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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3600, base_ring=CyclotomicField(60))
M = H._module
chi = DirichletCharacter(H, M([30,30,20,39]))
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pari:[g,chi] = znchar(Mod(967,3600))
\(\chi_{3600}(103,\cdot)\)
\(\chi_{3600}(247,\cdot)\)
\(\chi_{3600}(583,\cdot)\)
\(\chi_{3600}(727,\cdot)\)
\(\chi_{3600}(823,\cdot)\)
\(\chi_{3600}(967,\cdot)\)
\(\chi_{3600}(1303,\cdot)\)
\(\chi_{3600}(1447,\cdot)\)
\(\chi_{3600}(1687,\cdot)\)
\(\chi_{3600}(2023,\cdot)\)
\(\chi_{3600}(2167,\cdot)\)
\(\chi_{3600}(2263,\cdot)\)
\(\chi_{3600}(2887,\cdot)\)
\(\chi_{3600}(2983,\cdot)\)
\(\chi_{3600}(3127,\cdot)\)
\(\chi_{3600}(3463,\cdot)\)
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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 ]
\((3151,901,2801,577)\) → \((-1,-1,e\left(\frac{1}{3}\right),e\left(\frac{13}{20}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 3600 }(967, a) \) |
\(1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{4}{15}\right)\) |
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sage:chi.jacobi_sum(n)
