Not being a Chrome user myself, I find it surprising to hear that they to this day still only show the SHA1 fingerprint, especially since they (Google) are pushing for more TLS/encryption on the Internet you'd think they would be on top of this already.
I use Firefox and they do show both SHA1 and SHA256 fingerprints in the Certificate Viewer window.
Also, ZNC shows the SHA256 fingerprint when connecting to a server which uses self-signed certificates.
