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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2432, base_ring=CyclotomicField(288))
M = H._module
chi = DirichletCharacter(H, M([0,225,208]))
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pari:[g,chi] = znchar(Mod(421,2432))
| Modulus: | \(2432\) | |
| Conductor: | \(2432\) |
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sage:chi.conductor()
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pari:znconreyconductor(g,chi)
|
| Order: | \(288\) |
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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: | odd |
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sage:chi.is_odd()
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pari:zncharisodd(g,chi)
|
\(\chi_{2432}(13,\cdot)\)
\(\chi_{2432}(21,\cdot)\)
\(\chi_{2432}(29,\cdot)\)
\(\chi_{2432}(53,\cdot)\)
\(\chi_{2432}(109,\cdot)\)
\(\chi_{2432}(117,\cdot)\)
\(\chi_{2432}(165,\cdot)\)
\(\chi_{2432}(173,\cdot)\)
\(\chi_{2432}(181,\cdot)\)
\(\chi_{2432}(205,\cdot)\)
\(\chi_{2432}(261,\cdot)\)
\(\chi_{2432}(269,\cdot)\)
\(\chi_{2432}(317,\cdot)\)
\(\chi_{2432}(325,\cdot)\)
\(\chi_{2432}(333,\cdot)\)
\(\chi_{2432}(357,\cdot)\)
\(\chi_{2432}(413,\cdot)\)
\(\chi_{2432}(421,\cdot)\)
\(\chi_{2432}(469,\cdot)\)
\(\chi_{2432}(477,\cdot)\)
\(\chi_{2432}(485,\cdot)\)
\(\chi_{2432}(509,\cdot)\)
\(\chi_{2432}(565,\cdot)\)
\(\chi_{2432}(573,\cdot)\)
\(\chi_{2432}(621,\cdot)\)
\(\chi_{2432}(629,\cdot)\)
\(\chi_{2432}(637,\cdot)\)
\(\chi_{2432}(661,\cdot)\)
\(\chi_{2432}(717,\cdot)\)
\(\chi_{2432}(725,\cdot)\)
...
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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 ]
\((1407,2053,1921)\) → \((1,e\left(\frac{25}{32}\right),e\left(\frac{13}{18}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 2432 }(421, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{211}{288}\right)\) | \(e\left(\frac{97}{288}\right)\) | \(e\left(\frac{7}{48}\right)\) | \(e\left(\frac{67}{144}\right)\) | \(e\left(\frac{7}{96}\right)\) | \(e\left(\frac{95}{288}\right)\) | \(e\left(\frac{5}{72}\right)\) | \(e\left(\frac{7}{72}\right)\) | \(e\left(\frac{253}{288}\right)\) | \(e\left(\frac{55}{144}\right)\) |
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sage:chi.jacobi_sum(n)
