from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(100315, base_ring=CyclotomicField(2866))
M = H._module
chi = DirichletCharacter(H, M([1433,1286]))
chi.galois_orbit()
[g,chi] = znchar(Mod(4,100315))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(100315\) | |
| Conductor: | \(100315\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(2866\) | 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: | $\Q(\zeta_{1433})$ |
| Fixed field: | Number field defined by a degree 2866 polynomial (not computed) |
First 21 of 1432 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{100315}(4,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{399}{2866}\right)\) | \(e\left(\frac{2513}{2866}\right)\) | \(e\left(\frac{399}{1433}\right)\) | \(e\left(\frac{23}{1433}\right)\) | \(e\left(\frac{2113}{2866}\right)\) | \(e\left(\frac{1197}{2866}\right)\) | \(e\left(\frac{1080}{1433}\right)\) | \(e\left(\frac{1093}{1433}\right)\) | \(e\left(\frac{445}{2866}\right)\) | \(e\left(\frac{1385}{2866}\right)\) |
| \(\chi_{100315}(64,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1197}{2866}\right)\) | \(e\left(\frac{1807}{2866}\right)\) | \(e\left(\frac{1197}{1433}\right)\) | \(e\left(\frac{69}{1433}\right)\) | \(e\left(\frac{607}{2866}\right)\) | \(e\left(\frac{725}{2866}\right)\) | \(e\left(\frac{374}{1433}\right)\) | \(e\left(\frac{413}{1433}\right)\) | \(e\left(\frac{1335}{2866}\right)\) | \(e\left(\frac{1289}{2866}\right)\) |
| \(\chi_{100315}(94,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2425}{2866}\right)\) | \(e\left(\frac{541}{2866}\right)\) | \(e\left(\frac{992}{1433}\right)\) | \(e\left(\frac{50}{1433}\right)\) | \(e\left(\frac{2039}{2866}\right)\) | \(e\left(\frac{1543}{2866}\right)\) | \(e\left(\frac{541}{1433}\right)\) | \(e\left(\frac{1130}{1433}\right)\) | \(e\left(\frac{2525}{2866}\right)\) | \(e\left(\frac{581}{2866}\right)\) |
| \(\chi_{100315}(174,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{905}{2866}\right)\) | \(e\left(\frac{521}{2866}\right)\) | \(e\left(\frac{905}{1433}\right)\) | \(e\left(\frac{713}{1433}\right)\) | \(e\left(\frac{2451}{2866}\right)\) | \(e\left(\frac{2715}{2866}\right)\) | \(e\left(\frac{521}{1433}\right)\) | \(e\left(\frac{924}{1433}\right)\) | \(e\left(\frac{2331}{2866}\right)\) | \(e\left(\frac{2811}{2866}\right)\) |
| \(\chi_{100315}(199,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1083}{2866}\right)\) | \(e\left(\frac{1089}{2866}\right)\) | \(e\left(\frac{1083}{1433}\right)\) | \(e\left(\frac{1086}{1433}\right)\) | \(e\left(\frac{1641}{2866}\right)\) | \(e\left(\frac{383}{2866}\right)\) | \(e\left(\frac{1089}{1433}\right)\) | \(e\left(\frac{1329}{1433}\right)\) | \(e\left(\frac{389}{2866}\right)\) | \(e\left(\frac{2531}{2866}\right)\) |
| \(\chi_{100315}(274,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1047}{2866}\right)\) | \(e\left(\frac{2069}{2866}\right)\) | \(e\left(\frac{1047}{1433}\right)\) | \(e\left(\frac{125}{1433}\right)\) | \(e\left(\frac{1515}{2866}\right)\) | \(e\left(\frac{275}{2866}\right)\) | \(e\left(\frac{636}{1433}\right)\) | \(e\left(\frac{1392}{1433}\right)\) | \(e\left(\frac{1297}{2866}\right)\) | \(e\left(\frac{2169}{2866}\right)\) |
| \(\chi_{100315}(479,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1373}{2866}\right)\) | \(e\left(\frac{2111}{2866}\right)\) | \(e\left(\frac{1373}{1433}\right)\) | \(e\left(\frac{309}{1433}\right)\) | \(e\left(\frac{1223}{2866}\right)\) | \(e\left(\frac{1253}{2866}\right)\) | \(e\left(\frac{678}{1433}\right)\) | \(e\left(\frac{105}{1433}\right)\) | \(e\left(\frac{1991}{2866}\right)\) | \(e\left(\frac{1785}{2866}\right)\) |
| \(\chi_{100315}(584,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2741}{2866}\right)\) | \(e\left(\frac{2129}{2866}\right)\) | \(e\left(\frac{1308}{1433}\right)\) | \(e\left(\frac{1002}{1433}\right)\) | \(e\left(\frac{279}{2866}\right)\) | \(e\left(\frac{2491}{2866}\right)\) | \(e\left(\frac{696}{1433}\right)\) | \(e\left(\frac{577}{1433}\right)\) | \(e\left(\frac{1879}{2866}\right)\) | \(e\left(\frac{1211}{2866}\right)\) |
| \(\chi_{100315}(634,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2085}{2866}\right)\) | \(e\left(\frac{1517}{2866}\right)\) | \(e\left(\frac{652}{1433}\right)\) | \(e\left(\frac{368}{1433}\right)\) | \(e\left(\frac{849}{2866}\right)\) | \(e\left(\frac{523}{2866}\right)\) | \(e\left(\frac{84}{1433}\right)\) | \(e\left(\frac{292}{1433}\right)\) | \(e\left(\frac{2821}{2866}\right)\) | \(e\left(\frac{665}{2866}\right)\) |
| \(\chi_{100315}(714,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1409}{2866}\right)\) | \(e\left(\frac{1131}{2866}\right)\) | \(e\left(\frac{1409}{1433}\right)\) | \(e\left(\frac{1270}{1433}\right)\) | \(e\left(\frac{1349}{2866}\right)\) | \(e\left(\frac{1361}{2866}\right)\) | \(e\left(\frac{1131}{1433}\right)\) | \(e\left(\frac{42}{1433}\right)\) | \(e\left(\frac{1083}{2866}\right)\) | \(e\left(\frac{2147}{2866}\right)\) |
| \(\chi_{100315}(754,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{341}{2866}\right)\) | \(e\left(\frac{589}{2866}\right)\) | \(e\left(\frac{341}{1433}\right)\) | \(e\left(\frac{465}{1433}\right)\) | \(e\left(\frac{477}{2866}\right)\) | \(e\left(\frac{1023}{2866}\right)\) | \(e\left(\frac{589}{1433}\right)\) | \(e\left(\frac{478}{1433}\right)\) | \(e\left(\frac{1271}{2866}\right)\) | \(e\left(\frac{961}{2866}\right)\) |
| \(\chi_{100315}(759,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{957}{2866}\right)\) | \(e\left(\frac{1653}{2866}\right)\) | \(e\left(\frac{957}{1433}\right)\) | \(e\left(\frac{1305}{1433}\right)\) | \(e\left(\frac{2633}{2866}\right)\) | \(e\left(\frac{5}{2866}\right)\) | \(e\left(\frac{220}{1433}\right)\) | \(e\left(\frac{833}{1433}\right)\) | \(e\left(\frac{701}{2866}\right)\) | \(e\left(\frac{2697}{2866}\right)\) |
| \(\chi_{100315}(844,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2233}{2866}\right)\) | \(e\left(\frac{991}{2866}\right)\) | \(e\left(\frac{800}{1433}\right)\) | \(e\left(\frac{179}{1433}\right)\) | \(e\left(\frac{1367}{2866}\right)\) | \(e\left(\frac{967}{2866}\right)\) | \(e\left(\frac{991}{1433}\right)\) | \(e\left(\frac{33}{1433}\right)\) | \(e\left(\frac{2591}{2866}\right)\) | \(e\left(\frac{561}{2866}\right)\) |
| \(\chi_{100315}(899,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1559}{2866}\right)\) | \(e\left(\frac{869}{2866}\right)\) | \(e\left(\frac{126}{1433}\right)\) | \(e\left(\frac{1214}{1433}\right)\) | \(e\left(\frac{441}{2866}\right)\) | \(e\left(\frac{1811}{2866}\right)\) | \(e\left(\frac{869}{1433}\right)\) | \(e\left(\frac{496}{1433}\right)\) | \(e\left(\frac{1121}{2866}\right)\) | \(e\left(\frac{1267}{2866}\right)\) |
