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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([0,20,0]))
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pari:[g,chi] = znchar(Mod(841,2268))
\(\chi_{2268}(85,\cdot)\)
\(\chi_{2268}(169,\cdot)\)
\(\chi_{2268}(337,\cdot)\)
\(\chi_{2268}(421,\cdot)\)
\(\chi_{2268}(589,\cdot)\)
\(\chi_{2268}(673,\cdot)\)
\(\chi_{2268}(841,\cdot)\)
\(\chi_{2268}(925,\cdot)\)
\(\chi_{2268}(1093,\cdot)\)
\(\chi_{2268}(1177,\cdot)\)
\(\chi_{2268}(1345,\cdot)\)
\(\chi_{2268}(1429,\cdot)\)
\(\chi_{2268}(1597,\cdot)\)
\(\chi_{2268}(1681,\cdot)\)
\(\chi_{2268}(1849,\cdot)\)
\(\chi_{2268}(1933,\cdot)\)
\(\chi_{2268}(2101,\cdot)\)
\(\chi_{2268}(2185,\cdot)\)
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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 ]
\((1135,1541,325)\) → \((1,e\left(\frac{10}{27}\right),1)\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 2268 }(841, a) \) |
\(1\) | \(1\) | \(e\left(\frac{14}{27}\right)\) | \(e\left(\frac{22}{27}\right)\) | \(e\left(\frac{26}{27}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{2}{27}\right)\) | \(e\left(\frac{1}{27}\right)\) | \(e\left(\frac{19}{27}\right)\) | \(e\left(\frac{11}{27}\right)\) | \(e\left(\frac{5}{9}\right)\) |
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sage:chi.jacobi_sum(n)
