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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3645, base_ring=CyclotomicField(54))
M = H._module
chi = DirichletCharacter(H, M([46,0]))
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pari:[g,chi] = znchar(Mod(3376,3645))
\(\chi_{3645}(136,\cdot)\)
\(\chi_{3645}(271,\cdot)\)
\(\chi_{3645}(541,\cdot)\)
\(\chi_{3645}(676,\cdot)\)
\(\chi_{3645}(946,\cdot)\)
\(\chi_{3645}(1081,\cdot)\)
\(\chi_{3645}(1351,\cdot)\)
\(\chi_{3645}(1486,\cdot)\)
\(\chi_{3645}(1756,\cdot)\)
\(\chi_{3645}(1891,\cdot)\)
\(\chi_{3645}(2161,\cdot)\)
\(\chi_{3645}(2296,\cdot)\)
\(\chi_{3645}(2566,\cdot)\)
\(\chi_{3645}(2701,\cdot)\)
\(\chi_{3645}(2971,\cdot)\)
\(\chi_{3645}(3106,\cdot)\)
\(\chi_{3645}(3376,\cdot)\)
\(\chi_{3645}(3511,\cdot)\)
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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 ]
\((731,2917)\) → \((e\left(\frac{23}{27}\right),1)\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 3645 }(3376, a) \) |
\(1\) | \(1\) | \(e\left(\frac{23}{27}\right)\) | \(e\left(\frac{19}{27}\right)\) | \(e\left(\frac{17}{27}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{2}{27}\right)\) | \(e\left(\frac{22}{27}\right)\) | \(e\left(\frac{13}{27}\right)\) | \(e\left(\frac{11}{27}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{8}{9}\right)\) |
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sage:chi.jacobi_sum(n)
