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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([17,9]))
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pari:[g,chi] = znchar(Mod(101,1734))
\(\chi_{1734}(101,\cdot)\)
\(\chi_{1734}(203,\cdot)\)
\(\chi_{1734}(305,\cdot)\)
\(\chi_{1734}(407,\cdot)\)
\(\chi_{1734}(509,\cdot)\)
\(\chi_{1734}(611,\cdot)\)
\(\chi_{1734}(713,\cdot)\)
\(\chi_{1734}(815,\cdot)\)
\(\chi_{1734}(917,\cdot)\)
\(\chi_{1734}(1019,\cdot)\)
\(\chi_{1734}(1121,\cdot)\)
\(\chi_{1734}(1223,\cdot)\)
\(\chi_{1734}(1325,\cdot)\)
\(\chi_{1734}(1427,\cdot)\)
\(\chi_{1734}(1529,\cdot)\)
\(\chi_{1734}(1631,\cdot)\)
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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 ]
\((1157,1159)\) → \((-1,e\left(\frac{9}{34}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 1734 }(101, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{1}{34}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{13}{34}\right)\) | \(e\left(\frac{5}{34}\right)\) |
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sage:chi.jacobi_sum(n)
