sage: H = DirichletGroup(8046)
pari: g = idealstar(,8046,2)
Character group
| sage: G.order()
pari: g.no
| ||
| Order | = | 2664 |
| sage: H.invariants()
pari: g.cyc
| ||
| Structure | = | \(C_{2}\times C_{1332}\) |
| sage: H.gens()
pari: g.gen
| ||
| Generators | = | $\chi_{8046}(299,\cdot)$, $\chi_{8046}(3727,\cdot)$ |
First 32 of 2664 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 | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{8046}(1,\cdot)\) | 8046.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(\chi_{8046}(5,\cdot)\) | 8046.bf | 666 | no | \(-1\) | \(1\) | \(e\left(\frac{313}{666}\right)\) | \(e\left(\frac{76}{333}\right)\) | \(e\left(\frac{137}{666}\right)\) | \(e\left(\frac{155}{333}\right)\) | \(e\left(\frac{67}{222}\right)\) | \(e\left(\frac{40}{111}\right)\) | \(e\left(\frac{541}{666}\right)\) | \(e\left(\frac{313}{333}\right)\) | \(e\left(\frac{401}{666}\right)\) | \(e\left(\frac{104}{333}\right)\) |
| \(\chi_{8046}(7,\cdot)\) | 8046.bh | 666 | no | \(1\) | \(1\) | \(e\left(\frac{76}{333}\right)\) | \(e\left(\frac{155}{333}\right)\) | \(e\left(\frac{91}{666}\right)\) | \(e\left(\frac{641}{666}\right)\) | \(e\left(\frac{34}{111}\right)\) | \(e\left(\frac{29}{111}\right)\) | \(e\left(\frac{617}{666}\right)\) | \(e\left(\frac{152}{333}\right)\) | \(e\left(\frac{8}{333}\right)\) | \(e\left(\frac{142}{333}\right)\) |
| \(\chi_{8046}(11,\cdot)\) | 8046.bi | 1332 | no | \(1\) | \(1\) | \(e\left(\frac{137}{666}\right)\) | \(e\left(\frac{91}{666}\right)\) | \(e\left(\frac{887}{1332}\right)\) | \(e\left(\frac{1081}{1332}\right)\) | \(e\left(\frac{35}{222}\right)\) | \(e\left(\frac{59}{111}\right)\) | \(e\left(\frac{1213}{1332}\right)\) | \(e\left(\frac{137}{333}\right)\) | \(e\left(\frac{67}{666}\right)\) | \(e\left(\frac{220}{333}\right)\) |
| \(\chi_{8046}(13,\cdot)\) | 8046.bj | 1332 | no | \(-1\) | \(1\) | \(e\left(\frac{155}{333}\right)\) | \(e\left(\frac{641}{666}\right)\) | \(e\left(\frac{1081}{1332}\right)\) | \(e\left(\frac{713}{1332}\right)\) | \(e\left(\frac{8}{111}\right)\) | \(e\left(\frac{46}{111}\right)\) | \(e\left(\frac{1211}{1332}\right)\) | \(e\left(\frac{310}{333}\right)\) | \(e\left(\frac{139}{333}\right)\) | \(e\left(\frac{53}{333}\right)\) |
| \(\chi_{8046}(17,\cdot)\) | 8046.z | 222 | no | \(-1\) | \(1\) | \(e\left(\frac{67}{222}\right)\) | \(e\left(\frac{34}{111}\right)\) | \(e\left(\frac{35}{222}\right)\) | \(e\left(\frac{8}{111}\right)\) | \(e\left(\frac{29}{74}\right)\) | \(e\left(\frac{14}{37}\right)\) | \(e\left(\frac{169}{222}\right)\) | \(e\left(\frac{67}{111}\right)\) | \(e\left(\frac{83}{222}\right)\) | \(e\left(\frac{29}{111}\right)\) |
