from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4256, base_ring=CyclotomicField(24))
M = H._module
chi = DirichletCharacter(H, M([12,15,0,20]))
chi.galois_orbit()
[g,chi] = znchar(Mod(715,4256))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
Modulus: | \(4256\) | |
Conductor: | \(608\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(24\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from 608.bn | 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: | \(\Q(\zeta_{24})\) |
Fixed field: | 24.24.372273065750166762311522006998539295982015765641428992.1 |
Characters in Galois orbit
Character | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{4256}(715,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{8}\right)\) |
\(\chi_{4256}(939,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{5}{8}\right)\) |
\(\chi_{4256}(1779,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{7}{8}\right)\) |
\(\chi_{4256}(2003,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{7}{8}\right)\) |
\(\chi_{4256}(2843,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{8}\right)\) |
\(\chi_{4256}(3067,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{8}\right)\) |
\(\chi_{4256}(3907,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{3}{8}\right)\) |
\(\chi_{4256}(4131,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{3}{8}\right)\) |