| \(\chi_{100315}(1024,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1995}{2866}\right)\) | \(e\left(\frac{1101}{2866}\right)\) | \(e\left(\frac{562}{1433}\right)\) | \(e\left(\frac{115}{1433}\right)\) | \(e\left(\frac{1967}{2866}\right)\) | \(e\left(\frac{253}{2866}\right)\) | \(e\left(\frac{1101}{1433}\right)\) | \(e\left(\frac{1166}{1433}\right)\) | \(e\left(\frac{2225}{2866}\right)\) | \(e\left(\frac{1193}{2866}\right)\) |
| \(\chi_{100315}(1124,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2255}{2866}\right)\) | \(e\left(\frac{1029}{2866}\right)\) | \(e\left(\frac{822}{1433}\right)\) | \(e\left(\frac{209}{1433}\right)\) | \(e\left(\frac{11}{2866}\right)\) | \(e\left(\frac{1033}{2866}\right)\) | \(e\left(\frac{1029}{1433}\right)\) | \(e\left(\frac{711}{1433}\right)\) | \(e\left(\frac{2673}{2866}\right)\) | \(e\left(\frac{623}{2866}\right)\) |
| \(\chi_{100315}(1254,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{635}{2866}\right)\) | \(e\left(\frac{2139}{2866}\right)\) | \(e\left(\frac{635}{1433}\right)\) | \(e\left(\frac{1387}{1433}\right)\) | \(e\left(\frac{73}{2866}\right)\) | \(e\left(\frac{1905}{2866}\right)\) | \(e\left(\frac{706}{1433}\right)\) | \(e\left(\frac{680}{1433}\right)\) | \(e\left(\frac{543}{2866}\right)\) | \(e\left(\frac{1529}{2866}\right)\) |
| \(\chi_{100315}(1329,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2363}{2866}\right)\) | \(e\left(\frac{955}{2866}\right)\) | \(e\left(\frac{930}{1433}\right)\) | \(e\left(\frac{226}{1433}\right)\) | \(e\left(\frac{389}{2866}\right)\) | \(e\left(\frac{1357}{2866}\right)\) | \(e\left(\frac{955}{1433}\right)\) | \(e\left(\frac{522}{1433}\right)\) | \(e\left(\frac{2815}{2866}\right)\) | \(e\left(\frac{1709}{2866}\right)\) |
| \(\chi_{100315}(1394,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1343}{2866}\right)\) | \(e\left(\frac{1017}{2866}\right)\) | \(e\left(\frac{1343}{1433}\right)\) | \(e\left(\frac{1180}{1433}\right)\) | \(e\left(\frac{2551}{2866}\right)\) | \(e\left(\frac{1163}{2866}\right)\) | \(e\left(\frac{1017}{1433}\right)\) | \(e\left(\frac{874}{1433}\right)\) | \(e\left(\frac{837}{2866}\right)\) | \(e\left(\frac{1961}{2866}\right)\) |
| \(\chi_{100315}(1504,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{357}{2866}\right)\) | \(e\left(\frac{2701}{2866}\right)\) | \(e\left(\frac{357}{1433}\right)\) | \(e\left(\frac{96}{1433}\right)\) | \(e\left(\frac{533}{2866}\right)\) | \(e\left(\frac{1071}{2866}\right)\) | \(e\left(\frac{1268}{1433}\right)\) | \(e\left(\frac{450}{1433}\right)\) | \(e\left(\frac{549}{2866}\right)\) | \(e\left(\frac{485}{2866}\right)\) |
| \(\chi_{100315}(1539,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1679}{2866}\right)\) | \(e\left(\frac{2379}{2866}\right)\) | \(e\left(\frac{246}{1433}\right)\) | \(e\left(\frac{596}{1433}\right)\) | \(e\left(\frac{861}{2866}\right)\) | \(e\left(\frac{2171}{2866}\right)\) | \(e\left(\frac{946}{1433}\right)\) | \(e\left(\frac{286}{1433}\right)\) | \(e\left(\frac{5}{2866}\right)\) | \(e\left(\frac{563}{2866}\right)\) |