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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7260, base_ring=CyclotomicField(22))
M = H._module
chi = DirichletCharacter(H, M([11,11,11,10]))
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pari:[g,chi] = znchar(Mod(3059,7260))
| Modulus: | \(7260\) | |
| Conductor: | \(7260\) |
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sage:chi.conductor()
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pari:znconreyconductor(g,chi)
|
| Order: | \(22\) |
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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)
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\(\chi_{7260}(419,\cdot)\)
\(\chi_{7260}(1079,\cdot)\)
\(\chi_{7260}(1739,\cdot)\)
\(\chi_{7260}(2399,\cdot)\)
\(\chi_{7260}(3059,\cdot)\)
\(\chi_{7260}(3719,\cdot)\)
\(\chi_{7260}(4379,\cdot)\)
\(\chi_{7260}(5039,\cdot)\)
\(\chi_{7260}(5699,\cdot)\)
\(\chi_{7260}(6359,\cdot)\)
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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 ]
\((3631,4841,4357,7141)\) → \((-1,-1,-1,e\left(\frac{5}{11}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 7260 }(3059, a) \) |
\(1\) | \(1\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{4}{11}\right)\) |
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sage:chi.jacobi_sum(n)
