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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3360, base_ring=CyclotomicField(24))
M = H._module
chi = DirichletCharacter(H, M([0,3,0,12,16]))
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pari:[g,chi] = znchar(Mod(2629,3360))
\(\chi_{3360}(109,\cdot)\)
\(\chi_{3360}(709,\cdot)\)
\(\chi_{3360}(949,\cdot)\)
\(\chi_{3360}(1549,\cdot)\)
\(\chi_{3360}(1789,\cdot)\)
\(\chi_{3360}(2389,\cdot)\)
\(\chi_{3360}(2629,\cdot)\)
\(\chi_{3360}(3229,\cdot)\)
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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 ]
\((1471,421,1121,2017,1921)\) → \((1,e\left(\frac{1}{8}\right),1,-1,e\left(\frac{2}{3}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 3360 }(2629, a) \) |
\(1\) | \(1\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(-i\) | \(e\left(\frac{1}{8}\right)\) |
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sage:chi.jacobi_sum(n)
