I am looking for FANTOM gene expression data. But I could only find transcript expression in this website: http://fantom.gsc.riken.jp/5/datafiles/reprocessed/hg38_latest/extra/CAGE_peaks_expression/
I previously downloaded from here http://fantom.gsc.riken.jp/5/datafiles/latest/extra/CAGE_peaks/, as recently as just a few months ago, and they have expression data over genes.
The FANTOM5 data has different promoter expression levels for each gene (CAGE, used by FANTOM, doesn't measure mRNA levels as per RNA-seq and instead measures the 5' cap mRNA, i.e. promoter activity and the transcription start site), generally going from p1-p4. p1 is the peak with the strongest signal and it is recommended to take that. It is a risky idea to average over the promoter expression levels because many genes will have 0 expression at p2-p4 (hint: you could try averaging over only those peaks that have non-zero expression).