| \(\chi_{8046}(19,\cdot)\) | 8046.w | 111 | no | \(1\) | \(1\) | \(e\left(\frac{40}{111}\right)\) | \(e\left(\frac{29}{111}\right)\) | \(e\left(\frac{59}{111}\right)\) | \(e\left(\frac{46}{111}\right)\) | \(e\left(\frac{14}{37}\right)\) | \(e\left(\frac{25}{37}\right)\) | \(e\left(\frac{28}{111}\right)\) | \(e\left(\frac{80}{111}\right)\) | \(e\left(\frac{86}{111}\right)\) | \(e\left(\frac{28}{111}\right)\) |
| \(\chi_{8046}(23,\cdot)\) | 8046.bi | 1332 | no | \(1\) | \(1\) | \(e\left(\frac{541}{666}\right)\) | \(e\left(\frac{617}{666}\right)\) | \(e\left(\frac{1213}{1332}\right)\) | \(e\left(\frac{1211}{1332}\right)\) | \(e\left(\frac{169}{222}\right)\) | \(e\left(\frac{28}{111}\right)\) | \(e\left(\frac{935}{1332}\right)\) | \(e\left(\frac{208}{333}\right)\) | \(e\left(\frac{425}{666}\right)\) | \(e\left(\frac{317}{333}\right)\) |
| \(\chi_{8046}(25,\cdot)\) | 8046.bc | 333 | no | \(1\) | \(1\) | \(e\left(\frac{313}{333}\right)\) | \(e\left(\frac{152}{333}\right)\) | \(e\left(\frac{137}{333}\right)\) | \(e\left(\frac{310}{333}\right)\) | \(e\left(\frac{67}{111}\right)\) | \(e\left(\frac{80}{111}\right)\) | \(e\left(\frac{208}{333}\right)\) | \(e\left(\frac{293}{333}\right)\) | \(e\left(\frac{68}{333}\right)\) | \(e\left(\frac{208}{333}\right)\) |
| \(\chi_{8046}(29,\cdot)\) | 8046.bf | 666 | no | \(-1\) | \(1\) | \(e\left(\frac{401}{666}\right)\) | \(e\left(\frac{8}{333}\right)\) | \(e\left(\frac{67}{666}\right)\) | \(e\left(\frac{139}{333}\right)\) | \(e\left(\frac{83}{222}\right)\) | \(e\left(\frac{86}{111}\right)\) | \(e\left(\frac{425}{666}\right)\) | \(e\left(\frac{68}{333}\right)\) | \(e\left(\frac{235}{666}\right)\) | \(e\left(\frac{46}{333}\right)\) |
| \(\chi_{8046}(31,\cdot)\) | 8046.bc | 333 | no | \(1\) | \(1\) | \(e\left(\frac{104}{333}\right)\) | \(e\left(\frac{142}{333}\right)\) | \(e\left(\frac{220}{333}\right)\) | \(e\left(\frac{53}{333}\right)\) | \(e\left(\frac{29}{111}\right)\) | \(e\left(\frac{28}{111}\right)\) | \(e\left(\frac{317}{333}\right)\) | \(e\left(\frac{208}{333}\right)\) | \(e\left(\frac{46}{333}\right)\) | \(e\left(\frac{317}{333}\right)\) |
| \(\chi_{8046}(35,\cdot)\) | 8046.ba | 222 | no | \(-1\) | \(1\) | \(e\left(\frac{155}{222}\right)\) | \(e\left(\frac{77}{111}\right)\) | \(e\left(\frac{38}{111}\right)\) | \(e\left(\frac{95}{222}\right)\) | \(e\left(\frac{45}{74}\right)\) | \(e\left(\frac{23}{37}\right)\) | \(e\left(\frac{82}{111}\right)\) | \(e\left(\frac{44}{111}\right)\) | \(e\left(\frac{139}{222}\right)\) | \(e\left(\frac{82}{111}\right)\) |
| \(\chi_{8046}(37,\cdot)\) | 8046.w | 111 | no | \(1\) | \(1\) | \(e\left(\frac{29}{111}\right)\) | \(e\left(\frac{46}{111}\right)\) | \(e\left(\frac{40}{111}\right)\) | \(e\left(\frac{50}{111}\right)\) | \(e\left(\frac{12}{37}\right)\) | \(e\left(\frac{32}{37}\right)\) | \(e\left(\frac{98}{111}\right)\) | \(e\left(\frac{58}{111}\right)\) | \(e\left(\frac{79}{111}\right)\) | \(e\left(\frac{98}{111}\right)\) |
