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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2667, base_ring=CyclotomicField(126))
M = H._module
chi = DirichletCharacter(H, M([63,21,19]))
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pari:[g,chi] = znchar(Mod(647,2667))
| Modulus: | \(2667\) | |
| Conductor: | \(2667\) |
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sage:chi.conductor()
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pari:znconreyconductor(g,chi)
|
| Order: | \(126\) |
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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)
|
\(\chi_{2667}(101,\cdot)\)
\(\chi_{2667}(110,\cdot)\)
\(\chi_{2667}(236,\cdot)\)
\(\chi_{2667}(299,\cdot)\)
\(\chi_{2667}(311,\cdot)\)
\(\chi_{2667}(395,\cdot)\)
\(\chi_{2667}(437,\cdot)\)
\(\chi_{2667}(467,\cdot)\)
\(\chi_{2667}(551,\cdot)\)
\(\chi_{2667}(593,\cdot)\)
\(\chi_{2667}(605,\cdot)\)
\(\chi_{2667}(614,\cdot)\)
\(\chi_{2667}(647,\cdot)\)
\(\chi_{2667}(731,\cdot)\)
\(\chi_{2667}(845,\cdot)\)
\(\chi_{2667}(1055,\cdot)\)
\(\chi_{2667}(1130,\cdot)\)
\(\chi_{2667}(1235,\cdot)\)
\(\chi_{2667}(1277,\cdot)\)
\(\chi_{2667}(1328,\cdot)\)
\(\chi_{2667}(1382,\cdot)\)
\(\chi_{2667}(1403,\cdot)\)
\(\chi_{2667}(1445,\cdot)\)
\(\chi_{2667}(1475,\cdot)\)
\(\chi_{2667}(1697,\cdot)\)
\(\chi_{2667}(1706,\cdot)\)
\(\chi_{2667}(1718,\cdot)\)
\(\chi_{2667}(1769,\cdot)\)
\(\chi_{2667}(1781,\cdot)\)
\(\chi_{2667}(1928,\cdot)\)
...
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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 ]
\((890,1144,2416)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{19}{126}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 2667 }(647, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{53}{126}\right)\) | \(e\left(\frac{85}{126}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{25}{63}\right)\) | \(-1\) |
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sage:chi.jacobi_sum(n)
