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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10627, base_ring=CyclotomicField(966))
M = H._module
chi = DirichletCharacter(H, M([949]))
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gp:[g,chi] = znchar(Mod(927, 10627))
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magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10627.927");
| Modulus: | \(10627\) |
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sage:chi.modulus()
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gp:g[1][1]
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magma:Modulus(chi);
|
| Conductor: | \(10627\) |
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sage:chi.conductor()
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gp:znconreyconductor(g,chi)
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magma:Conductor(chi);
|
| Order: | \(966\) |
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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);
|
\(\chi_{10627}(107,\cdot)\)
\(\chi_{10627}(113,\cdot)\)
\(\chi_{10627}(122,\cdot)\)
\(\chi_{10627}(158,\cdot)\)
\(\chi_{10627}(312,\cdot)\)
\(\chi_{10627}(377,\cdot)\)
\(\chi_{10627}(426,\cdot)\)
\(\chi_{10627}(449,\cdot)\)
\(\chi_{10627}(455,\cdot)\)
\(\chi_{10627}(543,\cdot)\)
\(\chi_{10627}(555,\cdot)\)
\(\chi_{10627}(566,\cdot)\)
\(\chi_{10627}(614,\cdot)\)
\(\chi_{10627}(654,\cdot)\)
\(\chi_{10627}(660,\cdot)\)
\(\chi_{10627}(716,\cdot)\)
\(\chi_{10627}(743,\cdot)\)
\(\chi_{10627}(758,\cdot)\)
\(\chi_{10627}(786,\cdot)\)
\(\chi_{10627}(894,\cdot)\)
\(\chi_{10627}(927,\cdot)\)
\(\chi_{10627}(959,\cdot)\)
\(\chi_{10627}(962,\cdot)\)
\(\chi_{10627}(1026,\cdot)\)
\(\chi_{10627}(1033,\cdot)\)
\(\chi_{10627}(1057,\cdot)\)
\(\chi_{10627}(1144,\cdot)\)
\(\chi_{10627}(1153,\cdot)\)
\(\chi_{10627}(1163,\cdot)\)
\(\chi_{10627}(1195,\cdot)\)
...
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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 };
\(5\) → \(e\left(\frac{949}{966}\right)\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 10627 }(927, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{31}{138}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{31}{69}\right)\) | \(e\left(\frac{949}{966}\right)\) | \(e\left(\frac{97}{483}\right)\) | \(e\left(\frac{131}{138}\right)\) | \(e\left(\frac{31}{46}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{100}{483}\right)\) | \(e\left(\frac{403}{966}\right)\) |
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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)
