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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2535, base_ring=CyclotomicField(78))
M = H._module
chi = DirichletCharacter(H, M([0,39,68]))
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pari:[g,chi] = znchar(Mod(289,2535))
\(\chi_{2535}(94,\cdot)\)
\(\chi_{2535}(139,\cdot)\)
\(\chi_{2535}(289,\cdot)\)
\(\chi_{2535}(334,\cdot)\)
\(\chi_{2535}(679,\cdot)\)
\(\chi_{2535}(724,\cdot)\)
\(\chi_{2535}(874,\cdot)\)
\(\chi_{2535}(919,\cdot)\)
\(\chi_{2535}(1069,\cdot)\)
\(\chi_{2535}(1114,\cdot)\)
\(\chi_{2535}(1264,\cdot)\)
\(\chi_{2535}(1309,\cdot)\)
\(\chi_{2535}(1459,\cdot)\)
\(\chi_{2535}(1504,\cdot)\)
\(\chi_{2535}(1654,\cdot)\)
\(\chi_{2535}(1699,\cdot)\)
\(\chi_{2535}(1849,\cdot)\)
\(\chi_{2535}(1894,\cdot)\)
\(\chi_{2535}(2044,\cdot)\)
\(\chi_{2535}(2089,\cdot)\)
\(\chi_{2535}(2239,\cdot)\)
\(\chi_{2535}(2284,\cdot)\)
\(\chi_{2535}(2434,\cdot)\)
\(\chi_{2535}(2479,\cdot)\)
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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 ]
\((1691,1522,1861)\) → \((1,-1,e\left(\frac{34}{39}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
| \( \chi_{ 2535 }(289, a) \) |
\(1\) | \(1\) | \(e\left(\frac{29}{78}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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sage:chi.jacobi_sum(n)
