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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2415, base_ring=CyclotomicField(22))
M = H._module
chi = DirichletCharacter(H, M([0,11,0,12]))
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pari:[g,chi] = znchar(Mod(64,2415))
\(\chi_{2415}(64,\cdot)\)
\(\chi_{2415}(169,\cdot)\)
\(\chi_{2415}(694,\cdot)\)
\(\chi_{2415}(1324,\cdot)\)
\(\chi_{2415}(1429,\cdot)\)
\(\chi_{2415}(1534,\cdot)\)
\(\chi_{2415}(1639,\cdot)\)
\(\chi_{2415}(1849,\cdot)\)
\(\chi_{2415}(2059,\cdot)\)
\(\chi_{2415}(2164,\cdot)\)
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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 ]
\((806,967,346,1891)\) → \((1,-1,1,e\left(\frac{6}{11}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(26\) |
| \( \chi_{ 2415 }(64, a) \) |
\(1\) | \(1\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(-1\) | \(e\left(\frac{8}{11}\right)\) |
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sage:chi.jacobi_sum(n)
