Magenta Corporation wants to raise $$51\mathrm{.}3$ million in a seasoned equity offering, net of all fees. Magenta stock currently sells for $$10$ per share. The underwriters will require a spread of $$0\mathrm{.}5$ per share, and indicate that the issue must be underpriced by $5$ percent. In addition to the underwriter's fee, the firm will incur $$2,300,000$ in legal, accounting, and other costs. How many shares must Magenta sell?

Note: Enter your answer in millions rounded to $3$ decimal places.

$5\mathrm{.}700$ million