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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1925, base_ring=CyclotomicField(12))
M = H._module
chi = DirichletCharacter(H, M([3,10,6]))
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pari:[g,chi] = znchar(Mod(1132,1925))
\(\chi_{1925}(318,\cdot)\)
\(\chi_{1925}(593,\cdot)\)
\(\chi_{1925}(857,\cdot)\)
\(\chi_{1925}(1132,\cdot)\)
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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 ]
\((1002,276,1751)\) → \((i,e\left(\frac{5}{6}\right),-1)\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(12\) | \(13\) | \(16\) | \(17\) |
| \( \chi_{ 1925 }(1132, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(i\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(-i\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{12}\right)\) |
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sage:chi.jacobi_sum(n)
