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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3025, base_ring=CyclotomicField(20))
M = H._module
chi = DirichletCharacter(H, M([17,4]))
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pari:[g,chi] = znchar(Mod(2622,3025))
\(\chi_{3025}(608,\cdot)\)
\(\chi_{3025}(928,\cdot)\)
\(\chi_{3025}(977,\cdot)\)
\(\chi_{3025}(1092,\cdot)\)
\(\chi_{3025}(1098,\cdot)\)
\(\chi_{3025}(1237,\cdot)\)
\(\chi_{3025}(1963,\cdot)\)
\(\chi_{3025}(2622,\cdot)\)
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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 ]
\((727,2301)\) → \((e\left(\frac{17}{20}\right),e\left(\frac{1}{5}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 3025 }(2622, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{7}{10}\right)\) |
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sage:chi.jacobi_sum(n)
