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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([0,11,11,9]))
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pari:[g,chi] = znchar(Mod(34,2415))
\(\chi_{2415}(34,\cdot)\)
\(\chi_{2415}(244,\cdot)\)
\(\chi_{2415}(454,\cdot)\)
\(\chi_{2415}(559,\cdot)\)
\(\chi_{2415}(664,\cdot)\)
\(\chi_{2415}(769,\cdot)\)
\(\chi_{2415}(1399,\cdot)\)
\(\chi_{2415}(1924,\cdot)\)
\(\chi_{2415}(2029,\cdot)\)
\(\chi_{2415}(2344,\cdot)\)
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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 ]
\((806,967,346,1891)\) → \((1,-1,-1,e\left(\frac{9}{22}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(26\) |
| \( \chi_{ 2415 }(34, a) \) |
\(1\) | \(1\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(1\) | \(e\left(\frac{1}{22}\right)\) |
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sage:chi.jacobi_sum(n)
