sage: H = DirichletGroup(2166)
pari: g = idealstar(,2166,2)
Character group
| sage: G.order()
pari: g.no
| ||
| Order | = | 684 |
| sage: H.invariants()
pari: g.cyc
| ||
| Structure | = | \(C_{2}\times C_{342}\) |
| sage: H.gens()
pari: g.gen
| ||
| Generators | = | $\chi_{2166}(1445,\cdot)$, $\chi_{2166}(1807,\cdot)$ |
First 32 of 684 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 | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{2166}(1,\cdot)\) | 2166.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(\chi_{2166}(5,\cdot)\) | 2166.w | 342 | no | \(-1\) | \(1\) | \(e\left(\frac{301}{342}\right)\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{79}{114}\right)\) | \(e\left(\frac{31}{171}\right)\) | \(e\left(\frac{277}{342}\right)\) | \(e\left(\frac{185}{342}\right)\) | \(e\left(\frac{130}{171}\right)\) | \(e\left(\frac{11}{342}\right)\) | \(e\left(\frac{31}{57}\right)\) | \(e\left(\frac{217}{342}\right)\) |
| \(\chi_{2166}(7,\cdot)\) | 2166.q | 57 | no | \(1\) | \(1\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{15}{19}\right)\) | \(e\left(\frac{14}{19}\right)\) | \(e\left(\frac{17}{57}\right)\) | \(e\left(\frac{7}{57}\right)\) | \(e\left(\frac{2}{57}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{26}{57}\right)\) | \(e\left(\frac{17}{19}\right)\) | \(e\left(\frac{31}{57}\right)\) |
| \(\chi_{2166}(11,\cdot)\) | 2166.s | 114 | no | \(-1\) | \(1\) | \(e\left(\frac{79}{114}\right)\) | \(e\left(\frac{14}{19}\right)\) | \(e\left(\frac{35}{38}\right)\) | \(e\left(\frac{7}{57}\right)\) | \(e\left(\frac{103}{114}\right)\) | \(e\left(\frac{5}{114}\right)\) | \(e\left(\frac{22}{57}\right)\) | \(e\left(\frac{65}{114}\right)\) | \(e\left(\frac{7}{19}\right)\) | \(e\left(\frac{49}{114}\right)\) |
| \(\chi_{2166}(13,\cdot)\) | 2166.x | 342 | no | \(-1\) | \(1\) | \(e\left(\frac{31}{171}\right)\) | \(e\left(\frac{17}{57}\right)\) | \(e\left(\frac{7}{57}\right)\) | \(e\left(\frac{169}{342}\right)\) | \(e\left(\frac{70}{171}\right)\) | \(e\left(\frac{77}{171}\right)\) | \(e\left(\frac{62}{171}\right)\) | \(e\left(\frac{121}{342}\right)\) | \(e\left(\frac{55}{114}\right)\) | \(e\left(\frac{82}{171}\right)\) |
| \(\chi_{2166}(17,\cdot)\) | 2166.w | 342 | no | \(-1\) | \(1\) | \(e\left(\frac{277}{342}\right)\) | \(e\left(\frac{7}{57}\right)\) | \(e\left(\frac{103}{114}\right)\) | \(e\left(\frac{70}{171}\right)\) | \(e\left(\frac{289}{342}\right)\) | \(e\left(\frac{335}{342}\right)\) | \(e\left(\frac{106}{171}\right)\) | \(e\left(\frac{251}{342}\right)\) | \(e\left(\frac{13}{57}\right)\) | \(e\left(\frac{319}{342}\right)\) |
