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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9800, base_ring=CyclotomicField(28))
M = H._module
chi = DirichletCharacter(H, M([0,0,21,18]))
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pari:[g,chi] = znchar(Mod(7993,9800))
\(\chi_{9800}(657,\cdot)\)
\(\chi_{9800}(993,\cdot)\)
\(\chi_{9800}(2393,\cdot)\)
\(\chi_{9800}(3457,\cdot)\)
\(\chi_{9800}(3793,\cdot)\)
\(\chi_{9800}(4857,\cdot)\)
\(\chi_{9800}(6257,\cdot)\)
\(\chi_{9800}(6593,\cdot)\)
\(\chi_{9800}(7657,\cdot)\)
\(\chi_{9800}(7993,\cdot)\)
\(\chi_{9800}(9057,\cdot)\)
\(\chi_{9800}(9393,\cdot)\)
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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 ]
\((7351,4901,1177,5001)\) → \((1,1,-i,e\left(\frac{9}{14}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
| \( \chi_{ 9800 }(7993, a) \) |
\(1\) | \(1\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(1\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(-1\) |
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sage:chi.jacobi_sum(n)
