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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2366, base_ring=CyclotomicField(156))
M = H._module
chi = DirichletCharacter(H, M([130,53]))
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pari:[g,chi] = znchar(Mod(1475,2366))
\(\chi_{2366}(33,\cdot)\)
\(\chi_{2366}(115,\cdot)\)
\(\chi_{2366}(171,\cdot)\)
\(\chi_{2366}(201,\cdot)\)
\(\chi_{2366}(215,\cdot)\)
\(\chi_{2366}(297,\cdot)\)
\(\chi_{2366}(353,\cdot)\)
\(\chi_{2366}(383,\cdot)\)
\(\chi_{2366}(397,\cdot)\)
\(\chi_{2366}(479,\cdot)\)
\(\chi_{2366}(535,\cdot)\)
\(\chi_{2366}(565,\cdot)\)
\(\chi_{2366}(579,\cdot)\)
\(\chi_{2366}(661,\cdot)\)
\(\chi_{2366}(717,\cdot)\)
\(\chi_{2366}(747,\cdot)\)
\(\chi_{2366}(761,\cdot)\)
\(\chi_{2366}(843,\cdot)\)
\(\chi_{2366}(899,\cdot)\)
\(\chi_{2366}(929,\cdot)\)
\(\chi_{2366}(943,\cdot)\)
\(\chi_{2366}(1025,\cdot)\)
\(\chi_{2366}(1081,\cdot)\)
\(\chi_{2366}(1111,\cdot)\)
\(\chi_{2366}(1125,\cdot)\)
\(\chi_{2366}(1207,\cdot)\)
\(\chi_{2366}(1293,\cdot)\)
\(\chi_{2366}(1307,\cdot)\)
\(\chi_{2366}(1389,\cdot)\)
\(\chi_{2366}(1445,\cdot)\)
...
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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 ]
\((339,2199)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{53}{156}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 2366 }(1475, a) \) |
\(1\) | \(1\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{35}{156}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{17}{52}\right)\) | \(e\left(\frac{29}{156}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(i\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{23}{26}\right)\) |
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sage:chi.jacobi_sum(n)
