Read and interpret mifare 4k data

Question

How can I interpret the data on my mifare 4k (14443-a) card? My goal is to be able to read and understand the data, but the card seems to work under a specific communication between it and the valid reader. I would like to decipher this communication.

When I try to translate to ascii I just get random characters. See the example:

| sector 03 / 0x03 | ascii
----+------------------------------------------ -------+-----------------
12 | 00 08 73 80 82 22 00 70 E1 F7 E7 DD E0 4C 4A B7 | ..s..".p.....LJ.
13 | 00 80 60 00 40 1B 80 00 00 08 AF 9F 18 00 00 00 | ..`.@...........
14 | 22 BE 75 C2 A0 00 00 00 00 00 00 00 00 00 B3 A8 | ".u.............
15 | 00 00 00 00 00 00 F7 8F 00 00 00 00 00 00 00 00 | ................

I tried to use the card and observe which sectors changed, but I didn't get anything very useful in my analysis. See below:

| sector 03 / 0x03                                | ascii
----+-------------------------------------------------+-----------------
12 | 00 0D 56 40 82 22 00 7C 2E 26 53 81 2B 1D 34 6A | ..V@.".|.&S.+.4j
13 | 00 C0 60 00 80 33 40 00 00 08 B0 1B F0 00 00 00 | ..`..3@.........
14 | 22 C0 67 42 E0 00 00 00 00 00 00 00 00 00 C5 2F | ".gB.........../
15 | 00 00 00 00 00 00 F7 8F 00 00 00 00 00 00 00 00 | ................

I have access to all keys and access to all sectors, and I can also print the data. My goal is to understand them.

I'm currently studying the access bits in the trailer sector, but I don't think I'm going in the right direction. What can I do next?