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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5766, base_ring=CyclotomicField(310))
M = H._module
chi = DirichletCharacter(H, M([0,54]))
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pari:[g,chi] = znchar(Mod(907,5766))
\(\chi_{5766}(97,\cdot)\)
\(\chi_{5766}(109,\cdot)\)
\(\chi_{5766}(157,\cdot)\)
\(\chi_{5766}(163,\cdot)\)
\(\chi_{5766}(283,\cdot)\)
\(\chi_{5766}(295,\cdot)\)
\(\chi_{5766}(343,\cdot)\)
\(\chi_{5766}(349,\cdot)\)
\(\chi_{5766}(469,\cdot)\)
\(\chi_{5766}(481,\cdot)\)
\(\chi_{5766}(529,\cdot)\)
\(\chi_{5766}(535,\cdot)\)
\(\chi_{5766}(655,\cdot)\)
\(\chi_{5766}(667,\cdot)\)
\(\chi_{5766}(715,\cdot)\)
\(\chi_{5766}(721,\cdot)\)
\(\chi_{5766}(841,\cdot)\)
\(\chi_{5766}(853,\cdot)\)
\(\chi_{5766}(901,\cdot)\)
\(\chi_{5766}(907,\cdot)\)
\(\chi_{5766}(1027,\cdot)\)
\(\chi_{5766}(1039,\cdot)\)
\(\chi_{5766}(1087,\cdot)\)
\(\chi_{5766}(1093,\cdot)\)
\(\chi_{5766}(1213,\cdot)\)
\(\chi_{5766}(1225,\cdot)\)
\(\chi_{5766}(1273,\cdot)\)
\(\chi_{5766}(1279,\cdot)\)
\(\chi_{5766}(1399,\cdot)\)
\(\chi_{5766}(1411,\cdot)\)
...
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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 ]
\((3845,3847)\) → \((1,e\left(\frac{27}{155}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(35\) |
| \( \chi_{ 5766 }(907, a) \) |
\(1\) | \(1\) | \(e\left(\frac{20}{31}\right)\) | \(e\left(\frac{96}{155}\right)\) | \(e\left(\frac{41}{155}\right)\) | \(e\left(\frac{132}{155}\right)\) | \(e\left(\frac{99}{155}\right)\) | \(e\left(\frac{43}{155}\right)\) | \(e\left(\frac{24}{155}\right)\) | \(e\left(\frac{9}{31}\right)\) | \(e\left(\frac{148}{155}\right)\) | \(e\left(\frac{41}{155}\right)\) |
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sage:chi.jacobi_sum(n)
