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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5963, base_ring=CyclotomicField(264))
M = H._module
chi = DirichletCharacter(H, M([136,81]))
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gp:[g,chi] = znchar(Mod(2477, 5963))
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magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5963.2477");
| Modulus: | \(5963\) |
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sage:chi.modulus()
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gp:g[1][1]
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magma:Modulus(chi);
|
| Conductor: | \(5963\) |
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sage:chi.conductor()
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gp:znconreyconductor(g,chi)
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magma:Conductor(chi);
|
| Order: | \(264\) |
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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: | odd |
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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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\(\chi_{5963}(65,\cdot)\)
\(\chi_{5963}(155,\cdot)\)
\(\chi_{5963}(438,\cdot)\)
\(\chi_{5963}(505,\cdot)\)
\(\chi_{5963}(557,\cdot)\)
\(\chi_{5963}(592,\cdot)\)
\(\chi_{5963}(620,\cdot)\)
\(\chi_{5963}(726,\cdot)\)
\(\chi_{5963}(920,\cdot)\)
\(\chi_{5963}(1003,\cdot)\)
\(\chi_{5963}(1009,\cdot)\)
\(\chi_{5963}(1040,\cdot)\)
\(\chi_{5963}(1227,\cdot)\)
\(\chi_{5963}(1308,\cdot)\)
\(\chi_{5963}(1400,\cdot)\)
\(\chi_{5963}(1462,\cdot)\)
\(\chi_{5963}(1500,\cdot)\)
\(\chi_{5963}(1507,\cdot)\)
\(\chi_{5963}(1729,\cdot)\)
\(\chi_{5963}(1752,\cdot)\)
\(\chi_{5963}(1895,\cdot)\)
\(\chi_{5963}(1923,\cdot)\)
\(\chi_{5963}(2020,\cdot)\)
\(\chi_{5963}(2110,\cdot)\)
\(\chi_{5963}(2228,\cdot)\)
\(\chi_{5963}(2258,\cdot)\)
\(\chi_{5963}(2338,\cdot)\)
\(\chi_{5963}(2368,\cdot)\)
\(\chi_{5963}(2459,\cdot)\)
\(\chi_{5963}(2477,\cdot)\)
...
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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 };
\((5697,537)\) → \((e\left(\frac{17}{33}\right),e\left(\frac{27}{88}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 5963 }(2477, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{14}{33}\right)\) | \(e\left(\frac{35}{88}\right)\) | \(e\left(\frac{28}{33}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{217}{264}\right)\) | \(e\left(\frac{185}{264}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{83}{132}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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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)
