from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3015, base_ring=CyclotomicField(22))
M = H._module
chi = DirichletCharacter(H, M([11,0,17]))
chi.galois_orbit()
[g,chi] = znchar(Mod(161,3015))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(3015\) | |
| Conductor: | \(201\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(22\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 201.j | 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: | \(\Q(\zeta_{11})\) |
| Fixed field: | 22.22.39437071573367006679286233687044038294749249.1 |
Characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{3015}(161,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{8}{11}\right)\) |
| \(\chi_{3015}(206,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{3}{11}\right)\) |
| \(\chi_{3015}(521,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{2}{11}\right)\) |
| \(\chi_{3015}(611,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{5}{11}\right)\) |
| \(\chi_{3015}(656,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{7}{11}\right)\) |
| \(\chi_{3015}(1331,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{9}{11}\right)\) |
| \(\chi_{3015}(2186,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{6}{11}\right)\) |
| \(\chi_{3015}(2321,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{4}{11}\right)\) |
| \(\chi_{3015}(2591,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{1}{11}\right)\) |
| \(\chi_{3015}(2951,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{10}{11}\right)\) |