Developing LSTM neural networks that can accurately predict the future trajectory of ongoing cases and their remaining runtime is an active area of research in predictive process monitoring. In this work a novel complete remaining trace prediction (CRTP) LSTM is proposed. This model is trained to directly predict the complete remaining trace and runtime of cases in contrast to single event prediction as is considered in previously published research on this topic. This makes the CRTP-LSTM robust in terms of utilizing all available attributes of previously observed events for prediction, consequently it can be considered natively data aware. In an extensive experimental assessment the authors show that CRTP-LSTMs consistently outperform other considered approaches for both remaining trace and runtime prediction. Furthermore, the authors show that including all available information contained in previously observed events has a positive impact on the performance of the CRTP-LSTM model. This indicates that valuable information can be extracted from attributes of events in order to make more accurate trace and runtime predictions. This opens up interesting avenues for future research including the incorporation of inter-case features into a modeling setup when predicting the remaining trace and runtime of cases.