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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3267, base_ring=CyclotomicField(90))
M = H._module
chi = DirichletCharacter(H, M([40,9]))
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pari:[g,chi] = znchar(Mod(1201,3267))
\(\chi_{3267}(40,\cdot)\)
\(\chi_{3267}(94,\cdot)\)
\(\chi_{3267}(112,\cdot)\)
\(\chi_{3267}(403,\cdot)\)
\(\chi_{3267}(457,\cdot)\)
\(\chi_{3267}(475,\cdot)\)
\(\chi_{3267}(481,\cdot)\)
\(\chi_{3267}(844,\cdot)\)
\(\chi_{3267}(1129,\cdot)\)
\(\chi_{3267}(1183,\cdot)\)
\(\chi_{3267}(1201,\cdot)\)
\(\chi_{3267}(1492,\cdot)\)
\(\chi_{3267}(1546,\cdot)\)
\(\chi_{3267}(1564,\cdot)\)
\(\chi_{3267}(1570,\cdot)\)
\(\chi_{3267}(1933,\cdot)\)
\(\chi_{3267}(2218,\cdot)\)
\(\chi_{3267}(2272,\cdot)\)
\(\chi_{3267}(2290,\cdot)\)
\(\chi_{3267}(2581,\cdot)\)
\(\chi_{3267}(2635,\cdot)\)
\(\chi_{3267}(2653,\cdot)\)
\(\chi_{3267}(2659,\cdot)\)
\(\chi_{3267}(3022,\cdot)\)
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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 ]
\((3026,244)\) → \((e\left(\frac{4}{9}\right),e\left(\frac{1}{10}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 3267 }(1201, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{49}{90}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{73}{90}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{59}{90}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{17}{30}\right)\) |
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sage:chi.jacobi_sum(n)
