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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43904, base_ring=CyclotomicField(294))
M = H._module
chi = DirichletCharacter(H, M([0,147,118]))
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gp:[g,chi] = znchar(Mod(2881, 43904))
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magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43904.2881");
| Modulus: | \(43904\) |
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sage:chi.modulus()
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gp:g[1][1]
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magma:Modulus(chi);
|
| Conductor: | \(2744\) |
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sage:chi.conductor()
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gp:znconreyconductor(g,chi)
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magma:Conductor(chi);
|
| Order: | \(294\) |
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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 \(\chi_{2744}(1509,\cdot)\) |
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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: | 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);
|
\(\chi_{43904}(65,\cdot)\)
\(\chi_{43904}(193,\cdot)\)
\(\chi_{43904}(1089,\cdot)\)
\(\chi_{43904}(1857,\cdot)\)
\(\chi_{43904}(1985,\cdot)\)
\(\chi_{43904}(2753,\cdot)\)
\(\chi_{43904}(2881,\cdot)\)
\(\chi_{43904}(3649,\cdot)\)
\(\chi_{43904}(3777,\cdot)\)
\(\chi_{43904}(4545,\cdot)\)
\(\chi_{43904}(5441,\cdot)\)
\(\chi_{43904}(5569,\cdot)\)
\(\chi_{43904}(6337,\cdot)\)
\(\chi_{43904}(6465,\cdot)\)
\(\chi_{43904}(7361,\cdot)\)
\(\chi_{43904}(8129,\cdot)\)
\(\chi_{43904}(8257,\cdot)\)
\(\chi_{43904}(9025,\cdot)\)
\(\chi_{43904}(9153,\cdot)\)
\(\chi_{43904}(9921,\cdot)\)
\(\chi_{43904}(10049,\cdot)\)
\(\chi_{43904}(10817,\cdot)\)
\(\chi_{43904}(11713,\cdot)\)
\(\chi_{43904}(11841,\cdot)\)
\(\chi_{43904}(12609,\cdot)\)
\(\chi_{43904}(12737,\cdot)\)
\(\chi_{43904}(13633,\cdot)\)
\(\chi_{43904}(14401,\cdot)\)
\(\chi_{43904}(14529,\cdot)\)
\(\chi_{43904}(15297,\cdot)\)
...
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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 };
\((17151,9605,17153)\) → \((1,-1,e\left(\frac{59}{147}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 43904 }(2881, a) \) |
\(1\) | \(1\) | \(e\left(\frac{265}{294}\right)\) | \(e\left(\frac{41}{294}\right)\) | \(e\left(\frac{118}{147}\right)\) | \(e\left(\frac{289}{294}\right)\) | \(e\left(\frac{87}{98}\right)\) | \(e\left(\frac{2}{49}\right)\) | \(e\left(\frac{5}{147}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{121}{147}\right)\) | \(e\left(\frac{41}{147}\right)\) |
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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)
