2001 Cadillac STS GEAR RATIO.

I will give you what I have from GM service info, There is not a spec for RPM@Speed. Here is general info.
Transmission General Specifications
Transmission General Specifications (4T80-E) Name
Hydra-Matic 4T80-E

RPO Codes
MH1

Production Location
Willow Run, Ypsilanti, MI

Vehicle Platform, Engine/Transmission, Usage
E, G, K, Ksp

Transmission Drive
Transverse Mounted Front Wheel Drive

1st Gear Ratio
2.960:1

2nd Gear Ratio
1.626:1

3rd Gear Ratio
1.000:1

4th Gear Ratio
0.681:1

Reverse
2.130:1

Torque Converter Size, Diameter of Torque Converter Turbine
265 mm

Pressure Taps
Line Pressure

Transmission Fluid Type
DEXRON® III

Transmission Fluid Capacity, Approximate
Bottom Pan Removal: N/A

Complete Overhaul: 12.0 L (12.6 qts)

Dry: 14.2 L (15.0 qts)

Transmission Type: 4
Four Forward Gears

Transmission Type: T
Transverse Mount

Transmission Type: 80
Product Series

Transmission Type: E
Electronic Controls

Chain Ratios, Designates Number of Teeth on the Drive/Driven Sprockets
39/39

Final Drive Ratios
3.11, 3.71

Position Quadrant
P, R, N, Overdrive, 3, 2, 1