from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(694130, base_ring=CyclotomicField(1692))
M = H._module
chi = DirichletCharacter(H, M([1269,423,1057]))
chi.galois_orbit()
[g,chi] = znchar(Mod(893,694130))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(694130\) | |
| Conductor: | \(347065\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1692\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 347065.tb | 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: | $\Q(\zeta_{1692})$ |
| Fixed field: | Number field defined by a degree 1692 polynomial (not computed) |
First 31 of 552 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{694130}(893,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{367}{846}\right)\) | \(e\left(\frac{347}{1692}\right)\) | \(e\left(\frac{367}{423}\right)\) | \(e\left(\frac{55}{94}\right)\) | \(e\left(\frac{68}{141}\right)\) | \(e\left(\frac{1297}{1692}\right)\) | \(e\left(\frac{575}{846}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{106}{423}\right)\) | \(e\left(\frac{85}{282}\right)\) |
| \(\chi_{694130}(2533,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{263}{846}\right)\) | \(e\left(\frac{931}{1692}\right)\) | \(e\left(\frac{263}{423}\right)\) | \(e\left(\frac{43}{94}\right)\) | \(e\left(\frac{13}{141}\right)\) | \(e\left(\frac{1349}{1692}\right)\) | \(e\left(\frac{253}{846}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{182}{423}\right)\) | \(e\left(\frac{263}{282}\right)\) |
| \(\chi_{694130}(2797,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{355}{846}\right)\) | \(e\left(\frac{89}{1692}\right)\) | \(e\left(\frac{355}{423}\right)\) | \(e\left(\frac{3}{94}\right)\) | \(e\left(\frac{2}{141}\right)\) | \(e\left(\frac{1303}{1692}\right)\) | \(e\left(\frac{245}{846}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{310}{423}\right)\) | \(e\left(\frac{73}{282}\right)\) |
| \(\chi_{694130}(2943,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{149}{846}\right)\) | \(e\left(\frac{595}{1692}\right)\) | \(e\left(\frac{149}{423}\right)\) | \(e\left(\frac{19}{94}\right)\) | \(e\left(\frac{91}{141}\right)\) | \(e\left(\frac{137}{1692}\right)\) | \(e\left(\frac{79}{846}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{5}{423}\right)\) | \(e\left(\frac{149}{282}\right)\) |
| \(\chi_{694130}(3353,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{23}{846}\right)\) | \(e\left(\frac{847}{1692}\right)\) | \(e\left(\frac{23}{423}\right)\) | \(e\left(\frac{37}{94}\right)\) | \(e\left(\frac{103}{141}\right)\) | \(e\left(\frac{1469}{1692}\right)\) | \(e\left(\frac{421}{846}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{32}{423}\right)\) | \(e\left(\frac{23}{282}\right)\) |
| \(\chi_{694130}(3763,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{265}{846}\right)\) | \(e\left(\frac{1115}{1692}\right)\) | \(e\left(\frac{265}{423}\right)\) | \(e\left(\frac{83}{94}\right)\) | \(e\left(\frac{71}{141}\right)\) | \(e\left(\frac{925}{1692}\right)\) | \(e\left(\frac{731}{846}\right)\) | \(e\left(\frac{35}{36}\right)\) | \(e\left(\frac{148}{423}\right)\) | \(e\left(\frac{265}{282}\right)\) |
| \(\chi_{694130}(4027,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{295}{846}\right)\) | \(e\left(\frac{1337}{1692}\right)\) | \(e\left(\frac{295}{423}\right)\) | \(e\left(\frac{25}{94}\right)\) | \(e\left(\frac{95}{141}\right)\) | \(e\left(\frac{487}{1692}\right)\) | \(e\left(\frac{287}{846}\right)\) | \(e\left(\frac{5}{36}\right)\) | \(e\left(\frac{61}{423}\right)\) | \(e\left(\frac{13}{282}\right)\) |
| \(\chi_{694130}(5257,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{217}{846}\right)\) | \(e\left(\frac{929}{1692}\right)\) | \(e\left(\frac{217}{423}\right)\) | \(e\left(\frac{63}{94}\right)\) | \(e\left(\frac{89}{141}\right)\) | \(e\left(\frac{103}{1692}\right)\) | \(e\left(\frac{257}{846}\right)\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{118}{423}\right)\) | \(e\left(\frac{217}{282}\right)\) |
| \(\chi_{694130}(8127,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{439}{846}\right)\) | \(e\left(\frac{1049}{1692}\right)\) | \(e\left(\frac{16}{423}\right)\) | \(e\left(\frac{85}{94}\right)\) | \(e\left(\frac{41}{141}\right)\) | \(e\left(\frac{415}{1692}\right)\) | \(e\left(\frac{17}{846}\right)\) | \(e\left(\frac{5}{36}\right)\) | \(e\left(\frac{151}{423}\right)\) | \(e\left(\frac{157}{282}\right)\) |
