sage: H = DirichletGroup(2014)
pari: g = idealstar(,2014,2)
Character group
| sage: G.order()
pari: g.no
| ||
| Order | = | 936 |
| sage: H.invariants()
pari: g.cyc
| ||
| Structure | = | \(C_{2}\times C_{468}\) |
| sage: H.gens()
pari: g.gen
| ||
| Generators | = | $\chi_{2014}(743,\cdot)$, $\chi_{2014}(267,\cdot)$ |
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 | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{2014}(1,\cdot)\) | 2014.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(\chi_{2014}(3,\cdot)\) | 2014.bi | 468 | no | \(1\) | \(1\) | \(e\left(\frac{443}{468}\right)\) | \(e\left(\frac{431}{468}\right)\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{209}{234}\right)\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{107}{234}\right)\) | \(e\left(\frac{203}{234}\right)\) | \(e\left(\frac{115}{234}\right)\) | \(e\left(\frac{401}{468}\right)\) | \(e\left(\frac{7}{36}\right)\) |
| \(\chi_{2014}(5,\cdot)\) | 2014.bj | 468 | no | \(-1\) | \(1\) | \(e\left(\frac{431}{468}\right)\) | \(e\left(\frac{329}{468}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{197}{234}\right)\) | \(e\left(\frac{7}{78}\right)\) | \(e\left(\frac{16}{117}\right)\) | \(e\left(\frac{73}{117}\right)\) | \(e\left(\frac{217}{234}\right)\) | \(e\left(\frac{425}{468}\right)\) | \(e\left(\frac{1}{36}\right)\) |
| \(\chi_{2014}(7,\cdot)\) | 2014.z | 78 | no | \(1\) | \(1\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{1}{6}\right)\) |
| \(\chi_{2014}(9,\cdot)\) | 2014.bf | 234 | no | \(1\) | \(1\) | \(e\left(\frac{209}{234}\right)\) | \(e\left(\frac{197}{234}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{92}{117}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{107}{117}\right)\) | \(e\left(\frac{86}{117}\right)\) | \(e\left(\frac{115}{117}\right)\) | \(e\left(\frac{167}{234}\right)\) | \(e\left(\frac{7}{18}\right)\) |
| \(\chi_{2014}(11,\cdot)\) | 2014.z | 78 | no | \(1\) | \(1\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{7}{78}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{19}{78}\right)\) | \(e\left(\frac{5}{6}\right)\) |
| \(\chi_{2014}(13,\cdot)\) | 2014.bg | 234 | no | \(-1\) | \(1\) | \(e\left(\frac{107}{234}\right)\) | \(e\left(\frac{16}{117}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{107}{117}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{109}{234}\right)\) | \(e\left(\frac{139}{234}\right)\) | \(e\left(\frac{46}{117}\right)\) | \(e\left(\frac{137}{234}\right)\) | \(e\left(\frac{5}{9}\right)\) |
| \(\chi_{2014}(15,\cdot)\) | 2014.bg | 234 | no | \(-1\) | \(1\) | \(e\left(\frac{203}{234}\right)\) | \(e\left(\frac{73}{117}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{86}{117}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{139}{234}\right)\) | \(e\left(\frac{115}{234}\right)\) | \(e\left(\frac{49}{117}\right)\) | \(e\left(\frac{179}{234}\right)\) | \(e\left(\frac{2}{9}\right)\) |
| \(\chi_{2014}(17,\cdot)\) | 2014.bf | 234 | no | \(1\) | \(1\) | \(e\left(\frac{115}{234}\right)\) | \(e\left(\frac{217}{234}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{115}{117}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{46}{117}\right)\) | \(e\left(\frac{49}{117}\right)\) | \(e\left(\frac{56}{117}\right)\) | \(e\left(\frac{121}{234}\right)\) | \(e\left(\frac{11}{18}\right)\) |
| \(\chi_{2014}(21,\cdot)\) | 2014.bi | 468 | no | \(1\) | \(1\) | \(e\left(\frac{401}{468}\right)\) | \(e\left(\frac{425}{468}\right)\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{167}{234}\right)\) | \(e\left(\frac{19}{78}\right)\) | \(e\left(\frac{137}{234}\right)\) | \(e\left(\frac{179}{234}\right)\) | \(e\left(\frac{121}{234}\right)\) | \(e\left(\frac{251}{468}\right)\) | \(e\left(\frac{13}{36}\right)\) |
