My problem is to find a interpolating cubic spline to the points
$$\left\{(-2022,8043), (-4, 1989), (-2,1983), (0, 1977), (1, 1974), (3, 1968),(2022,-4089)\right\}$$
I know I can use a formula here or a naively solve it using or using a system of equations with 4n unknown variables, however my teacher told me that there is a way to solve it faster without too many calculations.Any ideas how to hack it?