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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(97020, base_ring=CyclotomicField(70))
M = H._module
chi = DirichletCharacter(H, M([35,35,0,10,56]))
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pari:[g,chi] = znchar(Mod(64331,97020))
\(\chi_{97020}(71,\cdot)\)
\(\chi_{97020}(8891,\cdot)\)
\(\chi_{97020}(10151,\cdot)\)
\(\chi_{97020}(11411,\cdot)\)
\(\chi_{97020}(13931,\cdot)\)
\(\chi_{97020}(22751,\cdot)\)
\(\chi_{97020}(25271,\cdot)\)
\(\chi_{97020}(27791,\cdot)\)
\(\chi_{97020}(36611,\cdot)\)
\(\chi_{97020}(37871,\cdot)\)
\(\chi_{97020}(39131,\cdot)\)
\(\chi_{97020}(51731,\cdot)\)
\(\chi_{97020}(52991,\cdot)\)
\(\chi_{97020}(55511,\cdot)\)
\(\chi_{97020}(64331,\cdot)\)
\(\chi_{97020}(65591,\cdot)\)
\(\chi_{97020}(66851,\cdot)\)
\(\chi_{97020}(69371,\cdot)\)
\(\chi_{97020}(78191,\cdot)\)
\(\chi_{97020}(79451,\cdot)\)
\(\chi_{97020}(80711,\cdot)\)
\(\chi_{97020}(83231,\cdot)\)
\(\chi_{97020}(92051,\cdot)\)
\(\chi_{97020}(93311,\cdot)\)
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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 ]
\((48511,43121,77617,9901,44101)\) → \((-1,-1,1,e\left(\frac{1}{7}\right),e\left(\frac{4}{5}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
| \( \chi_{ 97020 }(64331, a) \) |
\(1\) | \(1\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{3}{70}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{4}{35}\right)\) |
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sage:chi.jacobi_sum(n)
