Restoring lost encrypted partition

Restoring lost encrypted partition

I accidantally formatted the entire hard disk (quick format into NTFS)

it contains multiple partitions of different filesystem

1. ext4 encrypted with luks (whole partition encryption)
2. ext4 no encrypted
3. ntfs not encrtpted

I restored partition (ext4 no encrypted) & (ntfs not encrtpted) using testdisk but it seems complicated restoring the encrypted partition which is the partition that contains important files,

I searched for LUKS using grep and it shows many lines containing 'LUKS',

here is the first line:

9f175110 c5 df 3c de b8 a7 f1 cb 36 0a e9 e9 4c 55 4b 53 |..<.....6...LUKS|

I tried losetup then cryptsetup but cryptsetup shows an error:

Device /dev/loop is not a valid LUKS device

the encrypted partition shows on testdisk (it shows total size of partition, size of stored data , and partition label name):

                           start      End    size in sectors
 D Linux filesys. data         2046  591900669  591898624 
 D Linux filesys. data         2048  591900671  591898624

can someone help please??!