| \(\chi_{2166}(23,\cdot)\) | 2166.w | 342 | no | \(-1\) | \(1\) | \(e\left(\frac{185}{342}\right)\) | \(e\left(\frac{2}{57}\right)\) | \(e\left(\frac{5}{114}\right)\) | \(e\left(\frac{77}{171}\right)\) | \(e\left(\frac{335}{342}\right)\) | \(e\left(\frac{283}{342}\right)\) | \(e\left(\frac{14}{171}\right)\) | \(e\left(\frac{259}{342}\right)\) | \(e\left(\frac{20}{57}\right)\) | \(e\left(\frac{197}{342}\right)\) |
| \(\chi_{2166}(25,\cdot)\) | 2166.u | 171 | no | \(1\) | \(1\) | \(e\left(\frac{130}{171}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{22}{57}\right)\) | \(e\left(\frac{62}{171}\right)\) | \(e\left(\frac{106}{171}\right)\) | \(e\left(\frac{14}{171}\right)\) | \(e\left(\frac{89}{171}\right)\) | \(e\left(\frac{11}{171}\right)\) | \(e\left(\frac{5}{57}\right)\) | \(e\left(\frac{46}{171}\right)\) |
| \(\chi_{2166}(29,\cdot)\) | 2166.v | 342 | no | \(1\) | \(1\) | \(e\left(\frac{11}{342}\right)\) | \(e\left(\frac{26}{57}\right)\) | \(e\left(\frac{65}{114}\right)\) | \(e\left(\frac{121}{342}\right)\) | \(e\left(\frac{251}{342}\right)\) | \(e\left(\frac{259}{342}\right)\) | \(e\left(\frac{11}{171}\right)\) | \(e\left(\frac{59}{171}\right)\) | \(e\left(\frac{7}{114}\right)\) | \(e\left(\frac{167}{342}\right)\) |
| \(\chi_{2166}(31,\cdot)\) | 2166.t | 114 | no | \(-1\) | \(1\) | \(e\left(\frac{31}{57}\right)\) | \(e\left(\frac{17}{19}\right)\) | \(e\left(\frac{7}{19}\right)\) | \(e\left(\frac{55}{114}\right)\) | \(e\left(\frac{13}{57}\right)\) | \(e\left(\frac{20}{57}\right)\) | \(e\left(\frac{5}{57}\right)\) | \(e\left(\frac{7}{114}\right)\) | \(e\left(\frac{17}{38}\right)\) | \(e\left(\frac{25}{57}\right)\) |
| \(\chi_{2166}(35,\cdot)\) | 2166.w | 342 | no | \(-1\) | \(1\) | \(e\left(\frac{217}{342}\right)\) | \(e\left(\frac{31}{57}\right)\) | \(e\left(\frac{49}{114}\right)\) | \(e\left(\frac{82}{171}\right)\) | \(e\left(\frac{319}{342}\right)\) | \(e\left(\frac{197}{342}\right)\) | \(e\left(\frac{46}{171}\right)\) | \(e\left(\frac{167}{342}\right)\) | \(e\left(\frac{25}{57}\right)\) | \(e\left(\frac{61}{342}\right)\) |
| \(\chi_{2166}(37,\cdot)\) | 2166.n | 38 | no | \(-1\) | \(1\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{14}{19}\right)\) | \(e\left(\frac{8}{19}\right)\) | \(e\left(\frac{11}{38}\right)\) | \(e\left(\frac{14}{19}\right)\) | \(e\left(\frac{4}{19}\right)\) | \(e\left(\frac{1}{19}\right)\) | \(e\left(\frac{9}{38}\right)\) | \(e\left(\frac{33}{38}\right)\) | \(e\left(\frac{5}{19}\right)\) |
| \(\chi_{2166}(41,\cdot)\) | 2166.v | 342 | no | \(1\) | \(1\) | \(e\left(\frac{325}{342}\right)\) | \(e\left(\frac{22}{57}\right)\) | \(e\left(\frac{55}{114}\right)\) | \(e\left(\frac{155}{342}\right)\) | \(e\left(\frac{265}{342}\right)\) | \(e\left(\frac{35}{342}\right)\) | \(e\left(\frac{154}{171}\right)\) | \(e\left(\frac{142}{171}\right)\) | \(e\left(\frac{41}{114}\right)\) | \(e\left(\frac{115}{342}\right)\) |
