H = DirichletGroup(1041639)
chi = H[1041638]
pari: [g,chi] = znchar(Mod(1041638,1041639))
Kronecker symbol representation
sage: kronecker_character(-1041639)
pari: znchartokronecker(g,chi)
\(\displaystyle\left(\frac{-1041639}{\bullet}\right)\)
Basic properties
| Modulus: | \(1041639\) | |
| Conductor: | \(1041639\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(2\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | yes | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
|
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Related number fields
| Field of values: | \(\Q\) |
Values on generators
\((694427,495538,1004560)\) → \((-1,-1,-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) |
| \( \chi_{ 1041639 }(1041638, a) \) | \(-1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
sage: chi.jacobi_sum(n)