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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1824, base_ring=CyclotomicField(18))
M = H._module
chi = DirichletCharacter(H, M([0,0,0,14]))
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pari:[g,chi] = znchar(Mod(481,1824))
\(\chi_{1824}(289,\cdot)\)
\(\chi_{1824}(385,\cdot)\)
\(\chi_{1824}(481,\cdot)\)
\(\chi_{1824}(769,\cdot)\)
\(\chi_{1824}(1441,\cdot)\)
\(\chi_{1824}(1537,\cdot)\)
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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 ]
\((799,229,1217,97)\) → \((1,1,1,e\left(\frac{7}{9}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 1824 }(481, a) \) |
\(1\) | \(1\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{9}\right)\) |
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sage:chi.jacobi_sum(n)
