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Theta series of A_24 lattice.
0

%I #10 Sep 08 2022 08:44:48

%S 1,600,75900,3555800,77836050,924978120,6901688200,37479599400,

%T 162981777750,594965730200,1897531134180,5410666657200,14097598363900,

%U 33985515175800,76830818652600,164035898209360

%N Theta series of A_24 lattice.

%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 110.

%e 1 + 600*q^2 + 75900*q^4 + 3555800*q^6 + O(q^8).

%t terms = 16; f[q_] = LatticeData["A24", "ThetaSeriesFunction"][-I*Log[q]/Pi]; s = f[q] + O[q]^(2 terms); Partition[CoefficientList[s, q] // Round, 2][[All, 1]][[1 ;; terms]] (* _Jean-François Alcover_, Jul 06 2017 *)

%o (Magma) L:=Lattice("A",24); T1<q> := ThetaSeries(L,10);

%K nonn

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from Robert.Harley(AT)inria.fr, see A023902.