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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1932, base_ring=CyclotomicField(66))
M = H._module
chi = DirichletCharacter(H, M([33,33,11,57]))
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pari:[g,chi] = znchar(Mod(1571,1932))
| Modulus: | \(1932\) | |
| Conductor: | \(1932\) |
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sage:chi.conductor()
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pari:znconreyconductor(g,chi)
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| Order: | \(66\) |
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sage:chi.multiplicative_order()
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pari:charorder(g,chi)
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| 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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\(\chi_{1932}(143,\cdot)\)
\(\chi_{1932}(227,\cdot)\)
\(\chi_{1932}(383,\cdot)\)
\(\chi_{1932}(467,\cdot)\)
\(\chi_{1932}(479,\cdot)\)
\(\chi_{1932}(563,\cdot)\)
\(\chi_{1932}(635,\cdot)\)
\(\chi_{1932}(803,\cdot)\)
\(\chi_{1932}(815,\cdot)\)
\(\chi_{1932}(971,\cdot)\)
\(\chi_{1932}(983,\cdot)\)
\(\chi_{1932}(1055,\cdot)\)
\(\chi_{1932}(1307,\cdot)\)
\(\chi_{1932}(1391,\cdot)\)
\(\chi_{1932}(1487,\cdot)\)
\(\chi_{1932}(1571,\cdot)\)
\(\chi_{1932}(1643,\cdot)\)
\(\chi_{1932}(1739,\cdot)\)
\(\chi_{1932}(1811,\cdot)\)
\(\chi_{1932}(1907,\cdot)\)
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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 ]
\((967,1289,829,925)\) → \((-1,-1,e\left(\frac{1}{6}\right),e\left(\frac{19}{22}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 1932 }(1571, a) \) |
\(1\) | \(1\) | \(e\left(\frac{13}{66}\right)\) | \(e\left(\frac{29}{66}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{47}{66}\right)\) | \(e\left(\frac{19}{66}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{28}{33}\right)\) | \(e\left(\frac{31}{66}\right)\) | \(e\left(\frac{4}{11}\right)\) |
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sage:chi.jacobi_sum(n)
