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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, base_ring=CyclotomicField(66))
M = H._module
chi = DirichletCharacter(H, M([0,0,0,52]))
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pari:[g,chi] = znchar(Mod(121,4020))
\(\chi_{4020}(121,\cdot)\)
\(\chi_{4020}(181,\cdot)\)
\(\chi_{4020}(301,\cdot)\)
\(\chi_{4020}(361,\cdot)\)
\(\chi_{4020}(421,\cdot)\)
\(\chi_{4020}(601,\cdot)\)
\(\chi_{4020}(961,\cdot)\)
\(\chi_{4020}(1021,\cdot)\)
\(\chi_{4020}(1261,\cdot)\)
\(\chi_{4020}(1681,\cdot)\)
\(\chi_{4020}(2161,\cdot)\)
\(\chi_{4020}(2221,\cdot)\)
\(\chi_{4020}(2401,\cdot)\)
\(\chi_{4020}(2461,\cdot)\)
\(\chi_{4020}(2581,\cdot)\)
\(\chi_{4020}(2701,\cdot)\)
\(\chi_{4020}(2941,\cdot)\)
\(\chi_{4020}(3121,\cdot)\)
\(\chi_{4020}(3421,\cdot)\)
\(\chi_{4020}(3721,\cdot)\)
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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 ]
\((2011,2681,3217,1141)\) → \((1,1,1,e\left(\frac{26}{33}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 4020 }(121, a) \) |
\(1\) | \(1\) | \(e\left(\frac{4}{33}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{32}{33}\right)\) | \(e\left(\frac{14}{33}\right)\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{33}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{25}{33}\right)\) |
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sage:chi.jacobi_sum(n)
