vim, 49 bytes

Result

AC

Code [DL]

00000000  71 7a 63 63 12 3d 66 6d  6f 64 28 73 71 72 74 28  |qzcc.=fmod(sqrt(|
00000010  73 74 72 32 6e 72 28 40  40 2c 32 29 2a 38 2b 31  |str2nr(@@,2)*8+1|
00000020  29 2c 31 29 3d 3d 30 0a  1b 77 71 34 39 40 7a 5a  |),1)==0..wq49@zZ|
00000030  5a                                                |Z|
00000031

Disassembly

qzcc<C-R>=fmod(sqrt(str2nr(@@,2)*8+1),1)==0<NL><Esc>wq49@zZZ

stdin

00000001
01111000
10010100
10001000
00000110
11111101
00010111
11010010
11111001
11011000
10100011
00000011
11101111
01101001
00000011
00101101
00100100
10111110
01111100
11010010
10100111
00010100
00011011
10111010
00000010
10011001
00001010
00101100
00010110
11100111
00001111
11011101
10001011
01001110
01000010
00011100
01011001
00010101
10101011
00111011
11101001
11001111
10111001
10100110
00100000
01011011
00001110
11010110
00000000
00110111

stdout

1
1
0
1
1
1
0
1
0
0
0
1
0
1
1
1
1
1
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1

stderr

strace