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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(164025, base_ring=CyclotomicField(4860))
M = H._module
chi = DirichletCharacter(H, M([2180,729]))
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pari:[g,chi] = znchar(Mod(433,164025))
\(\chi_{164025}(28,\cdot)\)
\(\chi_{164025}(217,\cdot)\)
\(\chi_{164025}(298,\cdot)\)
\(\chi_{164025}(352,\cdot)\)
\(\chi_{164025}(433,\cdot)\)
\(\chi_{164025}(622,\cdot)\)
\(\chi_{164025}(703,\cdot)\)
\(\chi_{164025}(838,\cdot)\)
\(\chi_{164025}(1027,\cdot)\)
\(\chi_{164025}(1108,\cdot)\)
\(\chi_{164025}(1162,\cdot)\)
\(\chi_{164025}(1513,\cdot)\)
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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 ]
\((59051,104977)\) → \((e\left(\frac{109}{243}\right),e\left(\frac{3}{20}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 164025 }(433, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{2909}{4860}\right)\) | \(e\left(\frac{479}{2430}\right)\) | \(e\left(\frac{469}{972}\right)\) | \(e\left(\frac{1289}{1620}\right)\) | \(e\left(\frac{416}{1215}\right)\) | \(e\left(\frac{3751}{4860}\right)\) | \(e\left(\frac{197}{2430}\right)\) | \(e\left(\frac{479}{1215}\right)\) | \(e\left(\frac{1219}{1620}\right)\) | \(e\left(\frac{277}{810}\right)\) |
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sage:chi.jacobi_sum(n)
