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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2329, base_ring=CyclotomicField(34))
M = H._module
chi = DirichletCharacter(H, M([17,13]))
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pari:[g,chi] = znchar(Mod(288,2329))
| Modulus: | \(2329\) | |
| Conductor: | \(2329\) |
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sage:chi.conductor()
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pari:znconreyconductor(g,chi)
|
| Order: | \(34\) |
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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: | even |
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sage:chi.is_odd()
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pari:zncharisodd(g,chi)
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\(\chi_{2329}(152,\cdot)\)
\(\chi_{2329}(186,\cdot)\)
\(\chi_{2329}(288,\cdot)\)
\(\chi_{2329}(339,\cdot)\)
\(\chi_{2329}(373,\cdot)\)
\(\chi_{2329}(475,\cdot)\)
\(\chi_{2329}(492,\cdot)\)
\(\chi_{2329}(611,\cdot)\)
\(\chi_{2329}(900,\cdot)\)
\(\chi_{2329}(1036,\cdot)\)
\(\chi_{2329}(1529,\cdot)\)
\(\chi_{2329}(1648,\cdot)\)
\(\chi_{2329}(2005,\cdot)\)
\(\chi_{2329}(2039,\cdot)\)
\(\chi_{2329}(2073,\cdot)\)
\(\chi_{2329}(2158,\cdot)\)
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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 ]
\((275,2058)\) → \((-1,e\left(\frac{13}{34}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 2329 }(288, a) \) |
\(1\) | \(1\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{19}{34}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(1\) | \(e\left(\frac{5}{34}\right)\) |
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sage:chi.jacobi_sum(n)
