There are a couple formulas that will help you answer this.
To calculate the effective axle ratio of what will result from replacing the 31 inch tires with 33 inch tires.
Take the new tire revs/mile, divide by original tire revs/miles, multiply by original axle ratio, equals effective axle ratio
OR in your case
636 divided by 677 times 3.55 = 3.33
To choose an optional axle ratio based on the change in tire size you are making
Take the original tire revs/mile, divide by new tire revs/mile, multiply by original axle ratio, equals Equivalent Axle Ratio OR the desired axle ratio that will have no effect on your mileage or acceleration.
So the answer is
677 divided by 636 times 3.55 = 3.77
Depending on what you are looking for in performance vs. fuel mileage is also a consideration, the higher the axle ratio number the better your acceleration, but expect a trade off with decreased fuel economy.
The numbers I used for revs per mile will vary slightly from one tire company & tire type to another so you may want to look up the exact numbers for the tires you are using, although I believe you'll find these to be close enough to answer your question.