sage: H = DirichletGroup(7406)
pari: g = idealstar(,7406,2)
Character group
| sage: G.order()
pari: g.no
| ||
| Order | = | 3036 |
| sage: H.invariants()
pari: g.cyc
| ||
| Structure | = | \(C_{2}\times C_{1518}\) |
| sage: H.gens()
pari: g.gen
| ||
| Generators | = | $\chi_{7406}(2117,\cdot)$, $\chi_{7406}(3179,\cdot)$ |
First 32 of 3036 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 | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(25\) | \(27\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{7406}(1,\cdot)\) | 7406.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(\chi_{7406}(3,\cdot)\) | 7406.bf | 1518 | no | \(-1\) | \(1\) | \(e\left(\frac{1021}{1518}\right)\) | \(e\left(\frac{1313}{1518}\right)\) | \(e\left(\frac{262}{759}\right)\) | \(e\left(\frac{656}{759}\right)\) | \(e\left(\frac{257}{506}\right)\) | \(e\left(\frac{136}{253}\right)\) | \(e\left(\frac{127}{1518}\right)\) | \(e\left(\frac{929}{1518}\right)\) | \(e\left(\frac{554}{759}\right)\) | \(e\left(\frac{9}{506}\right)\) |
| \(\chi_{7406}(5,\cdot)\) | 7406.be | 1518 | no | \(1\) | \(1\) | \(e\left(\frac{1313}{1518}\right)\) | \(e\left(\frac{128}{759}\right)\) | \(e\left(\frac{554}{759}\right)\) | \(e\left(\frac{335}{1518}\right)\) | \(e\left(\frac{443}{506}\right)\) | \(e\left(\frac{17}{506}\right)\) | \(e\left(\frac{676}{759}\right)\) | \(e\left(\frac{116}{759}\right)\) | \(e\left(\frac{256}{759}\right)\) | \(e\left(\frac{301}{506}\right)\) |
| \(\chi_{7406}(9,\cdot)\) | 7406.bc | 759 | no | \(1\) | \(1\) | \(e\left(\frac{262}{759}\right)\) | \(e\left(\frac{554}{759}\right)\) | \(e\left(\frac{524}{759}\right)\) | \(e\left(\frac{553}{759}\right)\) | \(e\left(\frac{4}{253}\right)\) | \(e\left(\frac{19}{253}\right)\) | \(e\left(\frac{127}{759}\right)\) | \(e\left(\frac{170}{759}\right)\) | \(e\left(\frac{349}{759}\right)\) | \(e\left(\frac{9}{253}\right)\) |
| \(\chi_{7406}(11,\cdot)\) | 7406.bd | 1518 | no | \(-1\) | \(1\) | \(e\left(\frac{656}{759}\right)\) | \(e\left(\frac{335}{1518}\right)\) | \(e\left(\frac{553}{759}\right)\) | \(e\left(\frac{133}{1518}\right)\) | \(e\left(\frac{151}{253}\right)\) | \(e\left(\frac{43}{506}\right)\) | \(e\left(\frac{607}{1518}\right)\) | \(e\left(\frac{185}{1518}\right)\) | \(e\left(\frac{335}{759}\right)\) | \(e\left(\frac{150}{253}\right)\) |
| \(\chi_{7406}(13,\cdot)\) | 7406.z | 506 | no | \(-1\) | \(1\) | \(e\left(\frac{257}{506}\right)\) | \(e\left(\frac{443}{506}\right)\) | \(e\left(\frac{4}{253}\right)\) | \(e\left(\frac{151}{253}\right)\) | \(e\left(\frac{427}{506}\right)\) | \(e\left(\frac{97}{253}\right)\) | \(e\left(\frac{197}{506}\right)\) | \(e\left(\frac{441}{506}\right)\) | \(e\left(\frac{190}{253}\right)\) | \(e\left(\frac{265}{506}\right)\) |
