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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5766, base_ring=CyclotomicField(30))
M = H._module
chi = DirichletCharacter(H, M([15,7]))
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pari:[g,chi] = znchar(Mod(2435,5766))
\(\chi_{5766}(623,\cdot)\)
\(\chi_{5766}(2039,\cdot)\)
\(\chi_{5766}(2435,\cdot)\)
\(\chi_{5766}(3959,\cdot)\)
\(\chi_{5766}(3989,\cdot)\)
\(\chi_{5766}(4073,\cdot)\)
\(\chi_{5766}(5219,\cdot)\)
\(\chi_{5766}(5531,\cdot)\)
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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 ]
\((3845,3847)\) → \((-1,e\left(\frac{7}{30}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(35\) |
| \( \chi_{ 5766 }(2435, a) \) |
\(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) |
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sage:chi.jacobi_sum(n)
