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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1984, base_ring=CyclotomicField(20))
M = H._module
chi = DirichletCharacter(H, M([0,15,4]))
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pari:[g,chi] = znchar(Mod(977,1984))
\(\chi_{1984}(529,\cdot)\)
\(\chi_{1984}(593,\cdot)\)
\(\chi_{1984}(721,\cdot)\)
\(\chi_{1984}(977,\cdot)\)
\(\chi_{1984}(1521,\cdot)\)
\(\chi_{1984}(1585,\cdot)\)
\(\chi_{1984}(1713,\cdot)\)
\(\chi_{1984}(1969,\cdot)\)
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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 ]
\((63,1861,65)\) → \((1,-i,e\left(\frac{1}{5}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 1984 }(977, a) \) |
\(1\) | \(1\) | \(e\left(\frac{9}{20}\right)\) | \(-i\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{11}{20}\right)\) |
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sage:chi.jacobi_sum(n)
