from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(612, base_ring=CyclotomicField(2))
M = H._module
chi = DirichletCharacter(H, M([1,0,1]))
chi.galois_orbit()
[g,chi] = znchar(Mod(271,612))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
Modulus: | \(612\) | |
Conductor: | \(68\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(2\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | yes | |
Primitive: | no, induced from 68.d | 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: | \(\Q\) |
Fixed field: | \(\Q(\sqrt{-17}) \) |
Characters in Galois orbit
Character | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{612}(271,\cdot)\) | \(-1\) | \(1\) | \(-1\) | \(1\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(-1\) |