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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5160, base_ring=CyclotomicField(28))
M = H._module
chi = DirichletCharacter(H, M([14,14,14,21,6]))
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pari:[g,chi] = znchar(Mod(2483,5160))
| Modulus: | \(5160\) | |
| Conductor: | \(5160\) |
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sage:chi.conductor()
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pari:znconreyconductor(g,chi)
|
| Order: | \(28\) |
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sage:chi.multiplicative_order()
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pari:charorder(g,chi)
|
| Real: | no |
| Primitive: | yes |
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sage:chi.is_primitive()
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pari:#znconreyconductor(g,chi)==1
|
| Minimal: | yes |
| Parity: | even |
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sage:chi.is_odd()
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pari:zncharisodd(g,chi)
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\(\chi_{5160}(323,\cdot)\)
\(\chi_{5160}(1163,\cdot)\)
\(\chi_{5160}(1403,\cdot)\)
\(\chi_{5160}(1427,\cdot)\)
\(\chi_{5160}(2387,\cdot)\)
\(\chi_{5160}(2483,\cdot)\)
\(\chi_{5160}(2963,\cdot)\)
\(\chi_{5160}(3227,\cdot)\)
\(\chi_{5160}(3467,\cdot)\)
\(\chi_{5160}(4523,\cdot)\)
\(\chi_{5160}(4547,\cdot)\)
\(\chi_{5160}(5027,\cdot)\)
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sage:chi.galois_orbit()
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pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
\((3871,2581,1721,3097,4561)\) → \((-1,-1,-1,-i,e\left(\frac{3}{14}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 5160 }(2483, a) \) |
\(1\) | \(1\) | \(-i\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(-i\) | \(e\left(\frac{11}{14}\right)\) |
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sage:chi.jacobi_sum(n)
