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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4600, base_ring=CyclotomicField(44))
M = H._module
chi = DirichletCharacter(H, M([22,0,11,12]))
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pari:[g,chi] = znchar(Mod(2607,4600))
\(\chi_{4600}(407,\cdot)\)
\(\chi_{4600}(607,\cdot)\)
\(\chi_{4600}(807,\cdot)\)
\(\chi_{4600}(1007,\cdot)\)
\(\chi_{4600}(1143,\cdot)\)
\(\chi_{4600}(1343,\cdot)\)
\(\chi_{4600}(1407,\cdot)\)
\(\chi_{4600}(1543,\cdot)\)
\(\chi_{4600}(1743,\cdot)\)
\(\chi_{4600}(1807,\cdot)\)
\(\chi_{4600}(2007,\cdot)\)
\(\chi_{4600}(2143,\cdot)\)
\(\chi_{4600}(2543,\cdot)\)
\(\chi_{4600}(2607,\cdot)\)
\(\chi_{4600}(2743,\cdot)\)
\(\chi_{4600}(3343,\cdot)\)
\(\chi_{4600}(3407,\cdot)\)
\(\chi_{4600}(3807,\cdot)\)
\(\chi_{4600}(4143,\cdot)\)
\(\chi_{4600}(4543,\cdot)\)
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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 ]
\((1151,2301,2577,1201)\) → \((-1,1,i,e\left(\frac{3}{11}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(27\) | \(29\) |
| \( \chi_{ 4600 }(2607, a) \) |
\(1\) | \(1\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{9}{22}\right)\) |
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sage:chi.jacobi_sum(n)
