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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7803, base_ring=CyclotomicField(34))
M = H._module
chi = DirichletCharacter(H, M([0,10]))
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pari:[g,chi] = znchar(Mod(2296,7803))
\(\chi_{7803}(460,\cdot)\)
\(\chi_{7803}(919,\cdot)\)
\(\chi_{7803}(1378,\cdot)\)
\(\chi_{7803}(1837,\cdot)\)
\(\chi_{7803}(2296,\cdot)\)
\(\chi_{7803}(2755,\cdot)\)
\(\chi_{7803}(3214,\cdot)\)
\(\chi_{7803}(3673,\cdot)\)
\(\chi_{7803}(4132,\cdot)\)
\(\chi_{7803}(4591,\cdot)\)
\(\chi_{7803}(5050,\cdot)\)
\(\chi_{7803}(5509,\cdot)\)
\(\chi_{7803}(5968,\cdot)\)
\(\chi_{7803}(6427,\cdot)\)
\(\chi_{7803}(6886,\cdot)\)
\(\chi_{7803}(7345,\cdot)\)
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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 ]
\((2891,2026)\) → \((1,e\left(\frac{5}{17}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 7803 }(2296, a) \) |
\(1\) | \(1\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{9}{17}\right)\) |
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sage:chi.jacobi_sum(n)
