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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5184, base_ring=CyclotomicField(54))
M = H._module
chi = DirichletCharacter(H, M([27,27,41]))
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pari:[g,chi] = znchar(Mod(2975,5184))
\(\chi_{5184}(95,\cdot)\)
\(\chi_{5184}(479,\cdot)\)
\(\chi_{5184}(671,\cdot)\)
\(\chi_{5184}(1055,\cdot)\)
\(\chi_{5184}(1247,\cdot)\)
\(\chi_{5184}(1631,\cdot)\)
\(\chi_{5184}(1823,\cdot)\)
\(\chi_{5184}(2207,\cdot)\)
\(\chi_{5184}(2399,\cdot)\)
\(\chi_{5184}(2783,\cdot)\)
\(\chi_{5184}(2975,\cdot)\)
\(\chi_{5184}(3359,\cdot)\)
\(\chi_{5184}(3551,\cdot)\)
\(\chi_{5184}(3935,\cdot)\)
\(\chi_{5184}(4127,\cdot)\)
\(\chi_{5184}(4511,\cdot)\)
\(\chi_{5184}(4703,\cdot)\)
\(\chi_{5184}(5087,\cdot)\)
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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 ]
\((2431,325,1217)\) → \((-1,-1,e\left(\frac{41}{54}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 5184 }(2975, a) \) |
\(1\) | \(1\) | \(e\left(\frac{26}{27}\right)\) | \(e\left(\frac{35}{54}\right)\) | \(e\left(\frac{47}{54}\right)\) | \(e\left(\frac{31}{54}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{23}{27}\right)\) | \(e\left(\frac{25}{27}\right)\) | \(e\left(\frac{16}{27}\right)\) | \(e\left(\frac{37}{54}\right)\) |
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sage:chi.jacobi_sum(n)
