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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1710, base_ring=CyclotomicField(36))
M = H._module
chi = DirichletCharacter(H, M([0,27,10]))
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pari:[g,chi] = znchar(Mod(1153,1710))
\(\chi_{1710}(127,\cdot)\)
\(\chi_{1710}(307,\cdot)\)
\(\chi_{1710}(433,\cdot)\)
\(\chi_{1710}(523,\cdot)\)
\(\chi_{1710}(667,\cdot)\)
\(\chi_{1710}(793,\cdot)\)
\(\chi_{1710}(1117,\cdot)\)
\(\chi_{1710}(1153,\cdot)\)
\(\chi_{1710}(1207,\cdot)\)
\(\chi_{1710}(1333,\cdot)\)
\(\chi_{1710}(1477,\cdot)\)
\(\chi_{1710}(1693,\cdot)\)
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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 ]
\((191,1027,1351)\) → \((1,-i,e\left(\frac{5}{18}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 1710 }(1153, a) \) |
\(1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(i\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{25}{36}\right)\) |
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sage:chi.jacobi_sum(n)
