sage: H = DirichletGroup(930)
pari: g = idealstar(,930,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 240 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{2}\times C_{60}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{930}(311,\cdot)$, $\chi_{930}(187,\cdot)$, $\chi_{930}(871,\cdot)$ |
First 32 of 240 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 | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(37\) | \(41\) | \(43\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{930}(1,\cdot)\) | 930.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{930}(7,\cdot)\) | 930.bv | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{29}{60}\right)\) |
\(\chi_{930}(11,\cdot)\) | 930.br | 30 | no | \(1\) | \(1\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{17}{30}\right)\) |
\(\chi_{930}(13,\cdot)\) | 930.bt | 60 | no | \(1\) | \(1\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{13}{60}\right)\) |
\(\chi_{930}(17,\cdot)\) | 930.bu | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{11}{60}\right)\) |
\(\chi_{930}(19,\cdot)\) | 930.bn | 30 | no | \(1\) | \(1\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{1}{30}\right)\) |
\(\chi_{930}(23,\cdot)\) | 930.bi | 20 | no | \(-1\) | \(1\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(i\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{7}{20}\right)\) |
\(\chi_{930}(29,\cdot)\) | 930.y | 10 | no | \(1\) | \(1\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(1\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) |
\(\chi_{930}(37,\cdot)\) | 930.be | 12 | no | \(1\) | \(1\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(i\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{12}\right)\) |
\(\chi_{930}(41,\cdot)\) | 930.bq | 30 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{13}{15}\right)\) |
\(\chi_{930}(43,\cdot)\) | 930.bt | 60 | no | \(1\) | \(1\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{17}{60}\right)\) |
\(\chi_{930}(47,\cdot)\) | 930.bk | 20 | no | \(1\) | \(1\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(i\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{11}{20}\right)\) |
\(\chi_{930}(49,\cdot)\) | 930.bn | 30 | no | \(1\) | \(1\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{29}{30}\right)\) |
\(\chi_{930}(53,\cdot)\) | 930.bu | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{1}{60}\right)\) |
\(\chi_{930}(59,\cdot)\) | 930.bl | 30 | no | \(-1\) | \(1\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{19}{30}\right)\) |
\(\chi_{930}(61,\cdot)\) | 930.f | 2 | no | \(-1\) | \(1\) | \(1\) | \(-1\) | \(-1\) | \(-1\) | \(1\) | \(-1\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
\(\chi_{930}(67,\cdot)\) | 930.bc | 12 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(-i\) | \(-1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{12}\right)\) |
\(\chi_{930}(71,\cdot)\) | 930.bq | 30 | no | \(-1\) | \(1\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{4}{15}\right)\) |
\(\chi_{930}(73,\cdot)\) | 930.bt | 60 | no | \(1\) | \(1\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{49}{60}\right)\) |
\(\chi_{930}(77,\cdot)\) | 930.bi | 20 | no | \(-1\) | \(1\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(-i\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{20}\right)\) |
\(\chi_{930}(79,\cdot)\) | 930.bm | 30 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{14}{15}\right)\) |
\(\chi_{930}(83,\cdot)\) | 930.bu | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{37}{60}\right)\) |
\(\chi_{930}(89,\cdot)\) | 930.y | 10 | no | \(1\) | \(1\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(1\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) |
\(\chi_{930}(91,\cdot)\) | 930.x | 10 | no | \(-1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(-1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) |
\(\chi_{930}(97,\cdot)\) | 930.bh | 20 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(i\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{3}{20}\right)\) |
\(\chi_{930}(101,\cdot)\) | 930.w | 10 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(1\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) |
\(\chi_{930}(103,\cdot)\) | 930.bv | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{7}{60}\right)\) |
\(\chi_{930}(107,\cdot)\) | 930.bs | 60 | no | \(1\) | \(1\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{41}{60}\right)\) |
\(\chi_{930}(109,\cdot)\) | 930.z | 10 | no | \(1\) | \(1\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(-1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{10}\right)\) |
\(\chi_{930}(113,\cdot)\) | 930.bs | 60 | no | \(1\) | \(1\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{19}{60}\right)\) |
\(\chi_{930}(119,\cdot)\) | 930.r | 6 | no | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{930}(121,\cdot)\) | 930.bg | 15 | no | \(1\) | \(1\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) |