![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(40310, base_ring=CyclotomicField(966))
M = H._module
chi = DirichletCharacter(H, M([483,828,700]))
![Copy content]()
pari:[g,chi] = znchar(Mod(49,40310))
\(\chi_{40310}(49,\cdot)\)
\(\chi_{40310}(169,\cdot)\)
\(\chi_{40310}(719,\cdot)\)
\(\chi_{40310}(749,\cdot)\)
\(\chi_{40310}(819,\cdot)\)
\(\chi_{40310}(1039,\cdot)\)
\(\chi_{40310}(1109,\cdot)\)
\(\chi_{40310}(1329,\cdot)\)
\(\chi_{40310}(1399,\cdot)\)
\(\chi_{40310}(1649,\cdot)\)
\(\chi_{40310}(1789,\cdot)\)
\(\chi_{40310}(1959,\cdot)\)
\(\chi_{40310}(2229,\cdot)\)
\(\chi_{40310}(2249,\cdot)\)
\(\chi_{40310}(2539,\cdot)\)
\(\chi_{40310}(2809,\cdot)\)
\(\chi_{40310}(2829,\cdot)\)
\(\chi_{40310}(2849,\cdot)\)
\(\chi_{40310}(2949,\cdot)\)
\(\chi_{40310}(3039,\cdot)\)
\(\chi_{40310}(3069,\cdot)\)
\(\chi_{40310}(3099,\cdot)\)
\(\chi_{40310}(3139,\cdot)\)
\(\chi_{40310}(3529,\cdot)\)
\(\chi_{40310}(3619,\cdot)\)
\(\chi_{40310}(3649,\cdot)\)
\(\chi_{40310}(3819,\cdot)\)
\(\chi_{40310}(3939,\cdot)\)
\(\chi_{40310}(4009,\cdot)\)
\(\chi_{40310}(4109,\cdot)\)
...
![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 ]
\((24187,19461,16821)\) → \((-1,e\left(\frac{6}{7}\right),e\left(\frac{50}{69}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 40310 }(49, a) \) |
\(1\) | \(1\) | \(e\left(\frac{479}{966}\right)\) | \(e\left(\frac{17}{966}\right)\) | \(e\left(\frac{479}{483}\right)\) | \(e\left(\frac{242}{483}\right)\) | \(e\left(\frac{295}{966}\right)\) | \(e\left(\frac{5}{138}\right)\) | \(e\left(\frac{443}{483}\right)\) | \(e\left(\frac{248}{483}\right)\) | \(e\left(\frac{67}{322}\right)\) | \(e\left(\frac{157}{322}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
