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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2523, base_ring=CyclotomicField(28))
M = H._module
chi = DirichletCharacter(H, M([0,23]))
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pari:[g,chi] = znchar(Mod(2098,2523))
\(\chi_{2523}(781,\cdot)\)
\(\chi_{2523}(901,\cdot)\)
\(\chi_{2523}(1696,\cdot)\)
\(\chi_{2523}(1819,\cdot)\)
\(\chi_{2523}(1903,\cdot)\)
\(\chi_{2523}(2056,\cdot)\)
\(\chi_{2523}(2098,\cdot)\)
\(\chi_{2523}(2107,\cdot)\)
\(\chi_{2523}(2149,\cdot)\)
\(\chi_{2523}(2302,\cdot)\)
\(\chi_{2523}(2386,\cdot)\)
\(\chi_{2523}(2509,\cdot)\)
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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 ]
\((842,1684)\) → \((1,e\left(\frac{23}{28}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 2523 }(2098, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{2}{7}\right)\) |
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sage:chi.jacobi_sum(n)
