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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2898, base_ring=CyclotomicField(66))
M = H._module
chi = DirichletCharacter(H, M([22,33,51]))
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pari:[g,chi] = znchar(Mod(2407,2898))
\(\chi_{2898}(97,\cdot)\)
\(\chi_{2898}(475,\cdot)\)
\(\chi_{2898}(517,\cdot)\)
\(\chi_{2898}(727,\cdot)\)
\(\chi_{2898}(769,\cdot)\)
\(\chi_{2898}(895,\cdot)\)
\(\chi_{2898}(1147,\cdot)\)
\(\chi_{2898}(1399,\cdot)\)
\(\chi_{2898}(1483,\cdot)\)
\(\chi_{2898}(1525,\cdot)\)
\(\chi_{2898}(1735,\cdot)\)
\(\chi_{2898}(1861,\cdot)\)
\(\chi_{2898}(1903,\cdot)\)
\(\chi_{2898}(2029,\cdot)\)
\(\chi_{2898}(2113,\cdot)\)
\(\chi_{2898}(2365,\cdot)\)
\(\chi_{2898}(2407,\cdot)\)
\(\chi_{2898}(2491,\cdot)\)
\(\chi_{2898}(2659,\cdot)\)
\(\chi_{2898}(2869,\cdot)\)
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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 ]
\((1289,829,1891)\) → \((e\left(\frac{1}{3}\right),-1,e\left(\frac{17}{22}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 2898 }(2407, a) \) |
\(1\) | \(1\) | \(e\left(\frac{31}{33}\right)\) | \(e\left(\frac{19}{66}\right)\) | \(e\left(\frac{65}{66}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{53}{66}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{29}{66}\right)\) |
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sage:chi.jacobi_sum(n)
