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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2268, base_ring=CyclotomicField(54))
M = H._module
chi = DirichletCharacter(H, M([0,26,27]))
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pari:[g,chi] = znchar(Mod(769,2268))
\(\chi_{2268}(13,\cdot)\)
\(\chi_{2268}(97,\cdot)\)
\(\chi_{2268}(265,\cdot)\)
\(\chi_{2268}(349,\cdot)\)
\(\chi_{2268}(517,\cdot)\)
\(\chi_{2268}(601,\cdot)\)
\(\chi_{2268}(769,\cdot)\)
\(\chi_{2268}(853,\cdot)\)
\(\chi_{2268}(1021,\cdot)\)
\(\chi_{2268}(1105,\cdot)\)
\(\chi_{2268}(1273,\cdot)\)
\(\chi_{2268}(1357,\cdot)\)
\(\chi_{2268}(1525,\cdot)\)
\(\chi_{2268}(1609,\cdot)\)
\(\chi_{2268}(1777,\cdot)\)
\(\chi_{2268}(1861,\cdot)\)
\(\chi_{2268}(2029,\cdot)\)
\(\chi_{2268}(2113,\cdot)\)
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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 ]
\((1135,1541,325)\) → \((1,e\left(\frac{13}{27}\right),-1)\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 2268 }(769, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{31}{54}\right)\) | \(e\left(\frac{7}{27}\right)\) | \(e\left(\frac{19}{54}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{8}{27}\right)\) | \(e\left(\frac{4}{27}\right)\) | \(e\left(\frac{22}{27}\right)\) | \(e\left(\frac{7}{54}\right)\) | \(e\left(\frac{2}{9}\right)\) |
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sage:chi.jacobi_sum(n)
