![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8029, base_ring=CyclotomicField(60))
M = H._module
chi = DirichletCharacter(H, M([20,22,5]))
![Copy content]()
pari:[g,chi] = znchar(Mod(4818,8029))
| Modulus: | \(8029\) | |
| Conductor: | \(8029\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
pari:znconreyconductor(g,chi)
|
| Order: | \(60\) |
![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)
|
\(\chi_{8029}(177,\cdot)\)
\(\chi_{8029}(606,\cdot)\)
\(\chi_{8029}(695,\cdot)\)
\(\chi_{8029}(2132,\cdot)\)
\(\chi_{8029}(2678,\cdot)\)
\(\chi_{8029}(3196,\cdot)\)
\(\chi_{8029}(3427,\cdot)\)
\(\chi_{8029}(3803,\cdot)\)
\(\chi_{8029}(4041,\cdot)\)
\(\chi_{8029}(4300,\cdot)\)
\(\chi_{8029}(4818,\cdot)\)
\(\chi_{8029}(5499,\cdot)\)
\(\chi_{8029}(6017,\cdot)\)
\(\chi_{8029}(7340,\cdot)\)
\(\chi_{8029}(7926,\cdot)\)
\(\chi_{8029}(7947,\cdot)\)
![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 ]
\((5736,778,4775)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{11}{30}\right),e\left(\frac{1}{12}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 8029 }(4818, a) \) |
\(1\) | \(1\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{29}{30}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
