from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(390, base_ring=CyclotomicField(4))
M = H._module
chi = DirichletCharacter(H, M([2,0,3]))
chi.galois_orbit()
[g,chi] = znchar(Mod(161,390))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
Modulus: | \(390\) | |
Conductor: | \(39\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(4\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from 39.f | 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: | \(\mathbb{Q}(i)\) |
Fixed field: | 4.4.19773.1 |
Characters in Galois orbit
Character | \(-1\) | \(1\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{390}(161,\cdot)\) | \(1\) | \(1\) | \(i\) | \(-i\) | \(1\) | \(-i\) | \(1\) | \(-1\) | \(-i\) | \(i\) | \(i\) | \(-1\) |
\(\chi_{390}(281,\cdot)\) | \(1\) | \(1\) | \(-i\) | \(i\) | \(1\) | \(i\) | \(1\) | \(-1\) | \(i\) | \(-i\) | \(-i\) | \(-1\) |