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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9405, base_ring=CyclotomicField(18))
M = H._module
chi = DirichletCharacter(H, M([0,0,0,2]))
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pari:[g,chi] = znchar(Mod(1486,9405))
\(\chi_{9405}(1486,\cdot)\)
\(\chi_{9405}(1981,\cdot)\)
\(\chi_{9405}(2476,\cdot)\)
\(\chi_{9405}(3961,\cdot)\)
\(\chi_{9405}(7426,\cdot)\)
\(\chi_{9405}(7921,\cdot)\)
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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 ]
\((1046,1882,5986,496)\) → \((1,1,1,e\left(\frac{1}{9}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(23\) | \(26\) |
| \( \chi_{ 9405 }(1486, a) \) |
\(1\) | \(1\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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sage:chi.jacobi_sum(n)
