from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43904, base_ring=CyclotomicField(4704))
M = H._module
chi = DirichletCharacter(H, M([2352,3087,3328]))
chi.galois_orbit()
[g,chi] = znchar(Mod(11,43904))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(43904\) | |
| Conductor: | \(43904\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(4704\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Related number fields
| Field of values: | $\Q(\zeta_{4704})$ |
| Fixed field: | Number field defined by a degree 4704 polynomial (not computed) |
First 31 of 1344 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{43904}(11,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{829}{4704}\right)\) | \(e\left(\frac{815}{4704}\right)\) | \(e\left(\frac{829}{2352}\right)\) | \(e\left(\frac{2059}{4704}\right)\) | \(e\left(\frac{747}{1568}\right)\) | \(e\left(\frac{137}{392}\right)\) | \(e\left(\frac{73}{1176}\right)\) | \(e\left(\frac{89}{96}\right)\) | \(e\left(\frac{1681}{2352}\right)\) | \(e\left(\frac{815}{2352}\right)\) |
| \(\chi_{43904}(51,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{2327}{4704}\right)\) | \(e\left(\frac{2509}{4704}\right)\) | \(e\left(\frac{2327}{2352}\right)\) | \(e\left(\frac{1121}{4704}\right)\) | \(e\left(\frac{1153}{1568}\right)\) | \(e\left(\frac{11}{392}\right)\) | \(e\left(\frac{395}{1176}\right)\) | \(e\left(\frac{43}{96}\right)\) | \(e\left(\frac{1331}{2352}\right)\) | \(e\left(\frac{157}{2352}\right)\) |
| \(\chi_{43904}(107,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{2741}{4704}\right)\) | \(e\left(\frac{2167}{4704}\right)\) | \(e\left(\frac{389}{2352}\right)\) | \(e\left(\frac{3443}{4704}\right)\) | \(e\left(\frac{499}{1568}\right)\) | \(e\left(\frac{17}{392}\right)\) | \(e\left(\frac{1145}{1176}\right)\) | \(e\left(\frac{49}{96}\right)\) | \(e\left(\frac{2057}{2352}\right)\) | \(e\left(\frac{2167}{2352}\right)\) |
| \(\chi_{43904}(123,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1033}{4704}\right)\) | \(e\left(\frac{851}{4704}\right)\) | \(e\left(\frac{1033}{2352}\right)\) | \(e\left(\frac{1567}{4704}\right)\) | \(e\left(\frac{1311}{1568}\right)\) | \(e\left(\frac{157}{392}\right)\) | \(e\left(\frac{613}{1176}\right)\) | \(e\left(\frac{53}{96}\right)\) | \(e\left(\frac{1357}{2352}\right)\) | \(e\left(\frac{851}{2352}\right)\) |
| \(\chi_{43904}(163,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{2147}{4704}\right)\) | \(e\left(\frac{817}{4704}\right)\) | \(e\left(\frac{2147}{2352}\right)\) | \(e\left(\frac{725}{4704}\right)\) | \(e\left(\frac{1301}{1568}\right)\) | \(e\left(\frac{247}{392}\right)\) | \(e\left(\frac{887}{1176}\right)\) | \(e\left(\frac{7}{96}\right)\) | \(e\left(\frac{95}{2352}\right)\) | \(e\left(\frac{817}{2352}\right)\) |
| \(\chi_{43904}(179,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{3991}{4704}\right)\) | \(e\left(\frac{3725}{4704}\right)\) | \(e\left(\frac{1639}{2352}\right)\) | \(e\left(\frac{3841}{4704}\right)\) | \(e\left(\frac{865}{1568}\right)\) | \(e\left(\frac{251}{392}\right)\) | \(e\left(\frac{211}{1176}\right)\) | \(e\left(\frac{11}{96}\right)\) | \(e\left(\frac{1363}{2352}\right)\) | \(e\left(\frac{1373}{2352}\right)\) |
| \(\chi_{43904}(219,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{545}{4704}\right)\) | \(e\left(\frac{3163}{4704}\right)\) | \(e\left(\frac{545}{2352}\right)\) | \(e\left(\frac{2375}{4704}\right)\) | \(e\left(\frac{423}{1568}\right)\) | \(e\left(\frac{309}{392}\right)\) | \(e\left(\frac{797}{1176}\right)\) | \(e\left(\frac{13}{96}\right)\) | \(e\left(\frac{149}{2352}\right)\) | \(e\left(\frac{811}{2352}\right)\) |
