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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3864, base_ring=CyclotomicField(22))
M = H._module
chi = DirichletCharacter(H, M([11,0,0,0,21]))
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pari:[g,chi] = znchar(Mod(3487,3864))
\(\chi_{3864}(295,\cdot)\)
\(\chi_{3864}(631,\cdot)\)
\(\chi_{3864}(799,\cdot)\)
\(\chi_{3864}(1303,\cdot)\)
\(\chi_{3864}(1975,\cdot)\)
\(\chi_{3864}(2311,\cdot)\)
\(\chi_{3864}(3319,\cdot)\)
\(\chi_{3864}(3487,\cdot)\)
\(\chi_{3864}(3655,\cdot)\)
\(\chi_{3864}(3823,\cdot)\)
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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 ]
\((967,1933,1289,2761,2857)\) → \((-1,1,1,1,e\left(\frac{21}{22}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 3864 }(3487, a) \) |
\(1\) | \(1\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{5}{11}\right)\) |
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sage:chi.jacobi_sum(n)
