![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6223, base_ring=CyclotomicField(42))
M = H._module
chi = DirichletCharacter(H, M([29,23]))
![Copy content]()
pari:[g,chi] = znchar(Mod(2700,6223))
| Modulus: | \(6223\) | |
| Conductor: | \(6223\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
pari:znconreyconductor(g,chi)
|
| Order: | \(42\) |
![Copy content]()
sage:chi.multiplicative_order()
![Copy content]()
pari:charorder(g,chi)
|
| Real: | no |
| Primitive: | yes |
![Copy content]()
sage:chi.is_primitive()
![Copy content]()
pari:#znconreyconductor(g,chi)==1
|
| Minimal: | yes |
| Parity: | even |
![Copy content]()
sage:chi.is_odd()
![Copy content]()
pari:zncharisodd(g,chi)
|
\(\chi_{6223}(724,\cdot)\)
\(\chi_{6223}(894,\cdot)\)
\(\chi_{6223}(929,\cdot)\)
\(\chi_{6223}(1209,\cdot)\)
\(\chi_{6223}(1956,\cdot)\)
\(\chi_{6223}(2700,\cdot)\)
\(\chi_{6223}(2931,\cdot)\)
\(\chi_{6223}(3202,\cdot)\)
\(\chi_{6223}(3356,\cdot)\)
\(\chi_{6223}(3531,\cdot)\)
\(\chi_{6223}(4779,\cdot)\)
\(\chi_{6223}(5792,\cdot)\)
![Copy content]()
sage:chi.galois_orbit()
![Copy content]()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
\((5589,638)\) → \((e\left(\frac{29}{42}\right),e\left(\frac{23}{42}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 6223 }(2700, a) \) |
\(1\) | \(1\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(1\) |
![Copy content]()
sage:chi.jacobi_sum(n)
