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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(15800, base_ring=CyclotomicField(60))
M = H._module
chi = DirichletCharacter(H, M([0,30,33,50]))
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pari:[g,chi] = znchar(Mod(9773,15800))
| Modulus: | \(15800\) | |
| Conductor: | \(15800\) |
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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: | even |
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sage:chi.is_odd()
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pari:zncharisodd(g,chi)
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\(\chi_{15800}(3453,\cdot)\)
\(\chi_{15800}(4053,\cdot)\)
\(\chi_{15800}(4717,\cdot)\)
\(\chi_{15800}(5317,\cdot)\)
\(\chi_{15800}(6613,\cdot)\)
\(\chi_{15800}(7213,\cdot)\)
\(\chi_{15800}(7877,\cdot)\)
\(\chi_{15800}(8477,\cdot)\)
\(\chi_{15800}(9773,\cdot)\)
\(\chi_{15800}(10373,\cdot)\)
\(\chi_{15800}(11037,\cdot)\)
\(\chi_{15800}(11637,\cdot)\)
\(\chi_{15800}(12933,\cdot)\)
\(\chi_{15800}(13533,\cdot)\)
\(\chi_{15800}(14197,\cdot)\)
\(\chi_{15800}(14797,\cdot)\)
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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 ]
\((3951,7901,11377,12801)\) → \((1,-1,e\left(\frac{11}{20}\right),e\left(\frac{5}{6}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 15800 }(9773, a) \) |
\(1\) | \(1\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{11}{20}\right)\) |
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sage:chi.jacobi_sum(n)
