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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(232845, base_ring=CyclotomicField(2))
M = H._module
chi = DirichletCharacter(H, M([0,0,0,0]))
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pari:[g,chi] = znchar(Mod(1,232845))
| Modulus: | \(232845\) | |
| Conductor: | \(1\) |
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sage:chi.conductor()
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pari:znconreyconductor(g,chi)
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| Order: | \(1\) |
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sage:chi.multiplicative_order()
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pari:charorder(g,chi)
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| Real: | yes |
| Primitive: | no, induced from \(\chi_{1}(0,\cdot)\) |
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sage:chi.is_primitive()
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pari:#znconreyconductor(g,chi)==1
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| Minimal: | yes |
| Parity: | even |
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sage:chi.is_odd()
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pari:zncharisodd(g,chi)
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\(\chi_{232845}(1,\cdot)\)
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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 ]
\((155231,186277,48376,151621)\) → \((1,1,1,1)\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(22\) |
| \( \chi_{ 232845 }(1, a) \) |
\(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
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sage:chi.jacobi_sum(n)
