I'm going to coin some numbers, based on the heaven and the hell.
Immortial = 3 {365} 7 (Class 7: Up-arrow notation level)
Paradise = {5, 12, 16, 17} in BEAF (Class 8: Linear omega level)
Promised = {22, 51, 69, 77, 99} in BEAF (Class 9: Quadratic omega level)
Atmosphere = {100, 108, 130, 288, 449, 500} in BEAF (Class 10: Polynomial omega level)
Bliss = {517, 555, 569, 571, 700, 777, 800} in BEAF (Class 10: Polynomial omega level)
Dream = {841, 888, 900, 903, 936, 999, 1000, 1010} in BEAF (Class 10: Polynomial omega level)
Eternal = {1100, 1111, 1250, 1369, 1500, 1767, 1954, 2000, 2024, 2100} in BEAF (Class 10: Polynomial omega level)
Fairy = {2121, 2160, 2200, 2222, 2323, 2424, 2567, 2880, 2900, 3000, 3001} in BEAF (Class 10: Polynomial omega level)
Glory = {3062, 3500, 4176, 5000, 5200, 5432, 5454, 5555, 5678, 6000, 6500, 7000} in BEAF (Class 10: Polynomial omega level)
Happiness = {7121, 7200, 7500, 7777, 8000, 8250, 8311, 8888, 8989, 8999, 9000, 9123, 9999} in BEAF (Class 10: Polynomial omega level)
M̶̹̜̤̮̻̏̀̂͂̿a̸̢̢͈͚̺͈̬͋̂̒́̋͂͜ͅl̶̢͍͇͎̞̗̖̍̀͐͜i̷̯̱͍͙̒̆̉̿̃̉́̔̿͑̾̾͘͝c̶̡̜̯̥͉̳̺̰̰͊̍̈́é̵̡̨̜͍̝͙͈̩̖͔͇̫̉͆̉͂̈̉̇̅̃̂̈́ (Malice) = {666, 10 (1) 2} (Class 10: Polynomial omega level)
F̵̧̢̹̮͈̞̳̲̫̘͎̣̻͑́̿͋̿̀̄̐̒́̾̒̕͠͝e̸̡̯̙͕̮͈̙̳̭̮̊̐̉̌̇͒̇̓̈̂͛͐̃͑̌̈́̿ͅȧ̵̧̙̹͙̥͇̞͍̫̖̜̓̈́̃̊̏͐͜͝͠r̵̨̧̜͖̺̗͍͚̫̮͓̜̥̠͙̺͎̍͊̂͊̋ (Fear) = {666, 666 (1) 2} (Class 10: Polynomial omega level)
