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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2793, base_ring=CyclotomicField(126))
M = H._module
chi = DirichletCharacter(H, M([63,66,56]))
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pari:[g,chi] = znchar(Mod(389,2793))
| Modulus: | \(2793\) | |
| Conductor: | \(2793\) |
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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)
|
\(\chi_{2793}(137,\cdot)\)
\(\chi_{2793}(149,\cdot)\)
\(\chi_{2793}(158,\cdot)\)
\(\chi_{2793}(233,\cdot)\)
\(\chi_{2793}(359,\cdot)\)
\(\chi_{2793}(389,\cdot)\)
\(\chi_{2793}(536,\cdot)\)
\(\chi_{2793}(548,\cdot)\)
\(\chi_{2793}(632,\cdot)\)
\(\chi_{2793}(758,\cdot)\)
\(\chi_{2793}(788,\cdot)\)
\(\chi_{2793}(935,\cdot)\)
\(\chi_{2793}(947,\cdot)\)
\(\chi_{2793}(956,\cdot)\)
\(\chi_{2793}(1031,\cdot)\)
\(\chi_{2793}(1187,\cdot)\)
\(\chi_{2793}(1334,\cdot)\)
\(\chi_{2793}(1346,\cdot)\)
\(\chi_{2793}(1355,\cdot)\)
\(\chi_{2793}(1430,\cdot)\)
\(\chi_{2793}(1556,\cdot)\)
\(\chi_{2793}(1754,\cdot)\)
\(\chi_{2793}(1829,\cdot)\)
\(\chi_{2793}(1955,\cdot)\)
\(\chi_{2793}(1985,\cdot)\)
\(\chi_{2793}(2132,\cdot)\)
\(\chi_{2793}(2144,\cdot)\)
\(\chi_{2793}(2153,\cdot)\)
\(\chi_{2793}(2228,\cdot)\)
\(\chi_{2793}(2354,\cdot)\)
...
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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 ]
\((932,2110,2206)\) → \((-1,e\left(\frac{11}{21}\right),e\left(\frac{4}{9}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(20\) |
| \( \chi_{ 2793 }(389, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{71}{126}\right)\) | \(e\left(\frac{8}{63}\right)\) | \(e\left(\frac{101}{126}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{23}{63}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{32}{63}\right)\) | \(e\left(\frac{16}{63}\right)\) | \(e\left(\frac{5}{126}\right)\) | \(e\left(\frac{13}{14}\right)\) |
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sage:chi.jacobi_sum(n)
