H = DirichletGroup(1404928)
chi = H[983039]
pari: [g,chi] = znchar(Mod(983039,1404928))
Basic properties
| Modulus: | \(1404928\) | |
| Conductor: | \(4\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(2\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | yes | |
| Primitive: | no, induced from \(\chi_{4}(3,\cdot)\) | 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
\((983039,843781,983041)\) → \((-1,1,1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) |
| \( \chi_{ 1404928 }(983039, a) \) | \(-1\) | \(1\) | \(-1\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(-1\) | \(1\) | \(-1\) | \(-1\) |
sage: chi.jacobi_sum(n)