![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8464, base_ring=CyclotomicField(506))
M = H._module
chi = DirichletCharacter(H, M([0,0,34]))
![Copy content]()
pari:[g,chi] = znchar(Mod(225,8464))
\(\chi_{8464}(49,\cdot)\)
\(\chi_{8464}(81,\cdot)\)
\(\chi_{8464}(193,\cdot)\)
\(\chi_{8464}(209,\cdot)\)
\(\chi_{8464}(225,\cdot)\)
\(\chi_{8464}(257,\cdot)\)
\(\chi_{8464}(289,\cdot)\)
\(\chi_{8464}(305,\cdot)\)
\(\chi_{8464}(353,\cdot)\)
\(\chi_{8464}(417,\cdot)\)
\(\chi_{8464}(449,\cdot)\)
\(\chi_{8464}(545,\cdot)\)
\(\chi_{8464}(561,\cdot)\)
\(\chi_{8464}(577,\cdot)\)
\(\chi_{8464}(593,\cdot)\)
\(\chi_{8464}(625,\cdot)\)
\(\chi_{8464}(657,\cdot)\)
\(\chi_{8464}(673,\cdot)\)
\(\chi_{8464}(721,\cdot)\)
\(\chi_{8464}(785,\cdot)\)
\(\chi_{8464}(817,\cdot)\)
\(\chi_{8464}(913,\cdot)\)
\(\chi_{8464}(929,\cdot)\)
\(\chi_{8464}(945,\cdot)\)
\(\chi_{8464}(961,\cdot)\)
\(\chi_{8464}(993,\cdot)\)
\(\chi_{8464}(1025,\cdot)\)
\(\chi_{8464}(1041,\cdot)\)
\(\chi_{8464}(1089,\cdot)\)
\(\chi_{8464}(1153,\cdot)\)
...
![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 ]
\((7407,2117,6353)\) → \((1,1,e\left(\frac{17}{253}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 8464 }(225, a) \) |
\(1\) | \(1\) | \(e\left(\frac{19}{253}\right)\) | \(e\left(\frac{17}{253}\right)\) | \(e\left(\frac{169}{253}\right)\) | \(e\left(\frac{38}{253}\right)\) | \(e\left(\frac{43}{253}\right)\) | \(e\left(\frac{194}{253}\right)\) | \(e\left(\frac{36}{253}\right)\) | \(e\left(\frac{240}{253}\right)\) | \(e\left(\frac{134}{253}\right)\) | \(e\left(\frac{188}{253}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
