![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2420, base_ring=CyclotomicField(44))
M = H._module
chi = DirichletCharacter(H, M([22,11,34]))
![Copy content]()
pari:[g,chi] = znchar(Mod(1407,2420))
| Modulus: | \(2420\) | |
| Conductor: | \(2420\) |
![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: | odd |
![Copy content]()
sage:chi.is_odd()
![Copy content]()
pari:zncharisodd(g,chi)
|
\(\chi_{2420}(43,\cdot)\)
\(\chi_{2420}(87,\cdot)\)
\(\chi_{2420}(263,\cdot)\)
\(\chi_{2420}(307,\cdot)\)
\(\chi_{2420}(527,\cdot)\)
\(\chi_{2420}(703,\cdot)\)
\(\chi_{2420}(747,\cdot)\)
\(\chi_{2420}(923,\cdot)\)
\(\chi_{2420}(1143,\cdot)\)
\(\chi_{2420}(1187,\cdot)\)
\(\chi_{2420}(1363,\cdot)\)
\(\chi_{2420}(1407,\cdot)\)
\(\chi_{2420}(1583,\cdot)\)
\(\chi_{2420}(1627,\cdot)\)
\(\chi_{2420}(1803,\cdot)\)
\(\chi_{2420}(1847,\cdot)\)
\(\chi_{2420}(2023,\cdot)\)
\(\chi_{2420}(2067,\cdot)\)
\(\chi_{2420}(2243,\cdot)\)
\(\chi_{2420}(2287,\cdot)\)
![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 ]
\((1211,1937,2301)\) → \((-1,i,e\left(\frac{17}{22}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 2420 }(1407, a) \) |
\(-1\) | \(1\) | \(i\) | \(e\left(\frac{7}{44}\right)\) | \(-1\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(-i\) | \(e\left(\frac{7}{11}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
