from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9067, base_ring=CyclotomicField(3022))
M = H._module
chi = DirichletCharacter(H, M([2848]))
chi.galois_orbit()
[g,chi] = znchar(Mod(4,9067))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(9067\) | |
| Conductor: | \(9067\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1511\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | 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: | $\Q(\zeta_{1511})$ |
| Fixed field: | Number field defined by a degree 1511 polynomial (not computed) |
First 31 of 1510 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{9067}(4,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{42}{1511}\right)\) | \(e\left(\frac{1424}{1511}\right)\) | \(e\left(\frac{84}{1511}\right)\) | \(e\left(\frac{847}{1511}\right)\) | \(e\left(\frac{1466}{1511}\right)\) | \(e\left(\frac{1027}{1511}\right)\) | \(e\left(\frac{126}{1511}\right)\) | \(e\left(\frac{1337}{1511}\right)\) | \(e\left(\frac{889}{1511}\right)\) | \(e\left(\frac{15}{1511}\right)\) |
| \(\chi_{9067}(14,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1290}{1511}\right)\) | \(e\left(\frac{134}{1511}\right)\) | \(e\left(\frac{1069}{1511}\right)\) | \(e\left(\frac{328}{1511}\right)\) | \(e\left(\frac{1424}{1511}\right)\) | \(e\left(\frac{676}{1511}\right)\) | \(e\left(\frac{848}{1511}\right)\) | \(e\left(\frac{268}{1511}\right)\) | \(e\left(\frac{107}{1511}\right)\) | \(e\left(\frac{29}{1511}\right)\) |
| \(\chi_{9067}(16,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{84}{1511}\right)\) | \(e\left(\frac{1337}{1511}\right)\) | \(e\left(\frac{168}{1511}\right)\) | \(e\left(\frac{183}{1511}\right)\) | \(e\left(\frac{1421}{1511}\right)\) | \(e\left(\frac{543}{1511}\right)\) | \(e\left(\frac{252}{1511}\right)\) | \(e\left(\frac{1163}{1511}\right)\) | \(e\left(\frac{267}{1511}\right)\) | \(e\left(\frac{30}{1511}\right)\) |
| \(\chi_{9067}(22,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{784}{1511}\right)\) | \(e\left(\frac{1398}{1511}\right)\) | \(e\left(\frac{57}{1511}\right)\) | \(e\left(\frac{197}{1511}\right)\) | \(e\left(\frac{671}{1511}\right)\) | \(e\left(\frac{535}{1511}\right)\) | \(e\left(\frac{841}{1511}\right)\) | \(e\left(\frac{1285}{1511}\right)\) | \(e\left(\frac{981}{1511}\right)\) | \(e\left(\frac{280}{1511}\right)\) |
| \(\chi_{9067}(39,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{29}{1511}\right)\) | \(e\left(\frac{1343}{1511}\right)\) | \(e\left(\frac{58}{1511}\right)\) | \(e\left(\frac{333}{1511}\right)\) | \(e\left(\frac{1372}{1511}\right)\) | \(e\left(\frac{889}{1511}\right)\) | \(e\left(\frac{87}{1511}\right)\) | \(e\left(\frac{1175}{1511}\right)\) | \(e\left(\frac{362}{1511}\right)\) | \(e\left(\frac{550}{1511}\right)\) |
| \(\chi_{9067}(43,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{678}{1511}\right)\) | \(e\left(\frac{970}{1511}\right)\) | \(e\left(\frac{1356}{1511}\right)\) | \(e\left(\frac{74}{1511}\right)\) | \(e\left(\frac{137}{1511}\right)\) | \(e\left(\frac{1037}{1511}\right)\) | \(e\left(\frac{523}{1511}\right)\) | \(e\left(\frac{429}{1511}\right)\) | \(e\left(\frac{752}{1511}\right)\) | \(e\left(\frac{458}{1511}\right)\) |
| \(\chi_{9067}(49,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1027}{1511}\right)\) | \(e\left(\frac{355}{1511}\right)\) | \(e\left(\frac{543}{1511}\right)\) | \(e\left(\frac{1320}{1511}\right)\) | \(e\left(\frac{1382}{1511}\right)\) | \(e\left(\frac{325}{1511}\right)\) | \(e\left(\frac{59}{1511}\right)\) | \(e\left(\frac{710}{1511}\right)\) | \(e\left(\frac{836}{1511}\right)\) | \(e\left(\frac{43}{1511}\right)\) |
