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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3328, base_ring=CyclotomicField(192))
M = H._module
chi = DirichletCharacter(H, M([96,117,16]))
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pari:[g,chi] = znchar(Mod(1107,3328))
| Modulus: | \(3328\) | |
| Conductor: | \(3328\) |
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sage:chi.conductor()
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pari:znconreyconductor(g,chi)
|
| Order: | \(192\) |
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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)
|
\(\chi_{3328}(11,\cdot)\)
\(\chi_{3328}(19,\cdot)\)
\(\chi_{3328}(59,\cdot)\)
\(\chi_{3328}(67,\cdot)\)
\(\chi_{3328}(219,\cdot)\)
\(\chi_{3328}(227,\cdot)\)
\(\chi_{3328}(267,\cdot)\)
\(\chi_{3328}(275,\cdot)\)
\(\chi_{3328}(427,\cdot)\)
\(\chi_{3328}(435,\cdot)\)
\(\chi_{3328}(475,\cdot)\)
\(\chi_{3328}(483,\cdot)\)
\(\chi_{3328}(635,\cdot)\)
\(\chi_{3328}(643,\cdot)\)
\(\chi_{3328}(683,\cdot)\)
\(\chi_{3328}(691,\cdot)\)
\(\chi_{3328}(843,\cdot)\)
\(\chi_{3328}(851,\cdot)\)
\(\chi_{3328}(891,\cdot)\)
\(\chi_{3328}(899,\cdot)\)
\(\chi_{3328}(1051,\cdot)\)
\(\chi_{3328}(1059,\cdot)\)
\(\chi_{3328}(1099,\cdot)\)
\(\chi_{3328}(1107,\cdot)\)
\(\chi_{3328}(1259,\cdot)\)
\(\chi_{3328}(1267,\cdot)\)
\(\chi_{3328}(1307,\cdot)\)
\(\chi_{3328}(1315,\cdot)\)
\(\chi_{3328}(1467,\cdot)\)
\(\chi_{3328}(1475,\cdot)\)
...
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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 ]
\((1535,261,769)\) → \((-1,e\left(\frac{39}{64}\right),e\left(\frac{1}{12}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 3328 }(1107, a) \) |
\(1\) | \(1\) | \(e\left(\frac{31}{192}\right)\) | \(e\left(\frac{23}{64}\right)\) | \(e\left(\frac{49}{96}\right)\) | \(e\left(\frac{31}{96}\right)\) | \(e\left(\frac{169}{192}\right)\) | \(e\left(\frac{25}{48}\right)\) | \(e\left(\frac{11}{48}\right)\) | \(e\left(\frac{179}{192}\right)\) | \(e\left(\frac{43}{64}\right)\) | \(e\left(\frac{83}{96}\right)\) |
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sage:chi.jacobi_sum(n)
