Turing's Game

y=f(x)=(x+a)(x+b)

"x" and "y" are variables.

"a" and "b" are integer constants greater than -100 and less than +100.

Here are your data points:

When x = 1, y = -1386.

When x = 2, y = -1444.

When x = 3, y = -1500.

When x = 4, y = -1554.

When x = 5, y = -1606.

When x = 6, y = -1656.

When x = 7, y = -1704.

When x = 8, y = -1750.

When x = 9, y = -1794.

When x = 10, y = -1836.

When x = 11, y = -1876.

When x = 12, y = -1914.

When x = 13, y = -1950.

When x = 14, y = -1984.

When x = 15, y = -2016.

When x = 16, y = -2046.

When x = 17, y = -2074.

When x = 18, y = -2100.

When x = 19, y = -2124.

When x = 20, y = -2146.

When x = 21, y = -2166.

When x = 22, y = -2184.

When x = 23, y = -2200.

When x = 24, y = -2214.

When x = 25, y = -2226.

Find "a" and "b".