from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1088, base_ring=CyclotomicField(16))
M = H._module
chi = DirichletCharacter(H, M([8,13,5]))
pari: [g,chi] = znchar(Mod(107,1088))
Basic properties
Modulus: | \(1088\) | |
Conductor: | \(1088\) | 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 1088.ca
\(\chi_{1088}(107,\cdot)\) \(\chi_{1088}(163,\cdot)\) \(\chi_{1088}(267,\cdot)\) \(\chi_{1088}(411,\cdot)\) \(\chi_{1088}(507,\cdot)\) \(\chi_{1088}(691,\cdot)\) \(\chi_{1088}(1027,\cdot)\) \(\chi_{1088}(1043,\cdot)\)
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: | 16.16.1730228566815155980950535730783370329718784.5 |
Values on generators
\((511,69,513)\) → \((-1,e\left(\frac{13}{16}\right),e\left(\frac{5}{16}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
\( \chi_{ 1088 }(107, a) \) | \(1\) | \(1\) | \(i\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(-1\) | \(-i\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{9}{16}\right)\) |
sage: chi.jacobi_sum(n)