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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2496, base_ring=CyclotomicField(12))
M = H._module
chi = DirichletCharacter(H, M([6,9,6,10]))
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pari:[g,chi] = znchar(Mod(1583,2496))
\(\chi_{2496}(335,\cdot)\)
\(\chi_{2496}(719,\cdot)\)
\(\chi_{2496}(1583,\cdot)\)
\(\chi_{2496}(1967,\cdot)\)
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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 ]
\((703,1093,833,769)\) → \((-1,-i,-1,e\left(\frac{5}{6}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 2496 }(1583, a) \) |
\(1\) | \(1\) | \(-i\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(e\left(\frac{1}{12}\right)\) | \(1\) | \(e\left(\frac{11}{12}\right)\) |
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sage:chi.jacobi_sum(n)