| \(\chi_{9067}(53,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{307}{1511}\right)\) | \(e\left(\frac{983}{1511}\right)\) | \(e\left(\frac{614}{1511}\right)\) | \(e\left(\frac{399}{1511}\right)\) | \(e\left(\frac{1290}{1511}\right)\) | \(e\left(\frac{1283}{1511}\right)\) | \(e\left(\frac{921}{1511}\right)\) | \(e\left(\frac{455}{1511}\right)\) | \(e\left(\frac{706}{1511}\right)\) | \(e\left(\frac{1081}{1511}\right)\) |
| \(\chi_{9067}(54,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{646}{1511}\right)\) | \(e\left(\frac{1468}{1511}\right)\) | \(e\left(\frac{1292}{1511}\right)\) | \(e\left(\frac{436}{1511}\right)\) | \(e\left(\frac{603}{1511}\right)\) | \(e\left(\frac{1046}{1511}\right)\) | \(e\left(\frac{427}{1511}\right)\) | \(e\left(\frac{1425}{1511}\right)\) | \(e\left(\frac{1082}{1511}\right)\) | \(e\left(\frac{1310}{1511}\right)\) |
| \(\chi_{9067}(56,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1332}{1511}\right)\) | \(e\left(\frac{47}{1511}\right)\) | \(e\left(\frac{1153}{1511}\right)\) | \(e\left(\frac{1175}{1511}\right)\) | \(e\left(\frac{1379}{1511}\right)\) | \(e\left(\frac{192}{1511}\right)\) | \(e\left(\frac{974}{1511}\right)\) | \(e\left(\frac{94}{1511}\right)\) | \(e\left(\frac{996}{1511}\right)\) | \(e\left(\frac{44}{1511}\right)\) |
| \(\chi_{9067}(64,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{126}{1511}\right)\) | \(e\left(\frac{1250}{1511}\right)\) | \(e\left(\frac{252}{1511}\right)\) | \(e\left(\frac{1030}{1511}\right)\) | \(e\left(\frac{1376}{1511}\right)\) | \(e\left(\frac{59}{1511}\right)\) | \(e\left(\frac{378}{1511}\right)\) | \(e\left(\frac{989}{1511}\right)\) | \(e\left(\frac{1156}{1511}\right)\) | \(e\left(\frac{45}{1511}\right)\) |
| \(\chi_{9067}(65,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{496}{1511}\right)\) | \(e\left(\frac{1347}{1511}\right)\) | \(e\left(\frac{992}{1511}\right)\) | \(e\left(\frac{433}{1511}\right)\) | \(e\left(\frac{332}{1511}\right)\) | \(e\left(\frac{616}{1511}\right)\) | \(e\left(\frac{1488}{1511}\right)\) | \(e\left(\frac{1183}{1511}\right)\) | \(e\left(\frac{929}{1511}\right)\) | \(e\left(\frac{393}{1511}\right)\) |
| \(\chi_{9067}(77,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{521}{1511}\right)\) | \(e\left(\frac{108}{1511}\right)\) | \(e\left(\frac{1042}{1511}\right)\) | \(e\left(\frac{1189}{1511}\right)\) | \(e\left(\frac{629}{1511}\right)\) | \(e\left(\frac{184}{1511}\right)\) | \(e\left(\frac{52}{1511}\right)\) | \(e\left(\frac{216}{1511}\right)\) | \(e\left(\frac{199}{1511}\right)\) | \(e\left(\frac{294}{1511}\right)\) |
| \(\chi_{9067}(88,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{826}{1511}\right)\) | \(e\left(\frac{1311}{1511}\right)\) | \(e\left(\frac{141}{1511}\right)\) | \(e\left(\frac{1044}{1511}\right)\) | \(e\left(\frac{626}{1511}\right)\) | \(e\left(\frac{51}{1511}\right)\) | \(e\left(\frac{967}{1511}\right)\) | \(e\left(\frac{1111}{1511}\right)\) | \(e\left(\frac{359}{1511}\right)\) | \(e\left(\frac{295}{1511}\right)\) |
| \(\chi_{9067}(90,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1113}{1511}\right)\) | \(e\left(\frac{1472}{1511}\right)\) | \(e\left(\frac{715}{1511}\right)\) | \(e\left(\frac{536}{1511}\right)\) | \(e\left(\frac{1074}{1511}\right)\) | \(e\left(\frac{773}{1511}\right)\) | \(e\left(\frac{317}{1511}\right)\) | \(e\left(\frac{1433}{1511}\right)\) | \(e\left(\frac{138}{1511}\right)\) | \(e\left(\frac{1153}{1511}\right)\) |
