![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8464, base_ring=CyclotomicField(44))
M = H._module
chi = DirichletCharacter(H, M([22,33,6]))
![Copy content]()
pari:[g,chi] = znchar(Mod(6611,8464))
\(\chi_{8464}(195,\cdot)\)
\(\chi_{8464}(411,\cdot)\)
\(\chi_{8464}(571,\cdot)\)
\(\chi_{8464}(659,\cdot)\)
\(\chi_{8464}(803,\cdot)\)
\(\chi_{8464}(1939,\cdot)\)
\(\chi_{8464}(2179,\cdot)\)
\(\chi_{8464}(2379,\cdot)\)
\(\chi_{8464}(2475,\cdot)\)
\(\chi_{8464}(3731,\cdot)\)
\(\chi_{8464}(4427,\cdot)\)
\(\chi_{8464}(4643,\cdot)\)
\(\chi_{8464}(4803,\cdot)\)
\(\chi_{8464}(4891,\cdot)\)
\(\chi_{8464}(5035,\cdot)\)
\(\chi_{8464}(6171,\cdot)\)
\(\chi_{8464}(6411,\cdot)\)
\(\chi_{8464}(6611,\cdot)\)
\(\chi_{8464}(6707,\cdot)\)
\(\chi_{8464}(7963,\cdot)\)
![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 ]
\((7407,2117,6353)\) → \((-1,-i,e\left(\frac{3}{22}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 8464 }(6611, a) \) |
\(1\) | \(1\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{23}{44}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
