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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(961, base_ring=CyclotomicField(186))
M = H._module
chi = DirichletCharacter(H, M([148]))
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pari:[g,chi] = znchar(Mod(408,961))
| Modulus: | \(961\) | |
| Conductor: | \(961\) |
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sage:chi.conductor()
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pari:znconreyconductor(g,chi)
|
| Order: | \(93\) |
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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)
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\(\chi_{961}(5,\cdot)\)
\(\chi_{961}(25,\cdot)\)
\(\chi_{961}(36,\cdot)\)
\(\chi_{961}(56,\cdot)\)
\(\chi_{961}(67,\cdot)\)
\(\chi_{961}(87,\cdot)\)
\(\chi_{961}(98,\cdot)\)
\(\chi_{961}(118,\cdot)\)
\(\chi_{961}(129,\cdot)\)
\(\chi_{961}(149,\cdot)\)
\(\chi_{961}(160,\cdot)\)
\(\chi_{961}(180,\cdot)\)
\(\chi_{961}(191,\cdot)\)
\(\chi_{961}(211,\cdot)\)
\(\chi_{961}(222,\cdot)\)
\(\chi_{961}(242,\cdot)\)
\(\chi_{961}(253,\cdot)\)
\(\chi_{961}(273,\cdot)\)
\(\chi_{961}(284,\cdot)\)
\(\chi_{961}(304,\cdot)\)
\(\chi_{961}(315,\cdot)\)
\(\chi_{961}(335,\cdot)\)
\(\chi_{961}(346,\cdot)\)
\(\chi_{961}(366,\cdot)\)
\(\chi_{961}(377,\cdot)\)
\(\chi_{961}(397,\cdot)\)
\(\chi_{961}(408,\cdot)\)
\(\chi_{961}(428,\cdot)\)
\(\chi_{961}(459,\cdot)\)
\(\chi_{961}(470,\cdot)\)
...
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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 ]
\(3\) → \(e\left(\frac{74}{93}\right)\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 961 }(408, a) \) |
\(1\) | \(1\) | \(e\left(\frac{16}{31}\right)\) | \(e\left(\frac{74}{93}\right)\) | \(e\left(\frac{1}{31}\right)\) | \(e\left(\frac{10}{93}\right)\) | \(e\left(\frac{29}{93}\right)\) | \(e\left(\frac{53}{93}\right)\) | \(e\left(\frac{17}{31}\right)\) | \(e\left(\frac{55}{93}\right)\) | \(e\left(\frac{58}{93}\right)\) | \(e\left(\frac{1}{93}\right)\) |
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sage:chi.jacobi_sum(n)
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sage:chi.gauss_sum(a)
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pari:znchargauss(g,chi,a)
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sage:chi.jacobi_sum(n)
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sage:chi.kloosterman_sum(a,b)
