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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(14089, base_ring=CyclotomicField(576))
M = H._module
chi = DirichletCharacter(H, M([536,207]))
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gp:[g,chi] = znchar(Mod(2143, 14089))
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magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("14089.2143");
| 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: | \(576\) |
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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);
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\(\chi_{14089}(13,\cdot)\)
\(\chi_{14089}(33,\cdot)\)
\(\chi_{14089}(60,\cdot)\)
\(\chi_{14089}(68,\cdot)\)
\(\chi_{14089}(87,\cdot)\)
\(\chi_{14089}(133,\cdot)\)
\(\chi_{14089}(281,\cdot)\)
\(\chi_{14089}(312,\cdot)\)
\(\chi_{14089}(425,\cdot)\)
\(\chi_{14089}(685,\cdot)\)
\(\chi_{14089}(701,\cdot)\)
\(\chi_{14089}(759,\cdot)\)
\(\chi_{14089}(792,\cdot)\)
\(\chi_{14089}(889,\cdot)\)
\(\chi_{14089}(954,\cdot)\)
\(\chi_{14089}(978,\cdot)\)
\(\chi_{14089}(994,\cdot)\)
\(\chi_{14089}(1053,\cdot)\)
\(\chi_{14089}(1090,\cdot)\)
\(\chi_{14089}(1129,\cdot)\)
\(\chi_{14089}(1440,\cdot)\)
\(\chi_{14089}(1455,\cdot)\)
\(\chi_{14089}(1564,\cdot)\)
\(\chi_{14089}(1632,\cdot)\)
\(\chi_{14089}(1666,\cdot)\)
\(\chi_{14089}(1805,\cdot)\)
\(\chi_{14089}(1854,\cdot)\)
\(\chi_{14089}(2049,\cdot)\)
\(\chi_{14089}(2088,\cdot)\)
\(\chi_{14089}(2143,\cdot)\)
...
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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 };
\((10809,3286)\) → \((e\left(\frac{67}{72}\right),e\left(\frac{23}{64}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 14089 }(2143, a) \) |
\(1\) | \(1\) | \(e\left(\frac{191}{288}\right)\) | \(e\left(\frac{37}{48}\right)\) | \(e\left(\frac{47}{144}\right)\) | \(e\left(\frac{167}{576}\right)\) | \(e\left(\frac{125}{288}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{95}{96}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{61}{64}\right)\) | \(e\left(\frac{545}{576}\right)\) |
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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)
