H = DirichletGroup(11029607)
chi = H[11029606]
pari: [g,chi] = znchar(Mod(11029606,11029607))
Kronecker symbol representation
sage: kronecker_character(-11029607)
pari: znchartokronecker(g,chi)
\(\displaystyle\left(\frac{-11029607}{\bullet}\right)\)
Basic properties
Modulus: | \(11029607\) | |
Conductor: | \(11029607\) | 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
\((5597115,5432495)\) → \((-1,-1)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) |
\( \chi_{ 11029607 }(11029606, a) \) | \(-1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
sage: chi.jacobi_sum(n)