sage: H = DirichletGroup(33327)
pari: g = idealstar(,33327,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 18216 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{6}\times C_{1518}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{33327}(25922,\cdot)$, $\chi_{33327}(9523,\cdot)$, $\chi_{33327}(10585,\cdot)$ |
First 32 of 18216 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 | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{33327}(1,\cdot)\) | 33327.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{33327}(2,\cdot)\) | 33327.fp | 1518 | yes | \(-1\) | \(1\) | \(e\left(\frac{1343}{1518}\right)\) | \(e\left(\frac{584}{759}\right)\) | \(e\left(\frac{453}{506}\right)\) | \(e\left(\frac{331}{506}\right)\) | \(e\left(\frac{592}{759}\right)\) | \(e\left(\frac{491}{506}\right)\) | \(e\left(\frac{328}{759}\right)\) | \(e\left(\frac{409}{759}\right)\) | \(e\left(\frac{449}{1518}\right)\) | \(e\left(\frac{683}{759}\right)\) |
\(\chi_{33327}(4,\cdot)\) | 33327.fa | 759 | yes | \(1\) | \(1\) | \(e\left(\frac{584}{759}\right)\) | \(e\left(\frac{409}{759}\right)\) | \(e\left(\frac{200}{253}\right)\) | \(e\left(\frac{78}{253}\right)\) | \(e\left(\frac{425}{759}\right)\) | \(e\left(\frac{238}{253}\right)\) | \(e\left(\frac{656}{759}\right)\) | \(e\left(\frac{59}{759}\right)\) | \(e\left(\frac{449}{759}\right)\) | \(e\left(\frac{607}{759}\right)\) |
\(\chi_{33327}(5,\cdot)\) | 33327.fe | 1518 | yes | \(-1\) | \(1\) | \(e\left(\frac{453}{506}\right)\) | \(e\left(\frac{200}{253}\right)\) | \(e\left(\frac{509}{1518}\right)\) | \(e\left(\frac{347}{506}\right)\) | \(e\left(\frac{175}{759}\right)\) | \(e\left(\frac{41}{759}\right)\) | \(e\left(\frac{823}{1518}\right)\) | \(e\left(\frac{147}{253}\right)\) | \(e\left(\frac{593}{1518}\right)\) | \(e\left(\frac{116}{759}\right)\) |
\(\chi_{33327}(8,\cdot)\) | 33327.er | 506 | no | \(-1\) | \(1\) | \(e\left(\frac{331}{506}\right)\) | \(e\left(\frac{78}{253}\right)\) | \(e\left(\frac{347}{506}\right)\) | \(e\left(\frac{487}{506}\right)\) | \(e\left(\frac{86}{253}\right)\) | \(e\left(\frac{461}{506}\right)\) | \(e\left(\frac{75}{253}\right)\) | \(e\left(\frac{156}{253}\right)\) | \(e\left(\frac{449}{506}\right)\) | \(e\left(\frac{177}{253}\right)\) |
\(\chi_{33327}(10,\cdot)\) | 33327.fi | 1518 | no | \(1\) | \(1\) | \(e\left(\frac{592}{759}\right)\) | \(e\left(\frac{425}{759}\right)\) | \(e\left(\frac{175}{759}\right)\) | \(e\left(\frac{86}{253}\right)\) | \(e\left(\frac{8}{759}\right)\) | \(e\left(\frac{37}{1518}\right)\) | \(e\left(\frac{493}{506}\right)\) | \(e\left(\frac{91}{759}\right)\) | \(e\left(\frac{521}{759}\right)\) | \(e\left(\frac{40}{759}\right)\) |
