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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1734, base_ring=CyclotomicField(272))
M = H._module
chi = DirichletCharacter(H, M([136,243]))
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pari:[g,chi] = znchar(Mod(95,1734))
\(\chi_{1734}(5,\cdot)\)
\(\chi_{1734}(11,\cdot)\)
\(\chi_{1734}(23,\cdot)\)
\(\chi_{1734}(29,\cdot)\)
\(\chi_{1734}(41,\cdot)\)
\(\chi_{1734}(71,\cdot)\)
\(\chi_{1734}(95,\cdot)\)
\(\chi_{1734}(107,\cdot)\)
\(\chi_{1734}(113,\cdot)\)
\(\chi_{1734}(125,\cdot)\)
\(\chi_{1734}(143,\cdot)\)
\(\chi_{1734}(167,\cdot)\)
\(\chi_{1734}(173,\cdot)\)
\(\chi_{1734}(197,\cdot)\)
\(\chi_{1734}(209,\cdot)\)
\(\chi_{1734}(215,\cdot)\)
\(\chi_{1734}(227,\cdot)\)
\(\chi_{1734}(233,\cdot)\)
\(\chi_{1734}(245,\cdot)\)
\(\chi_{1734}(269,\cdot)\)
\(\chi_{1734}(275,\cdot)\)
\(\chi_{1734}(299,\cdot)\)
\(\chi_{1734}(311,\cdot)\)
\(\chi_{1734}(317,\cdot)\)
\(\chi_{1734}(335,\cdot)\)
\(\chi_{1734}(347,\cdot)\)
\(\chi_{1734}(371,\cdot)\)
\(\chi_{1734}(377,\cdot)\)
\(\chi_{1734}(401,\cdot)\)
\(\chi_{1734}(413,\cdot)\)
...
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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 ]
\((1157,1159)\) → \((-1,e\left(\frac{243}{272}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 1734 }(95, a) \) |
\(1\) | \(1\) | \(e\left(\frac{23}{272}\right)\) | \(e\left(\frac{129}{272}\right)\) | \(e\left(\frac{13}{272}\right)\) | \(e\left(\frac{7}{68}\right)\) | \(e\left(\frac{69}{136}\right)\) | \(e\left(\frac{197}{272}\right)\) | \(e\left(\frac{23}{136}\right)\) | \(e\left(\frac{47}{272}\right)\) | \(e\left(\frac{11}{272}\right)\) | \(e\left(\frac{19}{34}\right)\) |
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sage:chi.jacobi_sum(n)
