There are 100 fractions in the following set.

{14,47,710,1013,...,292295,295298,298301} \Big\lbrace \frac{1}{4}, \frac{4}{7}, \frac{7}{10}, \frac{10}{13}, ... , \frac{292}{295}, \frac{295}{298}, \frac{298}{301} \Big\rbrace

Each fraction after the first is found by adding 3 to the preceding fraction's numerator and denominator. What is the product of these 100 fractions?