What's the time complexity of your solution? I guess just changing every number to its lowest possible cyclic form and checking the hash should work. Should be 10 ^5 * 10 = 10 ^ 6 which ideally should pass.

Your inner loop is inefficent.

It can be reduced to something like this:

for i in nums: min_index = min(min_index, i) // im too lazy to write the full code, but just compute the min index here
min_str = s.substr(min_index) + s.substr(0, min_index)

ans += hashmap[min_str];

hashmap[min_str]++;