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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(14089, base_ring=CyclotomicField(192))
M = H._module
chi = DirichletCharacter(H, M([120,115]))
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gp:[g,chi] = znchar(Mod(4297, 14089))
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magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("14089.4297");
| Modulus: | \(14089\) |
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sage:chi.modulus()
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gp:g[1][1]
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magma:Modulus(chi);
|
| Conductor: | \(14089\) |
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sage:chi.conductor()
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gp:znconreyconductor(g,chi)
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magma:Conductor(chi);
|
| Order: | \(192\) |
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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: | even |
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sage:chi.is_odd()
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gp:zncharisodd(g,chi)
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magma:IsOdd(chi);
|
\(\chi_{14089}(22,\cdot)\)
\(\chi_{14089}(501,\cdot)\)
\(\chi_{14089}(813,\cdot)\)
\(\chi_{14089}(886,\cdot)\)
\(\chi_{14089}(1085,\cdot)\)
\(\chi_{14089}(1231,\cdot)\)
\(\chi_{14089}(1803,\cdot)\)
\(\chi_{14089}(1815,\cdot)\)
\(\chi_{14089}(2200,\cdot)\)
\(\chi_{14089}(2326,\cdot)\)
\(\chi_{14089}(2346,\cdot)\)
\(\chi_{14089}(2492,\cdot)\)
\(\chi_{14089}(2504,\cdot)\)
\(\chi_{14089}(2650,\cdot)\)
\(\chi_{14089}(3149,\cdot)\)
\(\chi_{14089}(3190,\cdot)\)
\(\chi_{14089}(3514,\cdot)\)
\(\chi_{14089}(3526,\cdot)\)
\(\chi_{14089}(3672,\cdot)\)
\(\chi_{14089}(4297,\cdot)\)
\(\chi_{14089}(4723,\cdot)\)
\(\chi_{14089}(4735,\cdot)\)
\(\chi_{14089}(5173,\cdot)\)
\(\chi_{14089}(6110,\cdot)\)
\(\chi_{14089}(6154,\cdot)\)
\(\chi_{14089}(7030,\cdot)\)
\(\chi_{14089}(7071,\cdot)\)
\(\chi_{14089}(7290,\cdot)\)
\(\chi_{14089}(7833,\cdot)\)
\(\chi_{14089}(8125,\cdot)\)
...
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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 };
\((10809,3286)\) → \((e\left(\frac{5}{8}\right),e\left(\frac{115}{192}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 14089 }(4297, a) \) |
\(1\) | \(1\) | \(e\left(\frac{35}{96}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{35}{48}\right)\) | \(e\left(\frac{43}{192}\right)\) | \(e\left(\frac{41}{96}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{3}{32}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{113}{192}\right)\) | \(e\left(\frac{63}{64}\right)\) |
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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)
