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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3328, base_ring=CyclotomicField(48))
M = H._module
chi = DirichletCharacter(H, M([0,39,8]))
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pari:[g,chi] = znchar(Mod(433,3328))
\(\chi_{3328}(17,\cdot)\)
\(\chi_{3328}(49,\cdot)\)
\(\chi_{3328}(433,\cdot)\)
\(\chi_{3328}(465,\cdot)\)
\(\chi_{3328}(849,\cdot)\)
\(\chi_{3328}(881,\cdot)\)
\(\chi_{3328}(1265,\cdot)\)
\(\chi_{3328}(1297,\cdot)\)
\(\chi_{3328}(1681,\cdot)\)
\(\chi_{3328}(1713,\cdot)\)
\(\chi_{3328}(2097,\cdot)\)
\(\chi_{3328}(2129,\cdot)\)
\(\chi_{3328}(2513,\cdot)\)
\(\chi_{3328}(2545,\cdot)\)
\(\chi_{3328}(2929,\cdot)\)
\(\chi_{3328}(2961,\cdot)\)
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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 ]
\((1535,261,769)\) → \((1,e\left(\frac{13}{16}\right),e\left(\frac{1}{6}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 3328 }(433, a) \) |
\(1\) | \(1\) | \(e\left(\frac{5}{48}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{11}{48}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{25}{48}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{1}{24}\right)\) |
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sage:chi.jacobi_sum(n)
