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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1734, base_ring=CyclotomicField(34))
M = H._module
chi = DirichletCharacter(H, M([0,29]))
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pari:[g,chi] = znchar(Mod(1291,1734))
\(\chi_{1734}(67,\cdot)\)
\(\chi_{1734}(169,\cdot)\)
\(\chi_{1734}(271,\cdot)\)
\(\chi_{1734}(373,\cdot)\)
\(\chi_{1734}(475,\cdot)\)
\(\chi_{1734}(679,\cdot)\)
\(\chi_{1734}(781,\cdot)\)
\(\chi_{1734}(883,\cdot)\)
\(\chi_{1734}(985,\cdot)\)
\(\chi_{1734}(1087,\cdot)\)
\(\chi_{1734}(1189,\cdot)\)
\(\chi_{1734}(1291,\cdot)\)
\(\chi_{1734}(1393,\cdot)\)
\(\chi_{1734}(1495,\cdot)\)
\(\chi_{1734}(1597,\cdot)\)
\(\chi_{1734}(1699,\cdot)\)
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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 ]
\((1157,1159)\) → \((1,e\left(\frac{29}{34}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 1734 }(1291, a) \) |
\(1\) | \(1\) | \(e\left(\frac{11}{34}\right)\) | \(e\left(\frac{7}{34}\right)\) | \(e\left(\frac{21}{34}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{7}{34}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{21}{34}\right)\) | \(e\left(\frac{23}{34}\right)\) | \(e\left(\frac{9}{17}\right)\) |
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sage:chi.jacobi_sum(n)
