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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2900, base_ring=CyclotomicField(70))
M = H._module
chi = DirichletCharacter(H, M([0,14,5]))
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pari:[g,chi] = znchar(Mod(1541,2900))
\(\chi_{2900}(121,\cdot)\)
\(\chi_{2900}(241,\cdot)\)
\(\chi_{2900}(341,\cdot)\)
\(\chi_{2900}(361,\cdot)\)
\(\chi_{2900}(381,\cdot)\)
\(\chi_{2900}(441,\cdot)\)
\(\chi_{2900}(821,\cdot)\)
\(\chi_{2900}(921,\cdot)\)
\(\chi_{2900}(941,\cdot)\)
\(\chi_{2900}(961,\cdot)\)
\(\chi_{2900}(1021,\cdot)\)
\(\chi_{2900}(1281,\cdot)\)
\(\chi_{2900}(1521,\cdot)\)
\(\chi_{2900}(1541,\cdot)\)
\(\chi_{2900}(1861,\cdot)\)
\(\chi_{2900}(1981,\cdot)\)
\(\chi_{2900}(2081,\cdot)\)
\(\chi_{2900}(2121,\cdot)\)
\(\chi_{2900}(2181,\cdot)\)
\(\chi_{2900}(2441,\cdot)\)
\(\chi_{2900}(2561,\cdot)\)
\(\chi_{2900}(2661,\cdot)\)
\(\chi_{2900}(2681,\cdot)\)
\(\chi_{2900}(2761,\cdot)\)
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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 ]
\((1451,1277,901)\) → \((1,e\left(\frac{1}{5}\right),e\left(\frac{1}{14}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 2900 }(1541, a) \) |
\(1\) | \(1\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{69}{70}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{17}{70}\right)\) | \(e\left(\frac{43}{70}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{19}{70}\right)\) |
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sage:chi.jacobi_sum(n)
