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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1338, base_ring=CyclotomicField(74))
M = H._module
chi = DirichletCharacter(H, M([0,36]))
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pari:[g,chi] = znchar(Mod(925,1338))
\(\chi_{1338}(7,\cdot)\)
\(\chi_{1338}(49,\cdot)\)
\(\chi_{1338}(115,\cdot)\)
\(\chi_{1338}(169,\cdot)\)
\(\chi_{1338}(253,\cdot)\)
\(\chi_{1338}(283,\cdot)\)
\(\chi_{1338}(289,\cdot)\)
\(\chi_{1338}(343,\cdot)\)
\(\chi_{1338}(355,\cdot)\)
\(\chi_{1338}(433,\cdot)\)
\(\chi_{1338}(463,\cdot)\)
\(\chi_{1338}(487,\cdot)\)
\(\chi_{1338}(565,\cdot)\)
\(\chi_{1338}(643,\cdot)\)
\(\chi_{1338}(673,\cdot)\)
\(\chi_{1338}(685,\cdot)\)
\(\chi_{1338}(697,\cdot)\)
\(\chi_{1338}(703,\cdot)\)
\(\chi_{1338}(733,\cdot)\)
\(\chi_{1338}(751,\cdot)\)
\(\chi_{1338}(781,\cdot)\)
\(\chi_{1338}(805,\cdot)\)
\(\chi_{1338}(865,\cdot)\)
\(\chi_{1338}(907,\cdot)\)
\(\chi_{1338}(925,\cdot)\)
\(\chi_{1338}(997,\cdot)\)
\(\chi_{1338}(1063,\cdot)\)
\(\chi_{1338}(1117,\cdot)\)
\(\chi_{1338}(1123,\cdot)\)
\(\chi_{1338}(1129,\cdot)\)
...
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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 ]
\((893,895)\) → \((1,e\left(\frac{18}{37}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 1338 }(925, a) \) |
\(1\) | \(1\) | \(e\left(\frac{11}{37}\right)\) | \(e\left(\frac{6}{37}\right)\) | \(e\left(\frac{2}{37}\right)\) | \(e\left(\frac{19}{37}\right)\) | \(e\left(\frac{2}{37}\right)\) | \(e\left(\frac{25}{37}\right)\) | \(e\left(\frac{11}{37}\right)\) | \(e\left(\frac{22}{37}\right)\) | \(e\left(\frac{10}{37}\right)\) | \(e\left(\frac{33}{37}\right)\) |
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sage:chi.jacobi_sum(n)
