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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([33,0,33,11,3]))
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pari:[g,chi] = znchar(Mod(143,3864))
\(\chi_{3864}(143,\cdot)\)
\(\chi_{3864}(383,\cdot)\)
\(\chi_{3864}(479,\cdot)\)
\(\chi_{3864}(815,\cdot)\)
\(\chi_{3864}(983,\cdot)\)
\(\chi_{3864}(1055,\cdot)\)
\(\chi_{3864}(1391,\cdot)\)
\(\chi_{3864}(1487,\cdot)\)
\(\chi_{3864}(2159,\cdot)\)
\(\chi_{3864}(2399,\cdot)\)
\(\chi_{3864}(2495,\cdot)\)
\(\chi_{3864}(2567,\cdot)\)
\(\chi_{3864}(2735,\cdot)\)
\(\chi_{3864}(2903,\cdot)\)
\(\chi_{3864}(3239,\cdot)\)
\(\chi_{3864}(3503,\cdot)\)
\(\chi_{3864}(3575,\cdot)\)
\(\chi_{3864}(3671,\cdot)\)
\(\chi_{3864}(3743,\cdot)\)
\(\chi_{3864}(3839,\cdot)\)
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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 ]
\((967,1933,1289,2761,2857)\) → \((-1,1,-1,e\left(\frac{1}{6}\right),e\left(\frac{1}{22}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 3864 }(143, a) \) |
\(1\) | \(1\) | \(e\left(\frac{25}{66}\right)\) | \(e\left(\frac{5}{66}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{65}{66}\right)\) | \(e\left(\frac{1}{66}\right)\) | \(e\left(\frac{25}{33}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{31}{33}\right)\) | \(e\left(\frac{19}{66}\right)\) | \(e\left(\frac{6}{11}\right)\) |
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sage:chi.jacobi_sum(n)
