![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4563, base_ring=CyclotomicField(468))
M = H._module
chi = DirichletCharacter(H, M([182,459]))
![Copy content]()
pari:[g,chi] = znchar(Mod(317,4563))
| Modulus: | \(4563\) | |
| Conductor: | \(4563\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
pari:znconreyconductor(g,chi)
|
| Order: | \(468\) |
![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)
|
\(\chi_{4563}(5,\cdot)\)
\(\chi_{4563}(47,\cdot)\)
\(\chi_{4563}(83,\cdot)\)
\(\chi_{4563}(86,\cdot)\)
\(\chi_{4563}(122,\cdot)\)
\(\chi_{4563}(164,\cdot)\)
\(\chi_{4563}(200,\cdot)\)
\(\chi_{4563}(203,\cdot)\)
\(\chi_{4563}(281,\cdot)\)
\(\chi_{4563}(317,\cdot)\)
\(\chi_{4563}(320,\cdot)\)
\(\chi_{4563}(356,\cdot)\)
\(\chi_{4563}(398,\cdot)\)
\(\chi_{4563}(434,\cdot)\)
\(\chi_{4563}(473,\cdot)\)
\(\chi_{4563}(515,\cdot)\)
\(\chi_{4563}(551,\cdot)\)
\(\chi_{4563}(554,\cdot)\)
\(\chi_{4563}(590,\cdot)\)
\(\chi_{4563}(632,\cdot)\)
\(\chi_{4563}(668,\cdot)\)
\(\chi_{4563}(671,\cdot)\)
\(\chi_{4563}(707,\cdot)\)
\(\chi_{4563}(749,\cdot)\)
\(\chi_{4563}(785,\cdot)\)
\(\chi_{4563}(788,\cdot)\)
\(\chi_{4563}(824,\cdot)\)
\(\chi_{4563}(866,\cdot)\)
\(\chi_{4563}(902,\cdot)\)
\(\chi_{4563}(905,\cdot)\)
...
![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 ]
\((677,3889)\) → \((e\left(\frac{7}{18}\right),e\left(\frac{51}{52}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 4563 }(317, a) \) |
\(1\) | \(1\) | \(e\left(\frac{173}{468}\right)\) | \(e\left(\frac{173}{234}\right)\) | \(e\left(\frac{361}{468}\right)\) | \(e\left(\frac{77}{468}\right)\) | \(e\left(\frac{17}{156}\right)\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{35}{468}\right)\) | \(e\left(\frac{125}{234}\right)\) | \(e\left(\frac{56}{117}\right)\) | \(e\left(\frac{1}{39}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
