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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6304, base_ring=CyclotomicField(14))
M = H._module
chi = DirichletCharacter(H, M([0,0,1]))
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pari:[g,chi] = znchar(Mod(33,6304))
\(\chi_{6304}(33,\cdot)\)
\(\chi_{6304}(161,\cdot)\)
\(\chi_{6304}(4033,\cdot)\)
\(\chi_{6304}(4353,\cdot)\)
\(\chi_{6304}(4417,\cdot)\)
\(\chi_{6304}(6113,\cdot)\)
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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 ]
\((1183,3941,3745)\) → \((1,1,e\left(\frac{1}{14}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 6304 }(33, a) \) |
\(1\) | \(1\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(1\) | \(e\left(\frac{5}{14}\right)\) |
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sage:chi.jacobi_sum(n)
