vim, 47 bytes

Result

WA

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 29 2a 38 2b 31 29 2c  |str2nr(@@)*8+1),|
00000020  31 29 3d 3d 30 0a 1b 77  71 34 39 40 7a 5a 5a     |1)==0..wq49@zZZ|
0000002f

Disassembly

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

stdin

11111101
00001010
01101101
00111100
10001101
11001011
10001000
00101000
01110110
11100111
01000010
10010110
11100101
11001111
00101101
01100110
00100100
00000001
01100111
01011100
00000110
00000000
11101110
01111000
00001010
10000001
00011100
00101001
10011001
11101111
01011011
00010101
11101000
11011011
10110011
01001110
10101011
00001111
11010010
01101001
11010010
00110111
01111111
01011111
10011110
10101010
10000111
00000011
01011110
10111110

stdout

0
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0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
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0
0
0
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0
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0
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stderr

strace