Trench Mystery Cache

This cache is a tribute to "Trench", the phenomenal fifth album released by Twenty One Pilots.   DO NOT go to the coordinates posted or you will find yourself stuck in a literal trench!

After two world tours for their wildly successful album "Blurryface" -- the first album to ever have each track achieve at least gold status, including Stressed Out and Ride which each have at least one billion views -- the band Twenty One Pilots (TØP for short) went on hiatus for a full year, shutting down their social media and refusing interviews.

During that year fans were taken on a virtual scavenger hunt (almost like a puzzle Geocache!), collecting clues and scraps of information that eventually built a conceptual world with characters and lore that tie many of the band's songs and albums together into one narrative.  

To get the true coordinates of this cache you will need to take note of twelve key details relating to the album "Trench".

S =  Number of people in Twenty One Pilots.
c =  Number of concerts during their Tour De Columbus in 2017.  Two weeks later the band "went dark" and did not interact on social media or communicate directly with their fans for the next 12 months.
a =  The month in 2017 when TØP officially began their hiatus by Tweeting images of a red eye closing and the lyric “NOW I JUST SIT IN SILENCE” from their song Car Radio.
L =  On this day in July 2017, Josh accepted an Alternative Press Music Award.  Tyler was "off severing ties with Dema" and couldn't be there.  No one understood what he meant by that.
e =  On this day in April 2018, fans found a URL hidden on the TØP merch store.  Over the next three months, maps of a world called Trench and its capital city Dema would be posted on the site along with journal entries from someone named Clancy who wanted to explore beyond the walls of Dema against the wishes of the ruling bishops.  The site was full of hidden codes, cryptic images, and messages with double meanings that would be developed in the album.
d =  On this day in July 2018, fans were sent the message "ARE YOU STILL SLEEPING?" with a yellow eye that was beginning to open.  Days later billboards popped up around the world with the band's new yellow logo.

A =  On this day in July 2018, the single Jumpsuit was released, officially ending the band's hiatus.
n =  Total number of singles released by TØP that day.
D =  Number of mathematicians who founded Nicolas Bourbaki.

i =  Number of bishops in Dema.
C =  Hue of the color #FCE300, which the bishops are unable to see.
y =  Atomic number of 5th song on Trench.

For the correct Latitude, replace the last 3 digits with the 3-digit result of this calculation:

\(\Large{A(C+a-e)+S-y-n}\)

For the correct Longitude, replace the last 3 digits with the 3-digit result of this calculation:

\(\Large{c\left(d+L - \frac{i}{D}\right)}\)

If you've done your homework and solved the puzzle, then the container should be obvious and can be "levitated" for easy logging. Lots of parking nearby.