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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1444, base_ring=CyclotomicField(38))
M = H._module
chi = DirichletCharacter(H, M([19,30]))
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pari:[g,chi] = znchar(Mod(495,1444))
| Modulus: | \(1444\) | |
| Conductor: | \(1444\) |
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sage:chi.conductor()
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pari:znconreyconductor(g,chi)
|
| Order: | \(38\) |
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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
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| Minimal: | yes |
| Parity: | odd |
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sage:chi.is_odd()
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pari:zncharisodd(g,chi)
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\(\chi_{1444}(39,\cdot)\)
\(\chi_{1444}(115,\cdot)\)
\(\chi_{1444}(191,\cdot)\)
\(\chi_{1444}(267,\cdot)\)
\(\chi_{1444}(343,\cdot)\)
\(\chi_{1444}(419,\cdot)\)
\(\chi_{1444}(495,\cdot)\)
\(\chi_{1444}(571,\cdot)\)
\(\chi_{1444}(647,\cdot)\)
\(\chi_{1444}(799,\cdot)\)
\(\chi_{1444}(875,\cdot)\)
\(\chi_{1444}(951,\cdot)\)
\(\chi_{1444}(1027,\cdot)\)
\(\chi_{1444}(1103,\cdot)\)
\(\chi_{1444}(1179,\cdot)\)
\(\chi_{1444}(1255,\cdot)\)
\(\chi_{1444}(1331,\cdot)\)
\(\chi_{1444}(1407,\cdot)\)
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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 ]
\((723,1085)\) → \((-1,e\left(\frac{15}{19}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 1444 }(495, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{9}{38}\right)\) | \(e\left(\frac{3}{19}\right)\) | \(e\left(\frac{35}{38}\right)\) | \(e\left(\frac{9}{19}\right)\) | \(e\left(\frac{1}{38}\right)\) | \(e\left(\frac{14}{19}\right)\) | \(e\left(\frac{15}{38}\right)\) | \(e\left(\frac{8}{19}\right)\) | \(e\left(\frac{3}{19}\right)\) | \(e\left(\frac{29}{38}\right)\) |
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sage:chi.jacobi_sum(n)
