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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10002, base_ring=CyclotomicField(34))
M = H._module
chi = DirichletCharacter(H, M([17,3]))
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pari:[g,chi] = znchar(Mod(8747,10002))
\(\chi_{10002}(263,\cdot)\)
\(\chi_{10002}(479,\cdot)\)
\(\chi_{10002}(605,\cdot)\)
\(\chi_{10002}(845,\cdot)\)
\(\chi_{10002}(917,\cdot)\)
\(\chi_{10002}(1025,\cdot)\)
\(\chi_{10002}(4049,\cdot)\)
\(\chi_{10002}(5291,\cdot)\)
\(\chi_{10002}(5327,\cdot)\)
\(\chi_{10002}(6119,\cdot)\)
\(\chi_{10002}(7811,\cdot)\)
\(\chi_{10002}(8747,\cdot)\)
\(\chi_{10002}(8879,\cdot)\)
\(\chi_{10002}(9125,\cdot)\)
\(\chi_{10002}(9281,\cdot)\)
\(\chi_{10002}(9587,\cdot)\)
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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 ]
\((3335,1669)\) → \((-1,e\left(\frac{3}{34}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 10002 }(8747, a) \) |
\(1\) | \(1\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{33}{34}\right)\) | \(e\left(\frac{5}{34}\right)\) | \(1\) | \(e\left(\frac{33}{34}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{5}{34}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{9}{17}\right)\) |
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sage:chi.jacobi_sum(n)
