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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2183, base_ring=CyclotomicField(116))
M = H._module
chi = DirichletCharacter(H, M([87,74]))
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pari:[g,chi] = znchar(Mod(1042,2183))
| Modulus: | \(2183\) | |
| Conductor: | \(2183\) |
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sage:chi.conductor()
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pari:znconreyconductor(g,chi)
|
| Order: | \(116\) |
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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)
|
\(\chi_{2183}(6,\cdot)\)
\(\chi_{2183}(31,\cdot)\)
\(\chi_{2183}(43,\cdot)\)
\(\chi_{2183}(142,\cdot)\)
\(\chi_{2183}(179,\cdot)\)
\(\chi_{2183}(191,\cdot)\)
\(\chi_{2183}(216,\cdot)\)
\(\chi_{2183}(290,\cdot)\)
\(\chi_{2183}(327,\cdot)\)
\(\chi_{2183}(339,\cdot)\)
\(\chi_{2183}(364,\cdot)\)
\(\chi_{2183}(401,\cdot)\)
\(\chi_{2183}(450,\cdot)\)
\(\chi_{2183}(512,\cdot)\)
\(\chi_{2183}(524,\cdot)\)
\(\chi_{2183}(549,\cdot)\)
\(\chi_{2183}(561,\cdot)\)
\(\chi_{2183}(586,\cdot)\)
\(\chi_{2183}(598,\cdot)\)
\(\chi_{2183}(623,\cdot)\)
\(\chi_{2183}(660,\cdot)\)
\(\chi_{2183}(672,\cdot)\)
\(\chi_{2183}(746,\cdot)\)
\(\chi_{2183}(857,\cdot)\)
\(\chi_{2183}(882,\cdot)\)
\(\chi_{2183}(919,\cdot)\)
\(\chi_{2183}(968,\cdot)\)
\(\chi_{2183}(1005,\cdot)\)
\(\chi_{2183}(1042,\cdot)\)
\(\chi_{2183}(1104,\cdot)\)
...
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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 ]
\((1889,297)\) → \((-i,e\left(\frac{37}{58}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 2183 }(1042, a) \) |
\(1\) | \(1\) | \(e\left(\frac{45}{116}\right)\) | \(e\left(\frac{23}{58}\right)\) | \(e\left(\frac{45}{58}\right)\) | \(e\left(\frac{9}{116}\right)\) | \(e\left(\frac{91}{116}\right)\) | \(e\left(\frac{14}{29}\right)\) | \(e\left(\frac{19}{116}\right)\) | \(e\left(\frac{23}{29}\right)\) | \(e\left(\frac{27}{58}\right)\) | \(e\left(\frac{13}{29}\right)\) |
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sage:chi.jacobi_sum(n)
