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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(947, base_ring=CyclotomicField(86))
M = H._module
chi = DirichletCharacter(H, M([76]))
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pari:[g,chi] = znchar(Mod(30,947))
| Modulus: | \(947\) | |
| Conductor: | \(947\) |
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sage:chi.conductor()
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pari:znconreyconductor(g,chi)
|
| Order: | \(43\) |
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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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\(\chi_{947}(22,\cdot)\)
\(\chi_{947}(30,\cdot)\)
\(\chi_{947}(41,\cdot)\)
\(\chi_{947}(49,\cdot)\)
\(\chi_{947}(58,\cdot)\)
\(\chi_{947}(115,\cdot)\)
\(\chi_{947}(127,\cdot)\)
\(\chi_{947}(131,\cdot)\)
\(\chi_{947}(140,\cdot)\)
\(\chi_{947}(142,\cdot)\)
\(\chi_{947}(221,\cdot)\)
\(\chi_{947}(231,\cdot)\)
\(\chi_{947}(239,\cdot)\)
\(\chi_{947}(277,\cdot)\)
\(\chi_{947}(283,\cdot)\)
\(\chi_{947}(301,\cdot)\)
\(\chi_{947}(315,\cdot)\)
\(\chi_{947}(329,\cdot)\)
\(\chi_{947}(347,\cdot)\)
\(\chi_{947}(400,\cdot)\)
\(\chi_{947}(412,\cdot)\)
\(\chi_{947}(472,\cdot)\)
\(\chi_{947}(484,\cdot)\)
\(\chi_{947}(507,\cdot)\)
\(\chi_{947}(523,\cdot)\)
\(\chi_{947}(538,\cdot)\)
\(\chi_{947}(541,\cdot)\)
\(\chi_{947}(544,\cdot)\)
\(\chi_{947}(604,\cdot)\)
\(\chi_{947}(609,\cdot)\)
...
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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 ]
\(2\) → \(e\left(\frac{38}{43}\right)\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 947 }(30, a) \) |
\(1\) | \(1\) | \(e\left(\frac{38}{43}\right)\) | \(e\left(\frac{31}{43}\right)\) | \(e\left(\frac{33}{43}\right)\) | \(e\left(\frac{8}{43}\right)\) | \(e\left(\frac{26}{43}\right)\) | \(e\left(\frac{23}{43}\right)\) | \(e\left(\frac{28}{43}\right)\) | \(e\left(\frac{19}{43}\right)\) | \(e\left(\frac{3}{43}\right)\) | \(e\left(\frac{13}{43}\right)\) |
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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)
