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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2652, base_ring=CyclotomicField(48))
M = H._module
chi = DirichletCharacter(H, M([24,24,20,15]))
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pari:[g,chi] = znchar(Mod(1943,2652))
| Modulus: | \(2652\) | |
| Conductor: | \(2652\) |
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sage:chi.conductor()
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pari:znconreyconductor(g,chi)
|
| Order: | \(48\) |
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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
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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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\(\chi_{2652}(11,\cdot)\)
\(\chi_{2652}(71,\cdot)\)
\(\chi_{2652}(215,\cdot)\)
\(\chi_{2652}(275,\cdot)\)
\(\chi_{2652}(539,\cdot)\)
\(\chi_{2652}(635,\cdot)\)
\(\chi_{2652}(743,\cdot)\)
\(\chi_{2652}(839,\cdot)\)
\(\chi_{2652}(1571,\cdot)\)
\(\chi_{2652}(1727,\cdot)\)
\(\chi_{2652}(1775,\cdot)\)
\(\chi_{2652}(1931,\cdot)\)
\(\chi_{2652}(1943,\cdot)\)
\(\chi_{2652}(2147,\cdot)\)
\(\chi_{2652}(2411,\cdot)\)
\(\chi_{2652}(2615,\cdot)\)
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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 ]
\((1327,1769,613,1873)\) → \((-1,-1,e\left(\frac{5}{12}\right),e\left(\frac{5}{16}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) | \(37\) |
| \( \chi_{ 2652 }(1943, a) \) |
\(1\) | \(1\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{25}{48}\right)\) | \(e\left(\frac{5}{48}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{41}{48}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{11}{48}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{11}{48}\right)\) |
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sage:chi.jacobi_sum(n)
