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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(24400, base_ring=CyclotomicField(60))
M = H._module
chi = DirichletCharacter(H, M([30,45,27,11]))
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pari:[g,chi] = znchar(Mod(1987,24400))
| Modulus: | \(24400\) | |
| Conductor: | \(24400\) |
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sage:chi.conductor()
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pari:znconreyconductor(g,chi)
|
| Order: | \(60\) |
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sage:chi.multiplicative_order()
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pari:charorder(g,chi)
|
| Real: | no |
| Primitive: | yes |
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sage:chi.is_primitive()
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pari:#znconreyconductor(g,chi)==1
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| Minimal: | yes |
| Parity: | odd |
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sage:chi.is_odd()
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pari:zncharisodd(g,chi)
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\(\chi_{24400}(67,\cdot)\)
\(\chi_{24400}(1987,\cdot)\)
\(\chi_{24400}(2227,\cdot)\)
\(\chi_{24400}(6923,\cdot)\)
\(\chi_{24400}(7163,\cdot)\)
\(\chi_{24400}(9083,\cdot)\)
\(\chi_{24400}(11827,\cdot)\)
\(\chi_{24400}(14203,\cdot)\)
\(\chi_{24400}(15187,\cdot)\)
\(\chi_{24400}(15267,\cdot)\)
\(\chi_{24400}(16147,\cdot)\)
\(\chi_{24400}(17403,\cdot)\)
\(\chi_{24400}(18283,\cdot)\)
\(\chi_{24400}(18363,\cdot)\)
\(\chi_{24400}(19347,\cdot)\)
\(\chi_{24400}(21723,\cdot)\)
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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 ]
\((9151,6101,977,3601)\) → \((-1,-i,e\left(\frac{9}{20}\right),e\left(\frac{11}{60}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 24400 }(1987, a) \) |
\(-1\) | \(1\) | \(1\) | \(e\left(\frac{7}{30}\right)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(1\) |
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sage:chi.jacobi_sum(n)
