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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(15800, base_ring=CyclotomicField(30))
M = H._module
chi = DirichletCharacter(H, M([0,0,27,20]))
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pari:[g,chi] = znchar(Mod(13169,15800))
\(\chi_{15800}(529,\cdot)\)
\(\chi_{15800}(1129,\cdot)\)
\(\chi_{15800}(3689,\cdot)\)
\(\chi_{15800}(4289,\cdot)\)
\(\chi_{15800}(10009,\cdot)\)
\(\chi_{15800}(10609,\cdot)\)
\(\chi_{15800}(13169,\cdot)\)
\(\chi_{15800}(13769,\cdot)\)
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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 ]
\((3951,7901,11377,12801)\) → \((1,1,e\left(\frac{9}{10}\right),e\left(\frac{2}{3}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 15800 }(13169, a) \) |
\(1\) | \(1\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{9}{10}\right)\) |
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sage:chi.jacobi_sum(n)
