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We present multiwavelength modeling of the afterglow from the long gamma-ray burst GRB 160625B using Markov Chain Monte Carlo (MCMC) techniques of the afterglowpy Python package. GRB 160625B is an extremely bright burst with a rich set of observations spanning from radio to gamma-ray frequencies. These observations range from ~0.1 days to >1000 days, thus making this event extremely well-suited to such modeling. In this work we compare top-hat and Gaussian jet structure types in order to find best fit values for the GRB jet collimation angle, viewing angle, and other physical parameters. We find that a Gaussian-shaped jet is preferred (2.7-5.3 sigma) over the traditional top-hat model. Our estimate for the opening angle of the burst ranges from 1.26 to 3.90 degrees, depending on jet shape model. We also discuss the implications that assumptions on jet shape, viewing angle, and particularly the participation fraction of electrons have on the final estimation of GRB intrinsic energy release and the resulting energy budget of the relativistic outflow. Most notably, allowing the participation fraction to vary results in an estimated total relativistic energy of ~$10^{53}$ erg. This is two orders of magnitude higher than when the total fraction is assumed to be unity, thus this parameter has strong relevance for placing constraints on long GRB central engines, details of the circumburst media, and host environment.