from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9464, base_ring=CyclotomicField(26))
M = H._module
chi = DirichletCharacter(H, M([13,0,13,19]))
pari: [g,chi] = znchar(Mod(727,9464))
Basic properties
Modulus: | \(9464\) | |
Conductor: | \(4732\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(26\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{4732}(727,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9464.er
\(\chi_{9464}(727,\cdot)\) \(\chi_{9464}(1455,\cdot)\) \(\chi_{9464}(2183,\cdot)\) \(\chi_{9464}(2911,\cdot)\) \(\chi_{9464}(3639,\cdot)\) \(\chi_{9464}(4367,\cdot)\) \(\chi_{9464}(5095,\cdot)\) \(\chi_{9464}(5823,\cdot)\) \(\chi_{9464}(6551,\cdot)\) \(\chi_{9464}(7279,\cdot)\) \(\chi_{9464}(8007,\cdot)\) \(\chi_{9464}(8735,\cdot)\)
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: | \(\Q(\zeta_{13})\) |
Fixed field: | 26.26.24904548371754690207828206084673035814148045702609536001608390487104815104.1 |
Values on generators
\((2367,4733,2705,9297)\) → \((-1,1,-1,e\left(\frac{19}{26}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
\( \chi_{ 9464 }(727, a) \) | \(1\) | \(1\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(-1\) | \(-1\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{11}{13}\right)\) |
sage: chi.jacobi_sum(n)