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Abstract We present an analysis of a densely repeating sample of bursts from the first repeating fast radio burst, FRB 121102. We reanalyzed the data used by Gourdji et al. and detected 93 additional bursts using our single-pulse search pipeline. In total, we detected 133 bursts in three hours of data at a center frequency of 1.4 GHz using the Arecibo telescope, and develop robust modeling strategies to constrain the spectro-temporal properties of all of the bursts in the sample. Most of the burst profiles show a scattering tail, and burst spectra are well modeled by a Gaussian with a median width of 230 MHz. We find a lack of emission below 1300 MHz, consistent with previous studies of FRB 121102. We also find that the peak of the log-normal distribution of wait times decreases from 207 to 75 s using our larger sample of bursts, as compared to that of Gourdji et al. Our observations do not favor either Poissonian or Weibull distributions for the burst rate distribution. We searched for periodicity in the bursts using multiple techniques, but did not detect any significant period. The cumulative burst energy distribution exhibits a broken power-law shape, with the lower- andmore »higher-energy slopes of −0.4 ± 0.1 and −1.8 ± 0.2, with the break at (2.3 ± 0.2) × 10 37 erg. We provide our burst fitting routines as a Python package burstfit 4 4 https://github.com/thepetabyteproject/burstfit that can be used to model the spectrogram of any complex fast radio burst or pulsar pulse using robust fitting techniques. All of the other analysis scripts and results are publicly available. 5 5 https://github.com/thepetabyteproject/FRB121102« less