7. Given that the line $a x+b y=2017$ intersects the circle $x^{2}+y^{2}=100$ at points where both the x-coordinate and y-coordinate are integers, then the number of such lines is $\qquad$.
The integer points on the circle $x^{2}+y^{2}=100$ are $(10,0),(8,6),(6,8),(0,10),(-6,8),(-8,6),(-10,0)$, $(-8,-6),(-6,-8),(0,-10),(6,-8),(8,-6)$, a total of 12 points. The tangents through these points are 12 lines, and the lines connecting any two points are $C_{12}^{2}=66$ lines, among which 6 lines pass through the origin.
Therefore, the number of lines $a x+b y=2017$ that satisfy the condition is 72.