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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2156, base_ring=CyclotomicField(14))
M = H._module
chi = DirichletCharacter(H, M([0,13,0]))
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pari:[g,chi] = znchar(Mod(265,2156))
\(\chi_{2156}(265,\cdot)\)
\(\chi_{2156}(573,\cdot)\)
\(\chi_{2156}(1189,\cdot)\)
\(\chi_{2156}(1497,\cdot)\)
\(\chi_{2156}(1805,\cdot)\)
\(\chi_{2156}(2113,\cdot)\)
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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 ]
\((1079,1277,981)\) → \((1,e\left(\frac{13}{14}\right),1)\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 2156 }(265, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(-1\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{11}{14}\right)\) |
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sage:chi.jacobi_sum(n)
