H = DirichletGroup(374790)
chi = H[26911]
pari: [g,chi] = znchar(Mod(26911,374790))
Basic properties
Modulus: | \(374790\) | |
Conductor: | \(961\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(930\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{961}(3,\cdot)\) | 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: | $\Q(\zeta_{465})$ |
Values on generators
\((124931,149917,86491,26911)\) → \((1,1,1,e\left(\frac{1}{930}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(29\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 374790 }(26911, a) \) | \(-1\) | \(1\) | \(e\left(\frac{329}{465}\right)\) | \(e\left(\frac{323}{930}\right)\) | \(e\left(\frac{727}{930}\right)\) | \(e\left(\frac{107}{465}\right)\) | \(e\left(\frac{29}{310}\right)\) | \(e\left(\frac{153}{310}\right)\) | \(e\left(\frac{167}{186}\right)\) | \(e\left(\frac{37}{465}\right)\) | \(e\left(\frac{889}{930}\right)\) |
sage: chi.jacobi_sum(n)