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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4864, base_ring=CyclotomicField(72))
M = H._module
chi = DirichletCharacter(H, M([0,63,28]))
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pari:[g,chi] = znchar(Mod(33,4864))
\(\chi_{4864}(33,\cdot)\)
\(\chi_{4864}(97,\cdot)\)
\(\chi_{4864}(545,\cdot)\)
\(\chi_{4864}(737,\cdot)\)
\(\chi_{4864}(801,\cdot)\)
\(\chi_{4864}(865,\cdot)\)
\(\chi_{4864}(1249,\cdot)\)
\(\chi_{4864}(1313,\cdot)\)
\(\chi_{4864}(1761,\cdot)\)
\(\chi_{4864}(1953,\cdot)\)
\(\chi_{4864}(2017,\cdot)\)
\(\chi_{4864}(2081,\cdot)\)
\(\chi_{4864}(2465,\cdot)\)
\(\chi_{4864}(2529,\cdot)\)
\(\chi_{4864}(2977,\cdot)\)
\(\chi_{4864}(3169,\cdot)\)
\(\chi_{4864}(3233,\cdot)\)
\(\chi_{4864}(3297,\cdot)\)
\(\chi_{4864}(3681,\cdot)\)
\(\chi_{4864}(3745,\cdot)\)
\(\chi_{4864}(4193,\cdot)\)
\(\chi_{4864}(4385,\cdot)\)
\(\chi_{4864}(4449,\cdot)\)
\(\chi_{4864}(4513,\cdot)\)
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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 ]
\((3839,2053,4353)\) → \((1,e\left(\frac{7}{8}\right),e\left(\frac{7}{18}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 4864 }(33, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{49}{72}\right)\) | \(e\left(\frac{7}{72}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{5}{72}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{55}{72}\right)\) | \(e\left(\frac{1}{36}\right)\) |
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sage:chi.jacobi_sum(n)
