Title: Maass forms on SL_3(Z) Creator: David Farmer, Sally Koutsoliotas and Stefan Lemurell Program(s) used: Mathematica Operating system: Linux When created: June 2008 Rigor: The eigenvalue parameters we believe are correct to 8 or at least 7 decimal places. The prime fourier coefficents a2, a3 and a5 are correct to at least 7-8 places, a7 with 5-6 decimal places, a11 with 2-4 decimal places and a13 with 1-2 decimal places. These estimates are mainly based on checking the error in the Hecke relations for the computed composite coefficients. The composite coefficients given in the data are computed from the prime coefficients using the Hecke multiplicativity relations. The zeros of the L-functions are believed to be correct to 5-6 decimal places when the imaginary part is less than the imaginary part of any of the trivial zeros. For the largest eigenvalues this is (almost) true for all zeros in this range. For the smallest eigenvalues the precision in the zeros go down to 2-3 decimal places for zeros around 30. These estimates are based on comparing the result you get when perturbing the data with the error estimates and also by changing the flag -S in lcalc. Description: The data consists of 71 Maass forms on SL_3(Z). The files are in Lcalc format and could be run directly with lcalc. In particular rows 6-11 contains the parameters for the gamma function (i.e. the eigenvalue parameters) and the 16 last lines are the first 16 (complex) coefficients. The names of the files are gl3MaassX where X is any number from 1 to 71. The zeros are in the file ZeroList.txt. The data there are one line with the eigenvalue parameters separated by space, one empty line, the zeros one in each line, two empty lines and then the next L-function data. Encoded name: GL_3 Maass forms Data format: Lcalc-format Contents of files: Each file contains L-function data for a Maass form on SL_3(Z). Exception is the file ZeroList.txt which contains zeros (in the range [-30,30]) of the all the 71 L-functions. In total there are roughly 1500 zeros. File list: ZeroList.txt gl3Maass1 gl3Maass10 gl3Maass11 gl3Maass12 gl3Maass13 gl3Maass14 gl3Maass15 gl3Maass16 gl3Maass17 gl3Maass18 gl3Maass19 gl3Maass2 gl3Maass20 gl3Maass21 gl3Maass22 gl3Maass23 gl3Maass24 gl3Maass25 gl3Maass26 gl3Maass27 gl3Maass28 gl3Maass29 gl3Maass3 gl3Maass30 gl3Maass31 gl3Maass32 gl3Maass33 gl3Maass34 gl3Maass35 gl3Maass36 gl3Maass37 gl3Maass38 gl3Maass39 gl3Maass4 gl3Maass40 gl3Maass41 gl3Maass42 gl3Maass43 gl3Maass44 gl3Maass45 gl3Maass46 gl3Maass47 gl3Maass48 gl3Maass49 gl3Maass5 gl3Maass50 gl3Maass51 gl3Maass52 gl3Maass53 gl3Maass54 gl3Maass55 gl3Maass56 gl3Maass57 gl3Maass58 gl3Maass59 gl3Maass6 gl3Maass60 gl3Maass61 gl3Maass62 gl3Maass63 gl3Maass64 gl3Maass65 gl3Maass66 gl3Maass67 gl3Maass68 gl3Maass69 gl3Maass7 gl3Maass70 gl3Maass71 gl3Maass8 gl3Maass9