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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9595, base_ring=CyclotomicField(900))
M = H._module
chi = DirichletCharacter(H, M([450,50,297]))
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gp:[g,chi] = znchar(Mod(439, 9595))
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magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9595.439");
| Modulus: | \(9595\) |
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sage:chi.modulus()
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gp:g[1][1]
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magma:Modulus(chi);
|
| Conductor: | \(9595\) |
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sage:chi.conductor()
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gp:znconreyconductor(g,chi)
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magma:Conductor(chi);
|
| Order: | \(900\) |
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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);
|
\(\chi_{9595}(29,\cdot)\)
\(\chi_{9595}(34,\cdot)\)
\(\chi_{9595}(59,\cdot)\)
\(\chi_{9595}(89,\cdot)\)
\(\chi_{9595}(109,\cdot)\)
\(\chi_{9595}(129,\cdot)\)
\(\chi_{9595}(154,\cdot)\)
\(\chi_{9595}(174,\cdot)\)
\(\chi_{9595}(184,\cdot)\)
\(\chi_{9595}(204,\cdot)\)
\(\chi_{9595}(269,\cdot)\)
\(\chi_{9595}(314,\cdot)\)
\(\chi_{9595}(364,\cdot)\)
\(\chi_{9595}(439,\cdot)\)
\(\chi_{9595}(459,\cdot)\)
\(\chi_{9595}(534,\cdot)\)
\(\chi_{9595}(564,\cdot)\)
\(\chi_{9595}(599,\cdot)\)
\(\chi_{9595}(604,\cdot)\)
\(\chi_{9595}(659,\cdot)\)
\(\chi_{9595}(679,\cdot)\)
\(\chi_{9595}(699,\cdot)\)
\(\chi_{9595}(774,\cdot)\)
\(\chi_{9595}(819,\cdot)\)
\(\chi_{9595}(869,\cdot)\)
\(\chi_{9595}(944,\cdot)\)
\(\chi_{9595}(964,\cdot)\)
\(\chi_{9595}(984,\cdot)\)
\(\chi_{9595}(1039,\cdot)\)
\(\chi_{9595}(1104,\cdot)\)
...
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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 };
\((7677,3536,7981)\) → \((-1,e\left(\frac{1}{18}\right),e\left(\frac{33}{100}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 9595 }(439, a) \) |
\(1\) | \(1\) | \(e\left(\frac{797}{900}\right)\) | \(e\left(\frac{893}{900}\right)\) | \(e\left(\frac{347}{450}\right)\) | \(e\left(\frac{79}{90}\right)\) | \(e\left(\frac{241}{300}\right)\) | \(e\left(\frac{197}{300}\right)\) | \(e\left(\frac{443}{450}\right)\) | \(e\left(\frac{287}{300}\right)\) | \(e\left(\frac{229}{300}\right)\) | \(e\left(\frac{251}{450}\right)\) |
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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)
