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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1014, base_ring=CyclotomicField(78))
M = H._module
chi = DirichletCharacter(H, M([0,40]))
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pari:[g,chi] = znchar(Mod(841,1014))
\(\chi_{1014}(55,\cdot)\)
\(\chi_{1014}(61,\cdot)\)
\(\chi_{1014}(133,\cdot)\)
\(\chi_{1014}(139,\cdot)\)
\(\chi_{1014}(211,\cdot)\)
\(\chi_{1014}(217,\cdot)\)
\(\chi_{1014}(289,\cdot)\)
\(\chi_{1014}(295,\cdot)\)
\(\chi_{1014}(367,\cdot)\)
\(\chi_{1014}(373,\cdot)\)
\(\chi_{1014}(445,\cdot)\)
\(\chi_{1014}(451,\cdot)\)
\(\chi_{1014}(523,\cdot)\)
\(\chi_{1014}(601,\cdot)\)
\(\chi_{1014}(607,\cdot)\)
\(\chi_{1014}(679,\cdot)\)
\(\chi_{1014}(685,\cdot)\)
\(\chi_{1014}(757,\cdot)\)
\(\chi_{1014}(763,\cdot)\)
\(\chi_{1014}(835,\cdot)\)
\(\chi_{1014}(841,\cdot)\)
\(\chi_{1014}(913,\cdot)\)
\(\chi_{1014}(919,\cdot)\)
\(\chi_{1014}(997,\cdot)\)
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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 ]
\((677,847)\) → \((1,e\left(\frac{20}{39}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 1014 }(841, a) \) |
\(1\) | \(1\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{19}{39}\right)\) |
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sage:chi.jacobi_sum(n)
