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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3864, base_ring=CyclotomicField(66))
M = H._module
chi = DirichletCharacter(H, M([0,0,0,22,30]))
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pari:[g,chi] = znchar(Mod(1297,3864))
\(\chi_{3864}(25,\cdot)\)
\(\chi_{3864}(121,\cdot)\)
\(\chi_{3864}(193,\cdot)\)
\(\chi_{3864}(289,\cdot)\)
\(\chi_{3864}(361,\cdot)\)
\(\chi_{3864}(625,\cdot)\)
\(\chi_{3864}(961,\cdot)\)
\(\chi_{3864}(1129,\cdot)\)
\(\chi_{3864}(1297,\cdot)\)
\(\chi_{3864}(1369,\cdot)\)
\(\chi_{3864}(1465,\cdot)\)
\(\chi_{3864}(1705,\cdot)\)
\(\chi_{3864}(2377,\cdot)\)
\(\chi_{3864}(2473,\cdot)\)
\(\chi_{3864}(2809,\cdot)\)
\(\chi_{3864}(2881,\cdot)\)
\(\chi_{3864}(3049,\cdot)\)
\(\chi_{3864}(3385,\cdot)\)
\(\chi_{3864}(3481,\cdot)\)
\(\chi_{3864}(3721,\cdot)\)
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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 ]
\((967,1933,1289,2761,2857)\) → \((1,1,1,e\left(\frac{1}{3}\right),e\left(\frac{5}{11}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 3864 }(1297, a) \) |
\(1\) | \(1\) | \(e\left(\frac{4}{33}\right)\) | \(e\left(\frac{14}{33}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{17}{33}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{5}{11}\right)\) |
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sage:chi.jacobi_sum(n)