| \(\chi_{8046}(41,\cdot)\) | 8046.bi | 1332 | no | \(1\) | \(1\) | \(e\left(\frac{355}{666}\right)\) | \(e\left(\frac{299}{666}\right)\) | \(e\left(\frac{631}{1332}\right)\) | \(e\left(\frac{317}{1332}\right)\) | \(e\left(\frac{115}{222}\right)\) | \(e\left(\frac{67}{111}\right)\) | \(e\left(\frac{941}{1332}\right)\) | \(e\left(\frac{22}{333}\right)\) | \(e\left(\frac{125}{666}\right)\) | \(e\left(\frac{152}{333}\right)\) |
| \(\chi_{8046}(43,\cdot)\) | 8046.bj | 1332 | no | \(-1\) | \(1\) | \(e\left(\frac{154}{333}\right)\) | \(e\left(\frac{523}{666}\right)\) | \(e\left(\frac{509}{1332}\right)\) | \(e\left(\frac{109}{1332}\right)\) | \(e\left(\frac{28}{111}\right)\) | \(e\left(\frac{50}{111}\right)\) | \(e\left(\frac{187}{1332}\right)\) | \(e\left(\frac{308}{333}\right)\) | \(e\left(\frac{209}{333}\right)\) | \(e\left(\frac{130}{333}\right)\) |
| \(\chi_{8046}(47,\cdot)\) | 8046.bg | 666 | no | \(-1\) | \(1\) | \(e\left(\frac{611}{666}\right)\) | \(e\left(\frac{209}{333}\right)\) | \(e\left(\frac{230}{333}\right)\) | \(e\left(\frac{353}{666}\right)\) | \(e\left(\frac{101}{222}\right)\) | \(e\left(\frac{110}{111}\right)\) | \(e\left(\frac{286}{333}\right)\) | \(e\left(\frac{278}{333}\right)\) | \(e\left(\frac{187}{666}\right)\) | \(e\left(\frac{286}{333}\right)\) |
| \(\chi_{8046}(49,\cdot)\) | 8046.bc | 333 | no | \(1\) | \(1\) | \(e\left(\frac{152}{333}\right)\) | \(e\left(\frac{310}{333}\right)\) | \(e\left(\frac{91}{333}\right)\) | \(e\left(\frac{308}{333}\right)\) | \(e\left(\frac{68}{111}\right)\) | \(e\left(\frac{58}{111}\right)\) | \(e\left(\frac{284}{333}\right)\) | \(e\left(\frac{304}{333}\right)\) | \(e\left(\frac{16}{333}\right)\) | \(e\left(\frac{284}{333}\right)\) |
| \(\chi_{8046}(53,\cdot)\) | 8046.u | 74 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{74}\right)\) | \(e\left(\frac{10}{37}\right)\) | \(e\left(\frac{28}{37}\right)\) | \(e\left(\frac{33}{74}\right)\) | \(e\left(\frac{43}{74}\right)\) | \(e\left(\frac{8}{37}\right)\) | \(e\left(\frac{2}{37}\right)\) | \(e\left(\frac{11}{37}\right)\) | \(e\left(\frac{7}{74}\right)\) | \(e\left(\frac{2}{37}\right)\) |
| \(\chi_{8046}(55,\cdot)\) | 8046.x | 148 | no | \(-1\) | \(1\) | \(e\left(\frac{25}{37}\right)\) | \(e\left(\frac{27}{74}\right)\) | \(e\left(\frac{129}{148}\right)\) | \(e\left(\frac{41}{148}\right)\) | \(e\left(\frac{17}{37}\right)\) | \(e\left(\frac{33}{37}\right)\) | \(e\left(\frac{107}{148}\right)\) | \(e\left(\frac{13}{37}\right)\) | \(e\left(\frac{26}{37}\right)\) | \(e\left(\frac{36}{37}\right)\) |
