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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2312, base_ring=CyclotomicField(34))
M = H._module
chi = DirichletCharacter(H, M([0,0,6]))
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pari:[g,chi] = znchar(Mod(1089,2312))
\(\chi_{2312}(137,\cdot)\)
\(\chi_{2312}(273,\cdot)\)
\(\chi_{2312}(409,\cdot)\)
\(\chi_{2312}(545,\cdot)\)
\(\chi_{2312}(681,\cdot)\)
\(\chi_{2312}(817,\cdot)\)
\(\chi_{2312}(953,\cdot)\)
\(\chi_{2312}(1089,\cdot)\)
\(\chi_{2312}(1225,\cdot)\)
\(\chi_{2312}(1361,\cdot)\)
\(\chi_{2312}(1497,\cdot)\)
\(\chi_{2312}(1633,\cdot)\)
\(\chi_{2312}(1769,\cdot)\)
\(\chi_{2312}(1905,\cdot)\)
\(\chi_{2312}(2041,\cdot)\)
\(\chi_{2312}(2177,\cdot)\)
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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 ]
\((1735,1157,1737)\) → \((1,1,e\left(\frac{3}{17}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 2312 }(1089, a) \) |
\(1\) | \(1\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{6}{17}\right)\) |
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sage:chi.jacobi_sum(n)