| \(\chi_{694130}(8537,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{175}{846}\right)\) | \(e\left(\frac{449}{1692}\right)\) | \(e\left(\frac{175}{423}\right)\) | \(e\left(\frac{69}{94}\right)\) | \(e\left(\frac{140}{141}\right)\) | \(e\left(\frac{547}{1692}\right)\) | \(e\left(\frac{371}{846}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{409}{423}\right)\) | \(e\left(\frac{175}{282}\right)\) |
| \(\chi_{694130}(10587,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{821}{846}\right)\) | \(e\left(\frac{661}{1692}\right)\) | \(e\left(\frac{398}{423}\right)\) | \(e\left(\frac{17}{94}\right)\) | \(e\left(\frac{121}{141}\right)\) | \(e\left(\frac{647}{1692}\right)\) | \(e\left(\frac{793}{846}\right)\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{2}{423}\right)\) | \(e\left(\frac{257}{282}\right)\) |
| \(\chi_{694130}(12637,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{95}{846}\right)\) | \(e\left(\frac{1549}{1692}\right)\) | \(e\left(\frac{95}{423}\right)\) | \(e\left(\frac{67}{94}\right)\) | \(e\left(\frac{76}{141}\right)\) | \(e\left(\frac{587}{1692}\right)\) | \(e\left(\frac{709}{846}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{77}{423}\right)\) | \(e\left(\frac{95}{282}\right)\) |
| \(\chi_{694130}(15653,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{89}{846}\right)\) | \(e\left(\frac{151}{1692}\right)\) | \(e\left(\frac{89}{423}\right)\) | \(e\left(\frac{41}{94}\right)\) | \(e\left(\frac{43}{141}\right)\) | \(e\left(\frac{1013}{1692}\right)\) | \(e\left(\frac{121}{846}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{179}{423}\right)\) | \(e\left(\frac{89}{282}\right)\) |
| \(\chi_{694130}(15917,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{101}{846}\right)\) | \(e\left(\frac{409}{1692}\right)\) | \(e\left(\frac{101}{423}\right)\) | \(e\left(\frac{93}{94}\right)\) | \(e\left(\frac{109}{141}\right)\) | \(e\left(\frac{1007}{1692}\right)\) | \(e\left(\frac{451}{846}\right)\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{398}{423}\right)\) | \(e\left(\frac{101}{282}\right)\) |
| \(\chi_{694130}(16327,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{829}{846}\right)\) | \(e\left(\frac{1397}{1692}\right)\) | \(e\left(\frac{406}{423}\right)\) | \(e\left(\frac{83}{94}\right)\) | \(e\left(\frac{71}{141}\right)\) | \(e\left(\frac{643}{1692}\right)\) | \(e\left(\frac{167}{846}\right)\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{289}{423}\right)\) | \(e\left(\frac{265}{282}\right)\) |
| \(\chi_{694130}(16473,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{707}{846}\right)\) | \(e\left(\frac{1171}{1692}\right)\) | \(e\left(\frac{284}{423}\right)\) | \(e\left(\frac{87}{94}\right)\) | \(e\left(\frac{58}{141}\right)\) | \(e\left(\frac{281}{1692}\right)\) | \(e\left(\frac{619}{846}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{248}{423}\right)\) | \(e\left(\frac{143}{282}\right)\) |
| \(\chi_{694130}(17703,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{227}{846}\right)\) | \(e\left(\frac{1003}{1692}\right)\) | \(e\left(\frac{227}{423}\right)\) | \(e\left(\frac{75}{94}\right)\) | \(e\left(\frac{97}{141}\right)\) | \(e\left(\frac{521}{1692}\right)\) | \(e\left(\frac{109}{846}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{371}{423}\right)\) | \(e\left(\frac{227}{282}\right)\) |
| \(\chi_{694130}(18113,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{431}{846}\right)\) | \(e\left(\frac{1159}{1692}\right)\) | \(e\left(\frac{8}{423}\right)\) | \(e\left(\frac{19}{94}\right)\) | \(e\left(\frac{91}{141}\right)\) | \(e\left(\frac{1265}{1692}\right)\) | \(e\left(\frac{643}{846}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{287}{423}\right)\) | \(e\left(\frac{149}{282}\right)\) |
| \(\chi_{694130}(18787,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{613}{846}\right)\) | \(e\left(\frac{137}{1692}\right)\) | \(e\left(\frac{190}{423}\right)\) | \(e\left(\frac{87}{94}\right)\) | \(e\left(\frac{11}{141}\right)\) | \(e\left(\frac{751}{1692}\right)\) | \(e\left(\frac{149}{846}\right)\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{154}{423}\right)\) | \(e\left(\frac{49}{282}\right)\) |
| \(\chi_{694130}(19197,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{605}{846}\right)\) | \(e\left(\frac{1093}{1692}\right)\) | \(e\left(\frac{182}{423}\right)\) | \(e\left(\frac{21}{94}\right)\) | \(e\left(\frac{61}{141}\right)\) | \(e\left(\frac{755}{1692}\right)\) | \(e\left(\frac{775}{846}\right)\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{290}{423}\right)\) | \(e\left(\frac{41}{282}\right)\) |
