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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7350, base_ring=CyclotomicField(30))
M = H._module
chi = DirichletCharacter(H, M([0,3,20]))
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pari:[g,chi] = znchar(Mod(6829,7350))
\(\chi_{7350}(79,\cdot)\)
\(\chi_{7350}(2419,\cdot)\)
\(\chi_{7350}(3019,\cdot)\)
\(\chi_{7350}(3889,\cdot)\)
\(\chi_{7350}(4489,\cdot)\)
\(\chi_{7350}(5359,\cdot)\)
\(\chi_{7350}(5959,\cdot)\)
\(\chi_{7350}(6829,\cdot)\)
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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 ]
\((4901,1177,2551)\) → \((1,e\left(\frac{1}{10}\right),e\left(\frac{2}{3}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 7350 }(6829, a) \) |
\(1\) | \(1\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(-1\) |
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sage:chi.jacobi_sum(n)
