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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(508288, base_ring=CyclotomicField(13680))
M = H._module
chi = DirichletCharacter(H, M([0,7695,12312,5200]))
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pari:[g,chi] = znchar(Mod(985,508288))
\(\chi_{508288}(73,\cdot)\)
\(\chi_{508288}(233,\cdot)\)
\(\chi_{508288}(633,\cdot)\)
\(\chi_{508288}(745,\cdot)\)
\(\chi_{508288}(777,\cdot)\)
\(\chi_{508288}(921,\cdot)\)
\(\chi_{508288}(937,\cdot)\)
\(\chi_{508288}(985,\cdot)\)
\(\chi_{508288}(1289,\cdot)\)
\(\chi_{508288}(1449,\cdot)\)
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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 ]
\((166783,174725,323457,14081)\) → \((1,e\left(\frac{9}{16}\right),e\left(\frac{9}{10}\right),e\left(\frac{65}{171}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 508288 }(985, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{9901}{13680}\right)\) | \(e\left(\frac{4783}{13680}\right)\) | \(e\left(\frac{2149}{2280}\right)\) | \(e\left(\frac{3061}{6840}\right)\) | \(e\left(\frac{5417}{13680}\right)\) | \(e\left(\frac{251}{3420}\right)\) | \(e\left(\frac{2587}{3420}\right)\) | \(e\left(\frac{1823}{2736}\right)\) | \(e\left(\frac{509}{1368}\right)\) | \(e\left(\frac{4783}{6840}\right)\) |
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sage:chi.jacobi_sum(n)
