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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(11243, base_ring=CyclotomicField(146))
M = H._module
chi = DirichletCharacter(H, M([104]))
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gp:[g,chi] = znchar(Mod(2839, 11243))
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magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("11243.2839");
| Modulus: | \(11243\) |
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sage:chi.modulus()
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gp:g[1][1]
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magma:Modulus(chi);
|
| Conductor: | \(11243\) |
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sage:chi.conductor()
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gp:znconreyconductor(g,chi)
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magma:Conductor(chi);
|
| Order: | \(73\) |
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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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\(\chi_{11243}(3,\cdot)\)
\(\chi_{11243}(9,\cdot)\)
\(\chi_{11243}(27,\cdot)\)
\(\chi_{11243}(81,\cdot)\)
\(\chi_{11243}(243,\cdot)\)
\(\chi_{11243}(665,\cdot)\)
\(\chi_{11243}(729,\cdot)\)
\(\chi_{11243}(781,\cdot)\)
\(\chi_{11243}(796,\cdot)\)
\(\chi_{11243}(919,\cdot)\)
\(\chi_{11243}(1336,\cdot)\)
\(\chi_{11243}(1995,\cdot)\)
\(\chi_{11243}(2187,\cdot)\)
\(\chi_{11243}(2297,\cdot)\)
\(\chi_{11243}(2327,\cdot)\)
\(\chi_{11243}(2343,\cdot)\)
\(\chi_{11243}(2388,\cdot)\)
\(\chi_{11243}(2757,\cdot)\)
\(\chi_{11243}(2834,\cdot)\)
\(\chi_{11243}(2839,\cdot)\)
\(\chi_{11243}(3020,\cdot)\)
\(\chi_{11243}(3065,\cdot)\)
\(\chi_{11243}(3242,\cdot)\)
\(\chi_{11243}(3311,\cdot)\)
\(\chi_{11243}(3748,\cdot)\)
\(\chi_{11243}(4008,\cdot)\)
\(\chi_{11243}(4013,\cdot)\)
\(\chi_{11243}(4054,\cdot)\)
\(\chi_{11243}(4193,\cdot)\)
\(\chi_{11243}(4694,\cdot)\)
...
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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 };
\(5\) → \(e\left(\frac{52}{73}\right)\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 11243 }(2839, a) \) |
\(1\) | \(1\) | \(e\left(\frac{65}{73}\right)\) | \(e\left(\frac{60}{73}\right)\) | \(e\left(\frac{57}{73}\right)\) | \(e\left(\frac{52}{73}\right)\) | \(e\left(\frac{52}{73}\right)\) | \(e\left(\frac{28}{73}\right)\) | \(e\left(\frac{49}{73}\right)\) | \(e\left(\frac{47}{73}\right)\) | \(e\left(\frac{44}{73}\right)\) | \(e\left(\frac{22}{73}\right)\) |
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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)
