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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(164025, base_ring=CyclotomicField(14580))
M = H._module
chi = DirichletCharacter(H, M([6800,8019]))
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pari:[g,chi] = znchar(Mod(523,164025))
\(\chi_{164025}(37,\cdot)\)
\(\chi_{164025}(73,\cdot)\)
\(\chi_{164025}(127,\cdot)\)
\(\chi_{164025}(172,\cdot)\)
\(\chi_{164025}(208,\cdot)\)
\(\chi_{164025}(253,\cdot)\)
\(\chi_{164025}(262,\cdot)\)
\(\chi_{164025}(388,\cdot)\)
\(\chi_{164025}(397,\cdot)\)
\(\chi_{164025}(442,\cdot)\)
\(\chi_{164025}(478,\cdot)\)
\(\chi_{164025}(523,\cdot)\)
\(\chi_{164025}(577,\cdot)\)
\(\chi_{164025}(613,\cdot)\)
\(\chi_{164025}(658,\cdot)\)
\(\chi_{164025}(667,\cdot)\)
\(\chi_{164025}(712,\cdot)\)
\(\chi_{164025}(748,\cdot)\)
\(\chi_{164025}(802,\cdot)\)
\(\chi_{164025}(847,\cdot)\)
\(\chi_{164025}(883,\cdot)\)
\(\chi_{164025}(928,\cdot)\)
\(\chi_{164025}(937,\cdot)\)
\(\chi_{164025}(1063,\cdot)\)
\(\chi_{164025}(1072,\cdot)\)
\(\chi_{164025}(1117,\cdot)\)
\(\chi_{164025}(1153,\cdot)\)
\(\chi_{164025}(1198,\cdot)\)
\(\chi_{164025}(1252,\cdot)\)
\(\chi_{164025}(1288,\cdot)\)
...
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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 ]
\((59051,104977)\) → \((e\left(\frac{340}{729}\right),e\left(\frac{11}{20}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 164025 }(523, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{239}{14580}\right)\) | \(e\left(\frac{239}{7290}\right)\) | \(e\left(\frac{1483}{2916}\right)\) | \(e\left(\frac{239}{4860}\right)\) | \(e\left(\frac{1661}{3645}\right)\) | \(e\left(\frac{9121}{14580}\right)\) | \(e\left(\frac{3827}{7290}\right)\) | \(e\left(\frac{239}{3645}\right)\) | \(e\left(\frac{2629}{4860}\right)\) | \(e\left(\frac{517}{2430}\right)\) |
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sage:chi.jacobi_sum(n)
