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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1452, base_ring=CyclotomicField(22))
M = H._module
chi = DirichletCharacter(H, M([11,0,1]))
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pari:[g,chi] = znchar(Mod(1363,1452))
\(\chi_{1452}(43,\cdot)\)
\(\chi_{1452}(175,\cdot)\)
\(\chi_{1452}(307,\cdot)\)
\(\chi_{1452}(439,\cdot)\)
\(\chi_{1452}(571,\cdot)\)
\(\chi_{1452}(703,\cdot)\)
\(\chi_{1452}(835,\cdot)\)
\(\chi_{1452}(1099,\cdot)\)
\(\chi_{1452}(1231,\cdot)\)
\(\chi_{1452}(1363,\cdot)\)
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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 ]
\((727,485,1333)\) → \((-1,1,e\left(\frac{1}{22}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 1452 }(1363, a) \) |
\(1\) | \(1\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{2}{11}\right)\) |
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sage:chi.jacobi_sum(n)
