The Pisano period

The Fibonacci series starts with [0, 1, 1, 2, ...] and has ever increasing numbers further down the series. If you take these numbers modulo n, then the series will eventually become periodical.

This is called the Pisano period π(n). The series of Pisano numbers for n = [1, 2, 3, ...] is A001175.

The challenge

Write a function get_pisano_numbers() in Python, which for a list of numbers n returns the corresponding list of π(n). For example, get_pisano_numbers([1,3]) would return [1,8].

The winner is the function that is both the shortest and the fastest.

The rules

• The software used is Python 3.11. Only modules from the standard library can be used, no numpy or other dependencies.
• A submission should be a standalone .py file.
• The score is the sum of the file size in bytes and the time to execute get_pisano_numbers() in miliseconds. Lower score wins.
• Before scoring, the .py files are processed by autopep8 --max-line-length 99999, in order to limit tricks with removal of whitespace to some degree.
• The input is a list of randomly chosen numbers from the range 2..6000. The list is 400 numbers long and the same for each submission.
• The code is executed on a 16 core AMD CPU.

Examples

As an example there are two implementations in the repository, together with a test script that executes them and prints a score. Output of test.py:

    NAME                    RESULT    TIME    SIZE   SCORE
    pisano_example1         PASS         0   33004   33004
    pisano_example2         PASS    397668     794  398462

The first example includes all Pisano periods for 1..6000 hardcoded in the source. This makes the execution very fast, but has a high score because of the file size.

The second example calculates all the requested numbers. This is a lot smaller, but execution takes a very long time.