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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2952, base_ring=CyclotomicField(60))
M = H._module
chi = DirichletCharacter(H, M([0,30,10,27]))
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pari:[g,chi] = znchar(Mod(1181,2952))
| Modulus: | \(2952\) | |
| Conductor: | \(2952\) |
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sage:chi.conductor()
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pari:znconreyconductor(g,chi)
|
| Order: | \(60\) |
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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)
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\(\chi_{2952}(5,\cdot)\)
\(\chi_{2952}(77,\cdot)\)
\(\chi_{2952}(389,\cdot)\)
\(\chi_{2952}(677,\cdot)\)
\(\chi_{2952}(869,\cdot)\)
\(\chi_{2952}(941,\cdot)\)
\(\chi_{2952}(1109,\cdot)\)
\(\chi_{2952}(1181,\cdot)\)
\(\chi_{2952}(1373,\cdot)\)
\(\chi_{2952}(1661,\cdot)\)
\(\chi_{2952}(1973,\cdot)\)
\(\chi_{2952}(2045,\cdot)\)
\(\chi_{2952}(2093,\cdot)\)
\(\chi_{2952}(2165,\cdot)\)
\(\chi_{2952}(2837,\cdot)\)
\(\chi_{2952}(2909,\cdot)\)
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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 ]
\((2215,1477,2297,1441)\) → \((1,-1,e\left(\frac{1}{6}\right),e\left(\frac{9}{20}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 2952 }(1181, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{14}{15}\right)\) |
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sage:chi.jacobi_sum(n)