| \(\chi_{2014}(23,\cdot)\) | 2014.u | 36 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{17}{36}\right)\) |
| \(\chi_{2014}(25,\cdot)\) | 2014.bf | 234 | no | \(1\) | \(1\) | \(e\left(\frac{197}{234}\right)\) | \(e\left(\frac{95}{234}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{80}{117}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{32}{117}\right)\) | \(e\left(\frac{29}{117}\right)\) | \(e\left(\frac{100}{117}\right)\) | \(e\left(\frac{191}{234}\right)\) | \(e\left(\frac{1}{18}\right)\) |
| \(\chi_{2014}(27,\cdot)\) | 2014.bd | 156 | no | \(1\) | \(1\) | \(e\left(\frac{131}{156}\right)\) | \(e\left(\frac{119}{156}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{29}{78}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{89}{156}\right)\) | \(e\left(\frac{7}{12}\right)\) |
| \(\chi_{2014}(29,\cdot)\) | 2014.bh | 234 | no | \(-1\) | \(1\) | \(e\left(\frac{37}{117}\right)\) | \(e\left(\frac{161}{234}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{74}{117}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{223}{234}\right)\) | \(e\left(\frac{1}{234}\right)\) | \(e\left(\frac{34}{117}\right)\) | \(e\left(\frac{43}{117}\right)\) | \(e\left(\frac{7}{18}\right)\) |
| \(\chi_{2014}(31,\cdot)\) | 2014.bd | 156 | no | \(1\) | \(1\) | \(e\left(\frac{97}{156}\right)\) | \(e\left(\frac{25}{156}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{19}{78}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{79}{156}\right)\) | \(e\left(\frac{5}{12}\right)\) |
| \(\chi_{2014}(33,\cdot)\) | 2014.bi | 468 | no | \(1\) | \(1\) | \(e\left(\frac{269}{468}\right)\) | \(e\left(\frac{5}{468}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{35}{234}\right)\) | \(e\left(\frac{25}{78}\right)\) | \(e\left(\frac{131}{234}\right)\) | \(e\left(\frac{137}{234}\right)\) | \(e\left(\frac{73}{234}\right)\) | \(e\left(\frac{47}{468}\right)\) | \(e\left(\frac{1}{36}\right)\) |
| \(\chi_{2014}(35,\cdot)\) | 2014.bj | 468 | no | \(-1\) | \(1\) | \(e\left(\frac{389}{468}\right)\) | \(e\left(\frac{323}{468}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{155}{234}\right)\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{31}{117}\right)\) | \(e\left(\frac{61}{117}\right)\) | \(e\left(\frac{223}{234}\right)\) | \(e\left(\frac{275}{468}\right)\) | \(e\left(\frac{7}{36}\right)\) |
| \(\chi_{2014}(37,\cdot)\) | 2014.r | 26 | no | \(-1\) | \(1\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(-1\) |
| \(\chi_{2014}(39,\cdot)\) | 2014.x | 52 | no | \(-1\) | \(1\) | \(e\left(\frac{21}{52}\right)\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{23}{52}\right)\) | \(-i\) |
| \(\chi_{2014}(41,\cdot)\) | 2014.bi | 468 | no | \(1\) | \(1\) | \(e\left(\frac{47}{468}\right)\) | \(e\left(\frac{107}{468}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{47}{234}\right)\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{89}{234}\right)\) | \(e\left(\frac{77}{234}\right)\) | \(e\left(\frac{205}{234}\right)\) | \(e\left(\frac{257}{468}\right)\) | \(e\left(\frac{7}{36}\right)\) |
| \(\chi_{2014}(43,\cdot)\) | 2014.bf | 234 | no | \(1\) | \(1\) | \(e\left(\frac{175}{234}\right)\) | \(e\left(\frac{25}{234}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{58}{117}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{70}{117}\right)\) | \(e\left(\frac{100}{117}\right)\) | \(e\left(\frac{14}{117}\right)\) | \(e\left(\frac{1}{234}\right)\) | \(e\left(\frac{5}{18}\right)\) |
