Understanding multilevel model coefficients

Yes, there are 504 observations and every single datapoint gets an intercept. I understand what you’re saying and it does seem like it’s that because some of the values for different datapoints are the same (so if the actor, treatment and block are the same). But I can’t figure out how to calculate p from the coefficients of the other variables. For example:

a[0] = -0.368
g[0] = -0.165
b[0] = -0.133

Sum is -0.666, But I don’t see that value in the list of any of the intercepts for p.

Or is the p calculation totally separate and has no relation to the a, g, b intercepts?