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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1488, base_ring=CyclotomicField(60))
M = H._module
chi = DirichletCharacter(H, M([30,45,0,52]))
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pari:[g,chi] = znchar(Mod(979,1488))
\(\chi_{1488}(19,\cdot)\)
\(\chi_{1488}(235,\cdot)\)
\(\chi_{1488}(307,\cdot)\)
\(\chi_{1488}(355,\cdot)\)
\(\chi_{1488}(379,\cdot)\)
\(\chi_{1488}(475,\cdot)\)
\(\chi_{1488}(547,\cdot)\)
\(\chi_{1488}(691,\cdot)\)
\(\chi_{1488}(763,\cdot)\)
\(\chi_{1488}(979,\cdot)\)
\(\chi_{1488}(1051,\cdot)\)
\(\chi_{1488}(1099,\cdot)\)
\(\chi_{1488}(1123,\cdot)\)
\(\chi_{1488}(1219,\cdot)\)
\(\chi_{1488}(1291,\cdot)\)
\(\chi_{1488}(1435,\cdot)\)
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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 ]
\((559,373,497,1057)\) → \((-1,-i,1,e\left(\frac{13}{15}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(35\) |
| \( \chi_{ 1488 }(979, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{7}{20}\right)\) |
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sage:chi.jacobi_sum(n)
