![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2668, base_ring=CyclotomicField(44))
M = H._module
chi = DirichletCharacter(H, M([22,16,11]))
![Copy content]()
pari:[g,chi] = znchar(Mod(1143,2668))
| Modulus: | \(2668\) | |
| Conductor: | \(2668\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
pari:znconreyconductor(g,chi)
|
| Order: | \(44\) |
![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)
|
\(\chi_{2668}(75,\cdot)\)
\(\chi_{2668}(215,\cdot)\)
\(\chi_{2668}(307,\cdot)\)
\(\chi_{2668}(331,\cdot)\)
\(\chi_{2668}(423,\cdot)\)
\(\chi_{2668}(679,\cdot)\)
\(\chi_{2668}(771,\cdot)\)
\(\chi_{2668}(795,\cdot)\)
\(\chi_{2668}(887,\cdot)\)
\(\chi_{2668}(1143,\cdot)\)
\(\chi_{2668}(1235,\cdot)\)
\(\chi_{2668}(1375,\cdot)\)
\(\chi_{2668}(1467,\cdot)\)
\(\chi_{2668}(2187,\cdot)\)
\(\chi_{2668}(2279,\cdot)\)
\(\chi_{2668}(2303,\cdot)\)
\(\chi_{2668}(2395,\cdot)\)
\(\chi_{2668}(2419,\cdot)\)
\(\chi_{2668}(2511,\cdot)\)
\(\chi_{2668}(2651,\cdot)\)
![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 ]
\((1335,465,553)\) → \((-1,e\left(\frac{4}{11}\right),i)\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 2668 }(1143, a) \) |
\(1\) | \(1\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{43}{44}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
