![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(961, base_ring=CyclotomicField(310))
M = H._module
chi = DirichletCharacter(H, M([22]))
![Copy content]()
pari:[g,chi] = znchar(Mod(295,961))
| Modulus: | \(961\) | |
| Conductor: | \(961\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
pari:znconreyconductor(g,chi)
|
| Order: | \(155\) |
![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)
|
\(\chi_{961}(2,\cdot)\)
\(\chi_{961}(4,\cdot)\)
\(\chi_{961}(8,\cdot)\)
\(\chi_{961}(16,\cdot)\)
\(\chi_{961}(33,\cdot)\)
\(\chi_{961}(35,\cdot)\)
\(\chi_{961}(39,\cdot)\)
\(\chi_{961}(47,\cdot)\)
\(\chi_{961}(64,\cdot)\)
\(\chi_{961}(66,\cdot)\)
\(\chi_{961}(70,\cdot)\)
\(\chi_{961}(78,\cdot)\)
\(\chi_{961}(95,\cdot)\)
\(\chi_{961}(97,\cdot)\)
\(\chi_{961}(101,\cdot)\)
\(\chi_{961}(109,\cdot)\)
\(\chi_{961}(126,\cdot)\)
\(\chi_{961}(128,\cdot)\)
\(\chi_{961}(132,\cdot)\)
\(\chi_{961}(140,\cdot)\)
\(\chi_{961}(157,\cdot)\)
\(\chi_{961}(159,\cdot)\)
\(\chi_{961}(163,\cdot)\)
\(\chi_{961}(171,\cdot)\)
\(\chi_{961}(188,\cdot)\)
\(\chi_{961}(190,\cdot)\)
\(\chi_{961}(194,\cdot)\)
\(\chi_{961}(202,\cdot)\)
\(\chi_{961}(219,\cdot)\)
\(\chi_{961}(221,\cdot)\)
...
![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 ]
\(3\) → \(e\left(\frac{11}{155}\right)\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 961 }(295, a) \) |
\(1\) | \(1\) | \(e\left(\frac{44}{155}\right)\) | \(e\left(\frac{11}{155}\right)\) | \(e\left(\frac{88}{155}\right)\) | \(e\left(\frac{7}{31}\right)\) | \(e\left(\frac{11}{31}\right)\) | \(e\left(\frac{108}{155}\right)\) | \(e\left(\frac{132}{155}\right)\) | \(e\left(\frac{22}{155}\right)\) | \(e\left(\frac{79}{155}\right)\) | \(e\left(\frac{143}{155}\right)\) |
![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)
