Each lattice L is given as 
		
	[gram, mass, rs, red_mass, hbv] 

where:

-- gram is a Gram matrix of L 

-- mass is the mass of L (inverse of order of isometry group of L)

-- rs is the root system of L (an ADE root system)

-- red_mass is the reduced mass of L (mass * order of the Weyl group of L) 

-- hbv is the hashed BV invariant of L (see Unimodular Hunting II)