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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2864, base_ring=CyclotomicField(356))
M = H._module
chi = DirichletCharacter(H, M([0,267,228]))
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pari:[g,chi] = znchar(Mod(13,2864))
| Modulus: | \(2864\) | |
| Conductor: | \(2864\) |
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sage:chi.conductor()
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pari:znconreyconductor(g,chi)
|
| Order: | \(356\) |
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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)
|
\(\chi_{2864}(5,\cdot)\)
\(\chi_{2864}(13,\cdot)\)
\(\chi_{2864}(29,\cdot)\)
\(\chi_{2864}(45,\cdot)\)
\(\chi_{2864}(61,\cdot)\)
\(\chi_{2864}(77,\cdot)\)
\(\chi_{2864}(85,\cdot)\)
\(\chi_{2864}(93,\cdot)\)
\(\chi_{2864}(101,\cdot)\)
\(\chi_{2864}(117,\cdot)\)
\(\chi_{2864}(125,\cdot)\)
\(\chi_{2864}(141,\cdot)\)
\(\chi_{2864}(149,\cdot)\)
\(\chi_{2864}(173,\cdot)\)
\(\chi_{2864}(221,\cdot)\)
\(\chi_{2864}(245,\cdot)\)
\(\chi_{2864}(253,\cdot)\)
\(\chi_{2864}(261,\cdot)\)
\(\chi_{2864}(285,\cdot)\)
\(\chi_{2864}(317,\cdot)\)
\(\chi_{2864}(325,\cdot)\)
\(\chi_{2864}(373,\cdot)\)
\(\chi_{2864}(389,\cdot)\)
\(\chi_{2864}(397,\cdot)\)
\(\chi_{2864}(405,\cdot)\)
\(\chi_{2864}(445,\cdot)\)
\(\chi_{2864}(453,\cdot)\)
\(\chi_{2864}(493,\cdot)\)
\(\chi_{2864}(509,\cdot)\)
\(\chi_{2864}(541,\cdot)\)
...
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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 ]
\((1791,2149,897)\) → \((1,-i,e\left(\frac{57}{89}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 2864 }(13, a) \) |
\(1\) | \(1\) | \(e\left(\frac{149}{356}\right)\) | \(e\left(\frac{47}{356}\right)\) | \(e\left(\frac{3}{178}\right)\) | \(e\left(\frac{149}{178}\right)\) | \(e\left(\frac{127}{356}\right)\) | \(e\left(\frac{93}{356}\right)\) | \(e\left(\frac{49}{89}\right)\) | \(e\left(\frac{28}{89}\right)\) | \(e\left(\frac{297}{356}\right)\) | \(e\left(\frac{155}{356}\right)\) |
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sage:chi.jacobi_sum(n)
