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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5766, base_ring=CyclotomicField(930))
M = H._module
chi = DirichletCharacter(H, M([0,608]))
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pari:[g,chi] = znchar(Mod(175,5766))
\(\chi_{5766}(7,\cdot)\)
\(\chi_{5766}(19,\cdot)\)
\(\chi_{5766}(49,\cdot)\)
\(\chi_{5766}(103,\cdot)\)
\(\chi_{5766}(121,\cdot)\)
\(\chi_{5766}(133,\cdot)\)
\(\chi_{5766}(169,\cdot)\)
\(\chi_{5766}(175,\cdot)\)
\(\chi_{5766}(193,\cdot)\)
\(\chi_{5766}(205,\cdot)\)
\(\chi_{5766}(289,\cdot)\)
\(\chi_{5766}(307,\cdot)\)
\(\chi_{5766}(319,\cdot)\)
\(\chi_{5766}(355,\cdot)\)
\(\chi_{5766}(361,\cdot)\)
\(\chi_{5766}(379,\cdot)\)
\(\chi_{5766}(391,\cdot)\)
\(\chi_{5766}(421,\cdot)\)
\(\chi_{5766}(475,\cdot)\)
\(\chi_{5766}(493,\cdot)\)
\(\chi_{5766}(505,\cdot)\)
\(\chi_{5766}(541,\cdot)\)
\(\chi_{5766}(565,\cdot)\)
\(\chi_{5766}(577,\cdot)\)
\(\chi_{5766}(607,\cdot)\)
\(\chi_{5766}(661,\cdot)\)
\(\chi_{5766}(679,\cdot)\)
\(\chi_{5766}(691,\cdot)\)
\(\chi_{5766}(727,\cdot)\)
\(\chi_{5766}(733,\cdot)\)
...
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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 ]
\((3845,3847)\) → \((1,e\left(\frac{304}{465}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(35\) |
| \( \chi_{ 5766 }(175, a) \) |
\(1\) | \(1\) | \(e\left(\frac{61}{93}\right)\) | \(e\left(\frac{82}{465}\right)\) | \(e\left(\frac{77}{465}\right)\) | \(e\left(\frac{74}{465}\right)\) | \(e\left(\frac{133}{465}\right)\) | \(e\left(\frac{421}{465}\right)\) | \(e\left(\frac{136}{155}\right)\) | \(e\left(\frac{29}{93}\right)\) | \(e\left(\frac{12}{155}\right)\) | \(e\left(\frac{129}{155}\right)\) |
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sage:chi.jacobi_sum(n)
