Does Gertrude share in Claudius’s guilt? I need quotation and explanation

I think that it is fairly accepted that Gertrude knew nothing about the murder of her late husband until Hamlet informed her in act 3. In that context, she does not share this guilt. Claudius does have guilt or at least fear of judgment from God.

KING: Try what repentance can. What can it not? Yet what can it when one can not repent? O wretched state! O bosom black as death! O limèd soul that, struggling to be free, Act 3 sc 3.

Gertrude may feel some guilt for marrying so soon after her husband's death but is surprised to hear about her husband's murder.

Gertrude: What have I done, that thou darest wag thy tongue In noise so rude against me? Act 3 sc 4