W̶̡̖͔̾́́̆̑́̍͐͗̽͋͑͒͛͘͝r̵̛̮̗͕̔̎̈̈́̃͆̓̋̃͋̌̈̎̎͐̕͠a̷̡̡̨̱̱̱̜͓̲͍̘̳̭̫͂̂̑̂͌̉̊́̉͆͋͜͝͝ẗ̴̥͇̖͖͍̯̣͈̩̫́͑̌͒͐̀̊͂̔͜ẖ̶̢͖͉͙͓͍̥̘̙̱͉̙̖̫̼̉̍͆̐́̇͌̕ (Wrath) = {666, 666, 666 (1) 2} (Class 11: Exponentiated linear omega level)
H̶̼̖̖͈̖͇̪̝̤̺̼̬̳̳̼͔̥̒͋̒̈̄͑̈́̈̐́̃̋̃̚̚͠͝͝à̶̛̛͖͈͎̮͉͖̺̲͇͕̳̬̻̩͔̻̻́͋͋͒̍̈́̚͘͘͝ͅt̴̛̼̏͐̓͂͂̾̅̋́͗̐̒̍̕̕͝ř̷̩͋̑͌͐̌̀̈́̈́̔̍̃̆̚͘͝ȅ̸̡̧̼̰̟̣̖͚̯̥͈̼̗̻͔̓̀̏̍͒̄͛̑̅͆̎ͅḓ̷̨̨̨̙̗̥̖̩̺̲̣̞̙̳̺̣͕̖̹̂̾̃͗̊̚ͅ (Hatred) = {666, 666, 666 (1) 666} ((Class 11: Exponentiated linear omega level)
D̷̞͕̺̗̠͙̼̄̊̀̈͋̇̏̋̅͝͠e̷̛̼̩̞̬̺̪̱͚̘̙͊͘̕s̷̛͈͎̝͙̈́̇̐̆̔p̷̪̥͊à̶̢̡̤͉͖̺̹̝̞̥̻̠͇̆͒̏͋̅͐͐͒̉̇̃̿͌̈̅͆̓̎͒̓̎̆į̷̧̪͍͔̭͔͔̲̦̳̦̖͓̦͌̌̈́͋̓͂̊̀̎̽̽̓̈̈̅̾͑̿͆͘͝͠͝ṙ̸̫̪̝̯̫̮̤̲͎̘̰̜͎̓̃̈́̔̐̄͑̾̅̓̎͑̑͊̇̈́̕̕͝͝͠ (Despair) = {666, 666, 666 (1) 666, 666, 666} (Class 11: Exponentiated linear omega level)
S̶̛̛̱̖͗̈́̈́̓̐̒́̈́̅̂̋̍͜t̴̩̘̯̮͎̥̜̰̼̖̼̺̱̘̞͓̗͉̺̪́̋͐͛̀͊͐͑́́̓́̎̐̚͜r̶̨̰̻͖͍̻̣̆̍͐̒̉͌̽̊̐̂̂͝i̵̛̹̦̦̒̑͛͂̀́̃̋̀̓̽̄͐͌̓͝͝f̷̛̱̜̖̩̙̫̖̩͚́͒͊̐̑̓̏̋̒̈́͋̔͑͐̈́̑̀͛̀͘͝ẹ̵̡̢̡̦͕̜̲̤̝̙̞̗̗̰̹̠̜͐͋̏̎̏͜ͅ (Strife) = {666, 666, 666 (1) 666, 666, 666 (1) 666, 666, 666} (Class 11: Exponentiated linear omega level)
B̸̰̦͕͓̱͖̗̋ͅĺ̸͉̼̜͐̈̆̾͐̀͆̈́͂̆̉̔̓̒̆͗̽͛̓́̋̈̚ǫ̴̧̲̠̹̬̰͔͔̖̖̋̈́̈́̓̊̂̈́͗̈o̵̢͈̟͎̟̱̫̰͈̻̞͔̜͉̦̟̲̥̖̩̤͔͖͋̉͑̋̈́͊̈́́̉̾̐̓̆̓̄̉͛̀̕͝͝d̷̼̣͖̀̉̽̊̀̐̉̓͂͊͂́̋͝͝͝t̵̢̨̡̬͔͍̔̆̀̈̏̀͊̀͊̊͂̂̑̓̕͝ḫ̶̨̼̭͒̑̽̌̅̈́̅̓̄́̀̐͗̀̊̀̓͘͘͠r̴̡̧̨̼̞͍̥͉̱̗̰̞͍̭̈́̈̎̊̑̈́̽̃i̶̲̟͍̪̹̪̰͈̘̖̝̲̞̘̦͇̭͇̜̿͜s̸̨̡̧̭̤̻̳̰̬͚̣̦͓̩͊͛̿̅͜t̸́̋̈́̓͑͊̔͂͠͝ͅ (Bloodthrist) = {666, 666, 666 (666) 666, 666, 666 (666) 666, 666, 666} (Class 12: Exponentiated polynomial omega level)
