sage: H = DirichletGroup(2415)
pari: g = idealstar(,2415,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 1056 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{2}\times C_{2}\times C_{132}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{2415}(806,\cdot)$, $\chi_{2415}(967,\cdot)$, $\chi_{2415}(346,\cdot)$, $\chi_{2415}(1891,\cdot)$ |
First 32 of 1056 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 | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(26\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{2415}(1,\cdot)\) | 2415.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{2415}(2,\cdot)\) | 2415.dk | 132 | yes | \(1\) | \(1\) | \(e\left(\frac{79}{132}\right)\) | \(e\left(\frac{13}{66}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{43}{66}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{95}{132}\right)\) | \(e\left(\frac{35}{66}\right)\) | \(i\) | \(e\left(\frac{41}{66}\right)\) |
\(\chi_{2415}(4,\cdot)\) | 2415.db | 66 | no | \(1\) | \(1\) | \(e\left(\frac{13}{66}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{26}{33}\right)\) | \(e\left(\frac{29}{66}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(-1\) | \(e\left(\frac{8}{33}\right)\) |
\(\chi_{2415}(8,\cdot)\) | 2415.ct | 44 | no | \(1\) | \(1\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(-i\) | \(e\left(\frac{19}{22}\right)\) |
\(\chi_{2415}(11,\cdot)\) | 2415.da | 66 | no | \(1\) | \(1\) | \(e\left(\frac{43}{66}\right)\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{28}{33}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{20}{33}\right)\) | \(e\left(\frac{1}{33}\right)\) | \(e\left(\frac{31}{66}\right)\) | \(-1\) | \(e\left(\frac{25}{66}\right)\) |
\(\chi_{2415}(13,\cdot)\) | 2415.co | 44 | no | \(1\) | \(1\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(-i\) | \(e\left(\frac{15}{22}\right)\) |
\(\chi_{2415}(16,\cdot)\) | 2415.cm | 33 | no | \(1\) | \(1\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{26}{33}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{20}{33}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{4}{33}\right)\) | \(1\) | \(e\left(\frac{16}{33}\right)\) |
\(\chi_{2415}(17,\cdot)\) | 2415.do | 132 | yes | \(1\) | \(1\) | \(e\left(\frac{95}{132}\right)\) | \(e\left(\frac{29}{66}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{1}{33}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{19}{132}\right)\) | \(e\left(\frac{7}{66}\right)\) | \(-i\) | \(e\left(\frac{14}{33}\right)\) |
\(\chi_{2415}(19,\cdot)\) | 2415.cv | 66 | no | \(1\) | \(1\) | \(e\left(\frac{35}{66}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{31}{66}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{4}{33}\right)\) | \(e\left(\frac{7}{66}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(1\) | \(e\left(\frac{5}{66}\right)\) |
\(\chi_{2415}(22,\cdot)\) | 2415.t | 4 | no | \(1\) | \(1\) | \(i\) | \(-1\) | \(-i\) | \(-1\) | \(-i\) | \(1\) | \(-i\) | \(1\) | \(-i\) | \(1\) |
\(\chi_{2415}(26,\cdot)\) | 2415.cy | 66 | no | \(1\) | \(1\) | \(e\left(\frac{41}{66}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{25}{66}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{14}{33}\right)\) | \(e\left(\frac{5}{66}\right)\) | \(1\) | \(e\left(\frac{10}{33}\right)\) |
\(\chi_{2415}(29,\cdot)\) | 2415.cd | 22 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(-1\) | \(e\left(\frac{13}{22}\right)\) |
\(\chi_{2415}(31,\cdot)\) | 2415.di | 66 | no | \(-1\) | \(1\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{25}{33}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{4}{33}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{17}{33}\right)\) | \(e\left(\frac{5}{66}\right)\) | \(e\left(\frac{61}{66}\right)\) | \(1\) | \(e\left(\frac{13}{66}\right)\) |
\(\chi_{2415}(32,\cdot)\) | 2415.dk | 132 | yes | \(1\) | \(1\) | \(e\left(\frac{131}{132}\right)\) | \(e\left(\frac{65}{66}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{17}{66}\right)\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{32}{33}\right)\) | \(e\left(\frac{79}{132}\right)\) | \(e\left(\frac{43}{66}\right)\) | \(i\) | \(e\left(\frac{7}{66}\right)\) |
\(\chi_{2415}(34,\cdot)\) | 2415.ci | 22 | no | \(1\) | \(1\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(1\) | \(e\left(\frac{1}{22}\right)\) |
\(\chi_{2415}(37,\cdot)\) | 2415.dn | 132 | no | \(1\) | \(1\) | \(e\left(\frac{109}{132}\right)\) | \(e\left(\frac{43}{66}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{61}{66}\right)\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{35}{132}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(-i\) | \(e\left(\frac{31}{33}\right)\) |