| \(\chi_{8046}(59,\cdot)\) | 8046.bi | 1332 | no | \(1\) | \(1\) | \(e\left(\frac{295}{666}\right)\) | \(e\left(\frac{89}{666}\right)\) | \(e\left(\frac{787}{1332}\right)\) | \(e\left(\frac{845}{1332}\right)\) | \(e\left(\frac{205}{222}\right)\) | \(e\left(\frac{76}{111}\right)\) | \(e\left(\frac{857}{1332}\right)\) | \(e\left(\frac{295}{333}\right)\) | \(e\left(\frac{329}{666}\right)\) | \(e\left(\frac{131}{333}\right)\) |
| \(\chi_{8046}(61,\cdot)\) | 8046.bh | 666 | no | \(1\) | \(1\) | \(e\left(\frac{49}{333}\right)\) | \(e\left(\frac{227}{333}\right)\) | \(e\left(\frac{361}{666}\right)\) | \(e\left(\frac{479}{666}\right)\) | \(e\left(\frac{19}{111}\right)\) | \(e\left(\frac{26}{111}\right)\) | \(e\left(\frac{113}{666}\right)\) | \(e\left(\frac{98}{333}\right)\) | \(e\left(\frac{233}{333}\right)\) | \(e\left(\frac{223}{333}\right)\) |
| \(\chi_{8046}(65,\cdot)\) | 8046.bi | 1332 | no | \(1\) | \(1\) | \(e\left(\frac{623}{666}\right)\) | \(e\left(\frac{127}{666}\right)\) | \(e\left(\frac{23}{1332}\right)\) | \(e\left(\frac{1}{1332}\right)\) | \(e\left(\frac{83}{222}\right)\) | \(e\left(\frac{86}{111}\right)\) | \(e\left(\frac{961}{1332}\right)\) | \(e\left(\frac{290}{333}\right)\) | \(e\left(\frac{13}{666}\right)\) | \(e\left(\frac{157}{333}\right)\) |
| \(\chi_{8046}(67,\cdot)\) | 8046.bc | 333 | no | \(1\) | \(1\) | \(e\left(\frac{245}{333}\right)\) | \(e\left(\frac{136}{333}\right)\) | \(e\left(\frac{70}{333}\right)\) | \(e\left(\frac{32}{333}\right)\) | \(e\left(\frac{95}{111}\right)\) | \(e\left(\frac{19}{111}\right)\) | \(e\left(\frac{116}{333}\right)\) | \(e\left(\frac{157}{333}\right)\) | \(e\left(\frac{166}{333}\right)\) | \(e\left(\frac{116}{333}\right)\) |
| \(\chi_{8046}(71,\cdot)\) | 8046.bd | 444 | no | \(1\) | \(1\) | \(e\left(\frac{55}{222}\right)\) | \(e\left(\frac{137}{222}\right)\) | \(e\left(\frac{79}{444}\right)\) | \(e\left(\frac{293}{444}\right)\) | \(e\left(\frac{47}{74}\right)\) | \(e\left(\frac{1}{37}\right)\) | \(e\left(\frac{77}{444}\right)\) | \(e\left(\frac{55}{111}\right)\) | \(e\left(\frac{35}{222}\right)\) | \(e\left(\frac{47}{111}\right)\) |
| \(\chi_{8046}(73,\cdot)\) | 8046.w | 111 | no | \(1\) | \(1\) | \(e\left(\frac{85}{111}\right)\) | \(e\left(\frac{20}{111}\right)\) | \(e\left(\frac{56}{111}\right)\) | \(e\left(\frac{70}{111}\right)\) | \(e\left(\frac{2}{37}\right)\) | \(e\left(\frac{30}{37}\right)\) | \(e\left(\frac{4}{111}\right)\) | \(e\left(\frac{59}{111}\right)\) | \(e\left(\frac{44}{111}\right)\) | \(e\left(\frac{4}{111}\right)\) |
| \(\chi_{8046}(77,\cdot)\) | 8046.bi | 1332 | no | \(1\) | \(1\) | \(e\left(\frac{289}{666}\right)\) | \(e\left(\frac{401}{666}\right)\) | \(e\left(\frac{1069}{1332}\right)\) | \(e\left(\frac{1031}{1332}\right)\) | \(e\left(\frac{103}{222}\right)\) | \(e\left(\frac{88}{111}\right)\) | \(e\left(\frac{1115}{1332}\right)\) | \(e\left(\frac{289}{333}\right)\) | \(e\left(\frac{83}{666}\right)\) | \(e\left(\frac{29}{333}\right)\) |
