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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8732, base_ring=CyclotomicField(36))
M = H._module
chi = DirichletCharacter(H, M([18,23,0]))
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pari:[g,chi] = znchar(Mod(3187,8732))
\(\chi_{8732}(355,\cdot)\)
\(\chi_{8732}(827,\cdot)\)
\(\chi_{8732}(1535,\cdot)\)
\(\chi_{8732}(1771,\cdot)\)
\(\chi_{8732}(3187,\cdot)\)
\(\chi_{8732}(3423,\cdot)\)
\(\chi_{8732}(4131,\cdot)\)
\(\chi_{8732}(4603,\cdot)\)
\(\chi_{8732}(5311,\cdot)\)
\(\chi_{8732}(6255,\cdot)\)
\(\chi_{8732}(7435,\cdot)\)
\(\chi_{8732}(8379,\cdot)\)
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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 ]
\((4367,1889,297)\) → \((-1,e\left(\frac{23}{36}\right),1)\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 8732 }(3187, a) \) |
\(1\) | \(1\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{1}{18}\right)\) |
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sage:chi.jacobi_sum(n)
