The challenge is the following,
We are also given the file message.txt which contains,
145 167 233 272 344 91 395 393 433 92 77 414 344 318 420 263 87 186 96 103 91 354 161
I followed what the challenge said, and applied mod 41 to each number and took the modular inverse using this Online Modular Multiplicative Inverse Calculator,
28 14 22 30 18 32 30 12 25 37 8 31 18 4 37 29 33 28 3 2 32 30 27
The number to character map used here is,
A: 1
B: 2
C: 3
D: 4
E: 5
F: 6
G: 7
H: 8
I: 9
J: 10
K: 11
L: 12
M: 13
N: 14
O: 15
P: 16
Q: 17
R: 18
S: 19
T: 20
U: 21
V: 22
W: 23
X: 24
Y: 25
Z: 26
0: 27
1: 28
2: 29
3: 30
4: 31
5: 32
6: 33
7: 34
8: 35
9: 36
_: 37
After I mapped the numbers to their respective characters, I got,
1 N V 3 R 5 3 L Y _ H 4 R D _ 2 6 1 C B 5 3 0
Therefore, the flag is,
picoCTF{1NV3R53LY_H4RD_261CB530}