from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4928, base_ring=CyclotomicField(2))
M = H._module
chi = DirichletCharacter(H, M([1,1,0,1]))
pari: [g,chi] = znchar(Mod(351,4928))
Basic properties
Modulus: | \(4928\) | |
Conductor: | \(88\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(2\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | yes | |
Primitive: | no, induced from \(\chi_{88}(43,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4928.l
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: | \(\Q(\sqrt{22}) \) |
Values on generators
\((4159,1541,2817,3137)\) → \((-1,-1,1,-1)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
\( \chi_{ 4928 }(351, a) \) | \(1\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(1\) | \(-1\) | \(-1\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
sage: chi.jacobi_sum(n)