| \(\chi_{43904}(235,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{2581}{4704}\right)\) | \(e\left(\frac{2231}{4704}\right)\) | \(e\left(\frac{229}{2352}\right)\) | \(e\left(\frac{3091}{4704}\right)\) | \(e\left(\frac{979}{1568}\right)\) | \(e\left(\frac{9}{392}\right)\) | \(e\left(\frac{145}{1176}\right)\) | \(e\left(\frac{17}{96}\right)\) | \(e\left(\frac{697}{2352}\right)\) | \(e\left(\frac{2231}{2352}\right)\) |
| \(\chi_{43904}(291,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1507}{4704}\right)\) | \(e\left(\frac{1073}{4704}\right)\) | \(e\left(\frac{1507}{2352}\right)\) | \(e\left(\frac{4021}{4704}\right)\) | \(e\left(\frac{85}{1568}\right)\) | \(e\left(\frac{215}{392}\right)\) | \(e\left(\frac{415}{1176}\right)\) | \(e\left(\frac{71}{96}\right)\) | \(e\left(\frac{1711}{2352}\right)\) | \(e\left(\frac{1073}{2352}\right)\) |
| \(\chi_{43904}(331,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{3725}{4704}\right)\) | \(e\left(\frac{127}{4704}\right)\) | \(e\left(\frac{1373}{2352}\right)\) | \(e\left(\frac{4667}{4704}\right)\) | \(e\left(\frac{1467}{1568}\right)\) | \(e\left(\frac{321}{392}\right)\) | \(e\left(\frac{1121}{1176}\right)\) | \(e\left(\frac{73}{96}\right)\) | \(e\left(\frac{1601}{2352}\right)\) | \(e\left(\frac{127}{2352}\right)\) |
| \(\chi_{43904}(347,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{769}{4704}\right)\) | \(e\left(\frac{251}{4704}\right)\) | \(e\left(\frac{769}{2352}\right)\) | \(e\left(\frac{1927}{4704}\right)\) | \(e\left(\frac{1319}{1568}\right)\) | \(e\left(\frac{85}{392}\right)\) | \(e\left(\frac{1021}{1176}\right)\) | \(e\left(\frac{77}{96}\right)\) | \(e\left(\frac{2053}{2352}\right)\) | \(e\left(\frac{251}{2352}\right)\) |
| \(\chi_{43904}(387,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{3803}{4704}\right)\) | \(e\left(\frac{4153}{4704}\right)\) | \(e\left(\frac{1451}{2352}\right)\) | \(e\left(\frac{605}{4704}\right)\) | \(e\left(\frac{253}{1568}\right)\) | \(e\left(\frac{271}{392}\right)\) | \(e\left(\frac{359}{1176}\right)\) | \(e\left(\frac{31}{96}\right)\) | \(e\left(\frac{647}{2352}\right)\) | \(e\left(\frac{1801}{2352}\right)\) |
| \(\chi_{43904}(403,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{367}{4704}\right)\) | \(e\left(\frac{4469}{4704}\right)\) | \(e\left(\frac{367}{2352}\right)\) | \(e\left(\frac{1513}{4704}\right)\) | \(e\left(\frac{1545}{1568}\right)\) | \(e\left(\frac{11}{392}\right)\) | \(e\left(\frac{787}{1176}\right)\) | \(e\left(\frac{35}{96}\right)\) | \(e\left(\frac{1723}{2352}\right)\) | \(e\left(\frac{2117}{2352}\right)\) |
| \(\chi_{43904}(443,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{2873}{4704}\right)\) | \(e\left(\frac{2467}{4704}\right)\) | \(e\left(\frac{521}{2352}\right)\) | \(e\left(\frac{911}{4704}\right)\) | \(e\left(\frac{495}{1568}\right)\) | \(e\left(\frac{53}{392}\right)\) | \(e\left(\frac{941}{1176}\right)\) | \(e\left(\frac{37}{96}\right)\) | \(e\left(\frac{1709}{2352}\right)\) | \(e\left(\frac{115}{2352}\right)\) |
| \(\chi_{43904}(499,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{935}{4704}\right)\) | \(e\left(\frac{4477}{4704}\right)\) | \(e\left(\frac{935}{2352}\right)\) | \(e\left(\frac{881}{4704}\right)\) | \(e\left(\frac{625}{1568}\right)\) | \(e\left(\frac{59}{392}\right)\) | \(e\left(\frac{515}{1176}\right)\) | \(e\left(\frac{91}{96}\right)\) | \(e\left(\frac{83}{2352}\right)\) | \(e\left(\frac{2125}{2352}\right)\) |
