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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3234, base_ring=CyclotomicField(70))
M = H._module
chi = DirichletCharacter(H, M([0,15,49]))
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pari:[g,chi] = znchar(Mod(1063,3234))
\(\chi_{3234}(13,\cdot)\)
\(\chi_{3234}(139,\cdot)\)
\(\chi_{3234}(349,\cdot)\)
\(\chi_{3234}(475,\cdot)\)
\(\chi_{3234}(601,\cdot)\)
\(\chi_{3234}(811,\cdot)\)
\(\chi_{3234}(853,\cdot)\)
\(\chi_{3234}(937,\cdot)\)
\(\chi_{3234}(1063,\cdot)\)
\(\chi_{3234}(1315,\cdot)\)
\(\chi_{3234}(1399,\cdot)\)
\(\chi_{3234}(1525,\cdot)\)
\(\chi_{3234}(1735,\cdot)\)
\(\chi_{3234}(1777,\cdot)\)
\(\chi_{3234}(1987,\cdot)\)
\(\chi_{3234}(2197,\cdot)\)
\(\chi_{3234}(2239,\cdot)\)
\(\chi_{3234}(2323,\cdot)\)
\(\chi_{3234}(2659,\cdot)\)
\(\chi_{3234}(2701,\cdot)\)
\(\chi_{3234}(2785,\cdot)\)
\(\chi_{3234}(2911,\cdot)\)
\(\chi_{3234}(3121,\cdot)\)
\(\chi_{3234}(3163,\cdot)\)
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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 ]
\((1079,199,2059)\) → \((1,e\left(\frac{3}{14}\right),e\left(\frac{7}{10}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 3234 }(1063, a) \) |
\(1\) | \(1\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{11}{35}\right)\) |
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sage:chi.jacobi_sum(n)
