The information you actually need is the # of issued shares, which is some fraction of # of authorized shares. You will have to make an assumption as to what that fraction is. From personal experience running several startups, I would recommend using 70%.
So, you need to:
1) Find out what state your employer's corporation is registered in
2) Request annual report from state's entity search website (e.g. https://icis.corp.delaware.gov/Ecorp/EntitySearch/NameSearch...)
3) Calculate issued shares based on some assumed fraction of authorized shares.
Given that, I tend to join the group that value options in an early stage private company as "worthless". If the cash comp doesn't work for me, it's unlikely the options will move the needle as I'll probably need to be there 5-9 years to actually see a positive event and I'll need to do that 5-10 times to have a solid chance of a couple of meaningful wins. Of course, some of the failures you can drop out after a year or two, but it's still many decades to have a reasonable possibility of a return from options.
It's hard enough for VCs who do this for a living and can make 10-50 simultaneous bets to come out well ahead - and the good ones have access to insane deal flow and all the docs during due diligence. Good luck being confident that you will beat that serially with limited deal flow and limited due diligence access.
To be clear, a certain proportion of people here DID beat that and are doing great with stock options, but the odds are not in your favor . . .