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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2592, base_ring=CyclotomicField(216))
M = H._module
chi = DirichletCharacter(H, M([0,189,124]))
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pari:[g,chi] = znchar(Mod(1037,2592))
| Modulus: | \(2592\) | |
| Conductor: | \(2592\) |
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sage:chi.conductor()
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pari:znconreyconductor(g,chi)
|
| Order: | \(216\) |
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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)
|
\(\chi_{2592}(5,\cdot)\)
\(\chi_{2592}(29,\cdot)\)
\(\chi_{2592}(77,\cdot)\)
\(\chi_{2592}(101,\cdot)\)
\(\chi_{2592}(149,\cdot)\)
\(\chi_{2592}(173,\cdot)\)
\(\chi_{2592}(221,\cdot)\)
\(\chi_{2592}(245,\cdot)\)
\(\chi_{2592}(293,\cdot)\)
\(\chi_{2592}(317,\cdot)\)
\(\chi_{2592}(365,\cdot)\)
\(\chi_{2592}(389,\cdot)\)
\(\chi_{2592}(437,\cdot)\)
\(\chi_{2592}(461,\cdot)\)
\(\chi_{2592}(509,\cdot)\)
\(\chi_{2592}(533,\cdot)\)
\(\chi_{2592}(581,\cdot)\)
\(\chi_{2592}(605,\cdot)\)
\(\chi_{2592}(653,\cdot)\)
\(\chi_{2592}(677,\cdot)\)
\(\chi_{2592}(725,\cdot)\)
\(\chi_{2592}(749,\cdot)\)
\(\chi_{2592}(797,\cdot)\)
\(\chi_{2592}(821,\cdot)\)
\(\chi_{2592}(869,\cdot)\)
\(\chi_{2592}(893,\cdot)\)
\(\chi_{2592}(941,\cdot)\)
\(\chi_{2592}(965,\cdot)\)
\(\chi_{2592}(1013,\cdot)\)
\(\chi_{2592}(1037,\cdot)\)
...
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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 ]
\((2431,325,1217)\) → \((1,e\left(\frac{7}{8}\right),e\left(\frac{31}{54}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 2592 }(1037, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{17}{216}\right)\) | \(e\left(\frac{101}{108}\right)\) | \(e\left(\frac{181}{216}\right)\) | \(e\left(\frac{155}{216}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{49}{72}\right)\) | \(e\left(\frac{61}{108}\right)\) | \(e\left(\frac{17}{108}\right)\) | \(e\left(\frac{187}{216}\right)\) | \(e\left(\frac{13}{27}\right)\) |
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sage:chi.jacobi_sum(n)
