![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(25410, base_ring=CyclotomicField(110))
M = H._module
chi = DirichletCharacter(H, M([0,55,55,27]))
![Copy content]()
pari:[g,chi] = znchar(Mod(7069,25410))
\(\chi_{25410}(139,\cdot)\)
\(\chi_{25410}(349,\cdot)\)
\(\chi_{25410}(1399,\cdot)\)
\(\chi_{25410}(2239,\cdot)\)
\(\chi_{25410}(2449,\cdot)\)
\(\chi_{25410}(3709,\cdot)\)
\(\chi_{25410}(4549,\cdot)\)
\(\chi_{25410}(4969,\cdot)\)
\(\chi_{25410}(6019,\cdot)\)
\(\chi_{25410}(6859,\cdot)\)
\(\chi_{25410}(7069,\cdot)\)
\(\chi_{25410}(7279,\cdot)\)
\(\chi_{25410}(8329,\cdot)\)
\(\chi_{25410}(9379,\cdot)\)
\(\chi_{25410}(9589,\cdot)\)
\(\chi_{25410}(11479,\cdot)\)
\(\chi_{25410}(11689,\cdot)\)
\(\chi_{25410}(11899,\cdot)\)
\(\chi_{25410}(12949,\cdot)\)
\(\chi_{25410}(13789,\cdot)\)
\(\chi_{25410}(13999,\cdot)\)
\(\chi_{25410}(14209,\cdot)\)
\(\chi_{25410}(15259,\cdot)\)
\(\chi_{25410}(16099,\cdot)\)
\(\chi_{25410}(16309,\cdot)\)
\(\chi_{25410}(16519,\cdot)\)
\(\chi_{25410}(17569,\cdot)\)
\(\chi_{25410}(18409,\cdot)\)
\(\chi_{25410}(18619,\cdot)\)
\(\chi_{25410}(18829,\cdot)\)
...
![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 ]
\((8471,15247,14521,7141)\) → \((1,-1,-1,e\left(\frac{27}{110}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
| \( \chi_{ 25410 }(7069, a) \) |
\(1\) | \(1\) | \(e\left(\frac{87}{110}\right)\) | \(e\left(\frac{3}{110}\right)\) | \(e\left(\frac{48}{55}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{19}{110}\right)\) | \(e\left(\frac{67}{110}\right)\) | \(e\left(\frac{89}{110}\right)\) | \(e\left(\frac{8}{55}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{3}{55}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
