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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2940, base_ring=CyclotomicField(84))
M = H._module
chi = DirichletCharacter(H, M([0,0,63,38]))
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pari:[g,chi] = znchar(Mod(1753,2940))
\(\chi_{2940}(73,\cdot)\)
\(\chi_{2940}(157,\cdot)\)
\(\chi_{2940}(397,\cdot)\)
\(\chi_{2940}(493,\cdot)\)
\(\chi_{2940}(577,\cdot)\)
\(\chi_{2940}(733,\cdot)\)
\(\chi_{2940}(817,\cdot)\)
\(\chi_{2940}(997,\cdot)\)
\(\chi_{2940}(1153,\cdot)\)
\(\chi_{2940}(1237,\cdot)\)
\(\chi_{2940}(1333,\cdot)\)
\(\chi_{2940}(1417,\cdot)\)
\(\chi_{2940}(1573,\cdot)\)
\(\chi_{2940}(1657,\cdot)\)
\(\chi_{2940}(1753,\cdot)\)
\(\chi_{2940}(1837,\cdot)\)
\(\chi_{2940}(1993,\cdot)\)
\(\chi_{2940}(2173,\cdot)\)
\(\chi_{2940}(2257,\cdot)\)
\(\chi_{2940}(2413,\cdot)\)
\(\chi_{2940}(2497,\cdot)\)
\(\chi_{2940}(2593,\cdot)\)
\(\chi_{2940}(2833,\cdot)\)
\(\chi_{2940}(2917,\cdot)\)
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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 ]
\((1471,1961,1177,1081)\) → \((1,1,-i,e\left(\frac{19}{42}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 2940 }(1753, a) \) |
\(1\) | \(1\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{37}{84}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{19}{84}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{27}{28}\right)\) |
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sage:chi.jacobi_sum(n)
