![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4830, base_ring=CyclotomicField(66))
M = H._module
chi = DirichletCharacter(H, M([33,0,22,39]))
![Copy content]()
pari:[g,chi] = znchar(Mod(4391,4830))
\(\chi_{4830}(11,\cdot)\)
\(\chi_{4830}(191,\cdot)\)
\(\chi_{4830}(221,\cdot)\)
\(\chi_{4830}(401,\cdot)\)
\(\chi_{4830}(431,\cdot)\)
\(\chi_{4830}(641,\cdot)\)
\(\chi_{4830}(1031,\cdot)\)
\(\chi_{4830}(1661,\cdot)\)
\(\chi_{4830}(1901,\cdot)\)
\(\chi_{4830}(2081,\cdot)\)
\(\chi_{4830}(2291,\cdot)\)
\(\chi_{4830}(2321,\cdot)\)
\(\chi_{4830}(2501,\cdot)\)
\(\chi_{4830}(2711,\cdot)\)
\(\chi_{4830}(2951,\cdot)\)
\(\chi_{4830}(3161,\cdot)\)
\(\chi_{4830}(3791,\cdot)\)
\(\chi_{4830}(3971,\cdot)\)
\(\chi_{4830}(4391,\cdot)\)
\(\chi_{4830}(4421,\cdot)\)
![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 ]
\((3221,967,2761,1891)\) → \((-1,1,e\left(\frac{1}{3}\right),e\left(\frac{13}{22}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
| \( \chi_{ 4830 }(4391, a) \) |
\(1\) | \(1\) | \(e\left(\frac{5}{33}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{32}{33}\right)\) | \(e\left(\frac{35}{66}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{5}{66}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{1}{6}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
