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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(45120, base_ring=CyclotomicField(92))
M = H._module
chi = DirichletCharacter(H, M([0,69,0,46,24]))
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gp:[g,chi] = znchar(Mod(5329, 45120))
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magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("45120.5329");
| Modulus: | \(45120\) |
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sage:chi.modulus()
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gp:g[1][1]
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magma:Modulus(chi);
|
| Conductor: | \(3760\) |
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sage:chi.conductor()
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gp:znconreyconductor(g,chi)
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magma:Conductor(chi);
|
| Order: | \(92\) |
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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 \(\chi_{3760}(2509,\cdot)\) |
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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);
|
\(\chi_{45120}(49,\cdot)\)
\(\chi_{45120}(529,\cdot)\)
\(\chi_{45120}(1489,\cdot)\)
\(\chi_{45120}(1969,\cdot)\)
\(\chi_{45120}(3409,\cdot)\)
\(\chi_{45120}(4849,\cdot)\)
\(\chi_{45120}(5329,\cdot)\)
\(\chi_{45120}(5809,\cdot)\)
\(\chi_{45120}(7729,\cdot)\)
\(\chi_{45120}(9169,\cdot)\)
\(\chi_{45120}(9649,\cdot)\)
\(\chi_{45120}(10129,\cdot)\)
\(\chi_{45120}(10609,\cdot)\)
\(\chi_{45120}(11569,\cdot)\)
\(\chi_{45120}(12049,\cdot)\)
\(\chi_{45120}(12529,\cdot)\)
\(\chi_{45120}(13009,\cdot)\)
\(\chi_{45120}(15889,\cdot)\)
\(\chi_{45120}(18289,\cdot)\)
\(\chi_{45120}(18769,\cdot)\)
\(\chi_{45120}(19729,\cdot)\)
\(\chi_{45120}(20689,\cdot)\)
\(\chi_{45120}(22609,\cdot)\)
\(\chi_{45120}(23089,\cdot)\)
\(\chi_{45120}(24049,\cdot)\)
\(\chi_{45120}(24529,\cdot)\)
\(\chi_{45120}(25969,\cdot)\)
\(\chi_{45120}(27409,\cdot)\)
\(\chi_{45120}(27889,\cdot)\)
\(\chi_{45120}(28369,\cdot)\)
...
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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 };
\((43711,2821,15041,36097,18241)\) → \((1,-i,1,-1,e\left(\frac{6}{23}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 45120 }(5329, a) \) |
\(1\) | \(1\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{53}{92}\right)\) | \(e\left(\frac{57}{92}\right)\) | \(e\left(\frac{31}{46}\right)\) | \(e\left(\frac{91}{92}\right)\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{35}{92}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{19}{92}\right)\) | \(e\left(\frac{19}{46}\right)\) |
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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)
