from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4928, base_ring=CyclotomicField(16))
M = H._module
chi = DirichletCharacter(H, M([0,15,8,8]))
pari: [g,chi] = znchar(Mod(461,4928))
Basic properties
Modulus: | \(4928\) | |
Conductor: | \(4928\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(16\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4928.da
\(\chi_{4928}(461,\cdot)\) \(\chi_{4928}(1077,\cdot)\) \(\chi_{4928}(1693,\cdot)\) \(\chi_{4928}(2309,\cdot)\) \(\chi_{4928}(2925,\cdot)\) \(\chi_{4928}(3541,\cdot)\) \(\chi_{4928}(4157,\cdot)\) \(\chi_{4928}(4773,\cdot)\)
sage: chi.galois_orbit()
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Related number fields
Field of values: | \(\Q(\zeta_{16})\) |
Fixed field: | 16.16.746956754543411303752080333032734588928.1 |
Values on generators
\((4159,1541,2817,3137)\) → \((1,e\left(\frac{15}{16}\right),-1,-1)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
\( \chi_{ 4928 }(461, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(-i\) | \(i\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{15}{16}\right)\) |
sage: chi.jacobi_sum(n)