sage: H = DirichletGroup(6378)
pari: g = idealstar(,6378,2)
Character group
| sage: G.order()
pari: g.no
| ||
| Order | = | 2124 |
| sage: H.invariants()
pari: g.cyc
| ||
| Structure | = | \(C_{2}\times C_{1062}\) |
| sage: H.gens()
pari: g.gen
| ||
| Generators | = | $\chi_{6378}(4253,\cdot)$, $\chi_{6378}(4255,\cdot)$ |
First 32 of 2124 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 | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{6378}(1,\cdot)\) | 6378.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(\chi_{6378}(5,\cdot)\) | 6378.r | 354 | no | \(1\) | \(1\) | \(e\left(\frac{44}{59}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{121}{354}\right)\) | \(e\left(\frac{49}{59}\right)\) | \(e\left(\frac{31}{118}\right)\) | \(e\left(\frac{142}{177}\right)\) | \(e\left(\frac{199}{354}\right)\) | \(e\left(\frac{29}{59}\right)\) | \(e\left(\frac{140}{177}\right)\) | \(e\left(\frac{313}{354}\right)\) |
| \(\chi_{6378}(7,\cdot)\) | 6378.i | 9 | no | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{7}{9}\right)\) |
| \(\chi_{6378}(11,\cdot)\) | 6378.w | 1062 | no | \(-1\) | \(1\) | \(e\left(\frac{121}{354}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{985}{1062}\right)\) | \(e\left(\frac{119}{177}\right)\) | \(e\left(\frac{115}{118}\right)\) | \(e\left(\frac{328}{531}\right)\) | \(e\left(\frac{163}{1062}\right)\) | \(e\left(\frac{121}{177}\right)\) | \(e\left(\frac{739}{1062}\right)\) | \(e\left(\frac{182}{531}\right)\) |
| \(\chi_{6378}(13,\cdot)\) | 6378.q | 177 | no | \(1\) | \(1\) | \(e\left(\frac{49}{59}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{119}{177}\right)\) | \(e\left(\frac{13}{59}\right)\) | \(e\left(\frac{30}{59}\right)\) | \(e\left(\frac{16}{177}\right)\) | \(e\left(\frac{86}{177}\right)\) | \(e\left(\frac{39}{59}\right)\) | \(e\left(\frac{113}{177}\right)\) | \(e\left(\frac{65}{177}\right)\) |
| \(\chi_{6378}(17,\cdot)\) | 6378.p | 118 | no | \(-1\) | \(1\) | \(e\left(\frac{31}{118}\right)\) | \(1\) | \(e\left(\frac{115}{118}\right)\) | \(e\left(\frac{30}{59}\right)\) | \(e\left(\frac{25}{118}\right)\) | \(e\left(\frac{35}{59}\right)\) | \(e\left(\frac{37}{118}\right)\) | \(e\left(\frac{31}{59}\right)\) | \(e\left(\frac{15}{118}\right)\) | \(e\left(\frac{50}{59}\right)\) |
| \(\chi_{6378}(19,\cdot)\) | 6378.u | 531 | no | \(1\) | \(1\) | \(e\left(\frac{142}{177}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{328}{531}\right)\) | \(e\left(\frac{16}{177}\right)\) | \(e\left(\frac{35}{59}\right)\) | \(e\left(\frac{233}{531}\right)\) | \(e\left(\frac{478}{531}\right)\) | \(e\left(\frac{107}{177}\right)\) | \(e\left(\frac{307}{531}\right)\) | \(e\left(\frac{139}{531}\right)\) |
| \(\chi_{6378}(23,\cdot)\) | 6378.w | 1062 | no | \(-1\) | \(1\) | \(e\left(\frac{199}{354}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{163}{1062}\right)\) | \(e\left(\frac{86}{177}\right)\) | \(e\left(\frac{37}{118}\right)\) | \(e\left(\frac{478}{531}\right)\) | \(e\left(\frac{979}{1062}\right)\) | \(e\left(\frac{22}{177}\right)\) | \(e\left(\frac{601}{1062}\right)\) | \(e\left(\frac{194}{531}\right)\) |
