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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(14688, base_ring=CyclotomicField(144))
M = H._module
chi = DirichletCharacter(H, M([72,72,80,27]))
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gp:[g,chi] = znchar(Mod(5263, 14688))
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magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("14688.5263");
| Modulus: | \(14688\) |
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sage:chi.modulus()
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gp:g[1][1]
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magma:Modulus(chi);
|
| Conductor: | \(3672\) |
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sage:chi.conductor()
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gp:znconreyconductor(g,chi)
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magma:Conductor(chi);
|
| Order: | \(144\) |
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sage:chi.multiplicative_order()
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gp:charorder(g,chi)
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magma:Order(chi);
|
| Real: | no |
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sage:chi.multiplicative_order() <= 2
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gp:charorder(g,chi) <= 2
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magma:Order(chi) le 2;
|
| Primitive: | no, induced from \(\chi_{3672}(3427,\cdot)\) |
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sage:chi.is_primitive()
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gp:#znconreyconductor(g,chi)==1
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magma:IsPrimitive(chi);
|
| Minimal: | no |
| Parity: | even |
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sage:chi.is_odd()
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gp:zncharisodd(g,chi)
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magma:IsOdd(chi);
|
\(\chi_{14688}(79,\cdot)\)
\(\chi_{14688}(175,\cdot)\)
\(\chi_{14688}(367,\cdot)\)
\(\chi_{14688}(751,\cdot)\)
\(\chi_{14688}(1231,\cdot)\)
\(\chi_{14688}(1519,\cdot)\)
\(\chi_{14688}(1807,\cdot)\)
\(\chi_{14688}(2383,\cdot)\)
\(\chi_{14688}(2479,\cdot)\)
\(\chi_{14688}(3055,\cdot)\)
\(\chi_{14688}(3343,\cdot)\)
\(\chi_{14688}(3631,\cdot)\)
\(\chi_{14688}(4111,\cdot)\)
\(\chi_{14688}(4495,\cdot)\)
\(\chi_{14688}(4687,\cdot)\)
\(\chi_{14688}(4783,\cdot)\)
\(\chi_{14688}(4975,\cdot)\)
\(\chi_{14688}(5071,\cdot)\)
\(\chi_{14688}(5263,\cdot)\)
\(\chi_{14688}(5647,\cdot)\)
\(\chi_{14688}(6127,\cdot)\)
\(\chi_{14688}(6415,\cdot)\)
\(\chi_{14688}(6703,\cdot)\)
\(\chi_{14688}(7279,\cdot)\)
\(\chi_{14688}(7375,\cdot)\)
\(\chi_{14688}(7951,\cdot)\)
\(\chi_{14688}(8239,\cdot)\)
\(\chi_{14688}(8527,\cdot)\)
\(\chi_{14688}(9007,\cdot)\)
\(\chi_{14688}(9391,\cdot)\)
...
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sage:chi.galois_orbit()
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gp:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
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magma:order := Order(chi);
{ chi^k : k in [1..order-1] | GCD(k,order) eq 1 };
\((11935,5509,3809,4321)\) → \((-1,-1,e\left(\frac{5}{9}\right),e\left(\frac{3}{16}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 14688 }(5263, a) \) |
\(1\) | \(1\) | \(e\left(\frac{31}{144}\right)\) | \(e\left(\frac{65}{144}\right)\) | \(e\left(\frac{77}{144}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{61}{144}\right)\) | \(e\left(\frac{31}{72}\right)\) | \(e\left(\frac{71}{144}\right)\) | \(e\left(\frac{43}{144}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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sage:chi(x)
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gp:chareval(g,chi,x) \\\\ x integer, value in Q/Z'
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magma:chi(x)
