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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4600, base_ring=CyclotomicField(22))
M = H._module
chi = DirichletCharacter(H, M([11,0,0,5]))
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pari:[g,chi] = znchar(Mod(4551,4600))
\(\chi_{4600}(751,\cdot)\)
\(\chi_{4600}(1351,\cdot)\)
\(\chi_{4600}(1551,\cdot)\)
\(\chi_{4600}(1951,\cdot)\)
\(\chi_{4600}(2351,\cdot)\)
\(\chi_{4600}(2551,\cdot)\)
\(\chi_{4600}(2751,\cdot)\)
\(\chi_{4600}(2951,\cdot)\)
\(\chi_{4600}(4151,\cdot)\)
\(\chi_{4600}(4551,\cdot)\)
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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 ]
\((1151,2301,2577,1201)\) → \((-1,1,1,e\left(\frac{5}{22}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(27\) | \(29\) |
| \( \chi_{ 4600 }(4551, a) \) |
\(1\) | \(1\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{1}{11}\right)\) |
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sage:chi.jacobi_sum(n)
