sage: H = DirichletGroup(1183)
pari: g = idealstar(,1183,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 936 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{6}\times C_{156}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{1183}(339,\cdot)$, $\chi_{1183}(1016,\cdot)$ |
First 32 of 936 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 | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{1183}(1,\cdot)\) | 1183.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{1183}(2,\cdot)\) | 1183.cg | 156 | yes | \(-1\) | \(1\) | \(e\left(\frac{35}{52}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{113}{156}\right)\) | \(e\left(\frac{125}{156}\right)\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{155}{156}\right)\) | \(e\left(\frac{37}{78}\right)\) |
\(\chi_{1183}(3,\cdot)\) | 1183.bx | 78 | yes | \(-1\) | \(1\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{77}{78}\right)\) |
\(\chi_{1183}(4,\cdot)\) | 1183.bz | 78 | yes | \(1\) | \(1\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{37}{39}\right)\) |
\(\chi_{1183}(5,\cdot)\) | 1183.cc | 156 | yes | \(1\) | \(1\) | \(e\left(\frac{113}{156}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{107}{156}\right)\) | \(e\left(\frac{37}{52}\right)\) | \(e\left(\frac{9}{52}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{43}{156}\right)\) | \(e\left(\frac{17}{39}\right)\) |
\(\chi_{1183}(6,\cdot)\) | 1183.cb | 156 | yes | \(1\) | \(1\) | \(e\left(\frac{125}{156}\right)\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{37}{52}\right)\) | \(e\left(\frac{103}{156}\right)\) | \(e\left(\frac{21}{52}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{83}{156}\right)\) | \(e\left(\frac{6}{13}\right)\) |
\(\chi_{1183}(8,\cdot)\) | 1183.bm | 52 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{9}{52}\right)\) | \(e\left(\frac{21}{52}\right)\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{51}{52}\right)\) | \(e\left(\frac{11}{26}\right)\) |
\(\chi_{1183}(9,\cdot)\) | 1183.bj | 39 | yes | \(1\) | \(1\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{38}{39}\right)\) |
\(\chi_{1183}(10,\cdot)\) | 1183.bu | 78 | yes | \(-1\) | \(1\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{71}{78}\right)\) |
\(\chi_{1183}(11,\cdot)\) | 1183.ca | 156 | yes | \(-1\) | \(1\) | \(e\left(\frac{155}{156}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{43}{156}\right)\) | \(e\left(\frac{83}{156}\right)\) | \(e\left(\frac{51}{52}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{35}{52}\right)\) | \(e\left(\frac{41}{78}\right)\) |
\(\chi_{1183}(12,\cdot)\) | 1183.br | 78 | yes | \(-1\) | \(1\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{73}{78}\right)\) |
\(\chi_{1183}(15,\cdot)\) | 1183.cf | 156 | no | \(-1\) | \(1\) | \(e\left(\frac{133}{156}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{35}{52}\right)\) | \(e\left(\frac{89}{156}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{127}{156}\right)\) | \(e\left(\frac{11}{26}\right)\) |
\(\chi_{1183}(16,\cdot)\) | 1183.bi | 39 | yes | \(1\) | \(1\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{35}{39}\right)\) |
\(\chi_{1183}(17,\cdot)\) | 1183.by | 78 | yes | \(-1\) | \(1\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{17}{78}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{59}{78}\right)\) |
\(\chi_{1183}(18,\cdot)\) | 1183.ce | 156 | yes | \(-1\) | \(1\) | \(e\left(\frac{145}{156}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{109}{156}\right)\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{41}{52}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{11}{156}\right)\) | \(e\left(\frac{35}{78}\right)\) |
\(\chi_{1183}(19,\cdot)\) | 1183.w | 12 | no | \(1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(i\) | \(1\) | \(1\) | \(i\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{1183}(20,\cdot)\) | 1183.cb | 156 | yes | \(1\) | \(1\) | \(e\left(\frac{11}{156}\right)\) | \(e\left(\frac{19}{78}\right)\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{7}{52}\right)\) | \(e\left(\frac{49}{156}\right)\) | \(e\left(\frac{11}{52}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{41}{156}\right)\) | \(e\left(\frac{5}{13}\right)\) |
\(\chi_{1183}(22,\cdot)\) | 1183.f | 3 | no | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
\(\chi_{1183}(23,\cdot)\) | 1183.k | 6 | no | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{1183}(24,\cdot)\) | 1183.ch | 156 | yes | \(1\) | \(1\) | \(e\left(\frac{23}{156}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{23}{78}\right)\) | \(e\left(\frac{25}{156}\right)\) | \(e\left(\frac{41}{156}\right)\) | \(e\left(\frac{23}{52}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{16}{39}\right)\) |
\(\chi_{1183}(25,\cdot)\) | 1183.bs | 78 | yes | \(1\) | \(1\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{29}{78}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{34}{39}\right)\) |
\(\chi_{1183}(27,\cdot)\) | 1183.bf | 26 | yes | \(-1\) | \(1\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{25}{26}\right)\) |
\(\chi_{1183}(29,\cdot)\) | 1183.bk | 39 | no | \(1\) | \(1\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{4}{13}\right)\) |
\(\chi_{1183}(30,\cdot)\) | 1183.bp | 78 | yes | \(1\) | \(1\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{29}{78}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{35}{39}\right)\) |
\(\chi_{1183}(31,\cdot)\) | 1183.cc | 156 | yes | \(1\) | \(1\) | \(e\left(\frac{73}{156}\right)\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{7}{156}\right)\) | \(e\left(\frac{17}{52}\right)\) | \(e\left(\frac{21}{52}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{83}{156}\right)\) | \(e\left(\frac{31}{39}\right)\) |
\(\chi_{1183}(32,\cdot)\) | 1183.cg | 156 | yes | \(-1\) | \(1\) | \(e\left(\frac{19}{52}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{97}{156}\right)\) | \(e\left(\frac{1}{156}\right)\) | \(e\left(\frac{5}{52}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{151}{156}\right)\) | \(e\left(\frac{29}{78}\right)\) |
\(\chi_{1183}(33,\cdot)\) | 1183.ch | 156 | yes | \(1\) | \(1\) | \(e\left(\frac{19}{156}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{19}{78}\right)\) | \(e\left(\frac{41}{156}\right)\) | \(e\left(\frac{61}{156}\right)\) | \(e\left(\frac{19}{52}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{11}{52}\right)\) | \(e\left(\frac{20}{39}\right)\) |
\(\chi_{1183}(34,\cdot)\) | 1183.bn | 52 | yes | \(1\) | \(1\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{51}{52}\right)\) | \(e\left(\frac{15}{52}\right)\) | \(e\left(\frac{43}{52}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{3}{13}\right)\) |
\(\chi_{1183}(36,\cdot)\) | 1183.bt | 78 | no | \(1\) | \(1\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{25}{78}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{12}{13}\right)\) |
\(\chi_{1183}(37,\cdot)\) | 1183.cg | 156 | yes | \(-1\) | \(1\) | \(e\left(\frac{33}{52}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{59}{156}\right)\) | \(e\left(\frac{155}{156}\right)\) | \(e\left(\frac{47}{52}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{5}{156}\right)\) | \(e\left(\frac{49}{78}\right)\) |
\(\chi_{1183}(38,\cdot)\) | 1183.br | 78 | yes | \(-1\) | \(1\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{19}{78}\right)\) | \(e\left(\frac{11}{78}\right)\) |
\(\chi_{1183}(40,\cdot)\) | 1183.bv | 78 | yes | \(-1\) | \(1\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{29}{78}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{67}{78}\right)\) |