\(\chi_{33327}(11,\cdot)\) | 33327.fc | 1518 | yes | \(1\) | \(1\) | \(e\left(\frac{491}{506}\right)\) | \(e\left(\frac{238}{253}\right)\) | \(e\left(\frac{41}{759}\right)\) | \(e\left(\frac{461}{506}\right)\) | \(e\left(\frac{37}{1518}\right)\) | \(e\left(\frac{193}{759}\right)\) | \(e\left(\frac{706}{759}\right)\) | \(e\left(\frac{223}{253}\right)\) | \(e\left(\frac{683}{759}\right)\) | \(e\left(\frac{185}{1518}\right)\) |
\(\chi_{33327}(13,\cdot)\) | 33327.fk | 1518 | yes | \(-1\) | \(1\) | \(e\left(\frac{328}{759}\right)\) | \(e\left(\frac{656}{759}\right)\) | \(e\left(\frac{823}{1518}\right)\) | \(e\left(\frac{75}{253}\right)\) | \(e\left(\frac{493}{506}\right)\) | \(e\left(\frac{706}{759}\right)\) | \(e\left(\frac{775}{1518}\right)\) | \(e\left(\frac{553}{759}\right)\) | \(e\left(\frac{197}{506}\right)\) | \(e\left(\frac{441}{506}\right)\) |
\(\chi_{33327}(16,\cdot)\) | 33327.fa | 759 | yes | \(1\) | \(1\) | \(e\left(\frac{409}{759}\right)\) | \(e\left(\frac{59}{759}\right)\) | \(e\left(\frac{147}{253}\right)\) | \(e\left(\frac{156}{253}\right)\) | \(e\left(\frac{91}{759}\right)\) | \(e\left(\frac{223}{253}\right)\) | \(e\left(\frac{553}{759}\right)\) | \(e\left(\frac{118}{759}\right)\) | \(e\left(\frac{139}{759}\right)\) | \(e\left(\frac{455}{759}\right)\) |
\(\chi_{33327}(17,\cdot)\) | 33327.fv | 1518 | no | \(-1\) | \(1\) | \(e\left(\frac{449}{1518}\right)\) | \(e\left(\frac{449}{759}\right)\) | \(e\left(\frac{593}{1518}\right)\) | \(e\left(\frac{449}{506}\right)\) | \(e\left(\frac{521}{759}\right)\) | \(e\left(\frac{683}{759}\right)\) | \(e\left(\frac{197}{506}\right)\) | \(e\left(\frac{139}{759}\right)\) | \(e\left(\frac{499}{1518}\right)\) | \(e\left(\frac{328}{759}\right)\) |
\(\chi_{33327}(19,\cdot)\) | 33327.fi | 1518 | no | \(1\) | \(1\) | \(e\left(\frac{683}{759}\right)\) | \(e\left(\frac{607}{759}\right)\) | \(e\left(\frac{116}{759}\right)\) | \(e\left(\frac{177}{253}\right)\) | \(e\left(\frac{40}{759}\right)\) | \(e\left(\frac{185}{1518}\right)\) | \(e\left(\frac{441}{506}\right)\) | \(e\left(\frac{455}{759}\right)\) | \(e\left(\frac{328}{759}\right)\) | \(e\left(\frac{200}{759}\right)\) |
\(\chi_{33327}(20,\cdot)\) | 33327.fx | 1518 | yes | \(-1\) | \(1\) | \(e\left(\frac{1009}{1518}\right)\) | \(e\left(\frac{250}{759}\right)\) | \(e\left(\frac{191}{1518}\right)\) | \(e\left(\frac{503}{506}\right)\) | \(e\left(\frac{200}{253}\right)\) | \(e\left(\frac{755}{759}\right)\) | \(e\left(\frac{617}{1518}\right)\) | \(e\left(\frac{500}{759}\right)\) | \(e\left(\frac{497}{506}\right)\) | \(e\left(\frac{241}{253}\right)\) |
\(\chi_{33327}(22,\cdot)\) | 33327.eg | 138 | no | \(-1\) | \(1\) | \(e\left(\frac{59}{69}\right)\) | \(e\left(\frac{49}{69}\right)\) | \(e\left(\frac{131}{138}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{37}{46}\right)\) | \(e\left(\frac{31}{138}\right)\) | \(e\left(\frac{25}{69}\right)\) | \(e\left(\frac{29}{69}\right)\) | \(e\left(\frac{9}{46}\right)\) | \(e\left(\frac{1}{46}\right)\) |