\(\chi_{2415}(38,\cdot)\) | 2415.do | 132 | yes | \(1\) | \(1\) | \(e\left(\frac{17}{132}\right)\) | \(e\left(\frac{17}{66}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{4}{33}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{17}{33}\right)\) | \(e\left(\frac{109}{132}\right)\) | \(e\left(\frac{61}{66}\right)\) | \(i\) | \(e\left(\frac{23}{33}\right)\) |
\(\chi_{2415}(41,\cdot)\) | 2415.cl | 22 | no | \(1\) | \(1\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(1\) | \(e\left(\frac{8}{11}\right)\) |
\(\chi_{2415}(43,\cdot)\) | 2415.cs | 44 | no | \(1\) | \(1\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(i\) | \(e\left(\frac{7}{11}\right)\) |
\(\chi_{2415}(44,\cdot)\) | 2415.dj | 66 | yes | \(1\) | \(1\) | \(e\left(\frac{28}{33}\right)\) | \(e\left(\frac{23}{33}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{5}{33}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{31}{66}\right)\) | \(e\left(\frac{35}{66}\right)\) | \(1\) | \(e\left(\frac{41}{66}\right)\) |
\(\chi_{2415}(47,\cdot)\) | 2415.bu | 12 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(i\) | \(e\left(\frac{5}{6}\right)\) | \(i\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(i\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{2415}(52,\cdot)\) | 2415.dr | 132 | no | \(1\) | \(1\) | \(e\left(\frac{29}{132}\right)\) | \(e\left(\frac{29}{66}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{1}{33}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{19}{132}\right)\) | \(e\left(\frac{20}{33}\right)\) | \(i\) | \(e\left(\frac{61}{66}\right)\) |
\(\chi_{2415}(53,\cdot)\) | 2415.dq | 132 | yes | \(-1\) | \(1\) | \(e\left(\frac{41}{132}\right)\) | \(e\left(\frac{41}{66}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{31}{33}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{127}{132}\right)\) | \(e\left(\frac{26}{33}\right)\) | \(i\) | \(e\left(\frac{43}{66}\right)\) |
\(\chi_{2415}(58,\cdot)\) | 2415.dp | 132 | no | \(-1\) | \(1\) | \(e\left(\frac{31}{132}\right)\) | \(e\left(\frac{31}{66}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{17}{33}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{31}{33}\right)\) | \(e\left(\frac{59}{132}\right)\) | \(e\left(\frac{53}{66}\right)\) | \(-i\) | \(e\left(\frac{7}{33}\right)\) |
\(\chi_{2415}(59,\cdot)\) | 2415.de | 66 | yes | \(1\) | \(1\) | \(e\left(\frac{20}{33}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{59}{66}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{14}{33}\right)\) | \(e\left(\frac{41}{66}\right)\) | \(e\left(\frac{25}{66}\right)\) | \(-1\) | \(e\left(\frac{17}{33}\right)\) |
\(\chi_{2415}(61,\cdot)\) | 2415.df | 66 | no | \(1\) | \(1\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{14}{33}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{19}{66}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{28}{33}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{25}{33}\right)\) | \(-1\) | \(e\left(\frac{35}{66}\right)\) |
\(\chi_{2415}(62,\cdot)\) | 2415.cr | 44 | yes | \(-1\) | \(1\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(i\) | \(e\left(\frac{9}{11}\right)\) |
\(\chi_{2415}(64,\cdot)\) | 2415.cg | 22 | no | \(1\) | \(1\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(-1\) | \(e\left(\frac{8}{11}\right)\) |
\(\chi_{2415}(67,\cdot)\) | 2415.dn | 132 | no | \(1\) | \(1\) | \(e\left(\frac{101}{132}\right)\) | \(e\left(\frac{35}{66}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{65}{66}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{7}{132}\right)\) | \(e\left(\frac{23}{33}\right)\) | \(-i\) | \(e\left(\frac{26}{33}\right)\) |
\(\chi_{2415}(68,\cdot)\) | 2415.bs | 12 | yes | \(1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(-i\) | \(e\left(\frac{1}{3}\right)\) | \(-i\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(i\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{2415}(71,\cdot)\) | 2415.cj | 22 | no | \(-1\) | \(1\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(1\) | \(e\left(\frac{21}{22}\right)\) |
\(\chi_{2415}(73,\cdot)\) | 2415.dr | 132 | no | \(1\) | \(1\) | \(e\left(\frac{59}{132}\right)\) | \(e\left(\frac{59}{66}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{26}{33}\right)\) | \(e\left(\frac{25}{132}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(-i\) | \(e\left(\frac{49}{66}\right)\) |