verilog, 75 bytes

Result

WA

Code [DL]

real x;initial repeat(50)$write("%d",$fscanf(1<<31,"%b",x)==(8*x+1)**0.5%2)

stdin

01111001
01101001
01000011
10000100
10001010
00011010
00000011
01011011
11010010
10000110
00100100
10001000
00110111
11100100
01010010
10011101
10100101
01000010
10111110
00001010
10101101
11010111
00111110
01111000
00001010
00010101
11111100
11010000
10101011
00001111
00011100
01001110
00101111
11111101
11100111
10001110
00000001
10001111
11100001
10011001
00101101
00011001
00000110
10101111
01101101
01101000
10111100
00110111
00011111
00000000

stdout

stderr

/volume/CODE:1: syntax error
I give up.
/home/esolang/bin/verilog: line 4: /tmp/code: No such file or directory
rm: cannot remove '/tmp/code': No such file or directory

strace