![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(508288, base_ring=CyclotomicField(114))
M = H._module
chi = DirichletCharacter(H, M([0,57,57,7]))
![Copy content]()
pari:[g,chi] = znchar(Mod(26817,508288))
\(\chi_{508288}(65,\cdot)\)
\(\chi_{508288}(2881,\cdot)\)
\(\chi_{508288}(26817,\cdot)\)
\(\chi_{508288}(29633,\cdot)\)
\(\chi_{508288}(53569,\cdot)\)
\(\chi_{508288}(80321,\cdot)\)
\(\chi_{508288}(83137,\cdot)\)
\(\chi_{508288}(107073,\cdot)\)
\(\chi_{508288}(109889,\cdot)\)
\(\chi_{508288}(133825,\cdot)\)
\(\chi_{508288}(136641,\cdot)\)
\(\chi_{508288}(163393,\cdot)\)
\(\chi_{508288}(187329,\cdot)\)
\(\chi_{508288}(190145,\cdot)\)
\(\chi_{508288}(214081,\cdot)\)
\(\chi_{508288}(216897,\cdot)\)
\(\chi_{508288}(240833,\cdot)\)
\(\chi_{508288}(243649,\cdot)\)
\(\chi_{508288}(267585,\cdot)\)
\(\chi_{508288}(270401,\cdot)\)
\(\chi_{508288}(294337,\cdot)\)
\(\chi_{508288}(297153,\cdot)\)
\(\chi_{508288}(321089,\cdot)\)
\(\chi_{508288}(323905,\cdot)\)
\(\chi_{508288}(347841,\cdot)\)
\(\chi_{508288}(350657,\cdot)\)
\(\chi_{508288}(374593,\cdot)\)
\(\chi_{508288}(377409,\cdot)\)
\(\chi_{508288}(401345,\cdot)\)
\(\chi_{508288}(404161,\cdot)\)
...
![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 ]
\((166783,174725,323457,14081)\) → \((1,-1,-1,e\left(\frac{7}{114}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 508288 }(26817, a) \) |
\(1\) | \(1\) | \(e\left(\frac{2}{57}\right)\) | \(e\left(\frac{85}{114}\right)\) | \(e\left(\frac{27}{38}\right)\) | \(e\left(\frac{4}{57}\right)\) | \(e\left(\frac{23}{114}\right)\) | \(e\left(\frac{89}{114}\right)\) | \(e\left(\frac{43}{114}\right)\) | \(e\left(\frac{85}{114}\right)\) | \(e\left(\frac{55}{57}\right)\) | \(e\left(\frac{28}{57}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