| \(\chi_{2166}(43,\cdot)\) | 2166.u | 171 | no | \(1\) | \(1\) | \(e\left(\frac{47}{171}\right)\) | \(e\left(\frac{46}{57}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{4}{171}\right)\) | \(e\left(\frac{62}{171}\right)\) | \(e\left(\frac{34}{171}\right)\) | \(e\left(\frac{94}{171}\right)\) | \(e\left(\frac{100}{171}\right)\) | \(e\left(\frac{4}{57}\right)\) | \(e\left(\frac{14}{171}\right)\) |
| \(\chi_{2166}(47,\cdot)\) | 2166.w | 342 | no | \(-1\) | \(1\) | \(e\left(\frac{47}{342}\right)\) | \(e\left(\frac{23}{57}\right)\) | \(e\left(\frac{29}{114}\right)\) | \(e\left(\frac{2}{171}\right)\) | \(e\left(\frac{233}{342}\right)\) | \(e\left(\frac{205}{342}\right)\) | \(e\left(\frac{47}{171}\right)\) | \(e\left(\frac{271}{342}\right)\) | \(e\left(\frac{2}{57}\right)\) | \(e\left(\frac{185}{342}\right)\) |
| \(\chi_{2166}(49,\cdot)\) | 2166.q | 57 | no | \(1\) | \(1\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{11}{19}\right)\) | \(e\left(\frac{9}{19}\right)\) | \(e\left(\frac{34}{57}\right)\) | \(e\left(\frac{14}{57}\right)\) | \(e\left(\frac{4}{57}\right)\) | \(e\left(\frac{1}{57}\right)\) | \(e\left(\frac{52}{57}\right)\) | \(e\left(\frac{15}{19}\right)\) | \(e\left(\frac{5}{57}\right)\) |
| \(\chi_{2166}(53,\cdot)\) | 2166.v | 342 | no | \(1\) | \(1\) | \(e\left(\frac{275}{342}\right)\) | \(e\left(\frac{23}{57}\right)\) | \(e\left(\frac{29}{114}\right)\) | \(e\left(\frac{289}{342}\right)\) | \(e\left(\frac{119}{342}\right)\) | \(e\left(\frac{319}{342}\right)\) | \(e\left(\frac{104}{171}\right)\) | \(e\left(\frac{107}{171}\right)\) | \(e\left(\frac{61}{114}\right)\) | \(e\left(\frac{71}{342}\right)\) |
| \(\chi_{2166}(55,\cdot)\) | 2166.u | 171 | no | \(1\) | \(1\) | \(e\left(\frac{98}{171}\right)\) | \(e\left(\frac{28}{57}\right)\) | \(e\left(\frac{35}{57}\right)\) | \(e\left(\frac{52}{171}\right)\) | \(e\left(\frac{122}{171}\right)\) | \(e\left(\frac{100}{171}\right)\) | \(e\left(\frac{25}{171}\right)\) | \(e\left(\frac{103}{171}\right)\) | \(e\left(\frac{52}{57}\right)\) | \(e\left(\frac{11}{171}\right)\) |
| \(\chi_{2166}(59,\cdot)\) | 2166.v | 342 | no | \(1\) | \(1\) | \(e\left(\frac{97}{342}\right)\) | \(e\left(\frac{22}{57}\right)\) | \(e\left(\frac{55}{114}\right)\) | \(e\left(\frac{41}{342}\right)\) | \(e\left(\frac{37}{342}\right)\) | \(e\left(\frac{263}{342}\right)\) | \(e\left(\frac{97}{171}\right)\) | \(e\left(\frac{85}{171}\right)\) | \(e\left(\frac{41}{114}\right)\) | \(e\left(\frac{229}{342}\right)\) |
