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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2900, base_ring=CyclotomicField(28))
M = H._module
chi = DirichletCharacter(H, M([14,14,27]))
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pari:[g,chi] = znchar(Mod(2799,2900))
\(\chi_{2900}(599,\cdot)\)
\(\chi_{2900}(699,\cdot)\)
\(\chi_{2900}(1099,\cdot)\)
\(\chi_{2900}(1199,\cdot)\)
\(\chi_{2900}(1899,\cdot)\)
\(\chi_{2900}(1999,\cdot)\)
\(\chi_{2900}(2099,\cdot)\)
\(\chi_{2900}(2299,\cdot)\)
\(\chi_{2900}(2399,\cdot)\)
\(\chi_{2900}(2599,\cdot)\)
\(\chi_{2900}(2699,\cdot)\)
\(\chi_{2900}(2799,\cdot)\)
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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 ]
\((1451,1277,901)\) → \((-1,-1,e\left(\frac{27}{28}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 2900 }(2799, a) \) |
\(1\) | \(1\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(-i\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{13}{28}\right)\) |
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sage:chi.jacobi_sum(n)
