![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(40310, base_ring=CyclotomicField(1932))
M = H._module
chi = DirichletCharacter(H, M([0,345,518]))
![Copy content]()
pari:[g,chi] = znchar(Mod(61,40310))
\(\chi_{40310}(21,\cdot)\)
\(\chi_{40310}(61,\cdot)\)
\(\chi_{40310}(101,\cdot)\)
\(\chi_{40310}(171,\cdot)\)
\(\chi_{40310}(211,\cdot)\)
\(\chi_{40310}(271,\cdot)\)
\(\chi_{40310}(351,\cdot)\)
\(\chi_{40310}(641,\cdot)\)
\(\chi_{40310}(751,\cdot)\)
\(\chi_{40310}(851,\cdot)\)
\(\chi_{40310}(1041,\cdot)\)
\(\chi_{40310}(1071,\cdot)\)
\(\chi_{40310}(1081,\cdot)\)
\(\chi_{40310}(1221,\cdot)\)
\(\chi_{40310}(1291,\cdot)\)
\(\chi_{40310}(1361,\cdot)\)
\(\chi_{40310}(1381,\cdot)\)
\(\chi_{40310}(1411,\cdot)\)
![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 ]
\((24187,19461,16821)\) → \((1,e\left(\frac{5}{28}\right),e\left(\frac{37}{138}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 40310 }(61, a) \) |
\(1\) | \(1\) | \(e\left(\frac{1711}{1932}\right)\) | \(e\left(\frac{265}{483}\right)\) | \(e\left(\frac{745}{966}\right)\) | \(e\left(\frac{1625}{1932}\right)\) | \(e\left(\frac{361}{966}\right)\) | \(e\left(\frac{121}{276}\right)\) | \(e\left(\frac{1859}{1932}\right)\) | \(e\left(\frac{839}{1932}\right)\) | \(e\left(\frac{261}{322}\right)\) | \(e\left(\frac{423}{644}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
