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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6936, base_ring=CyclotomicField(34))
M = H._module
chi = DirichletCharacter(H, M([0,17,0,10]))
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pari:[g,chi] = znchar(Mod(1429,6936))
\(\chi_{6936}(205,\cdot)\)
\(\chi_{6936}(613,\cdot)\)
\(\chi_{6936}(1021,\cdot)\)
\(\chi_{6936}(1429,\cdot)\)
\(\chi_{6936}(1837,\cdot)\)
\(\chi_{6936}(2245,\cdot)\)
\(\chi_{6936}(2653,\cdot)\)
\(\chi_{6936}(3061,\cdot)\)
\(\chi_{6936}(3877,\cdot)\)
\(\chi_{6936}(4285,\cdot)\)
\(\chi_{6936}(4693,\cdot)\)
\(\chi_{6936}(5101,\cdot)\)
\(\chi_{6936}(5509,\cdot)\)
\(\chi_{6936}(5917,\cdot)\)
\(\chi_{6936}(6325,\cdot)\)
\(\chi_{6936}(6733,\cdot)\)
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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 ]
\((1735,3469,4625,6361)\) → \((1,-1,1,e\left(\frac{5}{17}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 6936 }(1429, a) \) |
\(1\) | \(1\) | \(e\left(\frac{29}{34}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{9}{34}\right)\) | \(e\left(\frac{5}{34}\right)\) | \(e\left(\frac{21}{34}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{9}{34}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{15}{34}\right)\) |
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sage:chi.jacobi_sum(n)
