{'fraction_non_alphanumeric': 0.11746031746031746, 'fraction_numerical': 0.0380952380952381, 'mean_word_length': 3.1578947368421053, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Estimates of theta(x; k, l) for large values of x

We extend a result of Ramare and Rumely, 1996, about the Chebyshev function θ in arithmetic progressions. We find a map e(x) such that | θ(x; k, l) - x/φ(k) | 0), whereas e(x) is a constant. Now we are able to show that, for x ≥ 1531, |θ(x; 3, l) - x/2 | x/2 ln x.