| \(\chi_{2166}(61,\cdot)\) | 2166.u | 171 | no | \(1\) | \(1\) | \(e\left(\frac{70}{171}\right)\) | \(e\left(\frac{20}{57}\right)\) | \(e\left(\frac{25}{57}\right)\) | \(e\left(\frac{86}{171}\right)\) | \(e\left(\frac{136}{171}\right)\) | \(e\left(\frac{47}{171}\right)\) | \(e\left(\frac{140}{171}\right)\) | \(e\left(\frac{98}{171}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{130}{171}\right)\) |
| \(\chi_{2166}(65,\cdot)\) | 2166.r | 114 | no | \(1\) | \(1\) | \(e\left(\frac{7}{114}\right)\) | \(e\left(\frac{1}{19}\right)\) | \(e\left(\frac{31}{38}\right)\) | \(e\left(\frac{77}{114}\right)\) | \(e\left(\frac{25}{114}\right)\) | \(e\left(\frac{113}{114}\right)\) | \(e\left(\frac{7}{57}\right)\) | \(e\left(\frac{22}{57}\right)\) | \(e\left(\frac{1}{38}\right)\) | \(e\left(\frac{13}{114}\right)\) |
| \(\chi_{2166}(67,\cdot)\) | 2166.x | 342 | no | \(-1\) | \(1\) | \(e\left(\frac{82}{171}\right)\) | \(e\left(\frac{56}{57}\right)\) | \(e\left(\frac{13}{57}\right)\) | \(e\left(\frac{265}{342}\right)\) | \(e\left(\frac{130}{171}\right)\) | \(e\left(\frac{143}{171}\right)\) | \(e\left(\frac{164}{171}\right)\) | \(e\left(\frac{127}{342}\right)\) | \(e\left(\frac{37}{114}\right)\) | \(e\left(\frac{79}{171}\right)\) |
| \(\chi_{2166}(71,\cdot)\) | 2166.v | 342 | no | \(1\) | \(1\) | \(e\left(\frac{31}{342}\right)\) | \(e\left(\frac{37}{57}\right)\) | \(e\left(\frac{7}{114}\right)\) | \(e\left(\frac{341}{342}\right)\) | \(e\left(\frac{241}{342}\right)\) | \(e\left(\frac{77}{342}\right)\) | \(e\left(\frac{31}{171}\right)\) | \(e\left(\frac{73}{171}\right)\) | \(e\left(\frac{113}{114}\right)\) | \(e\left(\frac{253}{342}\right)\) |
| \(\chi_{2166}(73,\cdot)\) | 2166.u | 171 | no | \(1\) | \(1\) | \(e\left(\frac{167}{171}\right)\) | \(e\left(\frac{7}{57}\right)\) | \(e\left(\frac{23}{57}\right)\) | \(e\left(\frac{127}{171}\right)\) | \(e\left(\frac{2}{171}\right)\) | \(e\left(\frac{139}{171}\right)\) | \(e\left(\frac{163}{171}\right)\) | \(e\left(\frac{97}{171}\right)\) | \(e\left(\frac{13}{57}\right)\) | \(e\left(\frac{17}{171}\right)\) |
| \(\chi_{2166}(77,\cdot)\) | 2166.o | 38 | no | \(-1\) | \(1\) | \(e\left(\frac{17}{38}\right)\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{25}{38}\right)\) | \(e\left(\frac{8}{19}\right)\) | \(e\left(\frac{1}{38}\right)\) | \(e\left(\frac{3}{38}\right)\) | \(e\left(\frac{17}{19}\right)\) | \(e\left(\frac{1}{38}\right)\) | \(e\left(\frac{5}{19}\right)\) | \(e\left(\frac{37}{38}\right)\) |
| \(\chi_{2166}(79,\cdot)\) | 2166.x | 342 | no | \(-1\) | \(1\) | \(e\left(\frac{104}{171}\right)\) | \(e\left(\frac{46}{57}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{65}{342}\right)\) | \(e\left(\frac{119}{171}\right)\) | \(e\left(\frac{148}{171}\right)\) | \(e\left(\frac{37}{171}\right)\) | \(e\left(\frac{257}{342}\right)\) | \(e\left(\frac{65}{114}\right)\) | \(e\left(\frac{71}{171}\right)\) |
