sage: H = DirichletGroup(283920)
pari: g = idealstar(,283920,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 59904 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{12}\times C_{156}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{283920}(248431,\cdot)$, $\chi_{283920}(70981,\cdot)$, $\chi_{283920}(189281,\cdot)$, $\chi_{283920}(227137,\cdot)$, $\chi_{283920}(40561,\cdot)$, $\chi_{283920}(255361,\cdot)$ |
First 32 of 59904 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 | \(-1\) | \(1\) | \(11\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{283920}(1,\cdot)\) | 283920.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{283920}(11,\cdot)\) | 283920.czx | 156 | no | \(-1\) | \(1\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{103}{156}\right)\) | \(e\left(\frac{5}{156}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{19}{156}\right)\) | \(e\left(\frac{47}{156}\right)\) | \(e\left(\frac{145}{156}\right)\) |
\(\chi_{283920}(17,\cdot)\) | 283920.eds | 156 | no | \(-1\) | \(1\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(i\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{47}{52}\right)\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{145}{156}\right)\) | \(e\left(\frac{85}{156}\right)\) |
\(\chi_{283920}(19,\cdot)\) | 283920.wq | 12 | no | \(-1\) | \(1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{5}{12}\right)\) |
\(\chi_{283920}(23,\cdot)\) | 283920.ze | 12 | no | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(i\) | \(e\left(\frac{1}{3}\right)\) | \(i\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(-i\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{11}{12}\right)\) |
\(\chi_{283920}(29,\cdot)\) | 283920.dww | 156 | no | \(-1\) | \(1\) | \(e\left(\frac{103}{156}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{156}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{151}{156}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{83}{156}\right)\) | \(e\left(\frac{2}{13}\right)\) |
\(\chi_{283920}(31,\cdot)\) | 283920.duo | 156 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{156}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{77}{156}\right)\) | \(e\left(\frac{103}{156}\right)\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{127}{156}\right)\) |
\(\chi_{283920}(37,\cdot)\) | 283920.ecz | 156 | no | \(1\) | \(1\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{47}{52}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(-i\) | \(e\left(\frac{151}{156}\right)\) | \(e\left(\frac{103}{156}\right)\) | \(e\left(\frac{17}{52}\right)\) | \(e\left(\frac{121}{156}\right)\) | \(e\left(\frac{7}{78}\right)\) | \(e\left(\frac{35}{39}\right)\) |
\(\chi_{283920}(41,\cdot)\) | 283920.dii | 156 | no | \(-1\) | \(1\) | \(e\left(\frac{19}{156}\right)\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{121}{156}\right)\) | \(e\left(\frac{49}{156}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{17}{52}\right)\) |
\(\chi_{283920}(43,\cdot)\) | 283920.dni | 156 | no | \(1\) | \(1\) | \(e\left(\frac{47}{156}\right)\) | \(e\left(\frac{145}{156}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{83}{156}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{7}{78}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{27}{52}\right)\) |
\(\chi_{283920}(47,\cdot)\) | 283920.dkz | 156 | no | \(-1\) | \(1\) | \(e\left(\frac{145}{156}\right)\) | \(e\left(\frac{85}{156}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{127}{156}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{17}{52}\right)\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{67}{78}\right)\) |
\(\chi_{283920}(53,\cdot)\) | 283920.dqo | 156 | yes | \(1\) | \(1\) | \(e\left(\frac{101}{156}\right)\) | \(e\left(\frac{35}{156}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{7}{156}\right)\) |
\(\chi_{283920}(59,\cdot)\) | 283920.dzl | 156 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(e\left(\frac{35}{156}\right)\) | \(e\left(\frac{59}{156}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{89}{156}\right)\) | \(e\left(\frac{97}{156}\right)\) | \(e\left(\frac{73}{156}\right)\) |
\(\chi_{283920}(61,\cdot)\) | 283920.djo | 156 | no | \(-1\) | \(1\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{67}{78}\right)\) | \(-i\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{23}{156}\right)\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{145}{156}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{37}{156}\right)\) | \(e\left(\frac{55}{78}\right)\) |
\(\chi_{283920}(67,\cdot)\) | 283920.egd | 156 | no | \(-1\) | \(1\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{85}{156}\right)\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{37}{156}\right)\) | \(e\left(\frac{23}{156}\right)\) | \(e\left(\frac{23}{156}\right)\) | \(e\left(\frac{103}{156}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{1}{39}\right)\) |
\(\chi_{283920}(71,\cdot)\) | 283920.dxt | 156 | no | \(-1\) | \(1\) | \(e\left(\frac{149}{156}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{17}{156}\right)\) | \(e\left(\frac{23}{156}\right)\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{17}{52}\right)\) |
