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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7260, base_ring=CyclotomicField(22))
M = H._module
chi = DirichletCharacter(H, M([11,11,0,15]))
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pari:[g,chi] = znchar(Mod(131,7260))
\(\chi_{7260}(131,\cdot)\)
\(\chi_{7260}(791,\cdot)\)
\(\chi_{7260}(2111,\cdot)\)
\(\chi_{7260}(2771,\cdot)\)
\(\chi_{7260}(3431,\cdot)\)
\(\chi_{7260}(4091,\cdot)\)
\(\chi_{7260}(4751,\cdot)\)
\(\chi_{7260}(5411,\cdot)\)
\(\chi_{7260}(6071,\cdot)\)
\(\chi_{7260}(6731,\cdot)\)
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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 ]
\((3631,4841,4357,7141)\) → \((-1,-1,1,e\left(\frac{15}{22}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 7260 }(131, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{6}{11}\right)\) |
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sage:chi.jacobi_sum(n)
