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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8954, base_ring=CyclotomicField(18))
M = H._module
chi = DirichletCharacter(H, M([0,14]))
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pari:[g,chi] = znchar(Mod(7745,8954))
\(\chi_{8954}(969,\cdot)\)
\(\chi_{8954}(2179,\cdot)\)
\(\chi_{8954}(2421,\cdot)\)
\(\chi_{8954}(5325,\cdot)\)
\(\chi_{8954}(7261,\cdot)\)
\(\chi_{8954}(7745,\cdot)\)
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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 ]
\((1333,3147)\) → \((1,e\left(\frac{7}{9}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 8954 }(7745, a) \) |
\(1\) | \(1\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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sage:chi.jacobi_sum(n)
