from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(586971, base_ring=CyclotomicField(3630))
M = H._module
chi = DirichletCharacter(H, M([0,3025,3219]))
chi.galois_orbit()
[g,chi] = znchar(Mod(19,586971))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(586971\) | |
| Conductor: | \(9317\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(3630\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 9317.bu | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Related number fields
| Field of values: | $\Q(\zeta_{1815})$ |
| Fixed field: | Number field defined by a degree 3630 polynomial (not computed) |
First 31 of 880 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{586971}(19,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2009}{3630}\right)\) | \(e\left(\frac{194}{1815}\right)\) | \(e\left(\frac{1211}{3630}\right)\) | \(e\left(\frac{799}{1210}\right)\) | \(e\left(\frac{322}{363}\right)\) | \(e\left(\frac{314}{605}\right)\) | \(e\left(\frac{388}{1815}\right)\) | \(e\left(\frac{1508}{1815}\right)\) | \(e\left(\frac{1231}{1815}\right)\) | \(e\left(\frac{533}{1210}\right)\) |
| \(\chi_{586971}(325,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2287}{3630}\right)\) | \(e\left(\frac{472}{1815}\right)\) | \(e\left(\frac{1543}{3630}\right)\) | \(e\left(\frac{1077}{1210}\right)\) | \(e\left(\frac{20}{363}\right)\) | \(e\left(\frac{502}{605}\right)\) | \(e\left(\frac{944}{1815}\right)\) | \(e\left(\frac{619}{1815}\right)\) | \(e\left(\frac{338}{1815}\right)\) | \(e\left(\frac{829}{1210}\right)\) |
| \(\chi_{586971}(2224,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{983}{3630}\right)\) | \(e\left(\frac{983}{1815}\right)\) | \(e\left(\frac{1187}{3630}\right)\) | \(e\left(\frac{983}{1210}\right)\) | \(e\left(\frac{217}{363}\right)\) | \(e\left(\frac{38}{605}\right)\) | \(e\left(\frac{151}{1815}\right)\) | \(e\left(\frac{1616}{1815}\right)\) | \(e\left(\frac{727}{1815}\right)\) | \(e\left(\frac{1051}{1210}\right)\) |
| \(\chi_{586971}(3412,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1153}{3630}\right)\) | \(e\left(\frac{1153}{1815}\right)\) | \(e\left(\frac{3427}{3630}\right)\) | \(e\left(\frac{1153}{1210}\right)\) | \(e\left(\frac{95}{363}\right)\) | \(e\left(\frac{388}{605}\right)\) | \(e\left(\frac{491}{1815}\right)\) | \(e\left(\frac{1216}{1815}\right)\) | \(e\left(\frac{1787}{1815}\right)\) | \(e\left(\frac{701}{1210}\right)\) |
| \(\chi_{586971}(3988,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1157}{3630}\right)\) | \(e\left(\frac{1157}{1815}\right)\) | \(e\left(\frac{533}{3630}\right)\) | \(e\left(\frac{1157}{1210}\right)\) | \(e\left(\frac{169}{363}\right)\) | \(e\left(\frac{382}{605}\right)\) | \(e\left(\frac{499}{1815}\right)\) | \(e\left(\frac{929}{1815}\right)\) | \(e\left(\frac{1513}{1815}\right)\) | \(e\left(\frac{949}{1210}\right)\) |
| \(\chi_{586971}(4429,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3191}{3630}\right)\) | \(e\left(\frac{1376}{1815}\right)\) | \(e\left(\frac{899}{3630}\right)\) | \(e\left(\frac{771}{1210}\right)\) | \(e\left(\frac{46}{363}\right)\) | \(e\left(\frac{356}{605}\right)\) | \(e\left(\frac{937}{1815}\right)\) | \(e\left(\frac{1097}{1815}\right)\) | \(e\left(\frac{124}{1815}\right)\) | \(e\left(\frac{7}{1210}\right)\) |
| \(\chi_{586971}(4870,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1589}{3630}\right)\) | \(e\left(\frac{1589}{1815}\right)\) | \(e\left(\frac{161}{3630}\right)\) | \(e\left(\frac{379}{1210}\right)\) | \(e\left(\frac{175}{363}\right)\) | \(e\left(\frac{339}{605}\right)\) | \(e\left(\frac{1363}{1815}\right)\) | \(e\left(\frac{788}{1815}\right)\) | \(e\left(\frac{961}{1815}\right)\) | \(e\left(\frac{1113}{1210}\right)\) |
