)\) | 7920.jm | 30 | no | \(1\) | \(1\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{7920}(53,\cdot)\) | 7920.ht | 20 | no | \(1\) | \(1\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(i\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(-1\) |
\(\chi_{7920}(59,\cdot)\) | 7920.km | 60 | yes | \(1\) | \(1\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{7}{12}\right)\) |
\(\chi_{7920}(61,\cdot)\) | 7920.mh | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{11}{12}\right)\) |
\(\chi_{7920}(67,\cdot)\) | 7920.gd | 12 | no | \(1\) | \(1\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(i\) | \(i\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{7920}(71,\cdot)\) | 7920.fl | 10 | no | \(1\) | \(1\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(1\) |
\(\chi_{7920}(73,\cdot)\) | 7920.io | 20 | no | \(1\) | \(1\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(i\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(i\) |
\(\chi_{7920}(79,\cdot)\) | 7920.jp | 30 | no | \(1\) | \(1\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{7920}(83,\cdot)\) | 7920.lu | 60 | yes | \(1\) | \(1\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{7920}(89,\cdot)\) | 7920.o | 2 | no | \(-1\) | \(1\) | \(-1\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(-1\) | \(1\) |
\(\chi_{7920}(91,\cdot)\) | 7920.ho | 20 | no | \(-1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(1\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(-i\) |
\(\chi_{7920}(97,\cdot)\) | 7920.ln | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{5}{12}\right)\) |
\(\chi_{7920}(101,\cdot)\) | 7920.mb | 60 | no | \(1\) | \(1\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{5}{12}\right)\) |
\(\chi_{7920}(103,\cdot)\) | 7920.lp | 60 | no | \(1\) | \(1\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{7}{12}\right)\) |
\(\chi_{7920}(107,\cdot)\) | 7920.ia | 20 | no | \(1\) | \(1\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(i\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(1\) |
\(\chi_{7920}(109,\cdot)\) | 7920.bo | 4 | no | \(-1\) | \(1\) | \(-1\) | \(i\) | \(1\) | \(-i\) | \(1\) | \(-i\) | \(1\) | \(i\) | \(1\) | \(-i\) |
\(\chi_{7920}(113,\cdot)\) | 7920.lq | 60 | no | \(1\) | \(1\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{7}{12}\right)\) |
\(\chi_{7920}(119,\cdot)\) | 7920.kf | 30 | no | \(1\) | \(1\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{7920}(127,\cdot)\) | 7920.im | 20 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(i\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(-i\) |
\(\chi_{7920}(131,\cdot)\) | 7920.hj | 12 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(1\) | \(i\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(-i\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{12}\right)\) |