\(\chi_{283920}(73,\cdot)\) | 283920.dle | 156 | no | \(-1\) | \(1\) | \(e\left(\frac{131}{156}\right)\) | \(e\left(\frac{101}{156}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{5}{156}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{15}{52}\right)\) | \(e\left(\frac{33}{52}\right)\) | \(e\left(\frac{7}{39}\right)\) |
\(\chi_{283920}(79,\cdot)\) | 283920.crb | 78 | no | \(-1\) | \(1\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{23}{78}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{14}{39}\right)\) |
\(\chi_{283920}(83,\cdot)\) | 283920.cgo | 52 | yes | \(-1\) | \(1\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{45}{52}\right)\) | \(-1\) | \(i\) | \(e\left(\frac{41}{52}\right)\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{11}{26}\right)\) |
\(\chi_{283920}(89,\cdot)\) | 283920.buw | 12 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(1\) | \(e\left(\frac{7}{12}\right)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(-i\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{11}{12}\right)\) |
\(\chi_{283920}(97,\cdot)\) | 283920.dlp | 156 | no | \(-1\) | \(1\) | \(e\left(\frac{35}{156}\right)\) | \(e\left(\frac{103}{156}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{41}{52}\right)\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{119}{156}\right)\) | \(e\left(\frac{7}{156}\right)\) | \(e\left(\frac{8}{13}\right)\) |
\(\chi_{283920}(101,\cdot)\) | 283920.dvo | 156 | no | \(1\) | \(1\) | \(e\left(\frac{33}{52}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(-i\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{31}{156}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{53}{156}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{155}{156}\right)\) | \(e\left(\frac{47}{78}\right)\) |
\(\chi_{283920}(103,\cdot)\) | 283920.dcy | 156 | no | \(-1\) | \(1\) | \(e\left(\frac{29}{78}\right)\) | \(e\left(\frac{151}{156}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{17}{156}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{155}{156}\right)\) |
\(\chi_{283920}(107,\cdot)\) | 283920.dpk | 156 | yes | \(-1\) | \(1\) | \(e\left(\frac{95}{156}\right)\) | \(e\left(\frac{35}{52}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(i\) | \(e\left(\frac{61}{156}\right)\) | \(e\left(\frac{23}{78}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{47}{156}\right)\) |
\(\chi_{283920}(109,\cdot)\) | 283920.eeh | 156 | no | \(-1\) | \(1\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{45}{52}\right)\) | \(e\left(\frac{53}{156}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{43}{52}\right)\) | \(e\left(\frac{133}{156}\right)\) |
\(\chi_{283920}(113,\cdot)\) | 283920.dei | 156 | no | \(1\) | \(1\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{31}{156}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{113}{156}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{43}{156}\right)\) | \(e\left(\frac{9}{52}\right)\) |
\(\chi_{283920}(121,\cdot)\) | 283920.cpo | 78 | no | \(1\) | \(1\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{25}{78}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{19}{78}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{67}{78}\right)\) |
\(\chi_{283920}(127,\cdot)\) | 283920.eci | 156 | no | \(1\) | \(1\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{59}{156}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{49}{156}\right)\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{107}{156}\right)\) | \(e\left(\frac{49}{52}\right)\) |
\(\chi_{283920}(131,\cdot)\) | 283920.dxm | 156 | no | \(-1\) | \(1\) | \(e\left(\frac{25}{156}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{35}{52}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{125}{156}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{45}{52}\right)\) | \(e\left(\frac{25}{78}\right)\) |
\(\chi_{283920}(137,\cdot)\) | 283920.dmv | 156 | no | \(-1\) | \(1\) | \(e\left(\frac{73}{156}\right)\) | \(e\left(\frac{5}{52}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(-i\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{131}{156}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{113}{156}\right)\) | \(e\left(\frac{25}{156}\right)\) | \(e\left(\frac{47}{78}\right)\) |
\(\chi_{283920}(139,\cdot)\) | 283920.dwx | 156 | no | \(1\) | \(1\) | \(e\left(\frac{113}{156}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{17}{156}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{149}{156}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{7}{156}\right)\) | \(e\left(\frac{3}{26}\right)\) |
\(\chi_{283920}(149,\cdot)\) | 283920.cyj | 156 | yes | \(1\) | \(1\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{49}{78}\right)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{11}{156}\right)\) | \(e\left(\frac{49}{156}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{77}{156}\right)\) | \(e\left(\frac{55}{156}\right)\) | \(e\left(\frac{95}{156}\right)\) |