| \(\chi_{6378}(25,\cdot)\) | 6378.q | 177 | no | \(1\) | \(1\) | \(e\left(\frac{29}{59}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{121}{177}\right)\) | \(e\left(\frac{39}{59}\right)\) | \(e\left(\frac{31}{59}\right)\) | \(e\left(\frac{107}{177}\right)\) | \(e\left(\frac{22}{177}\right)\) | \(e\left(\frac{58}{59}\right)\) | \(e\left(\frac{103}{177}\right)\) | \(e\left(\frac{136}{177}\right)\) |
| \(\chi_{6378}(29,\cdot)\) | 6378.x | 1062 | no | \(1\) | \(1\) | \(e\left(\frac{140}{177}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{739}{1062}\right)\) | \(e\left(\frac{113}{177}\right)\) | \(e\left(\frac{15}{118}\right)\) | \(e\left(\frac{307}{531}\right)\) | \(e\left(\frac{601}{1062}\right)\) | \(e\left(\frac{103}{177}\right)\) | \(e\left(\frac{188}{531}\right)\) | \(e\left(\frac{127}{1062}\right)\) |
| \(\chi_{6378}(31,\cdot)\) | 6378.v | 1062 | no | \(-1\) | \(1\) | \(e\left(\frac{313}{354}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{182}{531}\right)\) | \(e\left(\frac{65}{177}\right)\) | \(e\left(\frac{50}{59}\right)\) | \(e\left(\frac{139}{531}\right)\) | \(e\left(\frac{194}{531}\right)\) | \(e\left(\frac{136}{177}\right)\) | \(e\left(\frac{127}{1062}\right)\) | \(e\left(\frac{355}{1062}\right)\) |
| \(\chi_{6378}(35,\cdot)\) | 6378.x | 1062 | no | \(1\) | \(1\) | \(e\left(\frac{14}{177}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{127}{1062}\right)\) | \(e\left(\frac{29}{177}\right)\) | \(e\left(\frac{31}{118}\right)\) | \(e\left(\frac{190}{531}\right)\) | \(e\left(\frac{7}{1062}\right)\) | \(e\left(\frac{28}{177}\right)\) | \(e\left(\frac{125}{531}\right)\) | \(e\left(\frac{703}{1062}\right)\) |
| \(\chi_{6378}(37,\cdot)\) | 6378.q | 177 | no | \(1\) | \(1\) | \(e\left(\frac{34}{59}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{32}{177}\right)\) | \(e\left(\frac{3}{59}\right)\) | \(e\left(\frac{16}{59}\right)\) | \(e\left(\frac{40}{177}\right)\) | \(e\left(\frac{38}{177}\right)\) | \(e\left(\frac{9}{59}\right)\) | \(e\left(\frac{17}{177}\right)\) | \(e\left(\frac{74}{177}\right)\) |
| \(\chi_{6378}(41,\cdot)\) | 6378.r | 354 | no | \(1\) | \(1\) | \(e\left(\frac{55}{59}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{343}{354}\right)\) | \(e\left(\frac{17}{59}\right)\) | \(e\left(\frac{83}{118}\right)\) | \(e\left(\frac{148}{177}\right)\) | \(e\left(\frac{175}{354}\right)\) | \(e\left(\frac{51}{59}\right)\) | \(e\left(\frac{116}{177}\right)\) | \(e\left(\frac{229}{354}\right)\) |
| \(\chi_{6378}(43,\cdot)\) | 6378.t | 354 | no | \(-1\) | \(1\) | \(e\left(\frac{75}{118}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{11}{177}\right)\) | \(e\left(\frac{25}{59}\right)\) | \(e\left(\frac{35}{59}\right)\) | \(e\left(\frac{58}{177}\right)\) | \(e\left(\frac{2}{177}\right)\) | \(e\left(\frac{16}{59}\right)\) | \(e\left(\frac{67}{354}\right)\) | \(e\left(\frac{73}{354}\right)\) |
| \(\chi_{6378}(47,\cdot)\) | 6378.w | 1062 | no | \(-1\) | \(1\) | \(e\left(\frac{293}{354}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{779}{1062}\right)\) | \(e\left(\frac{19}{177}\right)\) | \(e\left(\frac{61}{118}\right)\) | \(e\left(\frac{509}{531}\right)\) | \(e\left(\frac{737}{1062}\right)\) | \(e\left(\frac{116}{177}\right)\) | \(e\left(\frac{1061}{1062}\right)\) | \(e\left(\frac{331}{531}\right)\) |
