from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1196, base_ring=CyclotomicField(4))
M = H._module
chi = DirichletCharacter(H, M([2,3,2]))
pari: [g,chi] = znchar(Mod(551,1196))
Basic properties
| Modulus: | \(1196\) | |
| Conductor: | \(1196\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(4\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1196.k
\(\chi_{1196}(551,\cdot)\) \(\chi_{1196}(827,\cdot)\)
sage: chi.galois_orbit()
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Related number fields
| Field of values: | \(\mathbb{Q}(i)\) |
| Fixed field: | 4.0.18595408.2 |
Values on generators
\((599,93,833)\) → \((-1,-i,-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(25\) |
| \( \chi_{ 1196 }(551, a) \) | \(-1\) | \(1\) | \(-1\) | \(i\) | \(i\) | \(1\) | \(i\) | \(-i\) | \(1\) | \(-i\) | \(-i\) | \(-1\) |
sage: chi.jacobi_sum(n)