| \(\chi_{8046}(79,\cdot)\) | 8046.bj | 1332 | no | \(-1\) | \(1\) | \(e\left(\frac{115}{333}\right)\) | \(e\left(\frac{583}{666}\right)\) | \(e\left(\frac{845}{1332}\right)\) | \(e\left(\frac{529}{1332}\right)\) | \(e\left(\frac{31}{111}\right)\) | \(e\left(\frac{95}{111}\right)\) | \(e\left(\frac{211}{1332}\right)\) | \(e\left(\frac{230}{333}\right)\) | \(e\left(\frac{275}{333}\right)\) | \(e\left(\frac{136}{333}\right)\) |
| \(\chi_{8046}(83,\cdot)\) | 8046.bi | 1332 | no | \(1\) | \(1\) | \(e\left(\frac{473}{666}\right)\) | \(e\left(\frac{601}{666}\right)\) | \(e\left(\frac{413}{1332}\right)\) | \(e\left(\frac{655}{1332}\right)\) | \(e\left(\frac{197}{222}\right)\) | \(e\left(\frac{53}{111}\right)\) | \(e\left(\frac{751}{1332}\right)\) | \(e\left(\frac{140}{333}\right)\) | \(e\left(\frac{523}{666}\right)\) | \(e\left(\frac{271}{333}\right)\) |
| \(\chi_{8046}(85,\cdot)\) | 8046.bc | 333 | no | \(1\) | \(1\) | \(e\left(\frac{257}{333}\right)\) | \(e\left(\frac{178}{333}\right)\) | \(e\left(\frac{121}{333}\right)\) | \(e\left(\frac{179}{333}\right)\) | \(e\left(\frac{77}{111}\right)\) | \(e\left(\frac{82}{111}\right)\) | \(e\left(\frac{191}{333}\right)\) | \(e\left(\frac{181}{333}\right)\) | \(e\left(\frac{325}{333}\right)\) | \(e\left(\frac{191}{333}\right)\) |
| \(\chi_{8046}(89,\cdot)\) | 8046.bd | 444 | no | \(1\) | \(1\) | \(e\left(\frac{101}{222}\right)\) | \(e\left(\frac{187}{222}\right)\) | \(e\left(\frac{359}{444}\right)\) | \(e\left(\frac{421}{444}\right)\) | \(e\left(\frac{15}{74}\right)\) | \(e\left(\frac{20}{37}\right)\) | \(e\left(\frac{97}{444}\right)\) | \(e\left(\frac{101}{111}\right)\) | \(e\left(\frac{145}{222}\right)\) | \(e\left(\frac{52}{111}\right)\) |
| \(\chi_{8046}(91,\cdot)\) | 8046.be | 444 | no | \(-1\) | \(1\) | \(e\left(\frac{77}{111}\right)\) | \(e\left(\frac{95}{222}\right)\) | \(e\left(\frac{421}{444}\right)\) | \(e\left(\frac{221}{444}\right)\) | \(e\left(\frac{14}{37}\right)\) | \(e\left(\frac{25}{37}\right)\) | \(e\left(\frac{371}{444}\right)\) | \(e\left(\frac{43}{111}\right)\) | \(e\left(\frac{49}{111}\right)\) | \(e\left(\frac{65}{111}\right)\) |
| \(\chi_{8046}(95,\cdot)\) | 8046.bf | 666 | no | \(-1\) | \(1\) | \(e\left(\frac{553}{666}\right)\) | \(e\left(\frac{163}{333}\right)\) | \(e\left(\frac{491}{666}\right)\) | \(e\left(\frac{293}{333}\right)\) | \(e\left(\frac{151}{222}\right)\) | \(e\left(\frac{4}{111}\right)\) | \(e\left(\frac{43}{666}\right)\) | \(e\left(\frac{220}{333}\right)\) | \(e\left(\frac{251}{666}\right)\) | \(e\left(\frac{188}{333}\right)\) |