from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5950, base_ring=CyclotomicField(2))
M = H._module
chi = DirichletCharacter(H, M([1,0,1]))
pari: [g,chi] = znchar(Mod(2549,5950))
Basic properties
Modulus: | \(5950\) | |
Conductor: | \(85\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(2\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | yes | |
Primitive: | no, induced from \(\chi_{85}(84,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5950.g
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: | \(\Q\) |
Fixed field: | \(\Q(\sqrt{85}) \) |
Values on generators
\((477,2551,2451)\) → \((-1,1,-1)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(33\) |
\( \chi_{ 5950 }(2549, a) \) | \(1\) | \(1\) | \(1\) | \(1\) | \(-1\) | \(-1\) | \(1\) | \(1\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
sage: chi.jacobi_sum(n)