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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2432, base_ring=CyclotomicField(72))
M = H._module
chi = DirichletCharacter(H, M([0,9,40]))
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pari:[g,chi] = znchar(Mod(625,2432))
\(\chi_{2432}(17,\cdot)\)
\(\chi_{2432}(81,\cdot)\)
\(\chi_{2432}(177,\cdot)\)
\(\chi_{2432}(465,\cdot)\)
\(\chi_{2432}(529,\cdot)\)
\(\chi_{2432}(593,\cdot)\)
\(\chi_{2432}(625,\cdot)\)
\(\chi_{2432}(689,\cdot)\)
\(\chi_{2432}(785,\cdot)\)
\(\chi_{2432}(1073,\cdot)\)
\(\chi_{2432}(1137,\cdot)\)
\(\chi_{2432}(1201,\cdot)\)
\(\chi_{2432}(1233,\cdot)\)
\(\chi_{2432}(1297,\cdot)\)
\(\chi_{2432}(1393,\cdot)\)
\(\chi_{2432}(1681,\cdot)\)
\(\chi_{2432}(1745,\cdot)\)
\(\chi_{2432}(1809,\cdot)\)
\(\chi_{2432}(1841,\cdot)\)
\(\chi_{2432}(1905,\cdot)\)
\(\chi_{2432}(2001,\cdot)\)
\(\chi_{2432}(2289,\cdot)\)
\(\chi_{2432}(2353,\cdot)\)
\(\chi_{2432}(2417,\cdot)\)
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sage:chi.galois_orbit()
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pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
\((1407,2053,1921)\) → \((1,e\left(\frac{1}{8}\right),e\left(\frac{5}{9}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 2432 }(625, a) \) |
\(1\) | \(1\) | \(e\left(\frac{43}{72}\right)\) | \(e\left(\frac{1}{72}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{47}{72}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{13}{72}\right)\) | \(e\left(\frac{31}{36}\right)\) |
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sage:chi.jacobi_sum(n)
