X,Y to Lon, Lat conversion for New Zealand Transverse Mercator 2000

Hello, I need to convert X,Y coordinates in meters in the New Zealand Transverse Mercator 2000 projection (NZTM2000) to Lon, Lat values. NZTM2000 is based on the New Zealand Geodetic Datum 2000 (NZGD2000), the reference ellipsoid for which is GRS-80. Below are the details of the projection:

Origin latitude: 0° 00’ S
Origin longitude: 173° 00’ E
False northing: 10,000,000 meters N
False easting: 1,600,000 meters E
Central meridian scale factor: 0.9996

It does not seem like NZDG2000 is a datum supported by GMT, but I should be able to convert to lon, lat because I have the reference ellipsoid and the above information, correct? I have tried the following command:

gmt mapproject MOBIL_BasementPicks_NZTM2000.dat -R165.3/167/-46.7/-44.5 -Jt173/0.9996 -C1600000/10000000 -EGRS-80 -Qe -F -I -V > MOBIL_BasementPicks_NZGD2000_ll.dat

but it gives the error:

mapproject: Malformed or unrecognized <datum> argument (GRS-80)!

How do I specify it is the ellipsoid, not the datum that I am giving it? The -E option specifies it can take either. I suspect perhaps it is because I have not given it dx,dy,dz? If so, what are or where can I find those values for GRS-80? More generally, is this the correct way to convert NZTM X,Y values to Lon, Lat. I am using gmt 5.4.4. Thank you.

-EH

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