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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(33957, base_ring=CyclotomicField(30))
M = H._module
chi = DirichletCharacter(H, M([0,25,21]))
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pari:[g,chi] = znchar(Mod(9280,33957))
\(\chi_{33957}(19,\cdot)\)
\(\chi_{33957}(325,\cdot)\)
\(\chi_{33957}(3412,\cdot)\)
\(\chi_{33957}(9280,\cdot)\)
\(\chi_{33957}(15760,\cdot)\)
\(\chi_{33957}(18541,\cdot)\)
\(\chi_{33957}(21628,\cdot)\)
\(\chi_{33957}(25021,\cdot)\)
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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 ]
\((18866,14752,24697)\) → \((1,e\left(\frac{5}{6}\right),e\left(\frac{7}{10}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 33957 }(9280, a) \) |
\(1\) | \(1\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{7}{10}\right)\) |
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sage:chi.jacobi_sum(n)
