Cleanup printout of spin

[awvwgk]

• neither number of electrons nor spin available at this point
• cleanup some unused printout (removes one random_number call, among other things...)

Closes #575

[codecov]

Codecov Report

Merging #576 (5cfc0b2) into main (885af2f) will not change coverage.
The diff coverage is n/a.

❗ Current head 5cfc0b2 differs from pull request most recent head 3ecea47. Consider uploading reports for the commit 3ecea47 to get more accurate results

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