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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9386, base_ring=CyclotomicField(228))
M = H._module
chi = DirichletCharacter(H, M([133,182]))
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pari:[g,chi] = znchar(Mod(3599,9386))
\(\chi_{9386}(141,\cdot)\)
\(\chi_{9386}(449,\cdot)\)
\(\chi_{9386}(483,\cdot)\)
\(\chi_{9386}(487,\cdot)\)
\(\chi_{9386}(635,\cdot)\)
\(\chi_{9386}(943,\cdot)\)
\(\chi_{9386}(977,\cdot)\)
\(\chi_{9386}(981,\cdot)\)
\(\chi_{9386}(1129,\cdot)\)
\(\chi_{9386}(1437,\cdot)\)
\(\chi_{9386}(1471,\cdot)\)
\(\chi_{9386}(1475,\cdot)\)
\(\chi_{9386}(1623,\cdot)\)
\(\chi_{9386}(1931,\cdot)\)
\(\chi_{9386}(1965,\cdot)\)
\(\chi_{9386}(1969,\cdot)\)
\(\chi_{9386}(2117,\cdot)\)
\(\chi_{9386}(2425,\cdot)\)
\(\chi_{9386}(2463,\cdot)\)
\(\chi_{9386}(2611,\cdot)\)
\(\chi_{9386}(2919,\cdot)\)
\(\chi_{9386}(2953,\cdot)\)
\(\chi_{9386}(3105,\cdot)\)
\(\chi_{9386}(3413,\cdot)\)
\(\chi_{9386}(3447,\cdot)\)
\(\chi_{9386}(3451,\cdot)\)
\(\chi_{9386}(3599,\cdot)\)
\(\chi_{9386}(3907,\cdot)\)
\(\chi_{9386}(3941,\cdot)\)
\(\chi_{9386}(3945,\cdot)\)
...
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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 ]
\((1445,3251)\) → \((e\left(\frac{7}{12}\right),e\left(\frac{91}{114}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 9386 }(3599, a) \) |
\(1\) | \(1\) | \(e\left(\frac{11}{38}\right)\) | \(e\left(\frac{101}{228}\right)\) | \(e\left(\frac{35}{228}\right)\) | \(e\left(\frac{11}{19}\right)\) | \(e\left(\frac{115}{228}\right)\) | \(e\left(\frac{167}{228}\right)\) | \(e\left(\frac{65}{114}\right)\) | \(e\left(\frac{101}{228}\right)\) | \(e\left(\frac{43}{114}\right)\) | \(e\left(\frac{101}{114}\right)\) |
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sage:chi.jacobi_sum(n)
