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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2401, base_ring=CyclotomicField(98))
M = H._module
chi = DirichletCharacter(H, M([92]))
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pari:[g,chi] = znchar(Mod(834,2401))
\(\chi_{2401}(50,\cdot)\)
\(\chi_{2401}(99,\cdot)\)
\(\chi_{2401}(148,\cdot)\)
\(\chi_{2401}(197,\cdot)\)
\(\chi_{2401}(246,\cdot)\)
\(\chi_{2401}(295,\cdot)\)
\(\chi_{2401}(393,\cdot)\)
\(\chi_{2401}(442,\cdot)\)
\(\chi_{2401}(491,\cdot)\)
\(\chi_{2401}(540,\cdot)\)
\(\chi_{2401}(589,\cdot)\)
\(\chi_{2401}(638,\cdot)\)
\(\chi_{2401}(736,\cdot)\)
\(\chi_{2401}(785,\cdot)\)
\(\chi_{2401}(834,\cdot)\)
\(\chi_{2401}(883,\cdot)\)
\(\chi_{2401}(932,\cdot)\)
\(\chi_{2401}(981,\cdot)\)
\(\chi_{2401}(1079,\cdot)\)
\(\chi_{2401}(1128,\cdot)\)
\(\chi_{2401}(1177,\cdot)\)
\(\chi_{2401}(1226,\cdot)\)
\(\chi_{2401}(1275,\cdot)\)
\(\chi_{2401}(1324,\cdot)\)
\(\chi_{2401}(1422,\cdot)\)
\(\chi_{2401}(1471,\cdot)\)
\(\chi_{2401}(1520,\cdot)\)
\(\chi_{2401}(1569,\cdot)\)
\(\chi_{2401}(1618,\cdot)\)
\(\chi_{2401}(1667,\cdot)\)
...
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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 ]
\(3\) → \(e\left(\frac{46}{49}\right)\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 2401 }(834, a) \) |
\(1\) | \(1\) | \(e\left(\frac{6}{49}\right)\) | \(e\left(\frac{46}{49}\right)\) | \(e\left(\frac{12}{49}\right)\) | \(e\left(\frac{11}{49}\right)\) | \(e\left(\frac{3}{49}\right)\) | \(e\left(\frac{18}{49}\right)\) | \(e\left(\frac{43}{49}\right)\) | \(e\left(\frac{17}{49}\right)\) | \(e\left(\frac{13}{49}\right)\) | \(e\left(\frac{9}{49}\right)\) |
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sage:chi.jacobi_sum(n)
