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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([0,13,14]))
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pari:[g,chi] = znchar(Mod(1457,2028))
\(\chi_{2028}(53,\cdot)\)
\(\chi_{2028}(209,\cdot)\)
\(\chi_{2028}(365,\cdot)\)
\(\chi_{2028}(521,\cdot)\)
\(\chi_{2028}(833,\cdot)\)
\(\chi_{2028}(989,\cdot)\)
\(\chi_{2028}(1145,\cdot)\)
\(\chi_{2028}(1301,\cdot)\)
\(\chi_{2028}(1457,\cdot)\)
\(\chi_{2028}(1613,\cdot)\)
\(\chi_{2028}(1769,\cdot)\)
\(\chi_{2028}(1925,\cdot)\)
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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 ]
\((1015,677,1861)\) → \((1,-1,e\left(\frac{7}{13}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 2028 }(1457, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(1\) | \(-1\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{25}{26}\right)\) |
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sage:chi.jacobi_sum(n)