| \(\chi_{9067}(109,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{491}{1511}\right)\) | \(e\left(\frac{386}{1511}\right)\) | \(e\left(\frac{982}{1511}\right)\) | \(e\left(\frac{584}{1511}\right)\) | \(e\left(\frac{877}{1511}\right)\) | \(e\left(\frac{98}{1511}\right)\) | \(e\left(\frac{1473}{1511}\right)\) | \(e\left(\frac{772}{1511}\right)\) | \(e\left(\frac{1075}{1511}\right)\) | \(e\left(\frac{715}{1511}\right)\) |
| \(\chi_{9067}(111,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{38}{1511}\right)\) | \(e\left(\frac{353}{1511}\right)\) | \(e\left(\frac{76}{1511}\right)\) | \(e\left(\frac{1270}{1511}\right)\) | \(e\left(\frac{391}{1511}\right)\) | \(e\left(\frac{1217}{1511}\right)\) | \(e\left(\frac{114}{1511}\right)\) | \(e\left(\frac{706}{1511}\right)\) | \(e\left(\frac{1308}{1511}\right)\) | \(e\left(\frac{877}{1511}\right)\) |
| \(\chi_{9067}(121,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{15}{1511}\right)\) | \(e\left(\frac{1372}{1511}\right)\) | \(e\left(\frac{30}{1511}\right)\) | \(e\left(\frac{1058}{1511}\right)\) | \(e\left(\frac{1387}{1511}\right)\) | \(e\left(\frac{43}{1511}\right)\) | \(e\left(\frac{45}{1511}\right)\) | \(e\left(\frac{1233}{1511}\right)\) | \(e\left(\frac{1073}{1511}\right)\) | \(e\left(\frac{545}{1511}\right)\) |
| \(\chi_{9067}(138,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{893}{1511}\right)\) | \(e\left(\frac{1496}{1511}\right)\) | \(e\left(\frac{275}{1511}\right)\) | \(e\left(\frac{1136}{1511}\right)\) | \(e\left(\frac{878}{1511}\right)\) | \(e\left(\frac{646}{1511}\right)\) | \(e\left(\frac{1168}{1511}\right)\) | \(e\left(\frac{1481}{1511}\right)\) | \(e\left(\frac{518}{1511}\right)\) | \(e\left(\frac{211}{1511}\right)\) |
| \(\chi_{9067}(139,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1120}{1511}\right)\) | \(e\left(\frac{702}{1511}\right)\) | \(e\left(\frac{729}{1511}\right)\) | \(e\left(\frac{929}{1511}\right)\) | \(e\left(\frac{311}{1511}\right)\) | \(e\left(\frac{1196}{1511}\right)\) | \(e\left(\frac{338}{1511}\right)\) | \(e\left(\frac{1404}{1511}\right)\) | \(e\left(\frac{538}{1511}\right)\) | \(e\left(\frac{400}{1511}\right)\) |
| \(\chi_{9067}(150,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{69}{1511}\right)\) | \(e\left(\frac{1476}{1511}\right)\) | \(e\left(\frac{138}{1511}\right)\) | \(e\left(\frac{636}{1511}\right)\) | \(e\left(\frac{34}{1511}\right)\) | \(e\left(\frac{500}{1511}\right)\) | \(e\left(\frac{207}{1511}\right)\) | \(e\left(\frac{1441}{1511}\right)\) | \(e\left(\frac{705}{1511}\right)\) | \(e\left(\frac{996}{1511}\right)\) |
| \(\chi_{9067}(156,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{71}{1511}\right)\) | \(e\left(\frac{1256}{1511}\right)\) | \(e\left(\frac{142}{1511}\right)\) | \(e\left(\frac{1180}{1511}\right)\) | \(e\left(\frac{1327}{1511}\right)\) | \(e\left(\frac{405}{1511}\right)\) | \(e\left(\frac{213}{1511}\right)\) | \(e\left(\frac{1001}{1511}\right)\) | \(e\left(\frac{1251}{1511}\right)\) | \(e\left(\frac{565}{1511}\right)\) |
| \(\chi_{9067}(172,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{720}{1511}\right)\) | \(e\left(\frac{883}{1511}\right)\) | \(e\left(\frac{1440}{1511}\right)\) | \(e\left(\frac{921}{1511}\right)\) | \(e\left(\frac{92}{1511}\right)\) | \(e\left(\frac{553}{1511}\right)\) | \(e\left(\frac{649}{1511}\right)\) | \(e\left(\frac{255}{1511}\right)\) | \(e\left(\frac{130}{1511}\right)\) | \(e\left(\frac{473}{1511}\right)\) |
