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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(547, base_ring=CyclotomicField(182))
M = H._module
chi = DirichletCharacter(H, M([58]))
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pari:[g,chi] = znchar(Mod(154,547))
| Modulus: | \(547\) | |
| Conductor: | \(547\) |
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sage:chi.conductor()
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pari:znconreyconductor(g,chi)
|
| Order: | \(91\) |
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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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\(\chi_{547}(10,\cdot)\)
\(\chi_{547}(24,\cdot)\)
\(\chi_{547}(29,\cdot)\)
\(\chi_{547}(35,\cdot)\)
\(\chi_{547}(44,\cdot)\)
\(\chi_{547}(52,\cdot)\)
\(\chi_{547}(64,\cdot)\)
\(\chi_{547}(84,\cdot)\)
\(\chi_{547}(85,\cdot)\)
\(\chi_{547}(90,\cdot)\)
\(\chi_{547}(93,\cdot)\)
\(\chi_{547}(100,\cdot)\)
\(\chi_{547}(114,\cdot)\)
\(\chi_{547}(131,\cdot)\)
\(\chi_{547}(149,\cdot)\)
\(\chi_{547}(154,\cdot)\)
\(\chi_{547}(161,\cdot)\)
\(\chi_{547}(165,\cdot)\)
\(\chi_{547}(167,\cdot)\)
\(\chi_{547}(179,\cdot)\)
\(\chi_{547}(185,\cdot)\)
\(\chi_{547}(195,\cdot)\)
\(\chi_{547}(204,\cdot)\)
\(\chi_{547}(205,\cdot)\)
\(\chi_{547}(209,\cdot)\)
\(\chi_{547}(212,\cdot)\)
\(\chi_{547}(215,\cdot)\)
\(\chi_{547}(216,\cdot)\)
\(\chi_{547}(218,\cdot)\)
\(\chi_{547}(224,\cdot)\)
...
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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 ]
\(2\) → \(e\left(\frac{29}{91}\right)\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 547 }(154, a) \) |
\(1\) | \(1\) | \(e\left(\frac{29}{91}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{58}{91}\right)\) | \(e\left(\frac{4}{91}\right)\) | \(e\left(\frac{3}{91}\right)\) | \(e\left(\frac{75}{91}\right)\) | \(e\left(\frac{87}{91}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{33}{91}\right)\) | \(e\left(\frac{4}{13}\right)\) |
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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)