| \(\chi_{586971}(5617,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{301}{3630}\right)\) | \(e\left(\frac{301}{1815}\right)\) | \(e\left(\frac{2749}{3630}\right)\) | \(e\left(\frac{301}{1210}\right)\) | \(e\left(\frac{305}{363}\right)\) | \(e\left(\frac{456}{605}\right)\) | \(e\left(\frac{602}{1815}\right)\) | \(e\left(\frac{637}{1815}\right)\) | \(e\left(\frac{254}{1815}\right)\) | \(e\left(\frac{1117}{1210}\right)\) |
| \(\chi_{586971}(6058,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2539}{3630}\right)\) | \(e\left(\frac{724}{1815}\right)\) | \(e\left(\frac{721}{3630}\right)\) | \(e\left(\frac{119}{1210}\right)\) | \(e\left(\frac{326}{363}\right)\) | \(e\left(\frac{124}{605}\right)\) | \(e\left(\frac{1448}{1815}\right)\) | \(e\left(\frac{688}{1815}\right)\) | \(e\left(\frac{1226}{1815}\right)\) | \(e\left(\frac{723}{1210}\right)\) |
| \(\chi_{586971}(7075,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2933}{3630}\right)\) | \(e\left(\frac{1118}{1815}\right)\) | \(e\left(\frac{617}{3630}\right)\) | \(e\left(\frac{513}{1210}\right)\) | \(e\left(\frac{355}{363}\right)\) | \(e\left(\frac{138}{605}\right)\) | \(e\left(\frac{421}{1815}\right)\) | \(e\left(\frac{551}{1815}\right)\) | \(e\left(\frac{1462}{1815}\right)\) | \(e\left(\frac{951}{1210}\right)\) |
| \(\chi_{586971}(8263,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2773}{3630}\right)\) | \(e\left(\frac{958}{1815}\right)\) | \(e\left(\frac{217}{3630}\right)\) | \(e\left(\frac{353}{1210}\right)\) | \(e\left(\frac{299}{363}\right)\) | \(e\left(\frac{378}{605}\right)\) | \(e\left(\frac{101}{1815}\right)\) | \(e\left(\frac{1141}{1815}\right)\) | \(e\left(\frac{1532}{1815}\right)\) | \(e\left(\frac{711}{1210}\right)\) |
| \(\chi_{586971}(8839,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2357}{3630}\right)\) | \(e\left(\frac{542}{1815}\right)\) | \(e\left(\frac{3533}{3630}\right)\) | \(e\left(\frac{1147}{1210}\right)\) | \(e\left(\frac{226}{363}\right)\) | \(e\left(\frac{397}{605}\right)\) | \(e\left(\frac{1084}{1815}\right)\) | \(e\left(\frac{134}{1815}\right)\) | \(e\left(\frac{988}{1815}\right)\) | \(e\left(\frac{329}{1210}\right)\) |
| \(\chi_{586971}(9280,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{401}{3630}\right)\) | \(e\left(\frac{401}{1815}\right)\) | \(e\left(\frac{2999}{3630}\right)\) | \(e\left(\frac{401}{1210}\right)\) | \(e\left(\frac{340}{363}\right)\) | \(e\left(\frac{306}{605}\right)\) | \(e\left(\frac{802}{1815}\right)\) | \(e\left(\frac{722}{1815}\right)\) | \(e\left(\frac{664}{1815}\right)\) | \(e\left(\frac{57}{1210}\right)\) |
| \(\chi_{586971}(9721,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{839}{3630}\right)\) | \(e\left(\frac{839}{1815}\right)\) | \(e\left(\frac{101}{3630}\right)\) | \(e\left(\frac{839}{1210}\right)\) | \(e\left(\frac{94}{363}\right)\) | \(e\left(\frac{254}{605}\right)\) | \(e\left(\frac{1678}{1815}\right)\) | \(e\left(\frac{1058}{1815}\right)\) | \(e\left(\frac{1516}{1815}\right)\) | \(e\left(\frac{593}{1210}\right)\) |
| \(\chi_{586971}(10027,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2377}{3630}\right)\) | \(e\left(\frac{562}{1815}\right)\) | \(e\left(\frac{3583}{3630}\right)\) | \(e\left(\frac{1167}{1210}\right)\) | \(e\left(\frac{233}{363}\right)\) | \(e\left(\frac{367}{605}\right)\) | \(e\left(\frac{1124}{1815}\right)\) | \(e\left(\frac{514}{1815}\right)\) | \(e\left(\frac{1433}{1815}\right)\) | \(e\left(\frac{359}{1210}\right)\) |
