vim, 58 bytes

Result

WA

Code [DL]

:%s/.\+/\=!(float2nr(sqrt(("0b".submatch(0))*8+1)*99)%99)/

Disassembly

:%s/.\+/\=!(float2nr(sqrt(("0b".submatch(0))*8+1)*99)%99)/

stdin

10011001
10000100
01000010
00000000
01010110
11110100
00011100
00100101
01000111
10001000
10101011
11001110
11100111
00000011
00010010
01111111
01001110
11100001
00011010
00001111
00110111
00000001
10010101
10001000
00110111
11110101
11011000
01011011
10010111
10111010
11010010
11101110
00001010
00110011
01111110
11111101
00101101
00000110
11000101
01111011
10010001
10111110
00111111
00110100
01010111
10100101
01101001
00010101
01111000
00100100

stdout

10011001
10000100
01000010
00000000
01010110
11110100
00011100
00100101
01000111
10001000
10101011
11001110
11100111
00000011
00010010
01111111
01001110
11100001
00011010
00001111
00110111
00000001
10010101
10001000
00110111
11110101
11011000
01011011
10010111
10111010
11010010
11101110
00001010
00110011
01111110
11111101
00101101
00000110
11000101
01111011
10010001
10111110
00111111
00110100
01010111
10100101
01101001
00010101
01111000
00100100

stderr

strace