How was the Gamutmap data created? Which rendering intent did you use?  
Gamutmap was created using Adobe Photoshop with absolutely colorimetric rendering intent.

Why is the gray axis always displayed as H000 in any H table?  
Gray is gray, so we decided to leave the gray Axis as H000, but you can of course put in any H value - as long als C stays 0, it will be a neutral gray.

Can I assume that the colours here on my screen look correct?
A clear no. Colours over the web are very complex and not all browsers  display the colours the same way. sRGB, which is the internet standard, cannot display all LAB colours. If you have a colour-calibrated monitor and Adobe Acrobat Pro, it is worth downloading the free freeColour CIELAB HLC Colour Atlas XL. Otherwise you can also order a printed copy of the Atlas in our shop.

Can the printed freeColour CIELAB HLC Colour Atlas XL display all LAB colours?
No, the atlas shows a total of 13.383 colours with an accuracy for all colour swatches of Delta E00<1.

Gamutmap is really cool, but I still have suggestions for improvement. 
Write us at info@proof.de what you would miss or do better within gamutmap. We see gamutmap as a "work in progress", and would be happy if we could improve and expand gamutmap with your help.

I miss colour spaces in gamutmap
Write to us if you are missing individual colour spaces. We can quickly and easily add and integrate new colour spaces.