$#a1 is the index of the last element in the array @a1. To access the array referred to by $a1, you use additional syntax with that variable. For example:

$idx   = $#{$a1};       # index of last element
$idx   = $#$a1;         # same

$count = @{$a1};        # number of elements
$count = @$a1;          # same

$item  = $a1->[1];      # element 1
$item  = ${$a1}[1];     # same

@slice = @{$a1}[0, 1];  # slice of elements
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For more on using references, check out perlreftut (reference tutorial - offsite link), perlref (reference reference), perllol (lists of lists), and perldsc (data structures cookbook).