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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(373527, base_ring=CyclotomicField(22))
M = H._module
chi = DirichletCharacter(H, M([0,0,4]))
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pari:[g,chi] = znchar(Mod(101872,373527))
\(\chi_{373527}(33958,\cdot)\)
\(\chi_{373527}(67915,\cdot)\)
\(\chi_{373527}(101872,\cdot)\)
\(\chi_{373527}(135829,\cdot)\)
\(\chi_{373527}(169786,\cdot)\)
\(\chi_{373527}(203743,\cdot)\)
\(\chi_{373527}(237700,\cdot)\)
\(\chi_{373527}(271657,\cdot)\)
\(\chi_{373527}(305614,\cdot)\)
\(\chi_{373527}(339571,\cdot)\)
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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 ]
\((290522,286408,126568)\) → \((1,1,e\left(\frac{2}{11}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 373527 }(101872, a) \) |
\(1\) | \(1\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{9}{11}\right)\) |
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sage:chi.jacobi_sum(n)