| \(\chi_{2014}(45,\cdot)\) | 2014.be | 156 | no | \(-1\) | \(1\) | \(e\left(\frac{127}{156}\right)\) | \(e\left(\frac{85}{156}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{97}{156}\right)\) | \(e\left(\frac{5}{12}\right)\) |
| \(\chi_{2014}(47,\cdot)\) | 2014.bc | 117 | no | \(1\) | \(1\) | \(e\left(\frac{19}{117}\right)\) | \(e\left(\frac{103}{117}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{38}{117}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{62}{117}\right)\) | \(e\left(\frac{5}{117}\right)\) | \(e\left(\frac{106}{117}\right)\) | \(e\left(\frac{79}{117}\right)\) | \(e\left(\frac{8}{9}\right)\) |
| \(\chi_{2014}(49,\cdot)\) | 2014.w | 39 | no | \(1\) | \(1\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{1}{3}\right)\) |
| \(\chi_{2014}(51,\cdot)\) | 2014.bi | 468 | no | \(1\) | \(1\) | \(e\left(\frac{205}{468}\right)\) | \(e\left(\frac{397}{468}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{205}{234}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{199}{234}\right)\) | \(e\left(\frac{67}{234}\right)\) | \(e\left(\frac{227}{234}\right)\) | \(e\left(\frac{175}{468}\right)\) | \(e\left(\frac{29}{36}\right)\) |
| \(\chi_{2014}(55,\cdot)\) | 2014.bj | 468 | no | \(-1\) | \(1\) | \(e\left(\frac{257}{468}\right)\) | \(e\left(\frac{371}{468}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{23}{234}\right)\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{28}{117}\right)\) | \(e\left(\frac{40}{117}\right)\) | \(e\left(\frac{175}{234}\right)\) | \(e\left(\frac{71}{468}\right)\) | \(e\left(\frac{31}{36}\right)\) |
| \(\chi_{2014}(59,\cdot)\) | 2014.bh | 234 | no | \(-1\) | \(1\) | \(e\left(\frac{71}{117}\right)\) | \(e\left(\frac{37}{234}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{25}{117}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{137}{234}\right)\) | \(e\left(\frac{179}{234}\right)\) | \(e\left(\frac{2}{117}\right)\) | \(e\left(\frac{92}{117}\right)\) | \(e\left(\frac{11}{18}\right)\) |
| \(\chi_{2014}(61,\cdot)\) | 2014.bj | 468 | no | \(-1\) | \(1\) | \(e\left(\frac{199}{468}\right)\) | \(e\left(\frac{229}{468}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{199}{234}\right)\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{110}{117}\right)\) | \(e\left(\frac{107}{117}\right)\) | \(e\left(\frac{161}{234}\right)\) | \(e\left(\frac{421}{468}\right)\) | \(e\left(\frac{17}{36}\right)\) |
| \(\chi_{2014}(63,\cdot)\) | 2014.bc | 117 | no | \(1\) | \(1\) | \(e\left(\frac{94}{117}\right)\) | \(e\left(\frac{97}{117}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{71}{117}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{5}{117}\right)\) | \(e\left(\frac{74}{117}\right)\) | \(e\left(\frac{1}{117}\right)\) | \(e\left(\frac{46}{117}\right)\) | \(e\left(\frac{5}{9}\right)\) |
| \(\chi_{2014}(65,\cdot)\) | 2014.bd | 156 | no | \(1\) | \(1\) | \(e\left(\frac{59}{156}\right)\) | \(e\left(\frac{131}{156}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{17}{78}\right)\) | \(e\left(\frac{25}{78}\right)\) | \(e\left(\frac{77}{156}\right)\) | \(e\left(\frac{7}{12}\right)\) |
| \(\chi_{2014}(67,\cdot)\) | 2014.bi | 468 | no | \(1\) | \(1\) | \(e\left(\frac{85}{468}\right)\) | \(e\left(\frac{313}{468}\right)\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{85}{234}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{151}{234}\right)\) | \(e\left(\frac{199}{234}\right)\) | \(e\left(\frac{77}{234}\right)\) | \(e\left(\frac{415}{468}\right)\) | \(e\left(\frac{5}{36}\right)\) |
| \(\chi_{2014}(69,\cdot)\) | 2014.ba | 78 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{7}{78}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{17}{78}\right)\) | \(e\left(\frac{2}{3}\right)\) |