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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2816, base_ring=CyclotomicField(40))
M = H._module
chi = DirichletCharacter(H, M([20,15,36]))
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pari:[g,chi] = znchar(Mod(1887,2816))
\(\chi_{2816}(95,\cdot)\)
\(\chi_{2816}(415,\cdot)\)
\(\chi_{2816}(479,\cdot)\)
\(\chi_{2816}(607,\cdot)\)
\(\chi_{2816}(799,\cdot)\)
\(\chi_{2816}(1119,\cdot)\)
\(\chi_{2816}(1183,\cdot)\)
\(\chi_{2816}(1311,\cdot)\)
\(\chi_{2816}(1503,\cdot)\)
\(\chi_{2816}(1823,\cdot)\)
\(\chi_{2816}(1887,\cdot)\)
\(\chi_{2816}(2015,\cdot)\)
\(\chi_{2816}(2207,\cdot)\)
\(\chi_{2816}(2527,\cdot)\)
\(\chi_{2816}(2591,\cdot)\)
\(\chi_{2816}(2719,\cdot)\)
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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 ]
\((2047,1541,1025)\) → \((-1,e\left(\frac{3}{8}\right),e\left(\frac{9}{10}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 2816 }(1887, a) \) |
\(1\) | \(1\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(-i\) |
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sage:chi.jacobi_sum(n)
