![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9216, base_ring=CyclotomicField(384))
M = H._module
chi = DirichletCharacter(H, M([192,303,320]))
![Copy content]()
pari:[g,chi] = znchar(Mod(1031,9216))
\(\chi_{9216}(23,\cdot)\)
\(\chi_{9216}(119,\cdot)\)
\(\chi_{9216}(167,\cdot)\)
\(\chi_{9216}(263,\cdot)\)
\(\chi_{9216}(311,\cdot)\)
\(\chi_{9216}(407,\cdot)\)
\(\chi_{9216}(455,\cdot)\)
\(\chi_{9216}(551,\cdot)\)
\(\chi_{9216}(599,\cdot)\)
\(\chi_{9216}(695,\cdot)\)
\(\chi_{9216}(743,\cdot)\)
\(\chi_{9216}(839,\cdot)\)
\(\chi_{9216}(887,\cdot)\)
\(\chi_{9216}(983,\cdot)\)
\(\chi_{9216}(1031,\cdot)\)
\(\chi_{9216}(1127,\cdot)\)
\(\chi_{9216}(1175,\cdot)\)
\(\chi_{9216}(1271,\cdot)\)
\(\chi_{9216}(1319,\cdot)\)
\(\chi_{9216}(1415,\cdot)\)
\(\chi_{9216}(1463,\cdot)\)
\(\chi_{9216}(1559,\cdot)\)
\(\chi_{9216}(1607,\cdot)\)
\(\chi_{9216}(1703,\cdot)\)
\(\chi_{9216}(1751,\cdot)\)
\(\chi_{9216}(1847,\cdot)\)
\(\chi_{9216}(1895,\cdot)\)
\(\chi_{9216}(1991,\cdot)\)
\(\chi_{9216}(2039,\cdot)\)
\(\chi_{9216}(2135,\cdot)\)
...
![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 ]
\((8191,2053,4097)\) → \((-1,e\left(\frac{101}{128}\right),e\left(\frac{5}{6}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 9216 }(1031, a) \) |
\(1\) | \(1\) | \(e\left(\frac{367}{384}\right)\) | \(e\left(\frac{43}{192}\right)\) | \(e\left(\frac{155}{384}\right)\) | \(e\left(\frac{97}{384}\right)\) | \(e\left(\frac{19}{32}\right)\) | \(e\left(\frac{83}{128}\right)\) | \(e\left(\frac{137}{192}\right)\) | \(e\left(\frac{175}{192}\right)\) | \(e\left(\frac{341}{384}\right)\) | \(e\left(\frac{23}{48}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
