H = DirichletGroup(1033709)
chi = H[1033708]
pari: [g,chi] = znchar(Mod(1033708,1033709))
Kronecker symbol representation
sage: kronecker_character(1033709)
pari: znchartokronecker(g,chi)
\(\displaystyle\left(\frac{1033709}{\bullet}\right)\)
Basic properties
Modulus: | \(1033709\) | |
Conductor: | \(1033709\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Related number fields
Field of values: | \(\Q\) |
Values on generators
\((758746,407268)\) → \((-1,-1)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) |
\( \chi_{ 1033709 }(1033708, a) \) | \(1\) | \(1\) | \(-1\) | \(-1\) | \(1\) | \(1\) | \(1\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
sage: chi.jacobi_sum(n)