Complexity of accessing data in an object

In the worst case an JS object is represented as a hash table and has the same lookup complexity: O(1) on average but O(n) at worst. The hash table implementation is your case I guess, because you have so many items in the object. There is no difference how you access a property, obj.field and obj['filed'] are the same.

It's also worth to mention that the complexity isn't always equal to complexity of a hash table lookup, it's faster in much cases. Modern JS engines use techniques called hidden classes and inline caching to speed up the lookup. It's a pretty big question, how these techniques work, I've explained it in another answer.

Some relative resources:

• JavaScript engine fundamentals: Shapes and Inline Caches and a YouTube video as well.
• Fast properties in V8
• A tour of V8: object representation
• JavaScript Engines Hidden Classes (and Why You Should Keep Them in Mind)

Javascript objects are actually Hashes, so the complexity is O(1) for all engines.

obj.field is an alias for obj['field'], so they have the same performances.

You can find some JS hashes performance tests here, unfortunately only for your browser engine.