![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1502, base_ring=CyclotomicField(750))
M = H._module
chi = DirichletCharacter(H, M([254]))
![Copy content]()
pari:[g,chi] = znchar(Mod(95,1502))
\(\chi_{1502}(5,\cdot)\)
\(\chi_{1502}(9,\cdot)\)
\(\chi_{1502}(13,\cdot)\)
\(\chi_{1502}(19,\cdot)\)
\(\chi_{1502}(21,\cdot)\)
\(\chi_{1502}(23,\cdot)\)
\(\chi_{1502}(25,\cdot)\)
\(\chi_{1502}(33,\cdot)\)
\(\chi_{1502}(37,\cdot)\)
\(\chi_{1502}(47,\cdot)\)
\(\chi_{1502}(59,\cdot)\)
\(\chi_{1502}(65,\cdot)\)
\(\chi_{1502}(77,\cdot)\)
\(\chi_{1502}(81,\cdot)\)
\(\chi_{1502}(87,\cdot)\)
\(\chi_{1502}(89,\cdot)\)
\(\chi_{1502}(95,\cdot)\)
\(\chi_{1502}(97,\cdot)\)
\(\chi_{1502}(105,\cdot)\)
\(\chi_{1502}(109,\cdot)\)
\(\chi_{1502}(115,\cdot)\)
\(\chi_{1502}(123,\cdot)\)
\(\chi_{1502}(127,\cdot)\)
\(\chi_{1502}(139,\cdot)\)
\(\chi_{1502}(149,\cdot)\)
\(\chi_{1502}(167,\cdot)\)
\(\chi_{1502}(169,\cdot)\)
\(\chi_{1502}(181,\cdot)\)
\(\chi_{1502}(199,\cdot)\)
\(\chi_{1502}(201,\cdot)\)
...
![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 ]
\(3\) → \(e\left(\frac{127}{375}\right)\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 1502 }(95, a) \) |
\(1\) | \(1\) | \(e\left(\frac{127}{375}\right)\) | \(e\left(\frac{97}{375}\right)\) | \(e\left(\frac{59}{125}\right)\) | \(e\left(\frac{254}{375}\right)\) | \(e\left(\frac{11}{75}\right)\) | \(e\left(\frac{16}{375}\right)\) | \(e\left(\frac{224}{375}\right)\) | \(e\left(\frac{158}{375}\right)\) | \(e\left(\frac{286}{375}\right)\) | \(e\left(\frac{304}{375}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
