Precision of classical modular form eigenvalues (reviewed)

The Hecke eigenvalue field for classical newforms can often be embedded into $\C$ in multiple ways. The Hecke eigenvalues are computed numerically to high precision for each of these embeddings.

In the LMFDB, embeddings of $a_p$ for small $p$ are stored as floating point complex numbers to 53-bit precision. This data is made available on the website, to the precision the user requests up to a bound of several decimal places.

Users requiring more data can use the download links to get all the digits that are available.

When displaying floating point values, the round-to-nearest method is used, with half rounded to even as a tie breaker.