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I've done the simple but tedious first step of solving for the variables, which I assume is part of the puzzle.
1. 81β - 41Δ + 34μ + 64φ = 801
2. 41β - 41Δ + 56μ + 44φ = 3
3. 25β - 33Δ + 35μ + 54φ = 68
4. 63β - 24Δ + 30μ + 51φ = 6000
Ω cancels out of every equation.
β = 68
Δ = 553
μ = 231
φ = 158
I've thought a bit about the puzzle, but haven't really come up with anything at this point. Since Ω cancels out of each equation, I imagine it has some sort of other significance. I've thought about using congruence, but don't know where the Ω would fit in. Also, the fact that the variables are split up and parentheses are used might have some significance.