| \(\chi_{43904}(515,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{571}{4704}\right)\) | \(e\left(\frac{4505}{4704}\right)\) | \(e\left(\frac{571}{2352}\right)\) | \(e\left(\frac{1021}{4704}\right)\) | \(e\left(\frac{541}{1568}\right)\) | \(e\left(\frac{31}{392}\right)\) | \(e\left(\frac{151}{1176}\right)\) | \(e\left(\frac{95}{96}\right)\) | \(e\left(\frac{1399}{2352}\right)\) | \(e\left(\frac{2153}{2352}\right)\) |
| \(\chi_{43904}(555,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{2693}{4704}\right)\) | \(e\left(\frac{775}{4704}\right)\) | \(e\left(\frac{341}{2352}\right)\) | \(e\left(\frac{515}{4704}\right)\) | \(e\left(\frac{643}{1568}\right)\) | \(e\left(\frac{289}{392}\right)\) | \(e\left(\frac{257}{1176}\right)\) | \(e\left(\frac{1}{96}\right)\) | \(e\left(\frac{473}{2352}\right)\) | \(e\left(\frac{775}{2352}\right)\) |
| \(\chi_{43904}(571,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1177}{4704}\right)\) | \(e\left(\frac{323}{4704}\right)\) | \(e\left(\frac{1177}{2352}\right)\) | \(e\left(\frac{943}{4704}\right)\) | \(e\left(\frac{879}{1568}\right)\) | \(e\left(\frac{125}{392}\right)\) | \(e\left(\frac{925}{1176}\right)\) | \(e\left(\frac{5}{96}\right)\) | \(e\left(\frac{1405}{2352}\right)\) | \(e\left(\frac{323}{2352}\right)\) |
| \(\chi_{43904}(611,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{3443}{4704}\right)\) | \(e\left(\frac{769}{4704}\right)\) | \(e\left(\frac{1091}{2352}\right)\) | \(e\left(\frac{4517}{4704}\right)\) | \(e\left(\frac{549}{1568}\right)\) | \(e\left(\frac{351}{392}\right)\) | \(e\left(\frac{167}{1176}\right)\) | \(e\left(\frac{55}{96}\right)\) | \(e\left(\frac{527}{2352}\right)\) | \(e\left(\frac{769}{2352}\right)\) |
| \(\chi_{43904}(627,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{2119}{4704}\right)\) | \(e\left(\frac{1181}{4704}\right)\) | \(e\left(\frac{2119}{2352}\right)\) | \(e\left(\frac{2545}{4704}\right)\) | \(e\left(\frac{209}{1568}\right)\) | \(e\left(\frac{275}{392}\right)\) | \(e\left(\frac{859}{1176}\right)\) | \(e\left(\frac{59}{96}\right)\) | \(e\left(\frac{739}{2352}\right)\) | \(e\left(\frac{1181}{2352}\right)\) |
| \(\chi_{43904}(683,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{3397}{4704}\right)\) | \(e\left(\frac{2375}{4704}\right)\) | \(e\left(\frac{1045}{2352}\right)\) | \(e\left(\frac{1123}{4704}\right)\) | \(e\left(\frac{99}{1568}\right)\) | \(e\left(\frac{89}{392}\right)\) | \(e\left(\frac{1129}{1176}\right)\) | \(e\left(\frac{65}{96}\right)\) | \(e\left(\frac{1753}{2352}\right)\) | \(e\left(\frac{23}{2352}\right)\) |
| \(\chi_{43904}(723,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1919}{4704}\right)\) | \(e\left(\frac{2437}{4704}\right)\) | \(e\left(\frac{1919}{2352}\right)\) | \(e\left(\frac{2105}{4704}\right)\) | \(e\left(\frac{25}{1568}\right)\) | \(e\left(\frac{363}{392}\right)\) | \(e\left(\frac{491}{1176}\right)\) | \(e\left(\frac{19}{96}\right)\) | \(e\left(\frac{1979}{2352}\right)\) | \(e\left(\frac{85}{2352}\right)\) |
| \(\chi_{43904}(739,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{307}{4704}\right)\) | \(e\left(\frac{3905}{4704}\right)\) | \(e\left(\frac{307}{2352}\right)\) | \(e\left(\frac{1381}{4704}\right)\) | \(e\left(\frac{549}{1568}\right)\) | \(e\left(\frac{351}{392}\right)\) | \(e\left(\frac{559}{1176}\right)\) | \(e\left(\frac{23}{96}\right)\) | \(e\left(\frac{2095}{2352}\right)\) | \(e\left(\frac{1553}{2352}\right)\) |
