from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(100315, base_ring=CyclotomicField(2866))
M = H._module
chi = DirichletCharacter(H, M([0,2572]))
chi.galois_orbit()
[g,chi] = znchar(Mod(16,100315))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(100315\) | |
| Conductor: | \(20063\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1433\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 20063.e | 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: | $\Q(\zeta_{1433})$ |
| Fixed field: | Number field defined by a degree 1433 polynomial (not computed) |
First 31 of 1432 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{100315}(16,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{399}{1433}\right)\) | \(e\left(\frac{1080}{1433}\right)\) | \(e\left(\frac{798}{1433}\right)\) | \(e\left(\frac{46}{1433}\right)\) | \(e\left(\frac{680}{1433}\right)\) | \(e\left(\frac{1197}{1433}\right)\) | \(e\left(\frac{727}{1433}\right)\) | \(e\left(\frac{753}{1433}\right)\) | \(e\left(\frac{445}{1433}\right)\) | \(e\left(\frac{1385}{1433}\right)\) |
| \(\chi_{100315}(146,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1171}{1433}\right)\) | \(e\left(\frac{1241}{1433}\right)\) | \(e\left(\frac{909}{1433}\right)\) | \(e\left(\frac{979}{1433}\right)\) | \(e\left(\frac{516}{1433}\right)\) | \(e\left(\frac{647}{1433}\right)\) | \(e\left(\frac{1049}{1433}\right)\) | \(e\left(\frac{917}{1433}\right)\) | \(e\left(\frac{717}{1433}\right)\) | \(e\left(\frac{1346}{1433}\right)\) |
| \(\chi_{100315}(211,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{917}{1433}\right)\) | \(e\left(\frac{672}{1433}\right)\) | \(e\left(\frac{401}{1433}\right)\) | \(e\left(\frac{156}{1433}\right)\) | \(e\left(\frac{1060}{1433}\right)\) | \(e\left(\frac{1318}{1433}\right)\) | \(e\left(\frac{1344}{1433}\right)\) | \(e\left(\frac{373}{1433}\right)\) | \(e\left(\frac{1073}{1433}\right)\) | \(e\left(\frac{1021}{1433}\right)\) |
| \(\chi_{100315}(256,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{798}{1433}\right)\) | \(e\left(\frac{727}{1433}\right)\) | \(e\left(\frac{163}{1433}\right)\) | \(e\left(\frac{92}{1433}\right)\) | \(e\left(\frac{1360}{1433}\right)\) | \(e\left(\frac{961}{1433}\right)\) | \(e\left(\frac{21}{1433}\right)\) | \(e\left(\frac{73}{1433}\right)\) | \(e\left(\frac{890}{1433}\right)\) | \(e\left(\frac{1337}{1433}\right)\) |
| \(\chi_{100315}(281,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{928}{1433}\right)\) | \(e\left(\frac{691}{1433}\right)\) | \(e\left(\frac{423}{1433}\right)\) | \(e\left(\frac{186}{1433}\right)\) | \(e\left(\frac{382}{1433}\right)\) | \(e\left(\frac{1351}{1433}\right)\) | \(e\left(\frac{1382}{1433}\right)\) | \(e\left(\frac{1051}{1433}\right)\) | \(e\left(\frac{1114}{1433}\right)\) | \(e\left(\frac{1052}{1433}\right)\) |
| \(\chi_{100315}(376,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1412}{1433}\right)\) | \(e\left(\frac{94}{1433}\right)\) | \(e\left(\frac{1391}{1433}\right)\) | \(e\left(\frac{73}{1433}\right)\) | \(e\left(\frac{643}{1433}\right)\) | \(e\left(\frac{1370}{1433}\right)\) | \(e\left(\frac{188}{1433}\right)\) | \(e\left(\frac{790}{1433}\right)\) | \(e\left(\frac{52}{1433}\right)\) | \(e\left(\frac{983}{1433}\right)\) |
| \(\chi_{100315}(446,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{25}{1433}\right)\) | \(e\left(\frac{434}{1433}\right)\) | \(e\left(\frac{50}{1433}\right)\) | \(e\left(\frac{459}{1433}\right)\) | \(e\left(\frac{804}{1433}\right)\) | \(e\left(\frac{75}{1433}\right)\) | \(e\left(\frac{868}{1433}\right)\) | \(e\left(\frac{629}{1433}\right)\) | \(e\left(\frac{484}{1433}\right)\) | \(e\left(\frac{331}{1433}\right)\) |
