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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7350, base_ring=CyclotomicField(60))
M = H._module
chi = DirichletCharacter(H, M([30,3,20]))
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pari:[g,chi] = znchar(Mod(2627,7350))
\(\chi_{7350}(263,\cdot)\)
\(\chi_{7350}(863,\cdot)\)
\(\chi_{7350}(1733,\cdot)\)
\(\chi_{7350}(2027,\cdot)\)
\(\chi_{7350}(2333,\cdot)\)
\(\chi_{7350}(2627,\cdot)\)
\(\chi_{7350}(3203,\cdot)\)
\(\chi_{7350}(3497,\cdot)\)
\(\chi_{7350}(3803,\cdot)\)
\(\chi_{7350}(4097,\cdot)\)
\(\chi_{7350}(4673,\cdot)\)
\(\chi_{7350}(4967,\cdot)\)
\(\chi_{7350}(5273,\cdot)\)
\(\chi_{7350}(5567,\cdot)\)
\(\chi_{7350}(6437,\cdot)\)
\(\chi_{7350}(7037,\cdot)\)
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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 ]
\((4901,1177,2551)\) → \((-1,e\left(\frac{1}{20}\right),e\left(\frac{1}{3}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 7350 }(2627, a) \) |
\(1\) | \(1\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(-i\) |
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sage:chi.jacobi_sum(n)