| \(\chi_{7406}(15,\cdot)\) | 7406.bb | 506 | no | \(-1\) | \(1\) | \(e\left(\frac{136}{253}\right)\) | \(e\left(\frac{17}{506}\right)\) | \(e\left(\frac{19}{253}\right)\) | \(e\left(\frac{43}{506}\right)\) | \(e\left(\frac{97}{253}\right)\) | \(e\left(\frac{289}{506}\right)\) | \(e\left(\frac{493}{506}\right)\) | \(e\left(\frac{387}{506}\right)\) | \(e\left(\frac{17}{253}\right)\) | \(e\left(\frac{155}{253}\right)\) |
| \(\chi_{7406}(17,\cdot)\) | 7406.be | 1518 | no | \(1\) | \(1\) | \(e\left(\frac{127}{1518}\right)\) | \(e\left(\frac{676}{759}\right)\) | \(e\left(\frac{127}{759}\right)\) | \(e\left(\frac{607}{1518}\right)\) | \(e\left(\frac{197}{506}\right)\) | \(e\left(\frac{493}{506}\right)\) | \(e\left(\frac{629}{759}\right)\) | \(e\left(\frac{328}{759}\right)\) | \(e\left(\frac{593}{759}\right)\) | \(e\left(\frac{127}{506}\right)\) |
| \(\chi_{7406}(19,\cdot)\) | 7406.be | 1518 | no | \(1\) | \(1\) | \(e\left(\frac{929}{1518}\right)\) | \(e\left(\frac{116}{759}\right)\) | \(e\left(\frac{170}{759}\right)\) | \(e\left(\frac{185}{1518}\right)\) | \(e\left(\frac{441}{506}\right)\) | \(e\left(\frac{387}{506}\right)\) | \(e\left(\frac{328}{759}\right)\) | \(e\left(\frac{200}{759}\right)\) | \(e\left(\frac{232}{759}\right)\) | \(e\left(\frac{423}{506}\right)\) |
| \(\chi_{7406}(25,\cdot)\) | 7406.bc | 759 | no | \(1\) | \(1\) | \(e\left(\frac{554}{759}\right)\) | \(e\left(\frac{256}{759}\right)\) | \(e\left(\frac{349}{759}\right)\) | \(e\left(\frac{335}{759}\right)\) | \(e\left(\frac{190}{253}\right)\) | \(e\left(\frac{17}{253}\right)\) | \(e\left(\frac{593}{759}\right)\) | \(e\left(\frac{232}{759}\right)\) | \(e\left(\frac{512}{759}\right)\) | \(e\left(\frac{48}{253}\right)\) |
| \(\chi_{7406}(27,\cdot)\) | 7406.z | 506 | no | \(-1\) | \(1\) | \(e\left(\frac{9}{506}\right)\) | \(e\left(\frac{301}{506}\right)\) | \(e\left(\frac{9}{253}\right)\) | \(e\left(\frac{150}{253}\right)\) | \(e\left(\frac{265}{506}\right)\) | \(e\left(\frac{155}{253}\right)\) | \(e\left(\frac{127}{506}\right)\) | \(e\left(\frac{423}{506}\right)\) | \(e\left(\frac{48}{253}\right)\) | \(e\left(\frac{27}{506}\right)\) |
| \(\chi_{7406}(29,\cdot)\) | 7406.y | 253 | no | \(1\) | \(1\) | \(e\left(\frac{188}{253}\right)\) | \(e\left(\frac{75}{253}\right)\) | \(e\left(\frac{123}{253}\right)\) | \(e\left(\frac{26}{253}\right)\) | \(e\left(\frac{82}{253}\right)\) | \(e\left(\frac{10}{253}\right)\) | \(e\left(\frac{151}{253}\right)\) | \(e\left(\frac{234}{253}\right)\) | \(e\left(\frac{150}{253}\right)\) | \(e\left(\frac{58}{253}\right)\) |
| \(\chi_{7406}(31,\cdot)\) | 7406.bf | 1518 | no | \(-1\) | \(1\) | \(e\left(\frac{871}{1518}\right)\) | \(e\left(\frac{1019}{1518}\right)\) | \(e\left(\frac{112}{759}\right)\) | \(e\left(\frac{686}{759}\right)\) | \(e\left(\frac{359}{506}\right)\) | \(e\left(\frac{62}{253}\right)\) | \(e\left(\frac{709}{1518}\right)\) | \(e\left(\frac{1469}{1518}\right)\) | \(e\left(\frac{260}{759}\right)\) | \(e\left(\frac{365}{506}\right)\) |
