Populating a Map<Id,List<Contact>> for a comparison

Question

What I am trying to do here is populate a list from a callout to Looker (BI Tool) then create a Map of Salesforce Account IDs to associated Contact Emails. To do this I created this method:

public static Map<Id, List<Contact>> lookerById() {
   List<Contact> lookerList = zuoraContactSync.mergeList();
   system.debug(lookerList);
   Map<Id, List<Contact>> lookerByIds = new Map<Id, List<Contact>>();
   for(Contact con : lookerList) {
           List<Contact> contacts = lookerByIds.get(con.Email);
           system.debug(lookerByIds);
           lookerByIds.put(con.AccountId, contacts);      
       }                 
       //status__c is ROLE

   system.debug(lookerByIds.size());
   system.debug(lookerByIds);
   return lookerByIds;
}


   return lookerByIds;
}

When I use the put on this line :

lookerByIds = put(con.AccountId, contacts);

I am returned with an incorrect method signature error.

Method does not exist or incorrect signature: void put(Id, List<Contact>) from the type ClassName

I am reasonably certain I have the right logic to do this... mostly. What am I missing?