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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6080, base_ring=CyclotomicField(18))
M = H._module
chi = DirichletCharacter(H, M([9,9,9,13]))
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pari:[g,chi] = znchar(Mod(4639,6080))
\(\chi_{6080}(1439,\cdot)\)
\(\chi_{6080}(2719,\cdot)\)
\(\chi_{6080}(3359,\cdot)\)
\(\chi_{6080}(4639,\cdot)\)
\(\chi_{6080}(5599,\cdot)\)
\(\chi_{6080}(5919,\cdot)\)
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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 ]
\((191,5701,1217,1921)\) → \((-1,-1,-1,e\left(\frac{13}{18}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 6080 }(4639, a) \) |
\(1\) | \(1\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{9}\right)\) |
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sage:chi.jacobi_sum(n)
