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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2890, base_ring=CyclotomicField(34))
M = H._module
chi = DirichletCharacter(H, M([0,28]))
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pari:[g,chi] = znchar(Mod(2381,2890))
\(\chi_{2890}(171,\cdot)\)
\(\chi_{2890}(341,\cdot)\)
\(\chi_{2890}(511,\cdot)\)
\(\chi_{2890}(681,\cdot)\)
\(\chi_{2890}(851,\cdot)\)
\(\chi_{2890}(1021,\cdot)\)
\(\chi_{2890}(1191,\cdot)\)
\(\chi_{2890}(1361,\cdot)\)
\(\chi_{2890}(1531,\cdot)\)
\(\chi_{2890}(1701,\cdot)\)
\(\chi_{2890}(1871,\cdot)\)
\(\chi_{2890}(2041,\cdot)\)
\(\chi_{2890}(2211,\cdot)\)
\(\chi_{2890}(2381,\cdot)\)
\(\chi_{2890}(2551,\cdot)\)
\(\chi_{2890}(2721,\cdot)\)
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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 ]
\((1157,581)\) → \((1,e\left(\frac{14}{17}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 2890 }(2381, a) \) |
\(1\) | \(1\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{16}{17}\right)\) |
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sage:chi.jacobi_sum(n)
