sage: H = DirichletGroup(2576)
pari: g = idealstar(,2576,2)
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 | = | $\chi_{2576}(2255,\cdot)$, $\chi_{2576}(645,\cdot)$, $\chi_{2576}(1473,\cdot)$, $\chi_{2576}(1569,\cdot)$ |
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 | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(25\) | \(27\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{2576}(1,\cdot)\) | 2576.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{2576}(3,\cdot)\) | 2576.dp | 132 | yes | \(1\) | \(1\) | \(e\left(\frac{73}{132}\right)\) | \(e\left(\frac{41}{132}\right)\) | \(e\left(\frac{7}{66}\right)\) | \(e\left(\frac{61}{132}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{17}{66}\right)\) | \(e\left(\frac{65}{132}\right)\) | \(e\left(\frac{41}{66}\right)\) | \(e\left(\frac{29}{44}\right)\) |
\(\chi_{2576}(5,\cdot)\) | 2576.dq | 132 | yes | \(1\) | \(1\) | \(e\left(\frac{41}{132}\right)\) | \(e\left(\frac{61}{132}\right)\) | \(e\left(\frac{41}{66}\right)\) | \(e\left(\frac{131}{132}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{5}{33}\right)\) | \(e\left(\frac{79}{132}\right)\) | \(e\left(\frac{61}{66}\right)\) | \(e\left(\frac{41}{44}\right)\) |
\(\chi_{2576}(9,\cdot)\) | 2576.cw | 66 | no | \(1\) | \(1\) | \(e\left(\frac{7}{66}\right)\) | \(e\left(\frac{41}{66}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{61}{66}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{17}{33}\right)\) | \(e\left(\frac{65}{66}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{7}{22}\right)\) |
\(\chi_{2576}(11,\cdot)\) | 2576.dl | 132 | yes | \(1\) | \(1\) | \(e\left(\frac{61}{132}\right)\) | \(e\left(\frac{131}{132}\right)\) | \(e\left(\frac{61}{66}\right)\) | \(e\left(\frac{13}{132}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{35}{66}\right)\) | \(e\left(\frac{95}{132}\right)\) | \(e\left(\frac{65}{66}\right)\) | \(e\left(\frac{17}{44}\right)\) |
\(\chi_{2576}(13,\cdot)\) | 2576.cq | 44 | yes | \(-1\) | \(1\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{35}{44}\right)\) |
\(\chi_{2576}(15,\cdot)\) | 2576.ci | 22 | no | \(1\) | \(1\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{13}{22}\right)\) |
\(\chi_{2576}(17,\cdot)\) | 2576.da | 66 | no | \(1\) | \(1\) | \(e\left(\frac{17}{66}\right)\) | \(e\left(\frac{5}{33}\right)\) | \(e\left(\frac{17}{33}\right)\) | \(e\left(\frac{35}{66}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{20}{33}\right)\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{17}{22}\right)\) |
\(\chi_{2576}(19,\cdot)\) | 2576.dn | 132 | yes | \(-1\) | \(1\) | \(e\left(\frac{65}{132}\right)\) | \(e\left(\frac{79}{132}\right)\) | \(e\left(\frac{65}{66}\right)\) | \(e\left(\frac{95}{132}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{20}{33}\right)\) | \(e\left(\frac{19}{132}\right)\) | \(e\left(\frac{13}{66}\right)\) | \(e\left(\frac{21}{44}\right)\) |
\(\chi_{2576}(25,\cdot)\) | 2576.cw | 66 | no | \(1\) | \(1\) | \(e\left(\frac{41}{66}\right)\) | \(e\left(\frac{61}{66}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{65}{66}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{13}{66}\right)\) | \(e\left(\frac{28}{33}\right)\) | \(e\left(\frac{19}{22}\right)\) |
\(\chi_{2576}(27,\cdot)\) | 2576.ct | 44 | yes | \(1\) | \(1\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{43}{44}\right)\) |
\(\chi_{2576}(29,\cdot)\) | 2576.co | 44 | no | \(1\) | \(1\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{1}{44}\right)\) |
\(\chi_{2576}(31,\cdot)\) | 2576.de | 66 | no | \(1\) | \(1\) | \(e\left(\frac{1}{33}\right)\) | \(e\left(\frac{7}{66}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{41}{66}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{5}{66}\right)\) | \(e\left(\frac{14}{33}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{1}{11}\right)\) |
\(\chi_{2576}(33,\cdot)\) | 2576.da | 66 | no | \(1\) | \(1\) | \(e\left(\frac{1}{66}\right)\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{1}{33}\right)\) | \(e\left(\frac{37}{66}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{26}{33}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{20}{33}\right)\) | \(e\left(\frac{1}{22}\right)\) |
\(\chi_{2576}(37,\cdot)\) | 2576.do | 132 | yes | \(-1\) | \(1\) | \(e\left(\frac{47}{132}\right)\) | \(e\left(\frac{115}{132}\right)\) | \(e\left(\frac{47}{66}\right)\) | \(e\left(\frac{23}{132}\right)\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{1}{66}\right)\) | \(e\left(\frac{97}{132}\right)\) | \(e\left(\frac{49}{66}\right)\) | \(e\left(\frac{3}{44}\right)\) |