| \(\chi_{6378}(49,\cdot)\) | 6378.i | 9 | no | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{5}{9}\right)\) |
| \(\chi_{6378}(53,\cdot)\) | 6378.x | 1062 | no | \(1\) | \(1\) | \(e\left(\frac{70}{177}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{281}{1062}\right)\) | \(e\left(\frac{145}{177}\right)\) | \(e\left(\frac{37}{118}\right)\) | \(e\left(\frac{65}{531}\right)\) | \(e\left(\frac{743}{1062}\right)\) | \(e\left(\frac{140}{177}\right)\) | \(e\left(\frac{448}{531}\right)\) | \(e\left(\frac{1037}{1062}\right)\) |
| \(\chi_{6378}(55,\cdot)\) | 6378.v | 1062 | no | \(-1\) | \(1\) | \(e\left(\frac{31}{354}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{143}{531}\right)\) | \(e\left(\frac{89}{177}\right)\) | \(e\left(\frac{14}{59}\right)\) | \(e\left(\frac{223}{531}\right)\) | \(e\left(\frac{380}{531}\right)\) | \(e\left(\frac{31}{177}\right)\) | \(e\left(\frac{517}{1062}\right)\) | \(e\left(\frac{241}{1062}\right)\) |
| \(\chi_{6378}(59,\cdot)\) | 6378.r | 354 | no | \(1\) | \(1\) | \(e\left(\frac{36}{59}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{217}{354}\right)\) | \(e\left(\frac{24}{59}\right)\) | \(e\left(\frac{79}{118}\right)\) | \(e\left(\frac{25}{177}\right)\) | \(e\left(\frac{313}{354}\right)\) | \(e\left(\frac{13}{59}\right)\) | \(e\left(\frac{77}{177}\right)\) | \(e\left(\frac{181}{354}\right)\) |
| \(\chi_{6378}(61,\cdot)\) | 6378.v | 1062 | no | \(-1\) | \(1\) | \(e\left(\frac{67}{354}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{389}{531}\right)\) | \(e\left(\frac{101}{177}\right)\) | \(e\left(\frac{55}{59}\right)\) | \(e\left(\frac{265}{531}\right)\) | \(e\left(\frac{473}{531}\right)\) | \(e\left(\frac{67}{177}\right)\) | \(e\left(\frac{181}{1062}\right)\) | \(e\left(\frac{715}{1062}\right)\) |
| \(\chi_{6378}(65,\cdot)\) | 6378.r | 354 | no | \(1\) | \(1\) | \(e\left(\frac{34}{59}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{354}\right)\) | \(e\left(\frac{3}{59}\right)\) | \(e\left(\frac{91}{118}\right)\) | \(e\left(\frac{158}{177}\right)\) | \(e\left(\frac{17}{354}\right)\) | \(e\left(\frac{9}{59}\right)\) | \(e\left(\frac{76}{177}\right)\) | \(e\left(\frac{89}{354}\right)\) |
| \(\chi_{6378}(67,\cdot)\) | 6378.u | 531 | no | \(1\) | \(1\) | \(e\left(\frac{50}{177}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{113}{531}\right)\) | \(e\left(\frac{53}{177}\right)\) | \(e\left(\frac{9}{59}\right)\) | \(e\left(\frac{451}{531}\right)\) | \(e\left(\frac{278}{531}\right)\) | \(e\left(\frac{100}{177}\right)\) | \(e\left(\frac{143}{531}\right)\) | \(e\left(\frac{383}{531}\right)\) |
| \(\chi_{6378}(71,\cdot)\) | 6378.p | 118 | no | \(-1\) | \(1\) | \(e\left(\frac{117}{118}\right)\) | \(1\) | \(e\left(\frac{61}{118}\right)\) | \(e\left(\frac{39}{59}\right)\) | \(e\left(\frac{3}{118}\right)\) | \(e\left(\frac{16}{59}\right)\) | \(e\left(\frac{113}{118}\right)\) | \(e\left(\frac{58}{59}\right)\) | \(e\left(\frac{49}{118}\right)\) | \(e\left(\frac{6}{59}\right)\) |
