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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(25080, base_ring=CyclotomicField(180))
M = H._module
chi = DirichletCharacter(H, M([0,90,90,135,36,140]))
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gp:[g,chi] = znchar(Mod(3293, 25080))
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magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("25080.3293");
| Modulus: | \(25080\) |
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sage:chi.modulus()
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gp:g[1][1]
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magma:Modulus(chi);
|
| Conductor: | \(25080\) |
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sage:chi.conductor()
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gp:znconreyconductor(g,chi)
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magma:Conductor(chi);
|
| Order: | \(180\) |
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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);
|
\(\chi_{25080}(917,\cdot)\)
\(\chi_{25080}(1373,\cdot)\)
\(\chi_{25080}(1973,\cdot)\)
\(\chi_{25080}(3293,\cdot)\)
\(\chi_{25080}(3437,\cdot)\)
\(\chi_{25080}(3557,\cdot)\)
\(\chi_{25080}(4013,\cdot)\)
\(\chi_{25080}(4493,\cdot)\)
\(\chi_{25080}(5933,\cdot)\)
\(\chi_{25080}(6077,\cdot)\)
\(\chi_{25080}(6317,\cdot)\)
\(\chi_{25080}(7397,\cdot)\)
\(\chi_{25080}(8453,\cdot)\)
\(\chi_{25080}(8573,\cdot)\)
\(\chi_{25080}(10037,\cdot)\)
\(\chi_{25080}(10277,\cdot)\)
\(\chi_{25080}(10877,\cdot)\)
\(\chi_{25080}(11093,\cdot)\)
\(\chi_{25080}(11333,\cdot)\)
\(\chi_{25080}(12413,\cdot)\)
\(\chi_{25080}(12677,\cdot)\)
\(\chi_{25080}(12917,\cdot)\)
\(\chi_{25080}(14237,\cdot)\)
\(\chi_{25080}(14837,\cdot)\)
\(\chi_{25080}(15053,\cdot)\)
\(\chi_{25080}(15293,\cdot)\)
\(\chi_{25080}(15437,\cdot)\)
\(\chi_{25080}(15893,\cdot)\)
\(\chi_{25080}(16877,\cdot)\)
\(\chi_{25080}(17477,\cdot)\)
...
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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 };
\((6271,12541,16721,5017,9121,22441)\) → \((1,-1,-1,-i,e\left(\frac{1}{5}\right),e\left(\frac{7}{9}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(7\) | \(13\) | \(17\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
| \( \chi_{ 25080 }(3293, a) \) |
\(1\) | \(1\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{151}{180}\right)\) | \(e\left(\frac{149}{180}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{11}{90}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{19}{90}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{13}{180}\right)\) |
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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)
