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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3381, base_ring=CyclotomicField(14))
M = H._module
chi = DirichletCharacter(H, M([0,8,7]))
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pari:[g,chi] = znchar(Mod(22,3381))
\(\chi_{3381}(22,\cdot)\)
\(\chi_{3381}(505,\cdot)\)
\(\chi_{3381}(988,\cdot)\)
\(\chi_{3381}(1954,\cdot)\)
\(\chi_{3381}(2437,\cdot)\)
\(\chi_{3381}(2920,\cdot)\)
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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 ]
\((2255,346,442)\) → \((1,e\left(\frac{4}{7}\right),-1)\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 3381 }(22, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(-1\) |
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sage:chi.jacobi_sum(n)
