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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2541, base_ring=CyclotomicField(30))
M = H._module
chi = DirichletCharacter(H, M([15,10,12]))
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pari:[g,chi] = znchar(Mod(632,2541))
\(\chi_{2541}(632,\cdot)\)
\(\chi_{2541}(977,\cdot)\)
\(\chi_{2541}(1334,\cdot)\)
\(\chi_{2541}(1703,\cdot)\)
\(\chi_{2541}(1775,\cdot)\)
\(\chi_{2541}(2060,\cdot)\)
\(\chi_{2541}(2447,\cdot)\)
\(\chi_{2541}(2501,\cdot)\)
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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 ]
\((848,1816,2059)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{2}{5}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 2541 }(632, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{9}{10}\right)\) |
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sage:chi.jacobi_sum(n)
