This does what you asked for in the first screenful of your post. I wrote and tested it before noticing there was a lot more to the post, so here it is, maybe it is useful to you:

#! perl -sw
use strict;

my %fhs;

while( <DATA> ) {
    my @bits = split;
    my $abs = abs( $bits[ 3 ] );
    open $fhs{ $abs }, '>', 'output_' . $abs or die $! unless exists $
+fhs{ $abs };
    print { $fhs{ $abs } } $_;
}

__DATA__
-59.077    89.301   115.664       7
-61.251    77.435   117.760      -6
-60.950    71.712   116.061      -7
-56.247    83.685   114.576       1
-59.263    76.107   112.555      -2
-59.895    65.296   111.185       3
-60.141    63.694   111.257      -3
-61.667    63.707   116.937       2
-58.722    60.429   111.307      -1
-57.511    42.922   112.108       6
[download]

Produces:

C:\test>type output_*

output_1


-56.247    83.685   114.576       1
-58.722    60.429   111.307      -1

output_2


-59.263    76.107   112.555      -2
-61.667    63.707   116.937       2

output_3


-59.895    65.296   111.185       3
-60.141    63.694   111.257      -3

output_6


-61.251    77.435   117.760      -6
-57.511    42.922   112.108       6

output_7


-59.077    89.301   115.664       7
-60.950    71.712   116.061      -7
[download]