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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2527, base_ring=CyclotomicField(342))
M = H._module
chi = DirichletCharacter(H, M([114,166]))
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pari:[g,chi] = znchar(Mod(282,2527))
| Modulus: | \(2527\) | |
| Conductor: | \(2527\) |
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sage:chi.conductor()
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pari:znconreyconductor(g,chi)
|
| Order: | \(171\) |
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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)
|
\(\chi_{2527}(4,\cdot)\)
\(\chi_{2527}(16,\cdot)\)
\(\chi_{2527}(25,\cdot)\)
\(\chi_{2527}(93,\cdot)\)
\(\chi_{2527}(100,\cdot)\)
\(\chi_{2527}(123,\cdot)\)
\(\chi_{2527}(137,\cdot)\)
\(\chi_{2527}(149,\cdot)\)
\(\chi_{2527}(158,\cdot)\)
\(\chi_{2527}(226,\cdot)\)
\(\chi_{2527}(233,\cdot)\)
\(\chi_{2527}(256,\cdot)\)
\(\chi_{2527}(270,\cdot)\)
\(\chi_{2527}(282,\cdot)\)
\(\chi_{2527}(291,\cdot)\)
\(\chi_{2527}(359,\cdot)\)
\(\chi_{2527}(366,\cdot)\)
\(\chi_{2527}(403,\cdot)\)
\(\chi_{2527}(424,\cdot)\)
\(\chi_{2527}(492,\cdot)\)
\(\chi_{2527}(499,\cdot)\)
\(\chi_{2527}(522,\cdot)\)
\(\chi_{2527}(536,\cdot)\)
\(\chi_{2527}(548,\cdot)\)
\(\chi_{2527}(557,\cdot)\)
\(\chi_{2527}(625,\cdot)\)
\(\chi_{2527}(632,\cdot)\)
\(\chi_{2527}(655,\cdot)\)
\(\chi_{2527}(669,\cdot)\)
\(\chi_{2527}(681,\cdot)\)
...
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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 ]
\((1445,1807)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{83}{171}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 2527 }(282, a) \) |
\(1\) | \(1\) | \(e\left(\frac{26}{171}\right)\) | \(e\left(\frac{137}{171}\right)\) | \(e\left(\frac{52}{171}\right)\) | \(e\left(\frac{47}{171}\right)\) | \(e\left(\frac{163}{171}\right)\) | \(e\left(\frac{26}{57}\right)\) | \(e\left(\frac{103}{171}\right)\) | \(e\left(\frac{73}{171}\right)\) | \(e\left(\frac{16}{19}\right)\) | \(e\left(\frac{2}{19}\right)\) |
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sage:chi.jacobi_sum(n)
