from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(663, base_ring=CyclotomicField(24))
M = H._module
chi = DirichletCharacter(H, M([0,10,21]))
chi.galois_orbit()
[g,chi] = znchar(Mod(19,663))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
Modulus: | \(663\) | |
Conductor: | \(221\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(24\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from 221.bc | 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: | \(\Q(\zeta_{24})\) |
Fixed field: | 24.0.221912159494888970129181006529110805060115683312073.1 |
Characters in Galois orbit
Character | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(19\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{663}(19,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(1\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{663}(76,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(1\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{663}(223,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(1\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{663}(253,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(1\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{663}(280,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(1\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{663}(349,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(1\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{663}(457,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(1\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{663}(553,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(1\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |