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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(97020, base_ring=CyclotomicField(210))
M = H._module
chi = DirichletCharacter(H, M([105,140,0,50,63]))
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pari:[g,chi] = znchar(Mod(151,97020))
\(\chi_{97020}(151,\cdot)\)
\(\chi_{97020}(8971,\cdot)\)
\(\chi_{97020}(10831,\cdot)\)
\(\chi_{97020}(11491,\cdot)\)
\(\chi_{97020}(12091,\cdot)\)
\(\chi_{97020}(12751,\cdot)\)
\(\chi_{97020}(13351,\cdot)\)
\(\chi_{97020}(14011,\cdot)\)
\(\chi_{97020}(22171,\cdot)\)
\(\chi_{97020}(22831,\cdot)\)
\(\chi_{97020}(24691,\cdot)\)
\(\chi_{97020}(26611,\cdot)\)
\(\chi_{97020}(27211,\cdot)\)
\(\chi_{97020}(27871,\cdot)\)
\(\chi_{97020}(36031,\cdot)\)
\(\chi_{97020}(36691,\cdot)\)
\(\chi_{97020}(38551,\cdot)\)
\(\chi_{97020}(39211,\cdot)\)
\(\chi_{97020}(39811,\cdot)\)
\(\chi_{97020}(40471,\cdot)\)
\(\chi_{97020}(41071,\cdot)\)
\(\chi_{97020}(41731,\cdot)\)
\(\chi_{97020}(49891,\cdot)\)
\(\chi_{97020}(50551,\cdot)\)
\(\chi_{97020}(53071,\cdot)\)
\(\chi_{97020}(53671,\cdot)\)
\(\chi_{97020}(54331,\cdot)\)
\(\chi_{97020}(54931,\cdot)\)
\(\chi_{97020}(55591,\cdot)\)
\(\chi_{97020}(63751,\cdot)\)
...
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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 ]
\((48511,43121,77617,9901,44101)\) → \((-1,e\left(\frac{2}{3}\right),1,e\left(\frac{5}{21}\right),e\left(\frac{3}{10}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
| \( \chi_{ 97020 }(151, a) \) |
\(1\) | \(1\) | \(e\left(\frac{103}{210}\right)\) | \(e\left(\frac{137}{210}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{11}{210}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{23}{105}\right)\) | \(e\left(\frac{169}{210}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{53}{70}\right)\) |
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sage:chi.jacobi_sum(n)
