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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2900, base_ring=CyclotomicField(28))
M = H._module
chi = DirichletCharacter(H, M([0,21,15]))
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pari:[g,chi] = znchar(Mod(1593,2900))
\(\chi_{2900}(657,\cdot)\)
\(\chi_{2900}(693,\cdot)\)
\(\chi_{2900}(757,\cdot)\)
\(\chi_{2900}(793,\cdot)\)
\(\chi_{2900}(1593,\cdot)\)
\(\chi_{2900}(1893,\cdot)\)
\(\chi_{2900}(1957,\cdot)\)
\(\chi_{2900}(2157,\cdot)\)
\(\chi_{2900}(2193,\cdot)\)
\(\chi_{2900}(2393,\cdot)\)
\(\chi_{2900}(2457,\cdot)\)
\(\chi_{2900}(2757,\cdot)\)
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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 ]
\((1451,1277,901)\) → \((1,-i,e\left(\frac{15}{28}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 2900 }(1593, a) \) |
\(1\) | \(1\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(1\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{11}{14}\right)\) |
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sage:chi.jacobi_sum(n)
