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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2028, base_ring=CyclotomicField(26))
M = H._module
chi = DirichletCharacter(H, M([0,13,9]))
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pari:[g,chi] = znchar(Mod(77,2028))
\(\chi_{2028}(77,\cdot)\)
\(\chi_{2028}(233,\cdot)\)
\(\chi_{2028}(389,\cdot)\)
\(\chi_{2028}(545,\cdot)\)
\(\chi_{2028}(701,\cdot)\)
\(\chi_{2028}(857,\cdot)\)
\(\chi_{2028}(1169,\cdot)\)
\(\chi_{2028}(1325,\cdot)\)
\(\chi_{2028}(1481,\cdot)\)
\(\chi_{2028}(1637,\cdot)\)
\(\chi_{2028}(1793,\cdot)\)
\(\chi_{2028}(1949,\cdot)\)
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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 ]
\((1015,677,1861)\) → \((1,-1,e\left(\frac{9}{26}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 2028 }(77, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(-1\) | \(-1\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{17}{26}\right)\) |
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sage:chi.jacobi_sum(n)
