from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(100014, base_ring=CyclotomicField(2730))
M = H._module
chi = DirichletCharacter(H, M([1365,2065,1612]))
chi.galois_orbit()
[g,chi] = znchar(Mod(47,100014))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(100014\) | |
| Conductor: | \(50007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(2730\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 50007.lo | 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: | $\Q(\zeta_{1365})$ |
| Fixed field: | Number field defined by a degree 2730 polynomial (not computed) |
First 12 of 576 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{100014}(47,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{929}{2730}\right)\) | \(e\left(\frac{151}{910}\right)\) | \(e\left(\frac{1619}{2730}\right)\) | \(e\left(\frac{1019}{1365}\right)\) | \(e\left(\frac{1214}{1365}\right)\) | \(e\left(\frac{9}{65}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{929}{1365}\right)\) | \(e\left(\frac{704}{1365}\right)\) | \(e\left(\frac{24}{91}\right)\) |
| \(\chi_{100014}(53,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1223}{2730}\right)\) | \(e\left(\frac{907}{910}\right)\) | \(e\left(\frac{233}{2730}\right)\) | \(e\left(\frac{263}{1365}\right)\) | \(e\left(\frac{458}{1365}\right)\) | \(e\left(\frac{8}{65}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{1223}{1365}\right)\) | \(e\left(\frac{893}{1365}\right)\) | \(e\left(\frac{17}{91}\right)\) |
| \(\chi_{100014}(503,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{977}{2730}\right)\) | \(e\left(\frac{293}{910}\right)\) | \(e\left(\frac{2117}{2730}\right)\) | \(e\left(\frac{1007}{1365}\right)\) | \(e\left(\frac{617}{1365}\right)\) | \(e\left(\frac{42}{65}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{977}{1365}\right)\) | \(e\left(\frac{902}{1365}\right)\) | \(e\left(\frac{8}{91}\right)\) |
| \(\chi_{100014}(695,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{361}{2730}\right)\) | \(e\left(\frac{139}{910}\right)\) | \(e\left(\frac{2551}{2730}\right)\) | \(e\left(\frac{706}{1365}\right)\) | \(e\left(\frac{316}{1365}\right)\) | \(e\left(\frac{41}{65}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{361}{1365}\right)\) | \(e\left(\frac{181}{1365}\right)\) | \(e\left(\frac{1}{91}\right)\) |
| \(\chi_{100014}(983,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2329}{2730}\right)\) | \(e\left(\frac{501}{910}\right)\) | \(e\left(\frac{1129}{2730}\right)\) | \(e\left(\frac{214}{1365}\right)\) | \(e\left(\frac{409}{1365}\right)\) | \(e\left(\frac{29}{65}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{964}{1365}\right)\) | \(e\left(\frac{109}{1365}\right)\) | \(e\left(\frac{73}{91}\right)\) |
| \(\chi_{100014}(1007,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1867}{2730}\right)\) | \(e\left(\frac{613}{910}\right)\) | \(e\left(\frac{2137}{2730}\right)\) | \(e\left(\frac{1012}{1365}\right)\) | \(e\left(\frac{1207}{1365}\right)\) | \(e\left(\frac{12}{65}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{502}{1365}\right)\) | \(e\left(\frac{592}{1365}\right)\) | \(e\left(\frac{45}{91}\right)\) |
| \(\chi_{100014}(1061,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{79}{2730}\right)\) | \(e\left(\frac{101}{910}\right)\) | \(e\left(\frac{649}{2730}\right)\) | \(e\left(\frac{94}{1365}\right)\) | \(e\left(\frac{1264}{1365}\right)\) | \(e\left(\frac{34}{65}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{79}{1365}\right)\) | \(e\left(\frac{724}{1365}\right)\) | \(e\left(\frac{4}{91}\right)\) |
| \(\chi_{100014}(1181,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2501}{2730}\right)\) | \(e\left(\frac{479}{910}\right)\) | \(e\left(\frac{2231}{2730}\right)\) | \(e\left(\frac{626}{1365}\right)\) | \(e\left(\frac{431}{1365}\right)\) | \(e\left(\frac{1}{65}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{1136}{1365}\right)\) | \(e\left(\frac{1046}{1365}\right)\) | \(e\left(\frac{46}{91}\right)\) |
| \(\chi_{100014}(1259,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{419}{2730}\right)\) | \(e\left(\frac{121}{910}\right)\) | \(e\left(\frac{2129}{2730}\right)\) | \(e\left(\frac{464}{1365}\right)\) | \(e\left(\frac{1244}{1365}\right)\) | \(e\left(\frac{24}{65}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{419}{1365}\right)\) | \(e\left(\frac{989}{1365}\right)\) | \(e\left(\frac{12}{91}\right)\) |
| \(\chi_{100014}(1475,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{911}{2730}\right)\) | \(e\left(\frac{439}{910}\right)\) | \(e\left(\frac{1091}{2730}\right)\) | \(e\left(\frac{341}{1365}\right)\) | \(e\left(\frac{926}{1365}\right)\) | \(e\left(\frac{21}{65}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{911}{1365}\right)\) | \(e\left(\frac{971}{1365}\right)\) | \(e\left(\frac{30}{91}\right)\) |
| \(\chi_{100014}(1481,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1087}{2730}\right)\) | \(e\left(\frac{353}{910}\right)\) | \(e\left(\frac{187}{2730}\right)\) | \(e\left(\frac{1207}{1365}\right)\) | \(e\left(\frac{1012}{1365}\right)\) | \(e\left(\frac{12}{65}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{1087}{1365}\right)\) | \(e\left(\frac{787}{1365}\right)\) | \(e\left(\frac{32}{91}\right)\) |
| \(\chi_{100014}(1529,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2071}{2730}\right)\) | \(e\left(\frac{79}{910}\right)\) | \(e\left(\frac{841}{2730}\right)\) | \(e\left(\frac{961}{1365}\right)\) | \(e\left(\frac{376}{1365}\right)\) | \(e\left(\frac{6}{65}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{706}{1365}\right)\) | \(e\left(\frac{751}{1365}\right)\) | \(e\left(\frac{68}{91}\right)\) |