Rest API syntax for request & response for below conditions to retrive the projects

Hello Clarizen Developers,

Can you please help me with the syntax with rest api request and response with some sample data example to set the following condition to retrive the Projects.

ParentProject.Name does not contain “TEST”

AND

ParentProject.Name does not contain “Archive” 

AND 

Parent.Top Parent Project.Name begins with “TESTROOT_” 

AND 

Parent.Top Parent Project.Name is not one of "TEST2"