![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(30345, base_ring=CyclotomicField(408))
M = H._module
chi = DirichletCharacter(H, M([0,102,340,363]))
![Copy content]()
pari:[g,chi] = znchar(Mod(7642,30345))
\(\chi_{30345}(502,\cdot)\)
\(\chi_{30345}(892,\cdot)\)
\(\chi_{30345}(1018,\cdot)\)
\(\chi_{30345}(1522,\cdot)\)
\(\chi_{30345}(1657,\cdot)\)
\(\chi_{30345}(1753,\cdot)\)
\(\chi_{30345}(1783,\cdot)\)
\(\chi_{30345}(2287,\cdot)\)
\(\chi_{30345}(2518,\cdot)\)
\(\chi_{30345}(2677,\cdot)\)
\(\chi_{30345}(2803,\cdot)\)
\(\chi_{30345}(3307,\cdot)\)
\(\chi_{30345}(3442,\cdot)\)
\(\chi_{30345}(3538,\cdot)\)
\(\chi_{30345}(3568,\cdot)\)
\(\chi_{30345}(4072,\cdot)\)
\(\chi_{30345}(4303,\cdot)\)
\(\chi_{30345}(4462,\cdot)\)
\(\chi_{30345}(4588,\cdot)\)
\(\chi_{30345}(5227,\cdot)\)
\(\chi_{30345}(5323,\cdot)\)
\(\chi_{30345}(5353,\cdot)\)
\(\chi_{30345}(5857,\cdot)\)
\(\chi_{30345}(6088,\cdot)\)
\(\chi_{30345}(6247,\cdot)\)
\(\chi_{30345}(6373,\cdot)\)
\(\chi_{30345}(6877,\cdot)\)
\(\chi_{30345}(7012,\cdot)\)
\(\chi_{30345}(7108,\cdot)\)
\(\chi_{30345}(7138,\cdot)\)
...
![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 ]
\((20231,24277,4336,28036)\) → \((1,i,e\left(\frac{5}{6}\right),e\left(\frac{121}{136}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(19\) | \(22\) | \(23\) | \(26\) |
| \( \chi_{ 30345 }(7642, a) \) |
\(1\) | \(1\) | \(e\left(\frac{49}{51}\right)\) | \(e\left(\frac{47}{51}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{325}{408}\right)\) | \(e\left(\frac{43}{68}\right)\) | \(e\left(\frac{43}{51}\right)\) | \(e\left(\frac{25}{204}\right)\) | \(e\left(\frac{103}{136}\right)\) | \(e\left(\frac{335}{408}\right)\) | \(e\left(\frac{121}{204}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
