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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(18032, base_ring=CyclotomicField(154))
M = H._module
chi = DirichletCharacter(H, M([77,77,143,140]))
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gp:[g,chi] = znchar(Mod(2519, 18032))
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magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("18032.2519");
| Modulus: | \(18032\) |
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sage:chi.modulus()
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gp:g[1][1]
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magma:Modulus(chi);
|
| Conductor: | \(9016\) |
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sage:chi.conductor()
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gp:znconreyconductor(g,chi)
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magma:Conductor(chi);
|
| Order: | \(154\) |
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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 \(\chi_{9016}(7027,\cdot)\) |
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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);
|
\(\chi_{18032}(55,\cdot)\)
\(\chi_{18032}(167,\cdot)\)
\(\chi_{18032}(279,\cdot)\)
\(\chi_{18032}(951,\cdot)\)
\(\chi_{18032}(1511,\cdot)\)
\(\chi_{18032}(1623,\cdot)\)
\(\chi_{18032}(2295,\cdot)\)
\(\chi_{18032}(2519,\cdot)\)
\(\chi_{18032}(2631,\cdot)\)
\(\chi_{18032}(2855,\cdot)\)
\(\chi_{18032}(3751,\cdot)\)
\(\chi_{18032}(4087,\cdot)\)
\(\chi_{18032}(4199,\cdot)\)
\(\chi_{18032}(4535,\cdot)\)
\(\chi_{18032}(4871,\cdot)\)
\(\chi_{18032}(5207,\cdot)\)
\(\chi_{18032}(5319,\cdot)\)
\(\chi_{18032}(5431,\cdot)\)
\(\chi_{18032}(6103,\cdot)\)
\(\chi_{18032}(6327,\cdot)\)
\(\chi_{18032}(6775,\cdot)\)
\(\chi_{18032}(7111,\cdot)\)
\(\chi_{18032}(7671,\cdot)\)
\(\chi_{18032}(7783,\cdot)\)
\(\chi_{18032}(7895,\cdot)\)
\(\chi_{18032}(8007,\cdot)\)
\(\chi_{18032}(8679,\cdot)\)
\(\chi_{18032}(8903,\cdot)\)
\(\chi_{18032}(9239,\cdot)\)
\(\chi_{18032}(9351,\cdot)\)
...
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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 };
\((2255,13525,1473,1569)\) → \((-1,-1,e\left(\frac{13}{14}\right),e\left(\frac{10}{11}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(25\) | \(27\) |
| \( \chi_{ 18032 }(2519, a) \) |
\(1\) | \(1\) | \(e\left(\frac{73}{154}\right)\) | \(e\left(\frac{26}{77}\right)\) | \(e\left(\frac{73}{77}\right)\) | \(e\left(\frac{25}{77}\right)\) | \(e\left(\frac{67}{77}\right)\) | \(e\left(\frac{125}{154}\right)\) | \(e\left(\frac{89}{154}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{52}{77}\right)\) | \(e\left(\frac{65}{154}\right)\) |
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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)
