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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4225, base_ring=CyclotomicField(20))
M = H._module
chi = DirichletCharacter(H, M([11,5]))
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pari:[g,chi] = znchar(Mod(3648,4225))
\(\chi_{4225}(577,\cdot)\)
\(\chi_{4225}(1113,\cdot)\)
\(\chi_{4225}(1422,\cdot)\)
\(\chi_{4225}(1958,\cdot)\)
\(\chi_{4225}(2267,\cdot)\)
\(\chi_{4225}(2803,\cdot)\)
\(\chi_{4225}(3112,\cdot)\)
\(\chi_{4225}(3648,\cdot)\)
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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 ]
\((677,3551)\) → \((e\left(\frac{11}{20}\right),i)\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(14\) |
| \( \chi_{ 4225 }(3648, a) \) |
\(1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(-1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{3}{10}\right)\) |
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sage:chi.jacobi_sum(n)
