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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2366, base_ring=CyclotomicField(78))
M = H._module
chi = DirichletCharacter(H, M([26,2]))
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pari:[g,chi] = znchar(Mod(1199,2366))
\(\chi_{2366}(107,\cdot)\)
\(\chi_{2366}(165,\cdot)\)
\(\chi_{2366}(289,\cdot)\)
\(\chi_{2366}(347,\cdot)\)
\(\chi_{2366}(471,\cdot)\)
\(\chi_{2366}(711,\cdot)\)
\(\chi_{2366}(835,\cdot)\)
\(\chi_{2366}(893,\cdot)\)
\(\chi_{2366}(1017,\cdot)\)
\(\chi_{2366}(1075,\cdot)\)
\(\chi_{2366}(1199,\cdot)\)
\(\chi_{2366}(1257,\cdot)\)
\(\chi_{2366}(1381,\cdot)\)
\(\chi_{2366}(1439,\cdot)\)
\(\chi_{2366}(1563,\cdot)\)
\(\chi_{2366}(1621,\cdot)\)
\(\chi_{2366}(1745,\cdot)\)
\(\chi_{2366}(1803,\cdot)\)
\(\chi_{2366}(1927,\cdot)\)
\(\chi_{2366}(1985,\cdot)\)
\(\chi_{2366}(2109,\cdot)\)
\(\chi_{2366}(2167,\cdot)\)
\(\chi_{2366}(2291,\cdot)\)
\(\chi_{2366}(2349,\cdot)\)
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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 ]
\((339,2199)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{1}{39}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 2366 }(1199, a) \) |
\(1\) | \(1\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{7}{13}\right)\) |
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sage:chi.jacobi_sum(n)
