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What supply voltage do you have available? If just 5V you need to use a rail-to-rail op-amp. If higher like 12V you can use a common op-amp.
Btw, you need to decrease the signal -0.35V first, then amplify it x1.2 around middle (2.5V).
Btw, you need to decrease the signal -0.35V first, then amplify it x1.2.