sage: H = DirichletGroup(3150)
pari: g = idealstar(,3150,2)
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 | = | $\chi_{3150}(2801,\cdot)$, $\chi_{3150}(127,\cdot)$, $\chi_{3150}(451,\cdot)$ |
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 | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{3150}(1,\cdot)\) | 3150.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{3150}(11,\cdot)\) | 3150.di | 30 | no | \(-1\) | \(1\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{3150}(13,\cdot)\) | 3150.ei | 60 | no | \(1\) | \(1\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{7}{12}\right)\) |
\(\chi_{3150}(17,\cdot)\) | 3150.ef | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(-i\) |
\(\chi_{3150}(19,\cdot)\) | 3150.dn | 30 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(-1\) |
\(\chi_{3150}(23,\cdot)\) | 3150.ee | 60 | no | \(1\) | \(1\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{7}{12}\right)\) |
\(\chi_{3150}(29,\cdot)\) | 3150.dd | 30 | no | \(-1\) | \(1\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{3150}(31,\cdot)\) | 3150.cy | 30 | no | \(-1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{3150}(37,\cdot)\) | 3150.ek | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(-i\) |
\(\chi_{3150}(41,\cdot)\) | 3150.de | 30 | no | \(1\) | \(1\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{3150}(43,\cdot)\) | 3150.cc | 12 | no | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(-i\) | \(-1\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(-i\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{11}{12}\right)\) |
\(\chi_{3150}(47,\cdot)\) | 3150.ep | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{5}{12}\right)\) |
\(\chi_{3150}(53,\cdot)\) | 3150.ed | 60 | no | \(1\) | \(1\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(i\) |
\(\chi_{3150}(59,\cdot)\) | 3150.dy | 30 | no | \(1\) | \(1\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{3150}(61,\cdot)\) | 3150.cy | 30 | no | \(-1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{3150}(67,\cdot)\) | 3150.ea | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{1}{12}\right)\) |
\(\chi_{3150}(71,\cdot)\) | 3150.bw | 10 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(1\) |
\(\chi_{3150}(73,\cdot)\) | 3150.em | 60 | no | \(1\) | \(1\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(i\) |
\(\chi_{3150}(79,\cdot)\) | 3150.cz | 30 | no | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{3150}(83,\cdot)\) | 3150.ec | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{11}{12}\right)\) |
\(\chi_{3150}(89,\cdot)\) | 3150.db | 30 | no | \(1\) | \(1\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(-1\) |
\(\chi_{3150}(97,\cdot)\) | 3150.ei | 60 | no | \(1\) | \(1\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{5}{12}\right)\) |
\(\chi_{3150}(101,\cdot)\) | 3150.bl | 6 | no | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{3150}(103,\cdot)\) | 3150.el | 60 | no | \(1\) | \(1\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{7}{12}\right)\) |
\(\chi_{3150}(107,\cdot)\) | 3150.cm | 12 | no | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-i\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(-1\) | \(-i\) |
\(\chi_{3150}(109,\cdot)\) | 3150.dv | 30 | no | \(1\) | \(1\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(-1\) |
\(\chi_{3150}(113,\cdot)\) | 3150.eh | 60 | no | \(1\) | \(1\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{7}{12}\right)\) |
\(\chi_{3150}(121,\cdot)\) | 3150.ct | 15 | no | \(1\) | \(1\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{3150}(127,\cdot)\) | 3150.cv | 20 | no | \(-1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(-i\) |
\(\chi_{3150}(131,\cdot)\) | 3150.df | 30 | no | \(1\) | \(1\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{3150}(137,\cdot)\) | 3150.ee | 60 | no | \(1\) | \(1\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{5}{12}\right)\) |
\(\chi_{3150}(139,\cdot)\) | 3150.ds | 30 | no | \(-1\) | \(1\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{5}{6}\right)\) |