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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1224, base_ring=CyclotomicField(48))
M = H._module
chi = DirichletCharacter(H, M([24,0,32,33]))
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pari:[g,chi] = znchar(Mod(7,1224))
\(\chi_{1224}(7,\cdot)\)
\(\chi_{1224}(31,\cdot)\)
\(\chi_{1224}(79,\cdot)\)
\(\chi_{1224}(175,\cdot)\)
\(\chi_{1224}(295,\cdot)\)
\(\chi_{1224}(367,\cdot)\)
\(\chi_{1224}(439,\cdot)\)
\(\chi_{1224}(583,\cdot)\)
\(\chi_{1224}(607,\cdot)\)
\(\chi_{1224}(751,\cdot)\)
\(\chi_{1224}(823,\cdot)\)
\(\chi_{1224}(895,\cdot)\)
\(\chi_{1224}(1015,\cdot)\)
\(\chi_{1224}(1111,\cdot)\)
\(\chi_{1224}(1159,\cdot)\)
\(\chi_{1224}(1183,\cdot)\)
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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 ]
\((919,613,137,649)\) → \((-1,1,e\left(\frac{2}{3}\right),e\left(\frac{11}{16}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 1224 }(7, a) \) |
\(1\) | \(1\) | \(e\left(\frac{37}{48}\right)\) | \(e\left(\frac{35}{48}\right)\) | \(e\left(\frac{47}{48}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{7}{48}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{29}{48}\right)\) | \(e\left(\frac{1}{48}\right)\) | \(-1\) |
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sage:chi.jacobi_sum(n)
