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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(97693, base_ring=CyclotomicField(770))
M = H._module
chi = DirichletCharacter(H, M([88,610]))
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gp:[g,chi] = znchar(Mod(2927, 97693))
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magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("97693.2927");
| Modulus: | \(97693\) |
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sage:chi.modulus()
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gp:g[1][1]
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magma:Modulus(chi);
|
| Conductor: | \(97693\) |
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sage:chi.conductor()
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gp:znconreyconductor(g,chi)
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magma:Conductor(chi);
|
| Order: | \(385\) |
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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);
|
\(\chi_{97693}(547,\cdot)\)
\(\chi_{97693}(742,\cdot)\)
\(\chi_{97693}(1910,\cdot)\)
\(\chi_{97693}(1975,\cdot)\)
\(\chi_{97693}(2385,\cdot)\)
\(\chi_{97693}(2524,\cdot)\)
\(\chi_{97693}(2557,\cdot)\)
\(\chi_{97693}(2927,\cdot)\)
\(\chi_{97693}(3290,\cdot)\)
\(\chi_{97693}(4123,\cdot)\)
\(\chi_{97693}(4160,\cdot)\)
\(\chi_{97693}(5702,\cdot)\)
\(\chi_{97693}(6077,\cdot)\)
\(\chi_{97693}(6130,\cdot)\)
\(\chi_{97693}(6744,\cdot)\)
\(\chi_{97693}(7398,\cdot)\)
\(\chi_{97693}(7472,\cdot)\)
\(\chi_{97693}(7721,\cdot)\)
\(\chi_{97693}(7929,\cdot)\)
\(\chi_{97693}(8143,\cdot)\)
\(\chi_{97693}(8342,\cdot)\)
\(\chi_{97693}(8715,\cdot)\)
\(\chi_{97693}(8854,\cdot)\)
\(\chi_{97693}(8867,\cdot)\)
\(\chi_{97693}(8941,\cdot)\)
\(\chi_{97693}(9380,\cdot)\)
\(\chi_{97693}(9788,\cdot)\)
\(\chi_{97693}(10297,\cdot)\)
\(\chi_{97693}(10575,\cdot)\)
\(\chi_{97693}(11196,\cdot)\)
...
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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 };
\((81026,33339)\) → \((e\left(\frac{4}{35}\right),e\left(\frac{61}{77}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 97693 }(2927, a) \) |
\(1\) | \(1\) | \(e\left(\frac{19}{385}\right)\) | \(e\left(\frac{272}{385}\right)\) | \(e\left(\frac{38}{385}\right)\) | \(e\left(\frac{43}{385}\right)\) | \(e\left(\frac{291}{385}\right)\) | \(e\left(\frac{36}{385}\right)\) | \(e\left(\frac{57}{385}\right)\) | \(e\left(\frac{159}{385}\right)\) | \(e\left(\frac{62}{385}\right)\) | \(e\left(\frac{223}{385}\right)\) |
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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)
