![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(763, base_ring=CyclotomicField(54))
M = H._module
chi = DirichletCharacter(H, M([9,35]))
![Copy content]()
pari:[g,chi] = znchar(Mod(192,763))
| Modulus: | \(763\) | |
| Conductor: | \(763\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
pari:znconreyconductor(g,chi)
|
| Order: | \(54\) |
![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: | odd |
![Copy content]()
sage:chi.is_odd()
![Copy content]()
pari:zncharisodd(g,chi)
|
\(\chi_{763}(129,\cdot)\)
\(\chi_{763}(145,\cdot)\)
\(\chi_{763}(192,\cdot)\)
\(\chi_{763}(213,\cdot)\)
\(\chi_{763}(278,\cdot)\)
\(\chi_{763}(292,\cdot)\)
\(\chi_{763}(306,\cdot)\)
\(\chi_{763}(339,\cdot)\)
\(\chi_{763}(388,\cdot)\)
\(\chi_{763}(411,\cdot)\)
\(\chi_{763}(465,\cdot)\)
\(\chi_{763}(467,\cdot)\)
\(\chi_{763}(523,\cdot)\)
\(\chi_{763}(530,\cdot)\)
\(\chi_{763}(542,\cdot)\)
\(\chi_{763}(647,\cdot)\)
\(\chi_{763}(682,\cdot)\)
\(\chi_{763}(754,\cdot)\)
![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 ]
\((437,442)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{35}{54}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 763 }(192, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{47}{54}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{5}{54}\right)\) | \(e\left(\frac{4}{27}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{20}{27}\right)\) | \(e\left(\frac{10}{27}\right)\) | \(e\left(\frac{25}{54}\right)\) | \(e\left(\frac{23}{54}\right)\) |
![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)
