"Universal quadratic forms and the 290-Theorem" resource page

Tables

Results

The 29 critical integers in the 290-Theorem (data)
"Almost Universal" forms missing exactly one of each of the 29 critical integers (text)
All 6436 universal integer-valued (positive definite) quaternary forms (text, data)

Escalators and Auxiliary forms

Computational Details

Summary of computations to determine the square-free numbers represented by the quaternaries above
C++ Program Raw Output Logs for Basic and Auxiliary forms
C++ Program Persistent Datafiles for Basic and Auxiliary forms
Very large (152MB) list of 15 million primes used in the C++ code

Software

Making Escalators and Universal Forms

Producing the basic escalators (MAGMA, SAGE, Pari/GP)
Producing the auxiliary escalators (MAGMA, SAGE, Pari/GP)
Computing the universal quaternaries (MAGMA, SAGE, Pari/GP)

Quaternary Form Computations
Computing cuspidal constants and eigenform decompositions of theta functions (MAGMA, SAGE)
Checking representability of numbers by (positive definite integer-valued) quaternaries (Doxygen/C++, C++, SAGE)
Computing Eisenstein series by averaging over a genus (MAGMA)

Misc Python Scripts
Python script to distribute the C++ computations to a cluster using the Sun Grid Engine (SGE)
Python scripts to spawn multiple MAGMA processes to compute cuspidal constants for a range of forms (Basic, Aux)
Python script to parse a folder of Magma cuspidal constant output files
Python script to generate the HTML computation summaries for each quaternary from its C++ raw output log

Useful Software
Free software packages used above: SAGE, Pari/GP, Doxygen
Free libraries used in our computations: GMP, Pari/GP
Non-Free software used: MAGMA

References

The Beginning

The emergence of finiteness theorems

Effective bounds for representing a number by a definite form

Some nice survey papers related to these topics