| \(\chi_{43904}(779,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{4349}{4704}\right)\) | \(e\left(\frac{4111}{4704}\right)\) | \(e\left(\frac{1997}{2352}\right)\) | \(e\left(\frac{395}{4704}\right)\) | \(e\left(\frac{1163}{1568}\right)\) | \(e\left(\frac{313}{392}\right)\) | \(e\left(\frac{905}{1176}\right)\) | \(e\left(\frac{25}{96}\right)\) | \(e\left(\frac{1025}{2352}\right)\) | \(e\left(\frac{1759}{2352}\right)\) |
| \(\chi_{43904}(795,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{2257}{4704}\right)\) | \(e\left(\frac{1067}{4704}\right)\) | \(e\left(\frac{2257}{2352}\right)\) | \(e\left(\frac{3319}{4704}\right)\) | \(e\left(\frac{1559}{1568}\right)\) | \(e\left(\frac{277}{392}\right)\) | \(e\left(\frac{325}{1176}\right)\) | \(e\left(\frac{29}{96}\right)\) | \(e\left(\frac{1765}{2352}\right)\) | \(e\left(\frac{1067}{2352}\right)\) |
| \(\chi_{43904}(835,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1067}{4704}\right)\) | \(e\left(\frac{73}{4704}\right)\) | \(e\left(\frac{1067}{2352}\right)\) | \(e\left(\frac{3053}{4704}\right)\) | \(e\left(\frac{621}{1568}\right)\) | \(e\left(\frac{95}{392}\right)\) | \(e\left(\frac{311}{1176}\right)\) | \(e\left(\frac{79}{96}\right)\) | \(e\left(\frac{2087}{2352}\right)\) | \(e\left(\frac{73}{2352}\right)\) |
| \(\chi_{43904}(891,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1481}{4704}\right)\) | \(e\left(\frac{4435}{4704}\right)\) | \(e\left(\frac{1481}{2352}\right)\) | \(e\left(\frac{671}{4704}\right)\) | \(e\left(\frac{1535}{1568}\right)\) | \(e\left(\frac{101}{392}\right)\) | \(e\left(\frac{1061}{1176}\right)\) | \(e\left(\frac{85}{96}\right)\) | \(e\left(\frac{461}{2352}\right)\) | \(e\left(\frac{2083}{2352}\right)\) |
| \(\chi_{43904}(907,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{2461}{4704}\right)\) | \(e\left(\frac{1103}{4704}\right)\) | \(e\left(\frac{109}{2352}\right)\) | \(e\left(\frac{2827}{4704}\right)\) | \(e\left(\frac{555}{1568}\right)\) | \(e\left(\frac{297}{392}\right)\) | \(e\left(\frac{865}{1176}\right)\) | \(e\left(\frac{89}{96}\right)\) | \(e\left(\frac{1441}{2352}\right)\) | \(e\left(\frac{1103}{2352}\right)\) |
| \(\chi_{43904}(947,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{887}{4704}\right)\) | \(e\left(\frac{3085}{4704}\right)\) | \(e\left(\frac{887}{2352}\right)\) | \(e\left(\frac{2657}{4704}\right)\) | \(e\left(\frac{769}{1568}\right)\) | \(e\left(\frac{331}{392}\right)\) | \(e\left(\frac{803}{1176}\right)\) | \(e\left(\frac{43}{96}\right)\) | \(e\left(\frac{851}{2352}\right)\) | \(e\left(\frac{733}{2352}\right)\) |
| \(\chi_{43904}(963,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{715}{4704}\right)\) | \(e\left(\frac{3977}{4704}\right)\) | \(e\left(\frac{715}{2352}\right)\) | \(e\left(\frac{397}{4704}\right)\) | \(e\left(\frac{109}{1568}\right)\) | \(e\left(\frac{391}{392}\right)\) | \(e\left(\frac{463}{1176}\right)\) | \(e\left(\frac{47}{96}\right)\) | \(e\left(\frac{1447}{2352}\right)\) | \(e\left(\frac{1625}{2352}\right)\) |
| \(\chi_{43904}(1003,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{3989}{4704}\right)\) | \(e\left(\frac{727}{4704}\right)\) | \(e\left(\frac{1637}{2352}\right)\) | \(e\left(\frac{4307}{4704}\right)\) | \(e\left(\frac{1459}{1568}\right)\) | \(e\left(\frac{1}{392}\right)\) | \(e\left(\frac{713}{1176}\right)\) | \(e\left(\frac{49}{96}\right)\) | \(e\left(\frac{905}{2352}\right)\) | \(e\left(\frac{727}{2352}\right)\) |