We give two improved explicit versions of the prime number theorem for primes in arithmetic progressions: the first isolating the contribution of the Siegel zero and the second completely explicit, where the improvement is for medium-sized values of x. This will give an improved explicit Bombieri--Vinogradov-like result for non-exceptional moduli.

I would like to thank my supervisor Tim Trudgian for his help in developing this paper and his insightful comments. I would also like to thank the anonymous reviewer, Kevin O'Bryant and Daniel Johnston for the helpful comments and suggestions.