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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1120, base_ring=CyclotomicField(24))
M = H._module
chi = DirichletCharacter(H, M([0,15,0,16]))
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pari:[g,chi] = znchar(Mod(501,1120))
\(\chi_{1120}(221,\cdot)\)
\(\chi_{1120}(261,\cdot)\)
\(\chi_{1120}(501,\cdot)\)
\(\chi_{1120}(541,\cdot)\)
\(\chi_{1120}(781,\cdot)\)
\(\chi_{1120}(821,\cdot)\)
\(\chi_{1120}(1061,\cdot)\)
\(\chi_{1120}(1101,\cdot)\)
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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 ]
\((351,421,897,801)\) → \((1,e\left(\frac{5}{8}\right),1,e\left(\frac{2}{3}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
| \( \chi_{ 1120 }(501, a) \) |
\(1\) | \(1\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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sage:chi.jacobi_sum(n)
