![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1225, base_ring=CyclotomicField(84))
M = H._module
chi = DirichletCharacter(H, M([21,8]))
![Copy content]()
pari:[g,chi] = znchar(Mod(32,1225))
\(\chi_{1225}(32,\cdot)\)
\(\chi_{1225}(93,\cdot)\)
\(\chi_{1225}(107,\cdot)\)
\(\chi_{1225}(193,\cdot)\)
\(\chi_{1225}(207,\cdot)\)
\(\chi_{1225}(268,\cdot)\)
\(\chi_{1225}(282,\cdot)\)
\(\chi_{1225}(368,\cdot)\)
\(\chi_{1225}(382,\cdot)\)
\(\chi_{1225}(443,\cdot)\)
\(\chi_{1225}(457,\cdot)\)
\(\chi_{1225}(543,\cdot)\)
\(\chi_{1225}(632,\cdot)\)
\(\chi_{1225}(718,\cdot)\)
\(\chi_{1225}(732,\cdot)\)
\(\chi_{1225}(793,\cdot)\)
\(\chi_{1225}(807,\cdot)\)
\(\chi_{1225}(893,\cdot)\)
\(\chi_{1225}(907,\cdot)\)
\(\chi_{1225}(968,\cdot)\)
\(\chi_{1225}(982,\cdot)\)
\(\chi_{1225}(1068,\cdot)\)
\(\chi_{1225}(1082,\cdot)\)
\(\chi_{1225}(1143,\cdot)\)
![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 ]
\((1177,101)\) → \((i,e\left(\frac{2}{21}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 1225 }(32, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{71}{84}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{25}{84}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{19}{21}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
