from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(221760, base_ring=CyclotomicField(24))
M = H._module
chi = DirichletCharacter(H, M([12,21,20,18,8,0]))
chi.galois_orbit()
[g,chi] = znchar(Mod(23,221760))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(221760\) | |
| Conductor: | \(10080\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(24\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 10080.te | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Related number fields
| Field of values: | \(\Q(\zeta_{24})\) |
| Fixed field: | Number field defined by a degree 24 polynomial |
Characters in Galois orbit
| Character | \(-1\) | \(1\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{221760}(23,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(-1\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(i\) |
| \(\chi_{221760}(5303,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(-1\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(i\) |
| \(\chi_{221760}(33287,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(-1\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(-i\) |
| \(\chi_{221760}(38567,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(-1\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(-i\) |
| \(\chi_{221760}(110903,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(-1\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(i\) |
| \(\chi_{221760}(116183,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(-1\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(i\) |
| \(\chi_{221760}(144167,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(-1\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(-i\) |
| \(\chi_{221760}(149447,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(-1\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(-i\) |