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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(695, base_ring=CyclotomicField(92))
M = H._module
chi = DirichletCharacter(H, M([69,30]))
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pari:[g,chi] = znchar(Mod(48,695))
| Modulus: | \(695\) | |
| Conductor: | \(695\) |
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sage:chi.conductor()
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pari:znconreyconductor(g,chi)
|
| Order: | \(92\) |
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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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\(\chi_{695}(8,\cdot)\)
\(\chi_{695}(23,\cdot)\)
\(\chi_{695}(27,\cdot)\)
\(\chi_{695}(33,\cdot)\)
\(\chi_{695}(48,\cdot)\)
\(\chi_{695}(62,\cdot)\)
\(\chi_{695}(82,\cdot)\)
\(\chi_{695}(87,\cdot)\)
\(\chi_{695}(103,\cdot)\)
\(\chi_{695}(133,\cdot)\)
\(\chi_{695}(147,\cdot)\)
\(\chi_{695}(153,\cdot)\)
\(\chi_{695}(162,\cdot)\)
\(\chi_{695}(172,\cdot)\)
\(\chi_{695}(178,\cdot)\)
\(\chi_{695}(187,\cdot)\)
\(\chi_{695}(198,\cdot)\)
\(\chi_{695}(213,\cdot)\)
\(\chi_{695}(223,\cdot)\)
\(\chi_{695}(233,\cdot)\)
\(\chi_{695}(242,\cdot)\)
\(\chi_{695}(272,\cdot)\)
\(\chi_{695}(288,\cdot)\)
\(\chi_{695}(292,\cdot)\)
\(\chi_{695}(317,\cdot)\)
\(\chi_{695}(337,\cdot)\)
\(\chi_{695}(338,\cdot)\)
\(\chi_{695}(352,\cdot)\)
\(\chi_{695}(353,\cdot)\)
\(\chi_{695}(362,\cdot)\)
...
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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 ]
\((557,141)\) → \((-i,e\left(\frac{15}{46}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 695 }(48, a) \) |
\(1\) | \(1\) | \(e\left(\frac{7}{92}\right)\) | \(e\left(\frac{57}{92}\right)\) | \(e\left(\frac{7}{46}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{5}{92}\right)\) | \(e\left(\frac{21}{92}\right)\) | \(e\left(\frac{11}{46}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{71}{92}\right)\) | \(e\left(\frac{11}{92}\right)\) |
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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)
