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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3267, base_ring=CyclotomicField(18))
M = H._module
chi = DirichletCharacter(H, M([11,0]))
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pari:[g,chi] = znchar(Mod(1211,3267))
\(\chi_{3267}(122,\cdot)\)
\(\chi_{3267}(848,\cdot)\)
\(\chi_{3267}(1211,\cdot)\)
\(\chi_{3267}(1937,\cdot)\)
\(\chi_{3267}(2300,\cdot)\)
\(\chi_{3267}(3026,\cdot)\)
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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 ]
\((3026,244)\) → \((e\left(\frac{11}{18}\right),1)\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 3267 }(1211, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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sage:chi.jacobi_sum(n)