\(\chi_{2576}(39,\cdot)\) | 2576.dg | 66 | no | \(-1\) | \(1\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{13}{66}\right)\) | \(e\left(\frac{32}{33}\right)\) | \(e\left(\frac{31}{33}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{26}{33}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{5}{11}\right)\) |
\(\chi_{2576}(41,\cdot)\) | 2576.by | 22 | no | \(-1\) | \(1\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{2}{11}\right)\) |
\(\chi_{2576}(43,\cdot)\) | 2576.cp | 44 | no | \(1\) | \(1\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{29}{44}\right)\) |
\(\chi_{2576}(45,\cdot)\) | 2576.bq | 12 | yes | \(1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(-i\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(i\) |
\(\chi_{2576}(47,\cdot)\) | 2576.be | 6 | no | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
\(\chi_{2576}(51,\cdot)\) | 2576.dl | 132 | yes | \(1\) | \(1\) | \(e\left(\frac{107}{132}\right)\) | \(e\left(\frac{61}{132}\right)\) | \(e\left(\frac{41}{66}\right)\) | \(e\left(\frac{131}{132}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{43}{66}\right)\) | \(e\left(\frac{13}{132}\right)\) | \(e\left(\frac{61}{66}\right)\) | \(e\left(\frac{19}{44}\right)\) |
\(\chi_{2576}(53,\cdot)\) | 2576.do | 132 | yes | \(-1\) | \(1\) | \(e\left(\frac{31}{132}\right)\) | \(e\left(\frac{59}{132}\right)\) | \(e\left(\frac{31}{66}\right)\) | \(e\left(\frac{91}{132}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{47}{66}\right)\) | \(e\left(\frac{5}{132}\right)\) | \(e\left(\frac{59}{66}\right)\) | \(e\left(\frac{31}{44}\right)\) |
\(\chi_{2576}(55,\cdot)\) | 2576.ce | 22 | no | \(1\) | \(1\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{7}{22}\right)\) |
\(\chi_{2576}(57,\cdot)\) | 2576.cf | 22 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{3}{22}\right)\) |
\(\chi_{2576}(59,\cdot)\) | 2576.dp | 132 | yes | \(1\) | \(1\) | \(e\left(\frac{79}{132}\right)\) | \(e\left(\frac{95}{132}\right)\) | \(e\left(\frac{13}{66}\right)\) | \(e\left(\frac{19}{132}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{41}{66}\right)\) | \(e\left(\frac{83}{132}\right)\) | \(e\left(\frac{29}{66}\right)\) | \(e\left(\frac{35}{44}\right)\) |
\(\chi_{2576}(61,\cdot)\) | 2576.dq | 132 | yes | \(1\) | \(1\) | \(e\left(\frac{59}{132}\right)\) | \(e\left(\frac{91}{132}\right)\) | \(e\left(\frac{59}{66}\right)\) | \(e\left(\frac{5}{132}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{1}{132}\right)\) | \(e\left(\frac{25}{66}\right)\) | \(e\left(\frac{15}{44}\right)\) |
\(\chi_{2576}(65,\cdot)\) | 2576.dd | 66 | no | \(-1\) | \(1\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{23}{66}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{31}{66}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{7}{66}\right)\) | \(e\left(\frac{59}{66}\right)\) | \(e\left(\frac{23}{33}\right)\) | \(e\left(\frac{8}{11}\right)\) |
\(\chi_{2576}(67,\cdot)\) | 2576.dl | 132 | yes | \(1\) | \(1\) | \(e\left(\frac{115}{132}\right)\) | \(e\left(\frac{89}{132}\right)\) | \(e\left(\frac{49}{66}\right)\) | \(e\left(\frac{31}{132}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{53}{66}\right)\) | \(e\left(\frac{125}{132}\right)\) | \(e\left(\frac{23}{66}\right)\) | \(e\left(\frac{27}{44}\right)\) |
\(\chi_{2576}(71,\cdot)\) | 2576.cb | 22 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{4}{11}\right)\) |
\(\chi_{2576}(73,\cdot)\) | 2576.dh | 66 | no | \(-1\) | \(1\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{17}{33}\right)\) | \(e\left(\frac{5}{33}\right)\) | \(e\left(\frac{53}{66}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{29}{66}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{1}{33}\right)\) | \(e\left(\frac{8}{11}\right)\) |
\(\chi_{2576}(75,\cdot)\) | 2576.dp | 132 | yes | \(1\) | \(1\) | \(e\left(\frac{23}{132}\right)\) | \(e\left(\frac{31}{132}\right)\) | \(e\left(\frac{23}{66}\right)\) | \(e\left(\frac{59}{132}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{37}{66}\right)\) | \(e\left(\frac{91}{132}\right)\) | \(e\left(\frac{31}{66}\right)\) | \(e\left(\frac{23}{44}\right)\) |
\(\chi_{2576}(79,\cdot)\) | 2576.cx | 66 | no | \(1\) | \(1\) | \(e\left(\frac{1}{66}\right)\) | \(e\left(\frac{53}{66}\right)\) | \(e\left(\frac{1}{33}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{19}{66}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{20}{33}\right)\) | \(e\left(\frac{1}{22}\right)\) |