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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1617, base_ring=CyclotomicField(14))
M = H._module
chi = DirichletCharacter(H, M([0,9,7]))
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pari:[g,chi] = znchar(Mod(1231,1617))
\(\chi_{1617}(76,\cdot)\)
\(\chi_{1617}(307,\cdot)\)
\(\chi_{1617}(769,\cdot)\)
\(\chi_{1617}(1000,\cdot)\)
\(\chi_{1617}(1231,\cdot)\)
\(\chi_{1617}(1462,\cdot)\)
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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 ]
\((1079,199,442)\) → \((1,e\left(\frac{9}{14}\right),-1)\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 1617 }(1231, a) \) |
\(1\) | \(1\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(1\) | \(e\left(\frac{1}{14}\right)\) |
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sage:chi.jacobi_sum(n)