| \(\chi_{7406}(33,\cdot)\) | 7406.be | 1518 | no | \(1\) | \(1\) | \(e\left(\frac{815}{1518}\right)\) | \(e\left(\frac{65}{759}\right)\) | \(e\left(\frac{56}{759}\right)\) | \(e\left(\frac{1445}{1518}\right)\) | \(e\left(\frac{53}{506}\right)\) | \(e\left(\frac{315}{506}\right)\) | \(e\left(\frac{367}{759}\right)\) | \(e\left(\frac{557}{759}\right)\) | \(e\left(\frac{130}{759}\right)\) | \(e\left(\frac{309}{506}\right)\) |
| \(\chi_{7406}(37,\cdot)\) | 7406.bd | 1518 | no | \(-1\) | \(1\) | \(e\left(\frac{97}{759}\right)\) | \(e\left(\frac{613}{1518}\right)\) | \(e\left(\frac{194}{759}\right)\) | \(e\left(\frac{479}{1518}\right)\) | \(e\left(\frac{15}{253}\right)\) | \(e\left(\frac{269}{506}\right)\) | \(e\left(\frac{1079}{1518}\right)\) | \(e\left(\frac{769}{1518}\right)\) | \(e\left(\frac{613}{759}\right)\) | \(e\left(\frac{97}{253}\right)\) |
| \(\chi_{7406}(39,\cdot)\) | 7406.bc | 759 | no | \(1\) | \(1\) | \(e\left(\frac{137}{759}\right)\) | \(e\left(\frac{562}{759}\right)\) | \(e\left(\frac{274}{759}\right)\) | \(e\left(\frac{350}{759}\right)\) | \(e\left(\frac{89}{253}\right)\) | \(e\left(\frac{233}{253}\right)\) | \(e\left(\frac{359}{759}\right)\) | \(e\left(\frac{367}{759}\right)\) | \(e\left(\frac{365}{759}\right)\) | \(e\left(\frac{137}{253}\right)\) |
| \(\chi_{7406}(41,\cdot)\) | 7406.z | 506 | no | \(-1\) | \(1\) | \(e\left(\frac{71}{506}\right)\) | \(e\left(\frac{463}{506}\right)\) | \(e\left(\frac{71}{253}\right)\) | \(e\left(\frac{87}{253}\right)\) | \(e\left(\frac{179}{506}\right)\) | \(e\left(\frac{14}{253}\right)\) | \(e\left(\frac{271}{506}\right)\) | \(e\left(\frac{301}{506}\right)\) | \(e\left(\frac{210}{253}\right)\) | \(e\left(\frac{213}{506}\right)\) |
| \(\chi_{7406}(43,\cdot)\) | 7406.bb | 506 | no | \(-1\) | \(1\) | \(e\left(\frac{216}{253}\right)\) | \(e\left(\frac{27}{506}\right)\) | \(e\left(\frac{179}{253}\right)\) | \(e\left(\frac{485}{506}\right)\) | \(e\left(\frac{35}{253}\right)\) | \(e\left(\frac{459}{506}\right)\) | \(e\left(\frac{277}{506}\right)\) | \(e\left(\frac{317}{506}\right)\) | \(e\left(\frac{27}{253}\right)\) | \(e\left(\frac{142}{253}\right)\) |
| \(\chi_{7406}(45,\cdot)\) | 7406.w | 138 | no | \(1\) | \(1\) | \(e\left(\frac{29}{138}\right)\) | \(e\left(\frac{62}{69}\right)\) | \(e\left(\frac{29}{69}\right)\) | \(e\left(\frac{131}{138}\right)\) | \(e\left(\frac{41}{46}\right)\) | \(e\left(\frac{5}{46}\right)\) | \(e\left(\frac{4}{69}\right)\) | \(e\left(\frac{26}{69}\right)\) | \(e\left(\frac{55}{69}\right)\) | \(e\left(\frac{29}{46}\right)\) |