| \(\chi_{6378}(73,\cdot)\) | 6378.u | 531 | no | \(1\) | \(1\) | \(e\left(\frac{173}{177}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{83}{531}\right)\) | \(e\left(\frac{17}{177}\right)\) | \(e\left(\frac{4}{59}\right)\) | \(e\left(\frac{148}{531}\right)\) | \(e\left(\frac{176}{531}\right)\) | \(e\left(\frac{169}{177}\right)\) | \(e\left(\frac{293}{531}\right)\) | \(e\left(\frac{380}{531}\right)\) |
| \(\chi_{6378}(77,\cdot)\) | 6378.w | 1062 | no | \(-1\) | \(1\) | \(e\left(\frac{239}{354}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{749}{1062}\right)\) | \(e\left(\frac{1}{177}\right)\) | \(e\left(\frac{115}{118}\right)\) | \(e\left(\frac{92}{531}\right)\) | \(e\left(\frac{635}{1062}\right)\) | \(e\left(\frac{62}{177}\right)\) | \(e\left(\frac{149}{1062}\right)\) | \(e\left(\frac{64}{531}\right)\) |
| \(\chi_{6378}(79,\cdot)\) | 6378.v | 1062 | no | \(-1\) | \(1\) | \(e\left(\frac{241}{354}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{398}{531}\right)\) | \(e\left(\frac{41}{177}\right)\) | \(e\left(\frac{27}{59}\right)\) | \(e\left(\frac{409}{531}\right)\) | \(e\left(\frac{185}{531}\right)\) | \(e\left(\frac{64}{177}\right)\) | \(e\left(\frac{91}{1062}\right)\) | \(e\left(\frac{823}{1062}\right)\) |
| \(\chi_{6378}(83,\cdot)\) | 6378.w | 1062 | no | \(-1\) | \(1\) | \(e\left(\frac{55}{354}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{1027}{1062}\right)\) | \(e\left(\frac{38}{177}\right)\) | \(e\left(\frac{63}{118}\right)\) | \(e\left(\frac{487}{531}\right)\) | \(e\left(\frac{943}{1062}\right)\) | \(e\left(\frac{55}{177}\right)\) | \(e\left(\frac{529}{1062}\right)\) | \(e\left(\frac{131}{531}\right)\) |
| \(\chi_{6378}(85,\cdot)\) | 6378.t | 354 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{118}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{56}{177}\right)\) | \(e\left(\frac{20}{59}\right)\) | \(e\left(\frac{28}{59}\right)\) | \(e\left(\frac{70}{177}\right)\) | \(e\left(\frac{155}{177}\right)\) | \(e\left(\frac{1}{59}\right)\) | \(e\left(\frac{325}{354}\right)\) | \(e\left(\frac{259}{354}\right)\) |
| \(\chi_{6378}(89,\cdot)\) | 6378.s | 354 | no | \(-1\) | \(1\) | \(e\left(\frac{73}{118}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{211}{354}\right)\) | \(e\left(\frac{44}{59}\right)\) | \(e\left(\frac{17}{118}\right)\) | \(e\left(\frac{154}{177}\right)\) | \(e\left(\frac{151}{354}\right)\) | \(e\left(\frac{14}{59}\right)\) | \(e\left(\frac{7}{354}\right)\) | \(e\left(\frac{161}{177}\right)\) |
| \(\chi_{6378}(91,\cdot)\) | 6378.u | 531 | no | \(1\) | \(1\) | \(e\left(\frac{29}{177}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{239}{531}\right)\) | \(e\left(\frac{98}{177}\right)\) | \(e\left(\frac{30}{59}\right)\) | \(e\left(\frac{343}{531}\right)\) | \(e\left(\frac{494}{531}\right)\) | \(e\left(\frac{58}{177}\right)\) | \(e\left(\frac{44}{531}\right)\) | \(e\left(\frac{77}{531}\right)\) |
| \(\chi_{6378}(95,\cdot)\) | 6378.x | 1062 | no | \(1\) | \(1\) | \(e\left(\frac{97}{177}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{1019}{1062}\right)\) | \(e\left(\frac{163}{177}\right)\) | \(e\left(\frac{101}{118}\right)\) | \(e\left(\frac{128}{531}\right)\) | \(e\left(\frac{491}{1062}\right)\) | \(e\left(\frac{17}{177}\right)\) | \(e\left(\frac{196}{531}\right)\) | \(e\left(\frac{155}{1062}\right)\) |