H = DirichletGroup(1404928)
chi = H[1]
pari: [g,chi] = znchar(Mod(1,1404928))
Basic properties
Modulus: | \(1404928\) | |
Conductor: | \(1\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(1\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | yes | |
Primitive: | no, induced from \(\chi_{1}(0,\cdot)\) | 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
\((983039,843781,983041)\) → \((1,1,1)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) |
\( \chi_{ 1404928 }(1, a) \) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
sage: chi.jacobi_sum(n)