Compressing the Atomic Ionization Energies
Clean, 540 bytes + 64.396 Penalty = 604.396

Note: for the sake of readability, I've escaped every byte in the [Char] literal as most of them are non-printable. However, they are counted as only one byte per escape (except the null, quote, and newlines) as Clean naturally takes source files encoding-independently (except nulls).

import StdEnv,GenLib
c[h:t]=[(toInt h&gt;&gt;i)rem 2\\i&lt;-[0..7]]++c t
c[]=[]
r[]=[]
r l=[7&lt;&lt;29+2^62+sum[d&lt;&lt;p\\d&lt;-l&amp;p&lt;-[32..53]]:r(drop 22l)]
u::Maybe[Real]
u=uncompress{e\\e&lt;-[108:r(c['\145\062\353\227\045\336\021\131\341\224\212\225\230\140\121\241\231\027\321\306\361\254\075\154\161\041\144\255\346\110\371\126\172\155\361\127\152\023\350\222\117\116\341\222\155\357\351\072\341\153\315\025\171\317\141\367\076\232\377\323\206\301\257\235\103\154\157\274\035\010\347\167\142\370\355\074\172\320\347\036\165\262\210\364\177\025\144\176\303\223\143\116\340\270\012\172\062\377\257\141\265\320\342\261\225\347\215\165\044\152\017\011\133\251\027\347\243\307\231\304\165\351\325\035\036\053\010\341\344\131\363\207\072\045\327\012\130\347\167\023\312\023\210\013\347\244\236\020\172\153\362\370\142\123\276\116\226\341\211\245\105\136\145\146\130\367\123\026\312\244\225\347\152\225\145\142\207\164\227\145\360\105\140\201\041\271\141\273\274\230\020\101\166\101\133\171\063\155\302\062\036\061\335\147\130\365\175\201\203\035\357\341\272\172\270\067\047\002\200\223\342\156\230\253\152\347\105\322\335\117\203\220\242\342\316\137\311\247\004\155\164\124\131\205\325\203\116\306\365\170\325\032\143\337\017\331\232\006\266\122\176\305\334\137\214\312\130\035\110\306\206\227\001\000\150\353\121\132\146\246\226\231\071\365\050\140\063\063\333\314\314\307\314\354\231\231\171'])]}


Try it online!

This is the first challenge where I've been able to utilize Clean's generic compression ability (technically not actually compression, it's binary serialization) to gain an actual benefit.

I started with a [Real] - a list of 64-bit floating-point numbers, those from the question. After serializing this list, I simplified the top 10 bits (which were the same for each number), and the optimal configuration of the bottom 32 bits into the constant 7&lt;&lt;29+2^62. The remaining 22 bits per number were translated into 2.75 characters each, and encoded in a string.

This leaves the entire compressed constant at only 302 bytes, including every escape!