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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3060, base_ring=CyclotomicField(48))
M = H._module
chi = DirichletCharacter(H, M([0,32,36,15]))
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pari:[g,chi] = znchar(Mod(2113,3060))
\(\chi_{3060}(133,\cdot)\)
\(\chi_{3060}(517,\cdot)\)
\(\chi_{3060}(853,\cdot)\)
\(\chi_{3060}(877,\cdot)\)
\(\chi_{3060}(913,\cdot)\)
\(\chi_{3060}(997,\cdot)\)
\(\chi_{3060}(1093,\cdot)\)
\(\chi_{3060}(1417,\cdot)\)
\(\chi_{3060}(1537,\cdot)\)
\(\chi_{3060}(1897,\cdot)\)
\(\chi_{3060}(1933,\cdot)\)
\(\chi_{3060}(2113,\cdot)\)
\(\chi_{3060}(2173,\cdot)\)
\(\chi_{3060}(2437,\cdot)\)
\(\chi_{3060}(2893,\cdot)\)
\(\chi_{3060}(3037,\cdot)\)
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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 ]
\((1531,1361,1837,1261)\) → \((1,e\left(\frac{2}{3}\right),-i,e\left(\frac{5}{16}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 3060 }(2113, a) \) |
\(1\) | \(1\) | \(e\left(\frac{41}{48}\right)\) | \(e\left(\frac{41}{48}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{13}{48}\right)\) | \(e\left(\frac{11}{48}\right)\) | \(e\left(\frac{7}{48}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{37}{48}\right)\) | \(e\left(\frac{13}{24}\right)\) |
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sage:chi.jacobi_sum(n)
