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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6525, base_ring=CyclotomicField(28))
M = H._module
chi = DirichletCharacter(H, M([14,7,24]))
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pari:[g,chi] = znchar(Mod(107,6525))
\(\chi_{6525}(107,\cdot)\)
\(\chi_{6525}(368,\cdot)\)
\(\chi_{6525}(1457,\cdot)\)
\(\chi_{6525}(1718,\cdot)\)
\(\chi_{6525}(2807,\cdot)\)
\(\chi_{6525}(3032,\cdot)\)
\(\chi_{6525}(3068,\cdot)\)
\(\chi_{6525}(3293,\cdot)\)
\(\chi_{6525}(3707,\cdot)\)
\(\chi_{6525}(3968,\cdot)\)
\(\chi_{6525}(4607,\cdot)\)
\(\chi_{6525}(4868,\cdot)\)
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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 ]
\((1451,4177,901)\) → \((-1,i,e\left(\frac{6}{7}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 6525 }(107, a) \) |
\(1\) | \(1\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(-i\) | \(e\left(\frac{3}{14}\right)\) |
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sage:chi.jacobi_sum(n)