| \(\chi_{100315}(696,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{652}{1433}\right)\) | \(e\left(\frac{84}{1433}\right)\) | \(e\left(\frac{1304}{1433}\right)\) | \(e\left(\frac{736}{1433}\right)\) | \(e\left(\frac{849}{1433}\right)\) | \(e\left(\frac{523}{1433}\right)\) | \(e\left(\frac{168}{1433}\right)\) | \(e\left(\frac{584}{1433}\right)\) | \(e\left(\frac{1388}{1433}\right)\) | \(e\left(\frac{665}{1433}\right)\) |
| \(\chi_{100315}(726,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{388}{1433}\right)\) | \(e\left(\frac{1061}{1433}\right)\) | \(e\left(\frac{776}{1433}\right)\) | \(e\left(\frac{16}{1433}\right)\) | \(e\left(\frac{1358}{1433}\right)\) | \(e\left(\frac{1164}{1433}\right)\) | \(e\left(\frac{689}{1433}\right)\) | \(e\left(\frac{75}{1433}\right)\) | \(e\left(\frac{404}{1433}\right)\) | \(e\left(\frac{1354}{1433}\right)\) |
| \(\chi_{100315}(796,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{741}{1433}\right)\) | \(e\left(\frac{368}{1433}\right)\) | \(e\left(\frac{49}{1433}\right)\) | \(e\left(\frac{1109}{1433}\right)\) | \(e\left(\frac{444}{1433}\right)\) | \(e\left(\frac{790}{1433}\right)\) | \(e\left(\frac{736}{1433}\right)\) | \(e\left(\frac{989}{1433}\right)\) | \(e\left(\frac{417}{1433}\right)\) | \(e\left(\frac{525}{1433}\right)\) |
| \(\chi_{100315}(891,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{910}{1433}\right)\) | \(e\left(\frac{1181}{1433}\right)\) | \(e\left(\frac{387}{1433}\right)\) | \(e\left(\frac{658}{1433}\right)\) | \(e\left(\frac{319}{1433}\right)\) | \(e\left(\frac{1297}{1433}\right)\) | \(e\left(\frac{929}{1433}\right)\) | \(e\left(\frac{1114}{1433}\right)\) | \(e\left(\frac{135}{1433}\right)\) | \(e\left(\frac{871}{1433}\right)\) |
| \(\chi_{100315}(941,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1326}{1433}\right)\) | \(e\left(\frac{206}{1433}\right)\) | \(e\left(\frac{1219}{1433}\right)\) | \(e\left(\frac{99}{1433}\right)\) | \(e\left(\frac{342}{1433}\right)\) | \(e\left(\frac{1112}{1433}\right)\) | \(e\left(\frac{412}{1433}\right)\) | \(e\left(\frac{1091}{1433}\right)\) | \(e\left(\frac{1425}{1433}\right)\) | \(e\left(\frac{1392}{1433}\right)\) |
| \(\chi_{100315}(971,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1341}{1433}\right)\) | \(e\left(\frac{753}{1433}\right)\) | \(e\left(\frac{1249}{1433}\right)\) | \(e\left(\frac{661}{1433}\right)\) | \(e\left(\frac{1111}{1433}\right)\) | \(e\left(\frac{1157}{1433}\right)\) | \(e\left(\frac{73}{1433}\right)\) | \(e\left(\frac{322}{1433}\right)\) | \(e\left(\frac{569}{1433}\right)\) | \(e\left(\frac{1304}{1433}\right)\) |
| \(\chi_{100315}(981,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1107}{1433}\right)\) | \(e\left(\frac{1391}{1433}\right)\) | \(e\left(\frac{781}{1433}\right)\) | \(e\left(\frac{1065}{1433}\right)\) | \(e\left(\frac{292}{1433}\right)\) | \(e\left(\frac{455}{1433}\right)\) | \(e\left(\frac{1349}{1433}\right)\) | \(e\left(\frac{1141}{1433}\right)\) | \(e\left(\frac{739}{1433}\right)\) | \(e\left(\frac{384}{1433}\right)\) |
| \(\chi_{100315}(1096,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{723}{1433}\right)\) | \(e\left(\frac{858}{1433}\right)\) | \(e\left(\frac{13}{1433}\right)\) | \(e\left(\frac{148}{1433}\right)\) | \(e\left(\frac{381}{1433}\right)\) | \(e\left(\frac{736}{1433}\right)\) | \(e\left(\frac{283}{1433}\right)\) | \(e\left(\frac{1052}{1433}\right)\) | \(e\left(\frac{871}{1433}\right)\) | \(e\left(\frac{344}{1433}\right)\) |
