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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3025, base_ring=CyclotomicField(220))
M = H._module
chi = DirichletCharacter(H, M([143,186]))
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pari:[g,chi] = znchar(Mod(217,3025))
| Modulus: | \(3025\) | |
| Conductor: | \(3025\) |
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sage:chi.conductor()
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pari:znconreyconductor(g,chi)
|
| Order: | \(220\) |
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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)
|
\(\chi_{3025}(2,\cdot)\)
\(\chi_{3025}(8,\cdot)\)
\(\chi_{3025}(123,\cdot)\)
\(\chi_{3025}(128,\cdot)\)
\(\chi_{3025}(138,\cdot)\)
\(\chi_{3025}(172,\cdot)\)
\(\chi_{3025}(217,\cdot)\)
\(\chi_{3025}(237,\cdot)\)
\(\chi_{3025}(277,\cdot)\)
\(\chi_{3025}(283,\cdot)\)
\(\chi_{3025}(398,\cdot)\)
\(\chi_{3025}(413,\cdot)\)
\(\chi_{3025}(447,\cdot)\)
\(\chi_{3025}(492,\cdot)\)
\(\chi_{3025}(512,\cdot)\)
\(\chi_{3025}(552,\cdot)\)
\(\chi_{3025}(558,\cdot)\)
\(\chi_{3025}(673,\cdot)\)
\(\chi_{3025}(678,\cdot)\)
\(\chi_{3025}(688,\cdot)\)
\(\chi_{3025}(722,\cdot)\)
\(\chi_{3025}(767,\cdot)\)
\(\chi_{3025}(787,\cdot)\)
\(\chi_{3025}(827,\cdot)\)
\(\chi_{3025}(833,\cdot)\)
\(\chi_{3025}(948,\cdot)\)
\(\chi_{3025}(953,\cdot)\)
\(\chi_{3025}(963,\cdot)\)
\(\chi_{3025}(997,\cdot)\)
\(\chi_{3025}(1042,\cdot)\)
...
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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 ]
\((727,2301)\) → \((e\left(\frac{13}{20}\right),e\left(\frac{93}{110}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 3025 }(217, a) \) |
\(1\) | \(1\) | \(e\left(\frac{109}{220}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{109}{110}\right)\) | \(e\left(\frac{49}{110}\right)\) | \(e\left(\frac{37}{220}\right)\) | \(e\left(\frac{107}{220}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{207}{220}\right)\) | \(e\left(\frac{163}{220}\right)\) | \(e\left(\frac{73}{110}\right)\) |
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sage:chi.jacobi_sum(n)