| \(\chi_{586971}(10468,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{151}{3630}\right)\) | \(e\left(\frac{151}{1815}\right)\) | \(e\left(\frac{559}{3630}\right)\) | \(e\left(\frac{151}{1210}\right)\) | \(e\left(\frac{71}{363}\right)\) | \(e\left(\frac{76}{605}\right)\) | \(e\left(\frac{302}{1815}\right)\) | \(e\left(\frac{1417}{1815}\right)\) | \(e\left(\frac{1454}{1815}\right)\) | \(e\left(\frac{287}{1210}\right)\) |
| \(\chi_{586971}(10909,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2449}{3630}\right)\) | \(e\left(\frac{634}{1815}\right)\) | \(e\left(\frac{2311}{3630}\right)\) | \(e\left(\frac{29}{1210}\right)\) | \(e\left(\frac{113}{363}\right)\) | \(e\left(\frac{259}{605}\right)\) | \(e\left(\frac{1268}{1815}\right)\) | \(e\left(\frac{793}{1815}\right)\) | \(e\left(\frac{131}{1815}\right)\) | \(e\left(\frac{1193}{1210}\right)\) |
| \(\chi_{586971}(11926,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3233}{3630}\right)\) | \(e\left(\frac{1418}{1815}\right)\) | \(e\left(\frac{1367}{3630}\right)\) | \(e\left(\frac{813}{1210}\right)\) | \(e\left(\frac{97}{363}\right)\) | \(e\left(\frac{293}{605}\right)\) | \(e\left(\frac{1021}{1815}\right)\) | \(e\left(\frac{806}{1815}\right)\) | \(e\left(\frac{877}{1815}\right)\) | \(e\left(\frac{191}{1210}\right)\) |
| \(\chi_{586971}(13114,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2743}{3630}\right)\) | \(e\left(\frac{928}{1815}\right)\) | \(e\left(\frac{1957}{3630}\right)\) | \(e\left(\frac{323}{1210}\right)\) | \(e\left(\frac{107}{363}\right)\) | \(e\left(\frac{423}{605}\right)\) | \(e\left(\frac{41}{1815}\right)\) | \(e\left(\frac{571}{1815}\right)\) | \(e\left(\frac{1772}{1815}\right)\) | \(e\left(\frac{61}{1210}\right)\) |
| \(\chi_{586971}(13690,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2567}{3630}\right)\) | \(e\left(\frac{752}{1815}\right)\) | \(e\left(\frac{2243}{3630}\right)\) | \(e\left(\frac{147}{1210}\right)\) | \(e\left(\frac{118}{363}\right)\) | \(e\left(\frac{82}{605}\right)\) | \(e\left(\frac{1504}{1815}\right)\) | \(e\left(\frac{494}{1815}\right)\) | \(e\left(\frac{1123}{1815}\right)\) | \(e\left(\frac{39}{1210}\right)\) |
| \(\chi_{586971}(14131,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3551}{3630}\right)\) | \(e\left(\frac{1736}{1815}\right)\) | \(e\left(\frac{1799}{3630}\right)\) | \(e\left(\frac{1131}{1210}\right)\) | \(e\left(\frac{172}{363}\right)\) | \(e\left(\frac{421}{605}\right)\) | \(e\left(\frac{1657}{1815}\right)\) | \(e\left(\frac{677}{1815}\right)\) | \(e\left(\frac{874}{1815}\right)\) | \(e\left(\frac{547}{1210}\right)\) |
| \(\chi_{586971}(14572,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3389}{3630}\right)\) | \(e\left(\frac{1574}{1815}\right)\) | \(e\left(\frac{1031}{3630}\right)\) | \(e\left(\frac{969}{1210}\right)\) | \(e\left(\frac{79}{363}\right)\) | \(e\left(\frac{59}{605}\right)\) | \(e\left(\frac{1333}{1815}\right)\) | \(e\left(\frac{503}{1815}\right)\) | \(e\left(\frac{1081}{1815}\right)\) | \(e\left(\frac{183}{1210}\right)\) |
| \(\chi_{586971}(14878,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{937}{3630}\right)\) | \(e\left(\frac{937}{1815}\right)\) | \(e\left(\frac{3613}{3630}\right)\) | \(e\left(\frac{937}{1210}\right)\) | \(e\left(\frac{92}{363}\right)\) | \(e\left(\frac{107}{605}\right)\) | \(e\left(\frac{59}{1815}\right)\) | \(e\left(\frac{379}{1815}\right)\) | \(e\left(\frac{248}{1815}\right)\) | \(e\left(\frac{619}{1210}\right)\) |
