from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(33327, base_ring=CyclotomicField(1518))
M = H._module
chi = DirichletCharacter(H, M([759,1265,1170]))
chi.galois_orbit()
[g,chi] = znchar(Mod(26,33327))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(33327\) | |
| Conductor: | \(11109\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1518\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 11109.cj | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Related number fields
| Field of values: | $\Q(\zeta_{759})$ |
| Fixed field: | Number field defined by a degree 1518 polynomial (not computed) |
First 20 of 440 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{33327}(26,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{481}{1518}\right)\) | \(e\left(\frac{481}{759}\right)\) | \(e\left(\frac{332}{759}\right)\) | \(e\left(\frac{481}{506}\right)\) | \(e\left(\frac{1145}{1518}\right)\) | \(e\left(\frac{1367}{1518}\right)\) | \(e\left(\frac{477}{506}\right)\) | \(e\left(\frac{203}{759}\right)\) | \(e\left(\frac{520}{759}\right)\) | \(e\left(\frac{1171}{1518}\right)\) |
| \(\chi_{33327}(215,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{355}{1518}\right)\) | \(e\left(\frac{355}{759}\right)\) | \(e\left(\frac{548}{759}\right)\) | \(e\left(\frac{355}{506}\right)\) | \(e\left(\frac{1451}{1518}\right)\) | \(e\left(\frac{1031}{1518}\right)\) | \(e\left(\frac{7}{506}\right)\) | \(e\left(\frac{710}{759}\right)\) | \(e\left(\frac{712}{759}\right)\) | \(e\left(\frac{1183}{1518}\right)\) |
| \(\chi_{33327}(269,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{653}{1518}\right)\) | \(e\left(\frac{653}{759}\right)\) | \(e\left(\frac{1}{759}\right)\) | \(e\left(\frac{147}{506}\right)\) | \(e\left(\frac{655}{1518}\right)\) | \(e\left(\frac{139}{1518}\right)\) | \(e\left(\frac{211}{506}\right)\) | \(e\left(\frac{547}{759}\right)\) | \(e\left(\frac{29}{759}\right)\) | \(e\left(\frac{239}{1518}\right)\) |
| \(\chi_{33327}(278,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{133}{1518}\right)\) | \(e\left(\frac{133}{759}\right)\) | \(e\left(\frac{278}{759}\right)\) | \(e\left(\frac{133}{506}\right)\) | \(e\left(\frac{689}{1518}\right)\) | \(e\left(\frac{1451}{1518}\right)\) | \(e\left(\frac{215}{506}\right)\) | \(e\left(\frac{266}{759}\right)\) | \(e\left(\frac{472}{759}\right)\) | \(e\left(\frac{409}{1518}\right)\) |
| \(\chi_{33327}(395,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1091}{1518}\right)\) | \(e\left(\frac{332}{759}\right)\) | \(e\left(\frac{226}{759}\right)\) | \(e\left(\frac{79}{506}\right)\) | \(e\left(\frac{25}{1518}\right)\) | \(e\left(\frac{295}{1518}\right)\) | \(e\left(\frac{375}{506}\right)\) | \(e\left(\frac{664}{759}\right)\) | \(e\left(\frac{482}{759}\right)\) | \(e\left(\frac{125}{1518}\right)\) |
| \(\chi_{33327}(404,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{535}{1518}\right)\) | \(e\left(\frac{535}{759}\right)\) | \(e\left(\frac{131}{759}\right)\) | \(e\left(\frac{29}{506}\right)\) | \(e\left(\frac{797}{1518}\right)\) | \(e\left(\frac{1511}{1518}\right)\) | \(e\left(\frac{317}{506}\right)\) | \(e\left(\frac{311}{759}\right)\) | \(e\left(\frac{4}{759}\right)\) | \(e\left(\frac{949}{1518}\right)\) |
