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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1254, base_ring=CyclotomicField(18))
M = H._module
chi = DirichletCharacter(H, M([0,9,11]))
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pari:[g,chi] = znchar(Mod(1231,1254))
\(\chi_{1254}(109,\cdot)\)
\(\chi_{1254}(241,\cdot)\)
\(\chi_{1254}(307,\cdot)\)
\(\chi_{1254}(439,\cdot)\)
\(\chi_{1254}(637,\cdot)\)
\(\chi_{1254}(1231,\cdot)\)
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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 ]
\((419,343,1123)\) → \((1,-1,e\left(\frac{11}{18}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) | \(37\) |
| \( \chi_{ 1254 }(1231, a) \) |
\(1\) | \(1\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(-1\) |
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sage:chi.jacobi_sum(n)