| \(\chi_{7406}(47,\cdot)\) | 7406.v | 138 | no | \(-1\) | \(1\) | \(e\left(\frac{109}{138}\right)\) | \(e\left(\frac{83}{138}\right)\) | \(e\left(\frac{40}{69}\right)\) | \(e\left(\frac{38}{69}\right)\) | \(e\left(\frac{5}{46}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{61}{138}\right)\) | \(e\left(\frac{17}{138}\right)\) | \(e\left(\frac{14}{69}\right)\) | \(e\left(\frac{17}{46}\right)\) |
| \(\chi_{7406}(51,\cdot)\) | 7406.bd | 1518 | no | \(-1\) | \(1\) | \(e\left(\frac{574}{759}\right)\) | \(e\left(\frac{1147}{1518}\right)\) | \(e\left(\frac{389}{759}\right)\) | \(e\left(\frac{401}{1518}\right)\) | \(e\left(\frac{227}{253}\right)\) | \(e\left(\frac{259}{506}\right)\) | \(e\left(\frac{1385}{1518}\right)\) | \(e\left(\frac{67}{1518}\right)\) | \(e\left(\frac{388}{759}\right)\) | \(e\left(\frac{68}{253}\right)\) |
| \(\chi_{7406}(53,\cdot)\) | 7406.bd | 1518 | no | \(-1\) | \(1\) | \(e\left(\frac{236}{759}\right)\) | \(e\left(\frac{1421}{1518}\right)\) | \(e\left(\frac{472}{759}\right)\) | \(e\left(\frac{469}{1518}\right)\) | \(e\left(\frac{133}{253}\right)\) | \(e\left(\frac{125}{506}\right)\) | \(e\left(\frac{223}{1518}\right)\) | \(e\left(\frac{173}{1518}\right)\) | \(e\left(\frac{662}{759}\right)\) | \(e\left(\frac{236}{253}\right)\) |
| \(\chi_{7406}(55,\cdot)\) | 7406.z | 506 | no | \(-1\) | \(1\) | \(e\left(\frac{369}{506}\right)\) | \(e\left(\frac{197}{506}\right)\) | \(e\left(\frac{116}{253}\right)\) | \(e\left(\frac{78}{253}\right)\) | \(e\left(\frac{239}{506}\right)\) | \(e\left(\frac{30}{253}\right)\) | \(e\left(\frac{147}{506}\right)\) | \(e\left(\frac{139}{506}\right)\) | \(e\left(\frac{197}{253}\right)\) | \(e\left(\frac{95}{506}\right)\) |
| \(\chi_{7406}(57,\cdot)\) | 7406.bb | 506 | no | \(-1\) | \(1\) | \(e\left(\frac{72}{253}\right)\) | \(e\left(\frac{9}{506}\right)\) | \(e\left(\frac{144}{253}\right)\) | \(e\left(\frac{499}{506}\right)\) | \(e\left(\frac{96}{253}\right)\) | \(e\left(\frac{153}{506}\right)\) | \(e\left(\frac{261}{506}\right)\) | \(e\left(\frac{443}{506}\right)\) | \(e\left(\frac{9}{253}\right)\) | \(e\left(\frac{216}{253}\right)\) |
| \(\chi_{7406}(59,\cdot)\) | 7406.bf | 1518 | no | \(-1\) | \(1\) | \(e\left(\frac{727}{1518}\right)\) | \(e\left(\frac{251}{1518}\right)\) | \(e\left(\frac{727}{759}\right)\) | \(e\left(\frac{563}{759}\right)\) | \(e\left(\frac{295}{506}\right)\) | \(e\left(\frac{163}{253}\right)\) | \(e\left(\frac{1207}{1518}\right)\) | \(e\left(\frac{773}{1518}\right)\) | \(e\left(\frac{251}{759}\right)\) | \(e\left(\frac{221}{506}\right)\) |
| \(\chi_{7406}(61,\cdot)\) | 7406.be | 1518 | no | \(1\) | \(1\) | \(e\left(\frac{761}{1518}\right)\) | \(e\left(\frac{680}{759}\right)\) | \(e\left(\frac{2}{759}\right)\) | \(e\left(\frac{1163}{1518}\right)\) | \(e\left(\frac{29}{506}\right)\) | \(e\left(\frac{201}{506}\right)\) | \(e\left(\frac{745}{759}\right)\) | \(e\left(\frac{47}{759}\right)\) | \(e\left(\frac{601}{759}\right)\) | \(e\left(\frac{255}{506}\right)\) |
