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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1734, base_ring=CyclotomicField(16))
M = H._module
chi = DirichletCharacter(H, M([0,1]))
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pari:[g,chi] = znchar(Mod(1669,1734))
\(\chi_{1734}(643,\cdot)\)
\(\chi_{1734}(709,\cdot)\)
\(\chi_{1734}(907,\cdot)\)
\(\chi_{1734}(1081,\cdot)\)
\(\chi_{1734}(1231,\cdot)\)
\(\chi_{1734}(1405,\cdot)\)
\(\chi_{1734}(1603,\cdot)\)
\(\chi_{1734}(1669,\cdot)\)
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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 ]
\((1157,1159)\) → \((1,e\left(\frac{1}{16}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 1734 }(1669, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(i\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(1\) |
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sage:chi.jacobi_sum(n)
