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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([0,17,36]))
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pari:[g,chi] = znchar(Mod(1229,2268))
\(\chi_{2268}(65,\cdot)\)
\(\chi_{2268}(221,\cdot)\)
\(\chi_{2268}(317,\cdot)\)
\(\chi_{2268}(473,\cdot)\)
\(\chi_{2268}(569,\cdot)\)
\(\chi_{2268}(725,\cdot)\)
\(\chi_{2268}(821,\cdot)\)
\(\chi_{2268}(977,\cdot)\)
\(\chi_{2268}(1073,\cdot)\)
\(\chi_{2268}(1229,\cdot)\)
\(\chi_{2268}(1325,\cdot)\)
\(\chi_{2268}(1481,\cdot)\)
\(\chi_{2268}(1577,\cdot)\)
\(\chi_{2268}(1733,\cdot)\)
\(\chi_{2268}(1829,\cdot)\)
\(\chi_{2268}(1985,\cdot)\)
\(\chi_{2268}(2081,\cdot)\)
\(\chi_{2268}(2237,\cdot)\)
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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 ]
\((1135,1541,325)\) → \((1,e\left(\frac{17}{54}\right),e\left(\frac{2}{3}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 2268 }(1229, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{31}{54}\right)\) | \(e\left(\frac{41}{54}\right)\) | \(e\left(\frac{14}{27}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{43}{54}\right)\) | \(e\left(\frac{4}{27}\right)\) | \(e\left(\frac{35}{54}\right)\) | \(e\left(\frac{26}{27}\right)\) | \(e\left(\frac{5}{9}\right)\) |
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sage:chi.jacobi_sum(n)
