from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6019, base_ring=CyclotomicField(66))
M = H._module
chi = DirichletCharacter(H, M([11,58]))
pari: [g,chi] = znchar(Mod(95,6019))
Basic properties
Modulus: | \(6019\) | |
Conductor: | \(6019\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(66\) | 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 6019.cu
\(\chi_{6019}(95,\cdot)\) \(\chi_{6019}(179,\cdot)\) \(\chi_{6019}(920,\cdot)\) \(\chi_{6019}(1154,\cdot)\) \(\chi_{6019}(1219,\cdot)\) \(\chi_{6019}(1980,\cdot)\) \(\chi_{6019}(2383,\cdot)\) \(\chi_{6019}(2409,\cdot)\) \(\chi_{6019}(2630,\cdot)\) \(\chi_{6019}(2688,\cdot)\) \(\chi_{6019}(3007,\cdot)\) \(\chi_{6019}(3611,\cdot)\) \(\chi_{6019}(4203,\cdot)\) \(\chi_{6019}(4300,\cdot)\) \(\chi_{6019}(4762,\cdot)\) \(\chi_{6019}(5132,\cdot)\) \(\chi_{6019}(5236,\cdot)\) \(\chi_{6019}(5633,\cdot)\) \(\chi_{6019}(5678,\cdot)\) \(\chi_{6019}(5750,\cdot)\)
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: | \(\Q(\zeta_{33})\) |
Fixed field: | Number field defined by a degree 66 polynomial |
Values on generators
\((2316,1392)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{29}{33}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 6019 }(95, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{23}{66}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{19}{66}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{21}{22}\right)\) |
sage: chi.jacobi_sum(n)