![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(763, base_ring=CyclotomicField(54))
M = H._module
chi = DirichletCharacter(H, M([36,40]))
![Copy content]()
pari:[g,chi] = znchar(Mod(158,763))
| Modulus: | \(763\) | |
| Conductor: | \(763\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
pari:znconreyconductor(g,chi)
|
| Order: | \(27\) |
![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)
|
\(\chi_{763}(25,\cdot)\)
\(\chi_{763}(114,\cdot)\)
\(\chi_{763}(130,\cdot)\)
\(\chi_{763}(135,\cdot)\)
\(\chi_{763}(144,\cdot)\)
\(\chi_{763}(158,\cdot)\)
\(\chi_{763}(198,\cdot)\)
\(\chi_{763}(291,\cdot)\)
\(\chi_{763}(408,\cdot)\)
\(\chi_{763}(443,\cdot)\)
\(\chi_{763}(445,\cdot)\)
\(\chi_{763}(548,\cdot)\)
\(\chi_{763}(625,\cdot)\)
\(\chi_{763}(669,\cdot)\)
\(\chi_{763}(676,\cdot)\)
\(\chi_{763}(702,\cdot)\)
\(\chi_{763}(732,\cdot)\)
\(\chi_{763}(751,\cdot)\)
![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 ]
\((437,442)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{20}{27}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 763 }(158, a) \) |
\(1\) | \(1\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{5}{27}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{17}{27}\right)\) | \(e\left(\frac{20}{27}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{10}{27}\right)\) | \(e\left(\frac{5}{27}\right)\) | \(e\left(\frac{4}{27}\right)\) | \(e\left(\frac{8}{27}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
![Copy content]()
sage:chi.gauss_sum(a)
![Copy content]()
pari:znchargauss(g,chi,a)
![Copy content]()
sage:chi.jacobi_sum(n)
![Copy content]()
sage:chi.kloosterman_sum(a,b)
