![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(763, base_ring=CyclotomicField(108))
M = H._module
chi = DirichletCharacter(H, M([54,35]))
![Copy content]()
pari:[g,chi] = znchar(Mod(174,763))
| Modulus: | \(763\) | |
| Conductor: | \(763\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
pari:znconreyconductor(g,chi)
|
| Order: | \(108\) |
![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)
|
\(\chi_{763}(6,\cdot)\)
\(\chi_{763}(13,\cdot)\)
\(\chi_{763}(62,\cdot)\)
\(\chi_{763}(69,\cdot)\)
\(\chi_{763}(139,\cdot)\)
\(\chi_{763}(146,\cdot)\)
\(\chi_{763}(153,\cdot)\)
\(\chi_{763}(160,\cdot)\)
\(\chi_{763}(167,\cdot)\)
\(\chi_{763}(174,\cdot)\)
\(\chi_{763}(181,\cdot)\)
\(\chi_{763}(188,\cdot)\)
\(\chi_{763}(258,\cdot)\)
\(\chi_{763}(265,\cdot)\)
\(\chi_{763}(314,\cdot)\)
\(\chi_{763}(321,\cdot)\)
\(\chi_{763}(377,\cdot)\)
\(\chi_{763}(384,\cdot)\)
\(\chi_{763}(412,\cdot)\)
\(\chi_{763}(426,\cdot)\)
\(\chi_{763}(447,\cdot)\)
\(\chi_{763}(454,\cdot)\)
\(\chi_{763}(475,\cdot)\)
\(\chi_{763}(489,\cdot)\)
\(\chi_{763}(503,\cdot)\)
\(\chi_{763}(531,\cdot)\)
\(\chi_{763}(559,\cdot)\)
\(\chi_{763}(587,\cdot)\)
\(\chi_{763}(601,\cdot)\)
\(\chi_{763}(615,\cdot)\)
...
![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 ]
\((437,442)\) → \((-1,e\left(\frac{35}{108}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 763 }(174, a) \) |
\(1\) | \(1\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{19}{54}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{7}{54}\right)\) | \(e\left(\frac{89}{108}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{19}{27}\right)\) | \(e\left(\frac{65}{108}\right)\) | \(e\left(\frac{97}{108}\right)\) | \(e\left(\frac{8}{27}\right)\) |
![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)
