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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2925, base_ring=CyclotomicField(60))
M = H._module
chi = DirichletCharacter(H, M([50,18,25]))
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pari:[g,chi] = znchar(Mod(2489,2925))
| Modulus: | \(2925\) | |
| Conductor: | \(2925\) |
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sage:chi.conductor()
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pari:znconreyconductor(g,chi)
|
| Order: | \(60\) |
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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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\(\chi_{2925}(59,\cdot)\)
\(\chi_{2925}(119,\cdot)\)
\(\chi_{2925}(479,\cdot)\)
\(\chi_{2925}(644,\cdot)\)
\(\chi_{2925}(704,\cdot)\)
\(\chi_{2925}(734,\cdot)\)
\(\chi_{2925}(1064,\cdot)\)
\(\chi_{2925}(1229,\cdot)\)
\(\chi_{2925}(1289,\cdot)\)
\(\chi_{2925}(1319,\cdot)\)
\(\chi_{2925}(1814,\cdot)\)
\(\chi_{2925}(1904,\cdot)\)
\(\chi_{2925}(2234,\cdot)\)
\(\chi_{2925}(2459,\cdot)\)
\(\chi_{2925}(2489,\cdot)\)
\(\chi_{2925}(2819,\cdot)\)
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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 ]
\((326,352,2251)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{3}{10}\right),e\left(\frac{5}{12}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
| \( \chi_{ 2925 }(2489, a) \) |
\(1\) | \(1\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{1}{10}\right)\) |
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sage:chi.jacobi_sum(n)
