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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(12138, base_ring=CyclotomicField(34))
M = H._module
chi = DirichletCharacter(H, M([0,0,14]))
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pari:[g,chi] = znchar(Mod(9283,12138))
\(\chi_{12138}(715,\cdot)\)
\(\chi_{12138}(1429,\cdot)\)
\(\chi_{12138}(2143,\cdot)\)
\(\chi_{12138}(2857,\cdot)\)
\(\chi_{12138}(3571,\cdot)\)
\(\chi_{12138}(4285,\cdot)\)
\(\chi_{12138}(4999,\cdot)\)
\(\chi_{12138}(5713,\cdot)\)
\(\chi_{12138}(6427,\cdot)\)
\(\chi_{12138}(7141,\cdot)\)
\(\chi_{12138}(7855,\cdot)\)
\(\chi_{12138}(8569,\cdot)\)
\(\chi_{12138}(9283,\cdot)\)
\(\chi_{12138}(9997,\cdot)\)
\(\chi_{12138}(10711,\cdot)\)
\(\chi_{12138}(11425,\cdot)\)
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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 ]
\((8093,10405,9829)\) → \((1,1,e\left(\frac{7}{17}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 12138 }(9283, a) \) |
\(1\) | \(1\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{7}{17}\right)\) |
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sage:chi.jacobi_sum(n)