Ŗ̸̢̯̺̗̰̲͉͙̼̺̺̬̬͈͇̯̫̫͉̺̙͕̳̘͇͂͑̾́͒̄͂̒͆̿̀̎̿̋̈͛͘͘͠ͅͅu̴̹̮̤͐͗̑̐͆̈̿͂̓͒͋̽̏͆̅̀̎̋̌́̉̕͘͝i̴̛̛̦̯̰͇͕͓̩͖̗̰̥̓̅̒̊̆̌̅̃̐̓̈́̈́́̍͗̇̐̚̚̕͝͠͝͝ͅń̴̛̯̠͈̭͇̘̀͆̐̆̀́̐̂̒̇̇̄̈́̈́̈́̈́̒̀̒́͑̾̿̀̌̊͠ (Ruin) = {666, 666, 666 (666, 666, 666) 666, 666, 666 (666, 666, 666) 666, 666, 666} (Class 13: Double exponentiated polynomial omega level)
Ė̷̢̤͉̘͙̝̦̦̙̬̹̅̿͐́̒̔̓͘x̸͇͎͂͛̀t̸̠̞̿̇͑̍̾̇͂̔͌̾̐̎̅͋͂̈̈́̕̚e̴̡͍̣͉̟̬̭̪͍͖̦̳̅̿̍̈́̓̑̎̂̎̚͝ȓ̸̢̡̘̲̾̈̇̂̚m̴̢̨̧̧̢̨̢̤̘̹̘̜̝̜̮̤̦̗͇̩͖̦̟̺̰̯̖̣̜̓̂̓̑ͅi̴̢̠͈̺͋͆͆͊̐̑̾̌̎̋͋̔͐͌͗̏̄̉̒̒͘̚̕̚͠ͅn̶̡̳̩͙̲̰̬̓̓͛̃̐͌͝ă̶͓̈́̄̊́͛̓̃͂̆͑̓̄̃͛͛̑̽̎̍̒́̚͝͝͠t̶͍͎͉̟̓̈̑ī̸̧̛̛̯̠͔̻̟̘͍̾͋̒̎̆̋̽͋̈́̊̈͒̌̇͑̀̉̒͂͂͊̚͘͠͝͝͝ơ̵̡̡͎̮̥̳̝̪̙̟̱͎͕̰̮̬̖̙̗͍̬̤͍̤̯͚̺̦̈̾͌́̔̈́̉͠ṇ̶̡̡̨͔̦̰̪͖̰͖̳͖̺̺̰̠̩͔̼̩̮͍̌̆̀͛̎͊͆̆́̓͋́͛̑̄͑͋̌̊̄̓́̕̕̚͜͠͠ͅͅͅͅ (Extermination) = {666, 666, 666 (666 (666) 666) 666, 666, 666 (666 (666) 666) 666, 666, 666} (Class 15: Iterated Cantor normal form level)
Ę̵̛̪̘̞͉̑̑́̓̀̍͂̿͌̒̇̓͋̔̚̕̚͘ͅx̵̣͔͔̟͕̙̹̭̻̫̗̘̥̘̊̋ṱ̸̛̛̳̤̥͉̝̫̫̣̏̀̋͋̒̋̈́͑͆̃̅͒͆̊̉̊̏͌̍̾̃̍̔͂́͂̿̓̈́͗̀͋̆̽̋̅͑̕̕̕̕̕͝͝į̷̡̧̣̟̮͚̣͈̝̼͎͎͉̞̫͈̝̼̼̰͖̣͚̜̉̊̔̉͊̀͆͑͊͛̍͒̾̌͌̀̂͑͗͊̄͑̂́͗̊͒̏̌̑̈́̈́̊͂̃̕͝͝ͅn̶̢̲̠̝̬̬͕̣̙̭͍̼͕͓͕͖̩̯͔͓̰͖̯̺̪͚̈́́̍̄͊̓̐̑̇̏̃͌̌ͅͅc̶̢̧̨̡̧̡̧̛̤͙͖̭̯̘̘̭̘͖̠̪͉̠̱̫̺̖͚͎̅̈́͐̆̃͛̏͌̓͋̽͌͊͋͆̉͗̊͌̒̄̈́̊̑̽̿̕̕͠t̶̨̧̡̢̨͓͓͈̥̦̪̹̺̘͙̠̥̳̱̜̝̜̻̩̭̫͉̣̲̗̀̆́́͑̀̈́̏̔͊̾̑͊̅̃ͅï̸̡̢̧̱̙͚͖͍̤̙̯̳͇͕͈̱̝̯̝̺̭̘̠̰̭͓̯͔̬̮̬͎̥͙̰͍̭͉̰̫̝͔̝̬̲̮̏͒̓̅͌̈́̇̃̌͛͛̃̐̔̂̒͛͛̀̈̾͊͐́̾̇͒̎͋͐͘̕͠͝͠͠ͅò̴̠͎̙͎̥̟͌̐͒̋̎̎̑̉̀̈́͛͛̇̂̑̀̔͌͌͌̆̂̂̓̐̏̀́̚͝͝͠͠n̷̨̢̡̢̛̤͉̻͖̤͙̺̟̜̻̼̙͉̯̼̝̳̞̖̤̤͚̟̞͍͍̭̣̘̈́̄̊͆̈́̔̍̏̌͂̓ (Extinction) = X^^(X^^(X^^X & 666) & 666) & 666 = 666^^(666^^(666^^666 & 666) & 666) & 666 where X^^(a) & b = X^^c & b where c is the value of array a (Class 16: Epsilon level)