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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(11025, base_ring=CyclotomicField(42))
M = H._module
chi = DirichletCharacter(H, M([7,21,29]))
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pari:[g,chi] = znchar(Mod(299,11025))
\(\chi_{11025}(299,\cdot)\)
\(\chi_{11025}(1874,\cdot)\)
\(\chi_{11025}(1949,\cdot)\)
\(\chi_{11025}(3524,\cdot)\)
\(\chi_{11025}(5024,\cdot)\)
\(\chi_{11025}(5099,\cdot)\)
\(\chi_{11025}(6599,\cdot)\)
\(\chi_{11025}(6674,\cdot)\)
\(\chi_{11025}(8174,\cdot)\)
\(\chi_{11025}(8249,\cdot)\)
\(\chi_{11025}(9749,\cdot)\)
\(\chi_{11025}(9824,\cdot)\)
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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 ]
\((1226,4852,9901)\) → \((e\left(\frac{1}{6}\right),-1,e\left(\frac{29}{42}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
| \( \chi_{ 11025 }(299, a) \) |
\(1\) | \(1\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{4}{7}\right)\) |
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sage:chi.jacobi_sum(n)
