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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1183, base_ring=CyclotomicField(26))
M = H._module
chi = DirichletCharacter(H, M([0,12]))
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pari:[g,chi] = znchar(Mod(911,1183))
\(\chi_{1183}(92,\cdot)\)
\(\chi_{1183}(183,\cdot)\)
\(\chi_{1183}(274,\cdot)\)
\(\chi_{1183}(365,\cdot)\)
\(\chi_{1183}(456,\cdot)\)
\(\chi_{1183}(547,\cdot)\)
\(\chi_{1183}(638,\cdot)\)
\(\chi_{1183}(729,\cdot)\)
\(\chi_{1183}(820,\cdot)\)
\(\chi_{1183}(911,\cdot)\)
\(\chi_{1183}(1002,\cdot)\)
\(\chi_{1183}(1093,\cdot)\)
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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 ]
\((339,1016)\) → \((1,e\left(\frac{6}{13}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 1183 }(911, a) \) |
\(1\) | \(1\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{2}{13}\right)\) |
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sage:chi.jacobi_sum(n)
