How to center an existing JPG image as first page of existing PDF?

I would like to merge an existing JPG to an existing PDF in Format A4.
The picture has 649 x 1024 Pixels.

Unfortunately, I can't find the necessary option to CENTER such an existing JPG.
If I use
`-s A4 output_A4.pdf 1.jpg 1.pdf`
the picture will be truncated at the right side and at the bottom.
There is a small black border only on top and at the left side.

If I use
`-s A4 --scale-height --scale-width output_A4.pdf 1.jpg 1.pdf`
the picture is completely visible, but there is white margin.
There is a small black border on top, left, right and bottom.

If I use
`-s A4 --scale-width output_A4.pdf 1.jpg 1.pdf`
the picture is truncated at the bottom and the right side.
There is a small black border on top and left.

If I Use
`-s IMG-SIZE output_NEU.pdf 1.jpg 1.pdf`
the pictures appears as wanted, but the PDF itself is not A4 anymore,
it has a size - according to Acrobat Reader - of 229.0 x 361.2 mm.
The wanted A4 only has 210 x 297 mm.

What can I do do get an A4 PDF with a complete, centered (not truncated) picture?