Here is my very slope-y PhD thesis.
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Code: If you dont want to go to GitHub, here are the files you will need. If you just want to compute slopes, then I recommend you use Sage, but note that you will need both of these files, since the matrices are computed in magma and then sent to sage where you can get the slopes. You can look at the files to see the instructions on how to use the code. Also don't rename the files, unless you want to change the names in the sage code.
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MSci Project: This is my fourth year project titled: On the Langlands correspondence for algebraic tori. I did this at Imperial College under the supervision of Kevin Buzzard. It is based on a paper by R. Langlands called Representations of Abelian Algebraic Groups. Basically it is setting the ground work for what is known as the abelian or GL1 case of the Langlands program. In my project I generalize his results to work for the GL1 case of the p-adic Langlands program. It starts with a short exposition on Group Cohomology and a very brief introduction to Class Field Theory, and it ends with a short explanation of how Langlands ideas can be used to generalize Class Field Theory. Eventually it turned into this:
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Would you like a simple congruence condition on a prime number which guarantees it can be written in the form x^2+ny^2 for certain n? Then look no further, just click here
Also in my first year as an undergrad student I found myself needing to factor the following 150 digit number. It took my laptop 1 month of running at 100% to complete and it died shortly after, so in its memory I have the number and it factors:
9209927592397944934920379845651267773097680921924769291116603583273617641456927248867317822193720416353231538795723470673266303828 99130751718966390493
Factors: 979863517748281070738228384371465939352816287338433450546979231984403057791 and 939919430163324037588145448416699718267248619754167542463564282295611164323