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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2432, base_ring=CyclotomicField(144))
M = H._module
chi = DirichletCharacter(H, M([0,9,128]))
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pari:[g,chi] = znchar(Mod(537,2432))
\(\chi_{2432}(9,\cdot)\)
\(\chi_{2432}(25,\cdot)\)
\(\chi_{2432}(73,\cdot)\)
\(\chi_{2432}(137,\cdot)\)
\(\chi_{2432}(169,\cdot)\)
\(\chi_{2432}(233,\cdot)\)
\(\chi_{2432}(313,\cdot)\)
\(\chi_{2432}(329,\cdot)\)
\(\chi_{2432}(377,\cdot)\)
\(\chi_{2432}(441,\cdot)\)
\(\chi_{2432}(473,\cdot)\)
\(\chi_{2432}(537,\cdot)\)
\(\chi_{2432}(617,\cdot)\)
\(\chi_{2432}(633,\cdot)\)
\(\chi_{2432}(681,\cdot)\)
\(\chi_{2432}(745,\cdot)\)
\(\chi_{2432}(777,\cdot)\)
\(\chi_{2432}(841,\cdot)\)
\(\chi_{2432}(921,\cdot)\)
\(\chi_{2432}(937,\cdot)\)
\(\chi_{2432}(985,\cdot)\)
\(\chi_{2432}(1049,\cdot)\)
\(\chi_{2432}(1081,\cdot)\)
\(\chi_{2432}(1145,\cdot)\)
\(\chi_{2432}(1225,\cdot)\)
\(\chi_{2432}(1241,\cdot)\)
\(\chi_{2432}(1289,\cdot)\)
\(\chi_{2432}(1353,\cdot)\)
\(\chi_{2432}(1385,\cdot)\)
\(\chi_{2432}(1449,\cdot)\)
...
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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 ]
\((1407,2053,1921)\) → \((1,e\left(\frac{1}{16}\right),e\left(\frac{8}{9}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 2432 }(537, a) \) |
\(1\) | \(1\) | \(e\left(\frac{107}{144}\right)\) | \(e\left(\frac{41}{144}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{35}{72}\right)\) | \(e\left(\frac{47}{48}\right)\) | \(e\left(\frac{55}{144}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{101}{144}\right)\) | \(e\left(\frac{47}{72}\right)\) |
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sage:chi.jacobi_sum(n)
