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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5328, base_ring=CyclotomicField(36))
M = H._module
chi = DirichletCharacter(H, M([18,9,0,7]))
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pari:[g,chi] = znchar(Mod(91,5328))
\(\chi_{5328}(91,\cdot)\)
\(\chi_{5328}(163,\cdot)\)
\(\chi_{5328}(235,\cdot)\)
\(\chi_{5328}(523,\cdot)\)
\(\chi_{5328}(883,\cdot)\)
\(\chi_{5328}(1171,\cdot)\)
\(\chi_{5328}(1243,\cdot)\)
\(\chi_{5328}(1315,\cdot)\)
\(\chi_{5328}(2107,\cdot)\)
\(\chi_{5328}(2683,\cdot)\)
\(\chi_{5328}(4051,\cdot)\)
\(\chi_{5328}(4627,\cdot)\)
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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 ]
\((1999,1333,2369,1297)\) → \((-1,i,1,e\left(\frac{7}{36}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 5328 }(91, a) \) |
\(1\) | \(1\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(i\) |
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sage:chi.jacobi_sum(n)
