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Properties

Modulus $1440000$
Structure \(C_{2}\times C_{6}\times C_{64}\times C_{500}\)
Order $384000$

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Show commands: Magma / Pari/GP / SageMath

Copy content comment:Define the Dirichlet group
 
Copy content sage:G = DirichletGroup(1440000)
 
Copy content gp:g = idealstar(,1440000,2)
 
Copy content magma:G = FullDirichletGroup(1440000);
 

Character group

Order = 384000
Copy content comment:Order
 
Copy content sage:G.order()
 
Copy content gp:g.no
 
Copy content magma:Order(G);
 
Structure = \(C_{2}\times C_{6}\times C_{64}\times C_{500}\)
Copy content comment:Group structure
 
Copy content sage:sorted(g.order() for g in G.gens())
 
Copy content gp:g.cyc
 
Copy content magma:PrimaryInvariants(G);
 
Generators = $\chi_{1440000}(618751,\cdot)$, $\chi_{1440000}(202501,\cdot)$, $\chi_{1440000}(640001,\cdot)$, $\chi_{1440000}(389377,\cdot)$
Copy content comment:Generators
 
Copy content sage:G.gens()
 
Copy content gp:g.gen
 
Copy content magma:Generators(G);