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Please note that your utm_geo() routine provided to convert long/lat to UTM coordinates contains two 2 mistakes:

source file: utm_geo.f90

line 95:

wrong: f3=15.d0*e4/256.d0*45.d0*e6/1024.d0
correct would be: f3=15.d0*e4/256.d0 + 45.d0*e6/1024.d0

line 160:

wrong: f3=5.d0*3.d0*t1+10.d0*c1-4.d0*c1**2-9.d0*ep2
correct would be: f3=5.d0 + 3.d0*t1+10.d0*c1-4.d0*c1**2-9.d0*ep2

the above corrections could be verified by looking at the original publication:
Snyder, J.P., Map projections - a working manual, USGS professional paper 1395, 1987
https://doi.org/10.3133/pp1395

line 95 mistake/correction: see page 61, eq. 3-21 for M
line 160 mistake/correction: see page 63, eq. 8-17 for phi

the above error will lead to a positional error of ~7 m when converting lon/lat to UTM.

best regards,
daniel