| \(\chi_{2166}(83,\cdot)\) | 2166.s | 114 | no | \(-1\) | \(1\) | \(e\left(\frac{77}{114}\right)\) | \(e\left(\frac{11}{19}\right)\) | \(e\left(\frac{37}{38}\right)\) | \(e\left(\frac{53}{57}\right)\) | \(e\left(\frac{47}{114}\right)\) | \(e\left(\frac{103}{114}\right)\) | \(e\left(\frac{20}{57}\right)\) | \(e\left(\frac{85}{114}\right)\) | \(e\left(\frac{15}{19}\right)\) | \(e\left(\frac{29}{114}\right)\) |
| \(\chi_{2166}(85,\cdot)\) | 2166.u | 171 | no | \(1\) | \(1\) | \(e\left(\frac{118}{171}\right)\) | \(e\left(\frac{50}{57}\right)\) | \(e\left(\frac{34}{57}\right)\) | \(e\left(\frac{101}{171}\right)\) | \(e\left(\frac{112}{171}\right)\) | \(e\left(\frac{89}{171}\right)\) | \(e\left(\frac{65}{171}\right)\) | \(e\left(\frac{131}{171}\right)\) | \(e\left(\frac{44}{57}\right)\) | \(e\left(\frac{97}{171}\right)\) |
| \(\chi_{2166}(89,\cdot)\) | 2166.v | 342 | no | \(1\) | \(1\) | \(e\left(\frac{179}{342}\right)\) | \(e\left(\frac{50}{57}\right)\) | \(e\left(\frac{11}{114}\right)\) | \(e\left(\frac{259}{342}\right)\) | \(e\left(\frac{167}{342}\right)\) | \(e\left(\frac{235}{342}\right)\) | \(e\left(\frac{8}{171}\right)\) | \(e\left(\frac{74}{171}\right)\) | \(e\left(\frac{31}{114}\right)\) | \(e\left(\frac{137}{342}\right)\) |
| \(\chi_{2166}(91,\cdot)\) | 2166.x | 342 | no | \(-1\) | \(1\) | \(e\left(\frac{160}{171}\right)\) | \(e\left(\frac{5}{57}\right)\) | \(e\left(\frac{49}{57}\right)\) | \(e\left(\frac{271}{342}\right)\) | \(e\left(\frac{91}{171}\right)\) | \(e\left(\frac{83}{171}\right)\) | \(e\left(\frac{149}{171}\right)\) | \(e\left(\frac{277}{342}\right)\) | \(e\left(\frac{43}{114}\right)\) | \(e\left(\frac{4}{171}\right)\) |
| \(\chi_{2166}(97,\cdot)\) | 2166.x | 342 | no | \(-1\) | \(1\) | \(e\left(\frac{89}{171}\right)\) | \(e\left(\frac{1}{57}\right)\) | \(e\left(\frac{44}{57}\right)\) | \(e\left(\frac{77}{342}\right)\) | \(e\left(\frac{41}{171}\right)\) | \(e\left(\frac{28}{171}\right)\) | \(e\left(\frac{7}{171}\right)\) | \(e\left(\frac{215}{342}\right)\) | \(e\left(\frac{77}{114}\right)\) | \(e\left(\frac{92}{171}\right)\) |
| \(\chi_{2166}(101,\cdot)\) | 2166.w | 342 | no | \(-1\) | \(1\) | \(e\left(\frac{143}{342}\right)\) | \(e\left(\frac{53}{57}\right)\) | \(e\left(\frac{47}{114}\right)\) | \(e\left(\frac{17}{171}\right)\) | \(e\left(\frac{185}{342}\right)\) | \(e\left(\frac{289}{342}\right)\) | \(e\left(\frac{143}{171}\right)\) | \(e\left(\frac{337}{342}\right)\) | \(e\left(\frac{17}{57}\right)\) | \(e\left(\frac{119}{342}\right)\) |