\(\chi_{33327}(25,\cdot)\) | 33327.fb | 759 | yes | \(1\) | \(1\) | \(e\left(\frac{200}{253}\right)\) | \(e\left(\frac{147}{253}\right)\) | \(e\left(\frac{509}{759}\right)\) | \(e\left(\frac{94}{253}\right)\) | \(e\left(\frac{350}{759}\right)\) | \(e\left(\frac{82}{759}\right)\) | \(e\left(\frac{64}{759}\right)\) | \(e\left(\frac{41}{253}\right)\) | \(e\left(\frac{593}{759}\right)\) | \(e\left(\frac{232}{759}\right)\) |
\(\chi_{33327}(26,\cdot)\) | 33327.fu | 1518 | no | \(1\) | \(1\) | \(e\left(\frac{481}{1518}\right)\) | \(e\left(\frac{481}{759}\right)\) | \(e\left(\frac{332}{759}\right)\) | \(e\left(\frac{481}{506}\right)\) | \(e\left(\frac{1145}{1518}\right)\) | \(e\left(\frac{1367}{1518}\right)\) | \(e\left(\frac{477}{506}\right)\) | \(e\left(\frac{203}{759}\right)\) | \(e\left(\frac{520}{759}\right)\) | \(e\left(\frac{1171}{1518}\right)\) |
\(\chi_{33327}(29,\cdot)\) | 33327.fy | 1518 | no | \(-1\) | \(1\) | \(e\left(\frac{691}{1518}\right)\) | \(e\left(\frac{691}{759}\right)\) | \(e\left(\frac{197}{1518}\right)\) | \(e\left(\frac{185}{506}\right)\) | \(e\left(\frac{148}{253}\right)\) | \(e\left(\frac{409}{1518}\right)\) | \(e\left(\frac{499}{759}\right)\) | \(e\left(\frac{623}{759}\right)\) | \(e\left(\frac{49}{506}\right)\) | \(e\left(\frac{234}{253}\right)\) |
\(\chi_{33327}(31,\cdot)\) | 33327.fh | 1518 | yes | \(-1\) | \(1\) | \(e\left(\frac{194}{759}\right)\) | \(e\left(\frac{388}{759}\right)\) | \(e\left(\frac{171}{506}\right)\) | \(e\left(\frac{194}{253}\right)\) | \(e\left(\frac{901}{1518}\right)\) | \(e\left(\frac{60}{253}\right)\) | \(e\left(\frac{571}{1518}\right)\) | \(e\left(\frac{17}{759}\right)\) | \(e\left(\frac{709}{1518}\right)\) | \(e\left(\frac{1469}{1518}\right)\) |
\(\chi_{33327}(32,\cdot)\) | 33327.fp | 1518 | yes | \(-1\) | \(1\) | \(e\left(\frac{643}{1518}\right)\) | \(e\left(\frac{643}{759}\right)\) | \(e\left(\frac{241}{506}\right)\) | \(e\left(\frac{137}{506}\right)\) | \(e\left(\frac{683}{759}\right)\) | \(e\left(\frac{431}{506}\right)\) | \(e\left(\frac{122}{759}\right)\) | \(e\left(\frac{527}{759}\right)\) | \(e\left(\frac{727}{1518}\right)\) | \(e\left(\frac{379}{759}\right)\) |
\(\chi_{33327}(34,\cdot)\) | 33327.fj | 1518 | yes | \(1\) | \(1\) | \(e\left(\frac{137}{759}\right)\) | \(e\left(\frac{274}{759}\right)\) | \(e\left(\frac{217}{759}\right)\) | \(e\left(\frac{137}{253}\right)\) | \(e\left(\frac{118}{253}\right)\) | \(e\left(\frac{1321}{1518}\right)\) | \(e\left(\frac{1247}{1518}\right)\) | \(e\left(\frac{548}{759}\right)\) | \(e\left(\frac{158}{253}\right)\) | \(e\left(\frac{84}{253}\right)\) |
