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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(695, base_ring=CyclotomicField(276))
M = H._module
chi = DirichletCharacter(H, M([69,238]))
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pari:[g,chi] = znchar(Mod(132,695))
| Modulus: | \(695\) | |
| Conductor: | \(695\) |
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sage:chi.conductor()
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pari:znconreyconductor(g,chi)
|
| Order: | \(276\) |
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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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\(\chi_{695}(2,\cdot)\)
\(\chi_{695}(3,\cdot)\)
\(\chi_{695}(12,\cdot)\)
\(\chi_{695}(17,\cdot)\)
\(\chi_{695}(18,\cdot)\)
\(\chi_{695}(22,\cdot)\)
\(\chi_{695}(32,\cdot)\)
\(\chi_{695}(53,\cdot)\)
\(\chi_{695}(58,\cdot)\)
\(\chi_{695}(68,\cdot)\)
\(\chi_{695}(72,\cdot)\)
\(\chi_{695}(73,\cdot)\)
\(\chi_{695}(88,\cdot)\)
\(\chi_{695}(92,\cdot)\)
\(\chi_{695}(93,\cdot)\)
\(\chi_{695}(98,\cdot)\)
\(\chi_{695}(102,\cdot)\)
\(\chi_{695}(108,\cdot)\)
\(\chi_{695}(123,\cdot)\)
\(\chi_{695}(128,\cdot)\)
\(\chi_{695}(132,\cdot)\)
\(\chi_{695}(142,\cdot)\)
\(\chi_{695}(157,\cdot)\)
\(\chi_{695}(158,\cdot)\)
\(\chi_{695}(192,\cdot)\)
\(\chi_{695}(197,\cdot)\)
\(\chi_{695}(207,\cdot)\)
\(\chi_{695}(212,\cdot)\)
\(\chi_{695}(227,\cdot)\)
\(\chi_{695}(232,\cdot)\)
...
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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 ]
\((557,141)\) → \((i,e\left(\frac{119}{138}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 695 }(132, a) \) |
\(1\) | \(1\) | \(e\left(\frac{31}{276}\right)\) | \(e\left(\frac{29}{276}\right)\) | \(e\left(\frac{31}{138}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{101}{276}\right)\) | \(e\left(\frac{31}{92}\right)\) | \(e\left(\frac{29}{138}\right)\) | \(e\left(\frac{37}{69}\right)\) | \(e\left(\frac{91}{276}\right)\) | \(e\left(\frac{259}{276}\right)\) |
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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)
