![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8004, base_ring=CyclotomicField(154))
M = H._module
chi = DirichletCharacter(H, M([0,77,119,11]))
![Copy content]()
pari:[g,chi] = znchar(Mod(3281,8004))
\(\chi_{8004}(5,\cdot)\)
\(\chi_{8004}(125,\cdot)\)
\(\chi_{8004}(149,\cdot)\)
\(\chi_{8004}(245,\cdot)\)
\(\chi_{8004}(341,\cdot)\)
\(\chi_{8004}(497,\cdot)\)
\(\chi_{8004}(557,\cdot)\)
\(\chi_{8004}(701,\cdot)\)
\(\chi_{8004}(845,\cdot)\)
\(\chi_{8004}(941,\cdot)\)
\(\chi_{8004}(1049,\cdot)\)
\(\chi_{8004}(1169,\cdot)\)
\(\chi_{8004}(1193,\cdot)\)
\(\chi_{8004}(1253,\cdot)\)
\(\chi_{8004}(1385,\cdot)\)
\(\chi_{8004}(1397,\cdot)\)
\(\chi_{8004}(1601,\cdot)\)
\(\chi_{8004}(1745,\cdot)\)
\(\chi_{8004}(1949,\cdot)\)
\(\chi_{8004}(1985,\cdot)\)
\(\chi_{8004}(2081,\cdot)\)
\(\chi_{8004}(2213,\cdot)\)
\(\chi_{8004}(2297,\cdot)\)
\(\chi_{8004}(2333,\cdot)\)
\(\chi_{8004}(2429,\cdot)\)
\(\chi_{8004}(2777,\cdot)\)
\(\chi_{8004}(2909,\cdot)\)
\(\chi_{8004}(3125,\cdot)\)
\(\chi_{8004}(3257,\cdot)\)
\(\chi_{8004}(3281,\cdot)\)
...
![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 ]
\((4003,2669,3133,553)\) → \((1,-1,e\left(\frac{17}{22}\right),e\left(\frac{1}{14}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(31\) | \(35\) | \(37\) |
| \( \chi_{ 8004 }(3281, a) \) |
\(1\) | \(1\) | \(e\left(\frac{65}{77}\right)\) | \(e\left(\frac{83}{154}\right)\) | \(e\left(\frac{37}{154}\right)\) | \(e\left(\frac{8}{77}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{18}{77}\right)\) | \(e\left(\frac{53}{77}\right)\) | \(e\left(\frac{109}{154}\right)\) | \(e\left(\frac{59}{154}\right)\) | \(e\left(\frac{34}{77}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
