H = DirichletGroup(334620)
chi = H[174241]
pari: [g,chi] = znchar(Mod(174241,334620))
Basic properties
Modulus: | \(334620\) | |
Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{169}(2,\cdot)\) | 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: | $\Q(\zeta_{156})$ |
Values on generators
\((167311,37181,267697,273781,174241)\) → \((1,1,1,1,e\left(\frac{1}{156}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 334620 }(174241, a) \) | \(-1\) | \(1\) | \(e\left(\frac{107}{156}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{7}{52}\right)\) | \(e\left(\frac{151}{156}\right)\) | \(e\left(\frac{85}{156}\right)\) | \(e\left(\frac{61}{78}\right)\) |
sage: chi.jacobi_sum(n)