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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2900, base_ring=CyclotomicField(70))
M = H._module
chi = DirichletCharacter(H, M([0,49,50]))
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pari:[g,chi] = znchar(Mod(1009,2900))
\(\chi_{2900}(169,\cdot)\)
\(\chi_{2900}(429,\cdot)\)
\(\chi_{2900}(489,\cdot)\)
\(\chi_{2900}(509,\cdot)\)
\(\chi_{2900}(529,\cdot)\)
\(\chi_{2900}(629,\cdot)\)
\(\chi_{2900}(1009,\cdot)\)
\(\chi_{2900}(1069,\cdot)\)
\(\chi_{2900}(1089,\cdot)\)
\(\chi_{2900}(1109,\cdot)\)
\(\chi_{2900}(1209,\cdot)\)
\(\chi_{2900}(1329,\cdot)\)
\(\chi_{2900}(1589,\cdot)\)
\(\chi_{2900}(1669,\cdot)\)
\(\chi_{2900}(1689,\cdot)\)
\(\chi_{2900}(1789,\cdot)\)
\(\chi_{2900}(1909,\cdot)\)
\(\chi_{2900}(2169,\cdot)\)
\(\chi_{2900}(2229,\cdot)\)
\(\chi_{2900}(2269,\cdot)\)
\(\chi_{2900}(2369,\cdot)\)
\(\chi_{2900}(2489,\cdot)\)
\(\chi_{2900}(2809,\cdot)\)
\(\chi_{2900}(2829,\cdot)\)
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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 ]
\((1451,1277,901)\) → \((1,e\left(\frac{7}{10}\right),e\left(\frac{5}{7}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 2900 }(1009, a) \) |
\(1\) | \(1\) | \(e\left(\frac{33}{70}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{11}{70}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{69}{70}\right)\) | \(e\left(\frac{29}{70}\right)\) |
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sage:chi.jacobi_sum(n)
