Effective computations with Maass forms; data files

All decimals given in the files are expected to be correct, the last digit correctly rounded. All numbers were rounded from numbers which satisfied all tests of Hecke multiplicativity and of recomputing using a different parameter Y, to at least FIVE more decimal digits than shown here. For example, for the eigenvalues on PSL(2,Z), the first several Fourier coefficients (and the eigenvalue) presented should be correct to 1000 decimals, and ALL 455 coefficients should be correct to at least 900 decimals.

r=9.5336... (odd) | r=12.1730... (odd) | r=13.7797... (even) |

r=14.3585... (odd) | r=16.1380... (odd) | r=16.6442... (odd) |

r=17.7385... (even) | r=18.1809... (odd) | r=19.4234... (even) |

r=19.4847... (odd) |

r=5.4361... on Gamma_0(5), trivial character

r=3.2642... (a CM-form) on Gamma_0(5), non-trivial character (5/.)

r=4.8937... (double eigenvalue) on Gamma_0(5), non-trivial character (5/.)

r=2.5923... on Gamma_0(6), trivial character

Transcendence results in these cases.

(Cf. D. Farmer, S. Lemurell: "Deformations of Maass forms", to appear in J. Math. Comp. See also their web-page with data.)

Curve from r=4.1324...: [group [0.218,0.199...]; r=4.132...] [group [0.374,0.199...]; r=4.132...] [group [0.413,0.199...]; r=4.132...].

Curve from r=5.4361...: [group [0.071,0.193...]; r=5.370...] [group [0.143,0.184...]; r=5.287...] [group [0.279,0.189...]; r=5.338...].

Curve from r=6.8235...: [group [0.070,0.196...]; r=6.878...] [group [0.118,0.196...]; r=6.870...] [group [0.174,0.199...]; r=6.824...].

Parameters used in the computation of the K-Bessel function:
K-Bessel parameters.

Program for certification:
verify.c