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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1792, base_ring=CyclotomicField(192))
M = H._module
chi = DirichletCharacter(H, M([96,177,160]))
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pari:[g,chi] = znchar(Mod(1251,1792))
| Modulus: | \(1792\) | |
| Conductor: | \(1792\) |
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sage:chi.conductor()
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pari:znconreyconductor(g,chi)
|
| Order: | \(192\) |
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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
|
| Minimal: | yes |
| Parity: | even |
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sage:chi.is_odd()
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pari:zncharisodd(g,chi)
|
\(\chi_{1792}(3,\cdot)\)
\(\chi_{1792}(19,\cdot)\)
\(\chi_{1792}(59,\cdot)\)
\(\chi_{1792}(75,\cdot)\)
\(\chi_{1792}(115,\cdot)\)
\(\chi_{1792}(131,\cdot)\)
\(\chi_{1792}(171,\cdot)\)
\(\chi_{1792}(187,\cdot)\)
\(\chi_{1792}(227,\cdot)\)
\(\chi_{1792}(243,\cdot)\)
\(\chi_{1792}(283,\cdot)\)
\(\chi_{1792}(299,\cdot)\)
\(\chi_{1792}(339,\cdot)\)
\(\chi_{1792}(355,\cdot)\)
\(\chi_{1792}(395,\cdot)\)
\(\chi_{1792}(411,\cdot)\)
\(\chi_{1792}(451,\cdot)\)
\(\chi_{1792}(467,\cdot)\)
\(\chi_{1792}(507,\cdot)\)
\(\chi_{1792}(523,\cdot)\)
\(\chi_{1792}(563,\cdot)\)
\(\chi_{1792}(579,\cdot)\)
\(\chi_{1792}(619,\cdot)\)
\(\chi_{1792}(635,\cdot)\)
\(\chi_{1792}(675,\cdot)\)
\(\chi_{1792}(691,\cdot)\)
\(\chi_{1792}(731,\cdot)\)
\(\chi_{1792}(747,\cdot)\)
\(\chi_{1792}(787,\cdot)\)
\(\chi_{1792}(803,\cdot)\)
...
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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 ]
\((1023,1541,1025)\) → \((-1,e\left(\frac{59}{64}\right),e\left(\frac{5}{6}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 1792 }(1251, a) \) |
\(1\) | \(1\) | \(e\left(\frac{115}{192}\right)\) | \(e\left(\frac{17}{192}\right)\) | \(e\left(\frac{19}{96}\right)\) | \(e\left(\frac{37}{192}\right)\) | \(e\left(\frac{53}{64}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{31}{48}\right)\) | \(e\left(\frac{167}{192}\right)\) | \(e\left(\frac{7}{96}\right)\) | \(e\left(\frac{17}{96}\right)\) |
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sage:chi.jacobi_sum(n)
