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Since events are stored in the transaction receipts trie they should influence the gas a transaction costs since storage costs, right?

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The increase it by 375 + 375 * numberOfIndexedParameters + numberOfUnindexedBits.

For example:

event Event(uint16 indexed a, uint32 indexed b, uint64 c, uint128 d);
emit Event(1, 2, 3, 4);

The additional cost is 375 + 375 * 2 + 64 + 128.

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