H = DirichletGroup(1002413)
chi = H[1002412]
pari: [g,chi] = znchar(Mod(1002412,1002413))
Kronecker symbol representation
sage: kronecker_character(1002413)
pari: znchartokronecker(g,chi)
\(\displaystyle\left(\frac{1002413}{\bullet}\right)\)
Basic properties
| Modulus: | \(1002413\) | |
| Conductor: | \(1002413\) | 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
\((460125,82168)\) → \((-1,-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) |
| \( \chi_{ 1002413 }(1002412, a) \) | \(1\) | \(1\) | \(-1\) | \(-1\) | \(1\) | \(-1\) | \(1\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
sage: chi.jacobi_sum(n)