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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([8085,3685,15141]))
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pari:[g,chi] = znchar(Mod(899,373527))
\(\chi_{373527}(17,\cdot)\)
\(\chi_{373527}(206,\cdot)\)
\(\chi_{373527}(332,\cdot)\)
\(\chi_{373527}(404,\cdot)\)
\(\chi_{373527}(458,\cdot)\)
\(\chi_{373527}(530,\cdot)\)
\(\chi_{373527}(710,\cdot)\)
\(\chi_{373527}(899,\cdot)\)
\(\chi_{373527}(908,\cdot)\)
\(\chi_{373527}(1025,\cdot)\)
\(\chi_{373527}(1151,\cdot)\)
\(\chi_{373527}(1223,\cdot)\)
\(\chi_{373527}(1349,\cdot)\)
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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 ]
\((290522,286408,126568)\) → \((-1,e\left(\frac{67}{294}\right),e\left(\frac{103}{110}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 373527 }(899, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{5233}{8085}\right)\) | \(e\left(\frac{2381}{8085}\right)\) | \(e\left(\frac{3232}{8085}\right)\) | \(e\left(\frac{2538}{2695}\right)\) | \(e\left(\frac{76}{1617}\right)\) | \(e\left(\frac{1406}{2695}\right)\) | \(e\left(\frac{4762}{8085}\right)\) | \(e\left(\frac{1279}{16170}\right)\) | \(e\left(\frac{91}{165}\right)\) | \(e\left(\frac{1871}{2695}\right)\) |
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sage:chi.jacobi_sum(n)
