Pre-periodic parameters in the Mandelbrot set, up to type (pre-period + period) 28, rounded to nearest 10^{-26}

The Mandelbrot set is the set of parameters c such that the sequence z_{n+1} = z_n^2 + c starting from z_0=0 remains bounded. Misiurewicz-Thurston parameters are the parameters c for which the sequence (z_n) is pre-periodic, that is it becomes periodic of period k after the first m iterations. We classify pre-periodic parameters by their type or degree, the value of m+k, and sub-type, which is the pair (m,k) with the smallest positive integers m and k such that z_{m+k}=z_m; the set of such parameters is denoted by Mis(m,k). The sequence of polynomials p_n(c) defined recursively by p_n(c) = p_{n-1}^2(c) + c where p_0(c)=0 is related to this question. The roots of the polynomial p_{m+k}(c)-p_m(c) are composed of hyperbolic parameters whose period divides k and of pre-periodic parameters whose period divides k and whose pre-period does not exceed m. This data set contains a list of all Misiurewicz-Thurston (pre-periodic) parameters Mis(m,k) in the Mandelbrot set, up to type m+k=28, with non-negative imaginary part. Each file contains a list of roots, z=a+ib with a and b rounded to the nearest 10^{-26}, that is 85 bits of precision. The files are in CSV format (one file per sub-type), with one root per row, presented as the character chain "a, b". Note that b is always non-negative. For organization purposes, all the files of sub-type (m,k) for a given type n=m+k are collected together into a single TAR archive. The CSV files of types 26 to 28 where compressed individually using the BZ2 algorithm, before inserting them in the TAR archive; this choice provides a faster access to each individual sub-type. This data results from a conversion to human-readable decimal form of a high-precision and certified database, as explained in the reference [arXiv:2402.06083]. This larger database extends all the way to pre-periodic type m+k=35. Please contact the authors if you need access. For periodic / hyperbolic centers, please refer to the dataset [https://doi.org/10.5281/zenodo.15527027]. Note: please be careful that some programs mishandle CSV files that contain floating point numbers whose precision exceed machine precision (which is definitly the case here). To avoid such unpleasantness, we suggest accessing the CSV files programmatically, as text-based files. To add data protection to your workflow, we recommend using a certified file format, as explained in [arXiv:2402.06083] and implemented in [https://github.com/fvigneron/Mandelbrot].