| \(\chi_{7406}(65,\cdot)\) | 7406.bd | 1518 | no | \(-1\) | \(1\) | \(e\left(\frac{283}{759}\right)\) | \(e\left(\frac{67}{1518}\right)\) | \(e\left(\frac{566}{759}\right)\) | \(e\left(\frac{1241}{1518}\right)\) | \(e\left(\frac{182}{253}\right)\) | \(e\left(\frac{211}{506}\right)\) | \(e\left(\frac{425}{1518}\right)\) | \(e\left(\frac{37}{1518}\right)\) | \(e\left(\frac{67}{759}\right)\) | \(e\left(\frac{30}{253}\right)\) |
| \(\chi_{7406}(67,\cdot)\) | 7406.bd | 1518 | no | \(-1\) | \(1\) | \(e\left(\frac{587}{759}\right)\) | \(e\left(\frac{611}{1518}\right)\) | \(e\left(\frac{415}{759}\right)\) | \(e\left(\frac{1099}{1518}\right)\) | \(e\left(\frac{36}{253}\right)\) | \(e\left(\frac{89}{506}\right)\) | \(e\left(\frac{1021}{1518}\right)\) | \(e\left(\frac{1289}{1518}\right)\) | \(e\left(\frac{611}{759}\right)\) | \(e\left(\frac{81}{253}\right)\) |
| \(\chi_{7406}(71,\cdot)\) | 7406.y | 253 | no | \(1\) | \(1\) | \(e\left(\frac{137}{253}\right)\) | \(e\left(\frac{56}{253}\right)\) | \(e\left(\frac{21}{253}\right)\) | \(e\left(\frac{97}{253}\right)\) | \(e\left(\frac{14}{253}\right)\) | \(e\left(\frac{193}{253}\right)\) | \(e\left(\frac{106}{253}\right)\) | \(e\left(\frac{114}{253}\right)\) | \(e\left(\frac{112}{253}\right)\) | \(e\left(\frac{158}{253}\right)\) |
| \(\chi_{7406}(73,\cdot)\) | 7406.bf | 1518 | no | \(-1\) | \(1\) | \(e\left(\frac{643}{1518}\right)\) | \(e\left(\frac{815}{1518}\right)\) | \(e\left(\frac{643}{759}\right)\) | \(e\left(\frac{428}{759}\right)\) | \(e\left(\frac{89}{506}\right)\) | \(e\left(\frac{243}{253}\right)\) | \(e\left(\frac{865}{1518}\right)\) | \(e\left(\frac{1379}{1518}\right)\) | \(e\left(\frac{56}{759}\right)\) | \(e\left(\frac{137}{506}\right)\) |
| \(\chi_{7406}(75,\cdot)\) | 7406.bf | 1518 | no | \(-1\) | \(1\) | \(e\left(\frac{611}{1518}\right)\) | \(e\left(\frac{307}{1518}\right)\) | \(e\left(\frac{611}{759}\right)\) | \(e\left(\frac{232}{759}\right)\) | \(e\left(\frac{131}{506}\right)\) | \(e\left(\frac{153}{253}\right)\) | \(e\left(\frac{1313}{1518}\right)\) | \(e\left(\frac{1393}{1518}\right)\) | \(e\left(\frac{307}{759}\right)\) | \(e\left(\frac{105}{506}\right)\) |
| \(\chi_{7406}(79,\cdot)\) | 7406.bd | 1518 | no | \(-1\) | \(1\) | \(e\left(\frac{556}{759}\right)\) | \(e\left(\frac{955}{1518}\right)\) | \(e\left(\frac{353}{759}\right)\) | \(e\left(\frac{719}{1518}\right)\) | \(e\left(\frac{219}{253}\right)\) | \(e\left(\frac{183}{506}\right)\) | \(e\left(\frac{371}{1518}\right)\) | \(e\left(\frac{1411}{1518}\right)\) | \(e\left(\frac{196}{759}\right)\) | \(e\left(\frac{50}{253}\right)\) |