| \(\chi_{33327}(584,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1061}{1518}\right)\) | \(e\left(\frac{302}{759}\right)\) | \(e\left(\frac{169}{759}\right)\) | \(e\left(\frac{49}{506}\right)\) | \(e\left(\frac{1399}{1518}\right)\) | \(e\left(\frac{721}{1518}\right)\) | \(e\left(\frac{239}{506}\right)\) | \(e\left(\frac{604}{759}\right)\) | \(e\left(\frac{347}{759}\right)\) | \(e\left(\frac{923}{1518}\right)\) |
| \(\chi_{33327}(593,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{721}{1518}\right)\) | \(e\left(\frac{721}{759}\right)\) | \(e\left(\frac{29}{759}\right)\) | \(e\left(\frac{215}{506}\right)\) | \(e\left(\frac{779}{1518}\right)\) | \(e\left(\frac{995}{1518}\right)\) | \(e\left(\frac{47}{506}\right)\) | \(e\left(\frac{683}{759}\right)\) | \(e\left(\frac{82}{759}\right)\) | \(e\left(\frac{859}{1518}\right)\) |
| \(\chi_{33327}(656,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{571}{1518}\right)\) | \(e\left(\frac{571}{759}\right)\) | \(e\left(\frac{503}{759}\right)\) | \(e\left(\frac{65}{506}\right)\) | \(e\left(\frac{59}{1518}\right)\) | \(e\left(\frac{89}{1518}\right)\) | \(e\left(\frac{379}{506}\right)\) | \(e\left(\frac{383}{759}\right)\) | \(e\left(\frac{166}{759}\right)\) | \(e\left(\frac{295}{1518}\right)\) |
| \(\chi_{33327}(719,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1285}{1518}\right)\) | \(e\left(\frac{526}{759}\right)\) | \(e\left(\frac{38}{759}\right)\) | \(e\left(\frac{273}{506}\right)\) | \(e\left(\frac{1361}{1518}\right)\) | \(e\left(\frac{1487}{1518}\right)\) | \(e\left(\frac{175}{506}\right)\) | \(e\left(\frac{293}{759}\right)\) | \(e\left(\frac{343}{759}\right)\) | \(e\left(\frac{733}{1518}\right)\) |
| \(\chi_{33327}(836,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{971}{1518}\right)\) | \(e\left(\frac{212}{759}\right)\) | \(e\left(\frac{757}{759}\right)\) | \(e\left(\frac{465}{506}\right)\) | \(e\left(\frac{967}{1518}\right)\) | \(e\left(\frac{481}{1518}\right)\) | \(e\left(\frac{337}{506}\right)\) | \(e\left(\frac{424}{759}\right)\) | \(e\left(\frac{701}{759}\right)\) | \(e\left(\frac{281}{1518}\right)\) |
| \(\chi_{33327}(899,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1079}{1518}\right)\) | \(e\left(\frac{320}{759}\right)\) | \(e\left(\frac{355}{759}\right)\) | \(e\left(\frac{67}{506}\right)\) | \(e\left(\frac{271}{1518}\right)\) | \(e\left(\frac{769}{1518}\right)\) | \(e\left(\frac{17}{506}\right)\) | \(e\left(\frac{640}{759}\right)\) | \(e\left(\frac{428}{759}\right)\) | \(e\left(\frac{1355}{1518}\right)\) |
| \(\chi_{33327}(1025,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{953}{1518}\right)\) | \(e\left(\frac{194}{759}\right)\) | \(e\left(\frac{571}{759}\right)\) | \(e\left(\frac{447}{506}\right)\) | \(e\left(\frac{577}{1518}\right)\) | \(e\left(\frac{433}{1518}\right)\) | \(e\left(\frac{53}{506}\right)\) | \(e\left(\frac{388}{759}\right)\) | \(e\left(\frac{620}{759}\right)\) | \(e\left(\frac{1367}{1518}\right)\) |