\(\chi_{33327}(37,\cdot)\) | 33327.fn | 1518 | no | \(-1\) | \(1\) | \(e\left(\frac{74}{759}\right)\) | \(e\left(\frac{148}{759}\right)\) | \(e\left(\frac{613}{1518}\right)\) | \(e\left(\frac{74}{253}\right)\) | \(e\left(\frac{761}{1518}\right)\) | \(e\left(\frac{479}{1518}\right)\) | \(e\left(\frac{15}{253}\right)\) | \(e\left(\frac{296}{759}\right)\) | \(e\left(\frac{1079}{1518}\right)\) | \(e\left(\frac{769}{1518}\right)\) |
\(\chi_{33327}(38,\cdot)\) | 33327.fe | 1518 | yes | \(-1\) | \(1\) | \(e\left(\frac{397}{506}\right)\) | \(e\left(\frac{144}{253}\right)\) | \(e\left(\frac{73}{1518}\right)\) | \(e\left(\frac{179}{506}\right)\) | \(e\left(\frac{632}{759}\right)\) | \(e\left(\frac{70}{759}\right)\) | \(e\left(\frac{461}{1518}\right)\) | \(e\left(\frac{35}{253}\right)\) | \(e\left(\frac{1105}{1518}\right)\) | \(e\left(\frac{124}{759}\right)\) |
\(\chi_{33327}(40,\cdot)\) | 33327.gb | 1518 | yes | \(1\) | \(1\) | \(e\left(\frac{139}{253}\right)\) | \(e\left(\frac{25}{253}\right)\) | \(e\left(\frac{16}{759}\right)\) | \(e\left(\frac{164}{253}\right)\) | \(e\left(\frac{433}{759}\right)\) | \(e\left(\frac{1465}{1518}\right)\) | \(e\left(\frac{1273}{1518}\right)\) | \(e\left(\frac{50}{253}\right)\) | \(e\left(\frac{211}{759}\right)\) | \(e\left(\frac{647}{759}\right)\) |
\(\chi_{33327}(41,\cdot)\) | 33327.fs | 1518 | yes | \(1\) | \(1\) | \(e\left(\frac{1271}{1518}\right)\) | \(e\left(\frac{512}{759}\right)\) | \(e\left(\frac{62}{759}\right)\) | \(e\left(\frac{259}{506}\right)\) | \(e\left(\frac{465}{506}\right)\) | \(e\left(\frac{269}{1518}\right)\) | \(e\left(\frac{31}{1518}\right)\) | \(e\left(\frac{265}{759}\right)\) | \(e\left(\frac{9}{253}\right)\) | \(e\left(\frac{301}{506}\right)\) |
\(\chi_{33327}(43,\cdot)\) | 33327.fl | 1518 | no | \(-1\) | \(1\) | \(e\left(\frac{257}{759}\right)\) | \(e\left(\frac{514}{759}\right)\) | \(e\left(\frac{587}{1518}\right)\) | \(e\left(\frac{4}{253}\right)\) | \(e\left(\frac{367}{506}\right)\) | \(e\left(\frac{949}{1518}\right)\) | \(e\left(\frac{358}{759}\right)\) | \(e\left(\frac{269}{759}\right)\) | \(e\left(\frac{277}{506}\right)\) | \(e\left(\frac{317}{506}\right)\) |
\(\chi_{33327}(44,\cdot)\) | 33327.ft | 1518 | no | \(1\) | \(1\) | \(e\left(\frac{1123}{1518}\right)\) | \(e\left(\frac{364}{759}\right)\) | \(e\left(\frac{641}{759}\right)\) | \(e\left(\frac{111}{506}\right)\) | \(e\left(\frac{887}{1518}\right)\) | \(e\left(\frac{148}{759}\right)\) | \(e\left(\frac{201}{253}\right)\) | \(e\left(\frac{728}{759}\right)\) | \(e\left(\frac{373}{759}\right)\) | \(e\left(\frac{1399}{1518}\right)\) |
\(\chi_{33327}(47,\cdot)\) | 33327.ds | 138 | yes | \(1\) | \(1\) | \(e\left(\frac{109}{138}\right)\) | \(e\left(\frac{40}{69}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{17}{46}\right)\) | \(e\left(\frac{31}{138}\right)\) | \(e\left(\frac{33}{46}\right)\) | \(e\left(\frac{61}{138}\right)\) | \(e\left(\frac{11}{69}\right)\) | \(e\left(\frac{65}{69}\right)\) | \(e\left(\frac{17}{138}\right)\) |
