sage: H = DirichletGroup(2015)
pari: g = idealstar(,2015,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 1440 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{12}\times C_{60}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{2015}(807,\cdot)$, $\chi_{2015}(1861,\cdot)$, $\chi_{2015}(716,\cdot)$ |
First 32 of 1440 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 | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(14\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{2015}(1,\cdot)\) | 2015.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{2015}(2,\cdot)\) | 2015.hk | 60 | yes | \(1\) | \(1\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) |
\(\chi_{2015}(3,\cdot)\) | 2015.gn | 60 | yes | \(1\) | \(1\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(-1\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{7}{30}\right)\) |
\(\chi_{2015}(4,\cdot)\) | 2015.fm | 30 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) |
\(\chi_{2015}(6,\cdot)\) | 2015.cr | 12 | no | \(1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(i\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{2015}(7,\cdot)\) | 2015.gc | 60 | yes | \(1\) | \(1\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{1}{30}\right)\) |
\(\chi_{2015}(8,\cdot)\) | 2015.ej | 20 | yes | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(i\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{3}{10}\right)\) |
\(\chi_{2015}(9,\cdot)\) | 2015.fb | 30 | yes | \(1\) | \(1\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(1\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{7}{15}\right)\) |
\(\chi_{2015}(11,\cdot)\) | 2015.hi | 60 | no | \(1\) | \(1\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{13}{15}\right)\) |
\(\chi_{2015}(12,\cdot)\) | 2015.gz | 60 | yes | \(1\) | \(1\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{13}{30}\right)\) |
\(\chi_{2015}(14,\cdot)\) | 2015.ft | 30 | no | \(1\) | \(1\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{2}{15}\right)\) |
\(\chi_{2015}(16,\cdot)\) | 2015.eg | 15 | no | \(1\) | \(1\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) |
\(\chi_{2015}(17,\cdot)\) | 2015.gr | 60 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{19}{30}\right)\) |
\(\chi_{2015}(18,\cdot)\) | 2015.hr | 60 | yes | \(1\) | \(1\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{17}{30}\right)\) |
\(\chi_{2015}(19,\cdot)\) | 2015.hj | 60 | yes | \(-1\) | \(1\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{14}{15}\right)\) |
\(\chi_{2015}(21,\cdot)\) | 2015.gl | 60 | no | \(1\) | \(1\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{4}{15}\right)\) |
\(\chi_{2015}(22,\cdot)\) | 2015.gn | 60 | yes | \(1\) | \(1\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(-1\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{29}{30}\right)\) |
\(\chi_{2015}(23,\cdot)\) | 2015.gp | 60 | yes | \(1\) | \(1\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{3}{10}\right)\) |
\(\chi_{2015}(24,\cdot)\) | 2015.hc | 60 | yes | \(1\) | \(1\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(-i\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{8}{15}\right)\) |
\(\chi_{2015}(27,\cdot)\) | 2015.en | 20 | no | \(1\) | \(1\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(-1\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{7}{10}\right)\) |
\(\chi_{2015}(28,\cdot)\) | 2015.fy | 60 | yes | \(1\) | \(1\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(-i\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{7}{30}\right)\) |
\(\chi_{2015}(29,\cdot)\) | 2015.fg | 30 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) |
\(\chi_{2015}(32,\cdot)\) | 2015.cp | 12 | no | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(-i\) | \(-1\) |
\(\chi_{2015}(33,\cdot)\) | 2015.hk | 60 | yes | \(1\) | \(1\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) |
\(\chi_{2015}(34,\cdot)\) | 2015.hh | 60 | yes | \(1\) | \(1\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{11}{15}\right)\) |
\(\chi_{2015}(36,\cdot)\) | 2015.bx | 6 | no | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{2015}(37,\cdot)\) | 2015.ea | 12 | yes | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(-i\) | \(1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(i\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{2015}(38,\cdot)\) | 2015.hb | 60 | yes | \(-1\) | \(1\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{1}{30}\right)\) |
\(\chi_{2015}(41,\cdot)\) | 2015.gf | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{4}{15}\right)\) |
\(\chi_{2015}(42,\cdot)\) | 2015.gu | 60 | yes | \(1\) | \(1\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{11}{30}\right)\) |
\(\chi_{2015}(43,\cdot)\) | 2015.gr | 60 | yes | \(1\) | \(1\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{13}{30}\right)\) |
\(\chi_{2015}(44,\cdot)\) | 2015.hh | 60 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{1}{15}\right)\) |