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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(11025, base_ring=CyclotomicField(60))
M = H._module
chi = DirichletCharacter(H, M([10,57,40]))
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pari:[g,chi] = znchar(Mod(263,11025))
\(\chi_{11025}(263,\cdot)\)
\(\chi_{11025}(1598,\cdot)\)
\(\chi_{11025}(2027,\cdot)\)
\(\chi_{11025}(3362,\cdot)\)
\(\chi_{11025}(3803,\cdot)\)
\(\chi_{11025}(4673,\cdot)\)
\(\chi_{11025}(5567,\cdot)\)
\(\chi_{11025}(6008,\cdot)\)
\(\chi_{11025}(6437,\cdot)\)
\(\chi_{11025}(6878,\cdot)\)
\(\chi_{11025}(7772,\cdot)\)
\(\chi_{11025}(8213,\cdot)\)
\(\chi_{11025}(8642,\cdot)\)
\(\chi_{11025}(9083,\cdot)\)
\(\chi_{11025}(9977,\cdot)\)
\(\chi_{11025}(10847,\cdot)\)
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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 ]
\((1226,4852,9901)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{19}{20}\right),e\left(\frac{2}{3}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
| \( \chi_{ 11025 }(263, a) \) |
\(1\) | \(1\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{37}{60}\right)\) |
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sage:chi.jacobi_sum(n)
