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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(46255, base_ring=CyclotomicField(4060))
M = H._module
chi = DirichletCharacter(H, M([3045,1624,3130]))
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gp:[g,chi] = znchar(Mod(38, 46255))
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magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("46255.38");
| Modulus: | \(46255\) |
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sage:chi.modulus()
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gp:g[1][1]
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magma:Modulus(chi);
|
| Conductor: | \(46255\) |
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sage:chi.conductor()
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gp:znconreyconductor(g,chi)
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magma:Conductor(chi);
|
| Order: | \(4060\) |
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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: | yes |
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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: | yes |
| Parity: | odd |
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sage:chi.is_odd()
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gp:zncharisodd(g,chi)
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magma:IsOdd(chi);
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\(\chi_{46255}(38,\cdot)\)
\(\chi_{46255}(42,\cdot)\)
\(\chi_{46255}(92,\cdot)\)
\(\chi_{46255}(93,\cdot)\)
\(\chi_{46255}(158,\cdot)\)
\(\chi_{46255}(207,\cdot)\)
\(\chi_{46255}(212,\cdot)\)
\(\chi_{46255}(312,\cdot)\)
\(\chi_{46255}(323,\cdot)\)
\(\chi_{46255}(328,\cdot)\)
\(\chi_{46255}(357,\cdot)\)
\(\chi_{46255}(383,\cdot)\)
\(\chi_{46255}(412,\cdot)\)
\(\chi_{46255}(477,\cdot)\)
\(\chi_{46255}(498,\cdot)\)
\(\chi_{46255}(642,\cdot)\)
\(\chi_{46255}(643,\cdot)\)
\(\chi_{46255}(647,\cdot)\)
\(\chi_{46255}(702,\cdot)\)
\(\chi_{46255}(718,\cdot)\)
\(\chi_{46255}(763,\cdot)\)
\(\chi_{46255}(817,\cdot)\)
\(\chi_{46255}(818,\cdot)\)
\(\chi_{46255}(863,\cdot)\)
\(\chi_{46255}(883,\cdot)\)
\(\chi_{46255}(933,\cdot)\)
\(\chi_{46255}(962,\cdot)\)
\(\chi_{46255}(1028,\cdot)\)
\(\chi_{46255}(1048,\cdot)\)
\(\chi_{46255}(1082,\cdot)\)
...
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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 };
\((9252,16821,20186)\) → \((-i,e\left(\frac{2}{5}\right),e\left(\frac{313}{406}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 46255 }(38, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{3739}{4060}\right)\) | \(e\left(\frac{1797}{4060}\right)\) | \(e\left(\frac{1709}{2030}\right)\) | \(e\left(\frac{369}{1015}\right)\) | \(e\left(\frac{1713}{4060}\right)\) | \(e\left(\frac{3097}{4060}\right)\) | \(e\left(\frac{1797}{2030}\right)\) | \(e\left(\frac{33}{116}\right)\) | \(e\left(\frac{39}{4060}\right)\) | \(e\left(\frac{12}{35}\right)\) |
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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)
