![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(28665, base_ring=CyclotomicField(42))
M = H._module
chi = DirichletCharacter(H, M([28,21,22,14]))
![Copy content]()
pari:[g,chi] = znchar(Mod(28564,28665))
| Modulus: | \(28665\) | |
| Conductor: | \(28665\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
pari:znconreyconductor(g,chi)
|
| Order: | \(42\) |
![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)
|
\(\chi_{28665}(3649,\cdot)\)
\(\chi_{28665}(3994,\cdot)\)
\(\chi_{28665}(7744,\cdot)\)
\(\chi_{28665}(8089,\cdot)\)
\(\chi_{28665}(12184,\cdot)\)
\(\chi_{28665}(15934,\cdot)\)
\(\chi_{28665}(16279,\cdot)\)
\(\chi_{28665}(20029,\cdot)\)
\(\chi_{28665}(20374,\cdot)\)
\(\chi_{28665}(24124,\cdot)\)
\(\chi_{28665}(28219,\cdot)\)
\(\chi_{28665}(28564,\cdot)\)
![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 ]
\((25481,11467,18721,11026)\) → \((e\left(\frac{2}{3}\right),-1,e\left(\frac{11}{21}\right),e\left(\frac{1}{3}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) | \(29\) |
| \( \chi_{ 28665 }(28564, a) \) |
\(1\) | \(1\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(1\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{3}{7}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
