from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6760, base_ring=CyclotomicField(4))
M = H._module
chi = DirichletCharacter(H, M([2,0,2,3]))
pari: [g,chi] = znchar(Mod(239,6760))
Basic properties
Modulus: | \(6760\) | |
Conductor: | \(260\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(4\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{260}(239,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6760.bn
\(\chi_{6760}(239,\cdot)\) \(\chi_{6760}(3479,\cdot)\)
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: | 4.4.878800.1 |
Values on generators
\((5071,3381,4057,5241)\) → \((-1,1,-1,-i)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
\( \chi_{ 6760 }(239, a) \) | \(1\) | \(1\) | \(1\) | \(i\) | \(1\) | \(-i\) | \(1\) | \(i\) | \(i\) | \(-1\) | \(1\) | \(1\) |
sage: chi.jacobi_sum(n)