| \(\chi_{100315}(1201,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{864}{1433}\right)\) | \(e\left(\frac{841}{1433}\right)\) | \(e\left(\frac{295}{1433}\right)\) | \(e\left(\frac{272}{1433}\right)\) | \(e\left(\frac{158}{1433}\right)\) | \(e\left(\frac{1159}{1433}\right)\) | \(e\left(\frac{249}{1433}\right)\) | \(e\left(\frac{1275}{1433}\right)\) | \(e\left(\frac{1136}{1433}\right)\) | \(e\left(\frac{90}{1433}\right)\) |
| \(\chi_{100315}(1226,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{360}{1433}\right)\) | \(e\left(\frac{231}{1433}\right)\) | \(e\left(\frac{720}{1433}\right)\) | \(e\left(\frac{591}{1433}\right)\) | \(e\left(\frac{1260}{1433}\right)\) | \(e\left(\frac{1080}{1433}\right)\) | \(e\left(\frac{462}{1433}\right)\) | \(e\left(\frac{173}{1433}\right)\) | \(e\left(\frac{951}{1433}\right)\) | \(e\left(\frac{754}{1433}\right)\) |
| \(\chi_{100315}(1301,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{390}{1433}\right)\) | \(e\left(\frac{1325}{1433}\right)\) | \(e\left(\frac{780}{1433}\right)\) | \(e\left(\frac{282}{1433}\right)\) | \(e\left(\frac{1365}{1433}\right)\) | \(e\left(\frac{1170}{1433}\right)\) | \(e\left(\frac{1217}{1433}\right)\) | \(e\left(\frac{68}{1433}\right)\) | \(e\left(\frac{672}{1433}\right)\) | \(e\left(\frac{578}{1433}\right)\) |
| \(\chi_{100315}(1311,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{408}{1433}\right)\) | \(e\left(\frac{835}{1433}\right)\) | \(e\left(\frac{816}{1433}\right)\) | \(e\left(\frac{1243}{1433}\right)\) | \(e\left(\frac{1428}{1433}\right)\) | \(e\left(\frac{1224}{1433}\right)\) | \(e\left(\frac{237}{1433}\right)\) | \(e\left(\frac{5}{1433}\right)\) | \(e\left(\frac{218}{1433}\right)\) | \(e\left(\frac{759}{1433}\right)\) |
| \(\chi_{100315}(1461,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{990}{1433}\right)\) | \(e\left(\frac{277}{1433}\right)\) | \(e\left(\frac{547}{1433}\right)\) | \(e\left(\frac{1267}{1433}\right)\) | \(e\left(\frac{599}{1433}\right)\) | \(e\left(\frac{104}{1433}\right)\) | \(e\left(\frac{554}{1433}\right)\) | \(e\left(\frac{834}{1433}\right)\) | \(e\left(\frac{824}{1433}\right)\) | \(e\left(\frac{1357}{1433}\right)\) |
| \(\chi_{100315}(1506,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1247}{1433}\right)\) | \(e\left(\frac{1242}{1433}\right)\) | \(e\left(\frac{1061}{1433}\right)\) | \(e\left(\frac{1056}{1433}\right)\) | \(e\left(\frac{782}{1433}\right)\) | \(e\left(\frac{875}{1433}\right)\) | \(e\left(\frac{1051}{1433}\right)\) | \(e\left(\frac{651}{1433}\right)\) | \(e\left(\frac{870}{1433}\right)\) | \(e\left(\frac{518}{1433}\right)\) |
| \(\chi_{100315}(1751,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{948}{1433}\right)\) | \(e\left(\frac{465}{1433}\right)\) | \(e\left(\frac{463}{1433}\right)\) | \(e\left(\frac{1413}{1433}\right)\) | \(e\left(\frac{452}{1433}\right)\) | \(e\left(\frac{1411}{1433}\right)\) | \(e\left(\frac{930}{1433}\right)\) | \(e\left(\frac{981}{1433}\right)\) | \(e\left(\frac{928}{1433}\right)\) | \(e\left(\frac{457}{1433}\right)\) |
| \(\chi_{100315}(1801,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{363}{1433}\right)\) | \(e\left(\frac{627}{1433}\right)\) | \(e\left(\frac{726}{1433}\right)\) | \(e\left(\frac{990}{1433}\right)\) | \(e\left(\frac{554}{1433}\right)\) | \(e\left(\frac{1089}{1433}\right)\) | \(e\left(\frac{1254}{1433}\right)\) | \(e\left(\frac{879}{1433}\right)\) | \(e\left(\frac{1353}{1433}\right)\) | \(e\left(\frac{1023}{1433}\right)\) |
