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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(373527, base_ring=CyclotomicField(16170))
M = H._module
chi = DirichletCharacter(H, M([8085,605,8232]))
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pari:[g,chi] = znchar(Mod(845,373527))
\(\chi_{373527}(26,\cdot)\)
\(\chi_{373527}(152,\cdot)\)
\(\chi_{373527}(278,\cdot)\)
\(\chi_{373527}(467,\cdot)\)
\(\chi_{373527}(647,\cdot)\)
\(\chi_{373527}(719,\cdot)\)
\(\chi_{373527}(773,\cdot)\)
\(\chi_{373527}(845,\cdot)\)
\(\chi_{373527}(1160,\cdot)\)
\(\chi_{373527}(1214,\cdot)\)
\(\chi_{373527}(1466,\cdot)\)
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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 ]
\((290522,286408,126568)\) → \((-1,e\left(\frac{11}{294}\right),e\left(\frac{28}{55}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 373527 }(845, a) \) |
\(1\) | \(1\) | \(e\left(\frac{4327}{16170}\right)\) | \(e\left(\frac{4327}{8085}\right)\) | \(e\left(\frac{2084}{8085}\right)\) | \(e\left(\frac{4327}{5390}\right)\) | \(e\left(\frac{1699}{3234}\right)\) | \(e\left(\frac{439}{5390}\right)\) | \(e\left(\frac{569}{8085}\right)\) | \(e\left(\frac{3079}{8085}\right)\) | \(e\left(\frac{139}{330}\right)\) | \(e\left(\frac{2137}{2695}\right)\) |
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sage:chi.jacobi_sum(n)
