from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(91, base_ring=CyclotomicField(4))
M = H._module
chi = DirichletCharacter(H, M([0,1]))
chi.galois_orbit()
[g,chi] = znchar(Mod(8,91))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
Modulus: | \(91\) | |
Conductor: | \(13\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(4\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from 13.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: | \(\mathbb{Q}(i)\) |
Fixed field: | 4.0.2197.1 |
Characters in Galois orbit
Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{91}(8,\cdot)\) | \(-1\) | \(1\) | \(i\) | \(1\) | \(-1\) | \(i\) | \(i\) | \(-i\) | \(1\) | \(-1\) | \(-i\) | \(-1\) |
\(\chi_{91}(57,\cdot)\) | \(-1\) | \(1\) | \(-i\) | \(1\) | \(-1\) | \(-i\) | \(-i\) | \(i\) | \(1\) | \(-1\) | \(i\) | \(-1\) |