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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4600, base_ring=CyclotomicField(20))
M = H._module
chi = DirichletCharacter(H, M([0,0,17,10]))
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pari:[g,chi] = znchar(Mod(2897,4600))
\(\chi_{4600}(137,\cdot)\)
\(\chi_{4600}(873,\cdot)\)
\(\chi_{4600}(1977,\cdot)\)
\(\chi_{4600}(2713,\cdot)\)
\(\chi_{4600}(2897,\cdot)\)
\(\chi_{4600}(3633,\cdot)\)
\(\chi_{4600}(3817,\cdot)\)
\(\chi_{4600}(4553,\cdot)\)
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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 ]
\((1151,2301,2577,1201)\) → \((1,1,e\left(\frac{17}{20}\right),-1)\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(27\) | \(29\) |
| \( \chi_{ 4600 }(2897, a) \) |
\(1\) | \(1\) | \(e\left(\frac{19}{20}\right)\) | \(-i\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{7}{10}\right)\) |
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sage:chi.jacobi_sum(n)