| \(\chi_{100315}(1826,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1265}{1433}\right)\) | \(e\left(\frac{752}{1433}\right)\) | \(e\left(\frac{1097}{1433}\right)\) | \(e\left(\frac{584}{1433}\right)\) | \(e\left(\frac{845}{1433}\right)\) | \(e\left(\frac{929}{1433}\right)\) | \(e\left(\frac{71}{1433}\right)\) | \(e\left(\frac{588}{1433}\right)\) | \(e\left(\frac{416}{1433}\right)\) | \(e\left(\frac{699}{1433}\right)\) |
| \(\chi_{100315}(1916,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{886}{1433}\right)\) | \(e\left(\frac{879}{1433}\right)\) | \(e\left(\frac{339}{1433}\right)\) | \(e\left(\frac{332}{1433}\right)\) | \(e\left(\frac{235}{1433}\right)\) | \(e\left(\frac{1225}{1433}\right)\) | \(e\left(\frac{325}{1433}\right)\) | \(e\left(\frac{1198}{1433}\right)\) | \(e\left(\frac{1218}{1433}\right)\) | \(e\left(\frac{152}{1433}\right)\) |
| \(\chi_{100315}(1981,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{862}{1433}\right)\) | \(e\left(\frac{577}{1433}\right)\) | \(e\left(\frac{291}{1433}\right)\) | \(e\left(\frac{6}{1433}\right)\) | \(e\left(\frac{151}{1433}\right)\) | \(e\left(\frac{1153}{1433}\right)\) | \(e\left(\frac{1154}{1433}\right)\) | \(e\left(\frac{1282}{1433}\right)\) | \(e\left(\frac{868}{1433}\right)\) | \(e\left(\frac{866}{1433}\right)\) |
| \(\chi_{100315}(2086,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1117}{1433}\right)\) | \(e\left(\frac{1278}{1433}\right)\) | \(e\left(\frac{801}{1433}\right)\) | \(e\left(\frac{962}{1433}\right)\) | \(e\left(\frac{327}{1433}\right)\) | \(e\left(\frac{485}{1433}\right)\) | \(e\left(\frac{1123}{1433}\right)\) | \(e\left(\frac{1106}{1433}\right)\) | \(e\left(\frac{646}{1433}\right)\) | \(e\left(\frac{803}{1433}\right)\) |
| \(\chi_{100315}(2126,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1123}{1433}\right)\) | \(e\left(\frac{637}{1433}\right)\) | \(e\left(\frac{813}{1433}\right)\) | \(e\left(\frac{327}{1433}\right)\) | \(e\left(\frac{348}{1433}\right)\) | \(e\left(\frac{503}{1433}\right)\) | \(e\left(\frac{1274}{1433}\right)\) | \(e\left(\frac{1085}{1433}\right)\) | \(e\left(\frac{17}{1433}\right)\) | \(e\left(\frac{1341}{1433}\right)\) |
| \(\chi_{100315}(2166,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{247}{1433}\right)\) | \(e\left(\frac{1078}{1433}\right)\) | \(e\left(\frac{494}{1433}\right)\) | \(e\left(\frac{1325}{1433}\right)\) | \(e\left(\frac{148}{1433}\right)\) | \(e\left(\frac{741}{1433}\right)\) | \(e\left(\frac{723}{1433}\right)\) | \(e\left(\frac{1285}{1433}\right)\) | \(e\left(\frac{139}{1433}\right)\) | \(e\left(\frac{175}{1433}\right)\) |
| \(\chi_{100315}(2181,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1143}{1433}\right)\) | \(e\left(\frac{411}{1433}\right)\) | \(e\left(\frac{853}{1433}\right)\) | \(e\left(\frac{121}{1433}\right)\) | \(e\left(\frac{418}{1433}\right)\) | \(e\left(\frac{563}{1433}\right)\) | \(e\left(\frac{822}{1433}\right)\) | \(e\left(\frac{1015}{1433}\right)\) | \(e\left(\frac{1264}{1433}\right)\) | \(e\left(\frac{746}{1433}\right)\) |
| \(\chi_{100315}(2186,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1127}{1433}\right)\) | \(e\left(\frac{1165}{1433}\right)\) | \(e\left(\frac{821}{1433}\right)\) | \(e\left(\frac{859}{1433}\right)\) | \(e\left(\frac{362}{1433}\right)\) | \(e\left(\frac{515}{1433}\right)\) | \(e\left(\frac{897}{1433}\right)\) | \(e\left(\frac{1071}{1433}\right)\) | \(e\left(\frac{553}{1433}\right)\) | \(e\left(\frac{1222}{1433}\right)\) |