| \(\chi_{694130}(20017,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{151}{846}\right)\) | \(e\left(\frac{1625}{1692}\right)\) | \(e\left(\frac{151}{423}\right)\) | \(e\left(\frac{59}{94}\right)\) | \(e\left(\frac{8}{141}\right)\) | \(e\left(\frac{559}{1692}\right)\) | \(e\left(\frac{557}{846}\right)\) | \(e\left(\frac{5}{36}\right)\) | \(e\left(\frac{394}{423}\right)\) | \(e\left(\frac{151}{282}\right)\) |
| \(\chi_{694130}(20573,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{425}{846}\right)\) | \(e\left(\frac{607}{1692}\right)\) | \(e\left(\frac{2}{423}\right)\) | \(e\left(\frac{87}{94}\right)\) | \(e\left(\frac{58}{141}\right)\) | \(e\left(\frac{845}{1692}\right)\) | \(e\left(\frac{55}{846}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{389}{423}\right)\) | \(e\left(\frac{143}{282}\right)\) |
| \(\chi_{694130}(21247,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{215}{846}\right)\) | \(e\left(\frac{745}{1692}\right)\) | \(e\left(\frac{215}{423}\right)\) | \(e\left(\frac{23}{94}\right)\) | \(e\left(\frac{31}{141}\right)\) | \(e\left(\frac{527}{1692}\right)\) | \(e\left(\frac{625}{846}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{152}{423}\right)\) | \(e\left(\frac{215}{282}\right)\) |
| \(\chi_{694130}(22213,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{846}\right)\) | \(e\left(\frac{883}{1692}\right)\) | \(e\left(\frac{5}{423}\right)\) | \(e\left(\frac{53}{94}\right)\) | \(e\left(\frac{4}{141}\right)\) | \(e\left(\frac{209}{1692}\right)\) | \(e\left(\frac{349}{846}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{338}{423}\right)\) | \(e\left(\frac{5}{282}\right)\) |
| \(\chi_{694130}(23443,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{55}{846}\right)\) | \(e\left(\frac{407}{1692}\right)\) | \(e\left(\frac{55}{423}\right)\) | \(e\left(\frac{19}{94}\right)\) | \(e\left(\frac{44}{141}\right)\) | \(e\left(\frac{1453}{1692}\right)\) | \(e\left(\frac{455}{846}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{334}{423}\right)\) | \(e\left(\frac{55}{282}\right)\) |
| \(\chi_{694130}(23707,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{115}{846}\right)\) | \(e\left(\frac{5}{1692}\right)\) | \(e\left(\frac{115}{423}\right)\) | \(e\left(\frac{91}{94}\right)\) | \(e\left(\frac{92}{141}\right)\) | \(e\left(\frac{1423}{1692}\right)\) | \(e\left(\frac{413}{846}\right)\) | \(e\left(\frac{5}{36}\right)\) | \(e\left(\frac{160}{423}\right)\) | \(e\left(\frac{115}{282}\right)\) |
| \(\chi_{694130}(27953,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{685}{846}\right)\) | \(e\left(\frac{839}{1692}\right)\) | \(e\left(\frac{262}{423}\right)\) | \(e\left(\frac{23}{94}\right)\) | \(e\left(\frac{125}{141}\right)\) | \(e\left(\frac{1561}{1692}\right)\) | \(e\left(\frac{437}{846}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{199}{423}\right)\) | \(e\left(\frac{121}{282}\right)\) |
| \(\chi_{694130}(28363,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{846}\right)\) | \(e\left(\frac{1435}{1692}\right)\) | \(e\left(\frac{11}{423}\right)\) | \(e\left(\frac{79}{94}\right)\) | \(e\left(\frac{37}{141}\right)\) | \(e\left(\frac{629}{1692}\right)\) | \(e\left(\frac{91}{846}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{236}{423}\right)\) | \(e\left(\frac{11}{282}\right)\) |
| \(\chi_{694130}(29447,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{325}{846}\right)\) | \(e\left(\frac{713}{1692}\right)\) | \(e\left(\frac{325}{423}\right)\) | \(e\left(\frac{61}{94}\right)\) | \(e\left(\frac{119}{141}\right)\) | \(e\left(\frac{895}{1692}\right)\) | \(e\left(\frac{689}{846}\right)\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{397}{423}\right)\) | \(e\left(\frac{43}{282}\right)\) |
| \(\chi_{694130}(30003,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{846}\right)\) | \(e\left(\frac{515}{1692}\right)\) | \(e\left(\frac{1}{423}\right)\) | \(e\left(\frac{67}{94}\right)\) | \(e\left(\frac{29}{141}\right)\) | \(e\left(\frac{1057}{1692}\right)\) | \(e\left(\frac{239}{846}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{406}{423}\right)\) | \(e\left(\frac{1}{282}\right)\) |
| \(\chi_{694130}(30267,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{461}{846}\right)\) | \(e\left(\frac{1381}{1692}\right)\) | \(e\left(\frac{38}{423}\right)\) | \(e\left(\frac{55}{94}\right)\) | \(e\left(\frac{115}{141}\right)\) | \(e\left(\frac{827}{1692}\right)\) | \(e\left(\frac{199}{846}\right)\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{200}{423}\right)\) | \(e\left(\frac{179}{282}\right)\) |