| \(\chi_{33327}(1097,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{895}{1518}\right)\) | \(e\left(\frac{136}{759}\right)\) | \(e\left(\frac{56}{759}\right)\) | \(e\left(\frac{389}{506}\right)\) | \(e\left(\frac{1007}{1518}\right)\) | \(e\left(\frac{953}{1518}\right)\) | \(e\left(\frac{431}{506}\right)\) | \(e\left(\frac{272}{759}\right)\) | \(e\left(\frac{106}{759}\right)\) | \(e\left(\frac{481}{1518}\right)\) |
| \(\chi_{33327}(1214,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{545}{1518}\right)\) | \(e\left(\frac{545}{759}\right)\) | \(e\left(\frac{403}{759}\right)\) | \(e\left(\frac{39}{506}\right)\) | \(e\left(\frac{1351}{1518}\right)\) | \(e\left(\frac{1369}{1518}\right)\) | \(e\left(\frac{25}{506}\right)\) | \(e\left(\frac{331}{759}\right)\) | \(e\left(\frac{302}{759}\right)\) | \(e\left(\frac{683}{1518}\right)\) |
| \(\chi_{33327}(1223,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{541}{1518}\right)\) | \(e\left(\frac{541}{759}\right)\) | \(e\left(\frac{446}{759}\right)\) | \(e\left(\frac{35}{506}\right)\) | \(e\left(\frac{1433}{1518}\right)\) | \(e\left(\frac{515}{1518}\right)\) | \(e\left(\frac{243}{506}\right)\) | \(e\left(\frac{323}{759}\right)\) | \(e\left(\frac{31}{759}\right)\) | \(e\left(\frac{1093}{1518}\right)\) |
| \(\chi_{33327}(1277,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1319}{1518}\right)\) | \(e\left(\frac{560}{759}\right)\) | \(e\left(\frac{52}{759}\right)\) | \(e\left(\frac{307}{506}\right)\) | \(e\left(\frac{1423}{1518}\right)\) | \(e\left(\frac{397}{1518}\right)\) | \(e\left(\frac{93}{506}\right)\) | \(e\left(\frac{361}{759}\right)\) | \(e\left(\frac{749}{759}\right)\) | \(e\left(\frac{1043}{1518}\right)\) |
| \(\chi_{33327}(1340,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{251}{1518}\right)\) | \(e\left(\frac{251}{759}\right)\) | \(e\left(\frac{148}{759}\right)\) | \(e\left(\frac{251}{506}\right)\) | \(e\left(\frac{547}{1518}\right)\) | \(e\left(\frac{79}{1518}\right)\) | \(e\left(\frac{109}{506}\right)\) | \(e\left(\frac{502}{759}\right)\) | \(e\left(\frac{497}{759}\right)\) | \(e\left(\frac{1217}{1518}\right)\) |
| \(\chi_{33327}(1412,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1435}{1518}\right)\) | \(e\left(\frac{676}{759}\right)\) | \(e\left(\frac{323}{759}\right)\) | \(e\left(\frac{423}{506}\right)\) | \(e\left(\frac{563}{1518}\right)\) | \(e\left(\frac{875}{1518}\right)\) | \(e\left(\frac{349}{506}\right)\) | \(e\left(\frac{593}{759}\right)\) | \(e\left(\frac{259}{759}\right)\) | \(e\left(\frac{1297}{1518}\right)\) |
| \(\chi_{33327}(1475,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{547}{1518}\right)\) | \(e\left(\frac{547}{759}\right)\) | \(e\left(\frac{2}{759}\right)\) | \(e\left(\frac{41}{506}\right)\) | \(e\left(\frac{551}{1518}\right)\) | \(e\left(\frac{1037}{1518}\right)\) | \(e\left(\frac{169}{506}\right)\) | \(e\left(\frac{335}{759}\right)\) | \(e\left(\frac{58}{759}\right)\) | \(e\left(\frac{1237}{1518}\right)\) |