Khare, Larsen, and Ramakrishna created a set of techniques for constructing infinitely ramified Galois representations with prescribed properties, which Ramakrishna then used to construct transcendental l-adic Galois representations. Later, Pande used these techniques to create Galois-theoretic counterexamples to the Sato–Tate conjecture. I strengthen Pande's results to show that there exist Galois representations, ramified at an arbitrarily thin set of primes, whose Satake parameters converge at any specified rate to any fixed distribution.