\(\chi_{33327}(50,\cdot)\) | 33327.fy | 1518 | no | \(-1\) | \(1\) | \(e\left(\frac{1025}{1518}\right)\) | \(e\left(\frac{266}{759}\right)\) | \(e\left(\frac{859}{1518}\right)\) | \(e\left(\frac{13}{506}\right)\) | \(e\left(\frac{61}{253}\right)\) | \(e\left(\frac{119}{1518}\right)\) | \(e\left(\frac{392}{759}\right)\) | \(e\left(\frac{532}{759}\right)\) | \(e\left(\frac{39}{506}\right)\) | \(e\left(\frac{52}{253}\right)\) |
\(\chi_{33327}(52,\cdot)\) | 33327.gc | 1518 | yes | \(-1\) | \(1\) | \(e\left(\frac{51}{253}\right)\) | \(e\left(\frac{102}{253}\right)\) | \(e\left(\frac{505}{1518}\right)\) | \(e\left(\frac{153}{253}\right)\) | \(e\left(\frac{811}{1518}\right)\) | \(e\left(\frac{661}{759}\right)\) | \(e\left(\frac{569}{1518}\right)\) | \(e\left(\frac{204}{253}\right)\) | \(e\left(\frac{1489}{1518}\right)\) | \(e\left(\frac{1019}{1518}\right)\) |
\(\chi_{33327}(53,\cdot)\) | 33327.ft | 1518 | no | \(1\) | \(1\) | \(e\left(\frac{587}{1518}\right)\) | \(e\left(\frac{587}{759}\right)\) | \(e\left(\frac{331}{759}\right)\) | \(e\left(\frac{81}{506}\right)\) | \(e\left(\frac{1249}{1518}\right)\) | \(e\left(\frac{614}{759}\right)\) | \(e\left(\frac{133}{253}\right)\) | \(e\left(\frac{415}{759}\right)\) | \(e\left(\frac{491}{759}\right)\) | \(e\left(\frac{173}{1518}\right)\) |
\(\chi_{33327}(55,\cdot)\) | 33327.ew | 506 | no | \(-1\) | \(1\) | \(e\left(\frac{219}{253}\right)\) | \(e\left(\frac{185}{253}\right)\) | \(e\left(\frac{197}{506}\right)\) | \(e\left(\frac{151}{253}\right)\) | \(e\left(\frac{129}{506}\right)\) | \(e\left(\frac{78}{253}\right)\) | \(e\left(\frac{239}{506}\right)\) | \(e\left(\frac{117}{253}\right)\) | \(e\left(\frac{147}{506}\right)\) | \(e\left(\frac{139}{506}\right)\) |
\(\chi_{33327}(58,\cdot)\) | 33327.fb | 759 | yes | \(1\) | \(1\) | \(e\left(\frac{86}{253}\right)\) | \(e\left(\frac{172}{253}\right)\) | \(e\left(\frac{19}{759}\right)\) | \(e\left(\frac{5}{253}\right)\) | \(e\left(\frac{277}{759}\right)\) | \(e\left(\frac{182}{759}\right)\) | \(e\left(\frac{68}{759}\right)\) | \(e\left(\frac{91}{253}\right)\) | \(e\left(\frac{298}{759}\right)\) | \(e\left(\frac{626}{759}\right)\) |
\(\chi_{33327}(59,\cdot)\) | 33327.fz | 1518 | yes | \(1\) | \(1\) | \(e\left(\frac{865}{1518}\right)\) | \(e\left(\frac{106}{759}\right)\) | \(e\left(\frac{84}{253}\right)\) | \(e\left(\frac{359}{506}\right)\) | \(e\left(\frac{1369}{1518}\right)\) | \(e\left(\frac{291}{506}\right)\) | \(e\left(\frac{379}{1518}\right)\) | \(e\left(\frac{212}{759}\right)\) | \(e\left(\frac{224}{759}\right)\) | \(e\left(\frac{773}{1518}\right)\) |