| \(\chi_{586971}(15319,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2311}{3630}\right)\) | \(e\left(\frac{496}{1815}\right)\) | \(e\left(\frac{2329}{3630}\right)\) | \(e\left(\frac{1101}{1210}\right)\) | \(e\left(\frac{101}{363}\right)\) | \(e\left(\frac{466}{605}\right)\) | \(e\left(\frac{992}{1815}\right)\) | \(e\left(\frac{712}{1815}\right)\) | \(e\left(\frac{509}{1815}\right)\) | \(e\left(\frac{1107}{1210}\right)\) |
| \(\chi_{586971}(15760,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2029}{3630}\right)\) | \(e\left(\frac{214}{1815}\right)\) | \(e\left(\frac{1261}{3630}\right)\) | \(e\left(\frac{819}{1210}\right)\) | \(e\left(\frac{329}{363}\right)\) | \(e\left(\frac{284}{605}\right)\) | \(e\left(\frac{428}{1815}\right)\) | \(e\left(\frac{73}{1815}\right)\) | \(e\left(\frac{1676}{1815}\right)\) | \(e\left(\frac{563}{1210}\right)\) |
| \(\chi_{586971}(16777,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1883}{3630}\right)\) | \(e\left(\frac{68}{1815}\right)\) | \(e\left(\frac{3437}{3630}\right)\) | \(e\left(\frac{673}{1210}\right)\) | \(e\left(\frac{169}{363}\right)\) | \(e\left(\frac{503}{605}\right)\) | \(e\left(\frac{136}{1815}\right)\) | \(e\left(\frac{566}{1815}\right)\) | \(e\left(\frac{787}{1815}\right)\) | \(e\left(\frac{1191}{1210}\right)\) |
| \(\chi_{586971}(17965,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1063}{3630}\right)\) | \(e\left(\frac{1063}{1815}\right)\) | \(e\left(\frac{1387}{3630}\right)\) | \(e\left(\frac{1063}{1210}\right)\) | \(e\left(\frac{245}{363}\right)\) | \(e\left(\frac{523}{605}\right)\) | \(e\left(\frac{311}{1815}\right)\) | \(e\left(\frac{1321}{1815}\right)\) | \(e\left(\frac{692}{1815}\right)\) | \(e\left(\frac{1171}{1210}\right)\) |
| \(\chi_{586971}(18541,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1787}{3630}\right)\) | \(e\left(\frac{1787}{1815}\right)\) | \(e\left(\frac{293}{3630}\right)\) | \(e\left(\frac{577}{1210}\right)\) | \(e\left(\frac{208}{363}\right)\) | \(e\left(\frac{42}{605}\right)\) | \(e\left(\frac{1759}{1815}\right)\) | \(e\left(\frac{194}{1815}\right)\) | \(e\left(\frac{103}{1815}\right)\) | \(e\left(\frac{79}{1210}\right)\) |
| \(\chi_{586971}(18982,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1751}{3630}\right)\) | \(e\left(\frac{1751}{1815}\right)\) | \(e\left(\frac{929}{3630}\right)\) | \(e\left(\frac{541}{1210}\right)\) | \(e\left(\frac{268}{363}\right)\) | \(e\left(\frac{96}{605}\right)\) | \(e\left(\frac{1687}{1815}\right)\) | \(e\left(\frac{962}{1815}\right)\) | \(e\left(\frac{754}{1815}\right)\) | \(e\left(\frac{267}{1210}\right)\) |
| \(\chi_{586971}(19423,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1979}{3630}\right)\) | \(e\left(\frac{164}{1815}\right)\) | \(e\left(\frac{2951}{3630}\right)\) | \(e\left(\frac{769}{1210}\right)\) | \(e\left(\frac{130}{363}\right)\) | \(e\left(\frac{359}{605}\right)\) | \(e\left(\frac{328}{1815}\right)\) | \(e\left(\frac{938}{1815}\right)\) | \(e\left(\frac{1471}{1815}\right)\) | \(e\left(\frac{1093}{1210}\right)\) |
| \(\chi_{586971}(19729,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2137}{3630}\right)\) | \(e\left(\frac{322}{1815}\right)\) | \(e\left(\frac{2983}{3630}\right)\) | \(e\left(\frac{927}{1210}\right)\) | \(e\left(\frac{149}{363}\right)\) | \(e\left(\frac{122}{605}\right)\) | \(e\left(\frac{644}{1815}\right)\) | \(e\left(\frac{1399}{1815}\right)\) | \(e\left(\frac{1538}{1815}\right)\) | \(e\left(\frac{1209}{1210}\right)\) |