Post History

# [Pyth], 16 bytes

    .^RtJ^2yTyJ%2S97

[Try it online!][TIO-lt94lmtp]

This solution uses [Euler's formula](https://en.wikipedia.org/wiki/Modular_multiplicative_inverse#Using_Euler's_theorem), which states that if a is coprime to m,

    a^(phi(m)-1) = a^-1 mod m

where phi(m) is the totient function, the number of integers in the range [1, m-1] that are coprime to m. For a power of 2, this is m/2.

Using this formula, I calculate the modular inverse of the odd numbers 1-97 with the modulus 2^21, because it makes the code shorter.

    .^RtJ^2yTyJ%2S97
                 S97    Generate the list 1, 2, ..., 97
               %2       Take every other number, the odd ones.
    .^R                 Map the modular exponentiation function over the list,
                        with the odd numbers as the base
        J^2yT           Calculate 2^20 and save it in J.
       t                Exponent of J-1
             yJ         Modulus of 2*J

[Pyth]: https://github.com/isaacg1/pyth
[TIO-lt94lmtp]: https://tio.run/##K6gsyfj/Xy8uqMQrzqgypNJL1SjY0vz//3/5BSWZ@XnF/3VTAA "Pyth – Try It Online"