| \(\chi_{9067}(185,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{505}{1511}\right)\) | \(e\left(\frac{357}{1511}\right)\) | \(e\left(\frac{1010}{1511}\right)\) | \(e\left(\frac{1370}{1511}\right)\) | \(e\left(\frac{862}{1511}\right)\) | \(e\left(\frac{944}{1511}\right)\) | \(e\left(\frac{4}{1511}\right)\) | \(e\left(\frac{714}{1511}\right)\) | \(e\left(\frac{364}{1511}\right)\) | \(e\left(\frac{720}{1511}\right)\) |
| \(\chi_{9067}(189,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{383}{1511}\right)\) | \(e\left(\frac{178}{1511}\right)\) | \(e\left(\frac{766}{1511}\right)\) | \(e\left(\frac{1428}{1511}\right)\) | \(e\left(\frac{561}{1511}\right)\) | \(e\left(\frac{695}{1511}\right)\) | \(e\left(\frac{1149}{1511}\right)\) | \(e\left(\frac{356}{1511}\right)\) | \(e\left(\frac{300}{1511}\right)\) | \(e\left(\frac{1324}{1511}\right)\) |
| \(\chi_{9067}(194,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1410}{1511}\right)\) | \(e\left(\frac{533}{1511}\right)\) | \(e\left(\frac{1309}{1511}\right)\) | \(e\left(\frac{1237}{1511}\right)\) | \(e\left(\frac{432}{1511}\right)\) | \(e\left(\frac{1020}{1511}\right)\) | \(e\left(\frac{1208}{1511}\right)\) | \(e\left(\frac{1066}{1511}\right)\) | \(e\left(\frac{1136}{1511}\right)\) | \(e\left(\frac{1367}{1511}\right)\) |
| \(\chi_{9067}(196,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1069}{1511}\right)\) | \(e\left(\frac{268}{1511}\right)\) | \(e\left(\frac{627}{1511}\right)\) | \(e\left(\frac{656}{1511}\right)\) | \(e\left(\frac{1337}{1511}\right)\) | \(e\left(\frac{1352}{1511}\right)\) | \(e\left(\frac{185}{1511}\right)\) | \(e\left(\frac{536}{1511}\right)\) | \(e\left(\frac{214}{1511}\right)\) | \(e\left(\frac{58}{1511}\right)\) |
| \(\chi_{9067}(201,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1203}{1511}\right)\) | \(e\left(\frac{638}{1511}\right)\) | \(e\left(\frac{895}{1511}\right)\) | \(e\left(\frac{840}{1511}\right)\) | \(e\left(\frac{330}{1511}\right)\) | \(e\left(\frac{1031}{1511}\right)\) | \(e\left(\frac{587}{1511}\right)\) | \(e\left(\frac{1276}{1511}\right)\) | \(e\left(\frac{532}{1511}\right)\) | \(e\left(\frac{1401}{1511}\right)\) |
| \(\chi_{9067}(212,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{349}{1511}\right)\) | \(e\left(\frac{896}{1511}\right)\) | \(e\left(\frac{698}{1511}\right)\) | \(e\left(\frac{1246}{1511}\right)\) | \(e\left(\frac{1245}{1511}\right)\) | \(e\left(\frac{799}{1511}\right)\) | \(e\left(\frac{1047}{1511}\right)\) | \(e\left(\frac{281}{1511}\right)\) | \(e\left(\frac{84}{1511}\right)\) | \(e\left(\frac{1096}{1511}\right)\) |
| \(\chi_{9067}(216,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{688}{1511}\right)\) | \(e\left(\frac{1381}{1511}\right)\) | \(e\left(\frac{1376}{1511}\right)\) | \(e\left(\frac{1283}{1511}\right)\) | \(e\left(\frac{558}{1511}\right)\) | \(e\left(\frac{562}{1511}\right)\) | \(e\left(\frac{553}{1511}\right)\) | \(e\left(\frac{1251}{1511}\right)\) | \(e\left(\frac{460}{1511}\right)\) | \(e\left(\frac{1325}{1511}\right)\) |
| \(\chi_{9067}(221,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1366}{1511}\right)\) | \(e\left(\frac{840}{1511}\right)\) | \(e\left(\frac{1221}{1511}\right)\) | \(e\left(\frac{1357}{1511}\right)\) | \(e\left(\frac{695}{1511}\right)\) | \(e\left(\frac{88}{1511}\right)\) | \(e\left(\frac{1076}{1511}\right)\) | \(e\left(\frac{169}{1511}\right)\) | \(e\left(\frac{1212}{1511}\right)\) | \(e\left(\frac{272}{1511}\right)\) |