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There are no contemporary accounts. Even the gospels themselves are written decades after the death of Jesus and are not first hand accounts. There are a few historical sources (most notably Josephus) which are interesting because they mention Jesus and are independent of the gospels. The faq have a lot of discussions around these sources. But they the don't have a lot of information anyway. The most important source to the life of Jesus remains the gospels.
Sadly we don't have any court record stating "A guy named Jesus was crucified today for such and such offences". We dont even know exactly what year he was crucified.