![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8400, base_ring=CyclotomicField(60))
M = H._module
chi = DirichletCharacter(H, M([30,30,30,57,50]))
![Copy content]()
pari:[g,chi] = znchar(Mod(6263,8400))
\(\chi_{8400}(647,\cdot)\)
\(\chi_{8400}(887,\cdot)\)
\(\chi_{8400}(983,\cdot)\)
\(\chi_{8400}(1223,\cdot)\)
\(\chi_{8400}(2327,\cdot)\)
\(\chi_{8400}(2567,\cdot)\)
\(\chi_{8400}(2663,\cdot)\)
\(\chi_{8400}(2903,\cdot)\)
\(\chi_{8400}(4247,\cdot)\)
\(\chi_{8400}(4583,\cdot)\)
\(\chi_{8400}(5687,\cdot)\)
\(\chi_{8400}(5927,\cdot)\)
\(\chi_{8400}(6023,\cdot)\)
\(\chi_{8400}(6263,\cdot)\)
\(\chi_{8400}(7367,\cdot)\)
\(\chi_{8400}(7703,\cdot)\)
![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 ]
\((3151,2101,2801,5377,3601)\) → \((-1,-1,-1,e\left(\frac{19}{20}\right),e\left(\frac{5}{6}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 8400 }(6263, a) \) |
\(1\) | \(1\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(i\) |
![Copy content]()
sage:chi.jacobi_sum(n)
