Keyspace List for WPA on Default Routers

[miccee]

OUI: 38:3B:C8 = 2WIRE
ESSID: ATTXXXXXXX
Passphrase consists of:

a-z
0-9
=
?

Notice: No capital letter in my home router's passpharase. Length is exactly 12 char.
EDIT: Yes, this is the default passphrase. And yes, I have changed it

Is there a fixed pattern or they are completely random?

Good question. Arriving at the answer is partly why I posted. Since I can provide just one sample, it's too early to discern randomness from order. Honestly, I think the entropy is quite high, both in passwords and in ESSID assignment.

Can you please post the original passphrase? Does it have any relation to the last 6 characters of ATTXXXXXXX?