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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3800, base_ring=CyclotomicField(90))
M = H._module
chi = DirichletCharacter(H, M([0,0,9,20]))
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pari:[g,chi] = znchar(Mod(529,3800))
\(\chi_{3800}(9,\cdot)\)
\(\chi_{3800}(169,\cdot)\)
\(\chi_{3800}(289,\cdot)\)
\(\chi_{3800}(329,\cdot)\)
\(\chi_{3800}(529,\cdot)\)
\(\chi_{3800}(689,\cdot)\)
\(\chi_{3800}(769,\cdot)\)
\(\chi_{3800}(929,\cdot)\)
\(\chi_{3800}(1089,\cdot)\)
\(\chi_{3800}(1289,\cdot)\)
\(\chi_{3800}(1529,\cdot)\)
\(\chi_{3800}(1689,\cdot)\)
\(\chi_{3800}(1809,\cdot)\)
\(\chi_{3800}(2209,\cdot)\)
\(\chi_{3800}(2289,\cdot)\)
\(\chi_{3800}(2569,\cdot)\)
\(\chi_{3800}(2609,\cdot)\)
\(\chi_{3800}(2809,\cdot)\)
\(\chi_{3800}(2969,\cdot)\)
\(\chi_{3800}(3209,\cdot)\)
\(\chi_{3800}(3329,\cdot)\)
\(\chi_{3800}(3369,\cdot)\)
\(\chi_{3800}(3569,\cdot)\)
\(\chi_{3800}(3729,\cdot)\)
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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 ]
\((951,1901,1977,401)\) → \((1,1,e\left(\frac{1}{10}\right),e\left(\frac{2}{9}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 3800 }(529, a) \) |
\(1\) | \(1\) | \(e\left(\frac{53}{90}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{1}{90}\right)\) | \(e\left(\frac{47}{90}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{49}{90}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{44}{45}\right)\) |
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sage:chi.jacobi_sum(n)
