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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(22848, base_ring=CyclotomicField(24))
M = H._module
chi = DirichletCharacter(H, M([0,18,0,16,9]))
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pari:[g,chi] = znchar(Mod(18001,22848))
\(\chi_{22848}(529,\cdot)\)
\(\chi_{22848}(14737,\cdot)\)
\(\chi_{22848}(16753,\cdot)\)
\(\chi_{22848}(18001,\cdot)\)
\(\chi_{22848}(18097,\cdot)\)
\(\chi_{22848}(20017,\cdot)\)
\(\chi_{22848}(20113,\cdot)\)
\(\chi_{22848}(21361,\cdot)\)
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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 ]
\((13567,18565,15233,3265,2689)\) → \((1,-i,1,e\left(\frac{2}{3}\right),e\left(\frac{3}{8}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 22848 }(18001, a) \) |
\(1\) | \(1\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(-i\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{5}{8}\right)\) |
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sage:chi.jacobi_sum(n)
