Sorry, I'm not familiar with Singers although do know some models have a different needle system, such as slant while others use a slightly longer needle, which is not compatible with other makes of machines.
However in my Janome and Brother machines I would use a type HLX5 needle of size and tip to suit the fabric and thread. This type of needle has a heavier shaft which resists deflection when sewing difficult fabrics and/or while sewing at high speeds.
Can you phone your local Singer dealer to confirm which needle system your machine uses? Maybe join an online group for Singers, I'm sure they would know.
Sorry, I know I'm not much help but I haven't used a Singer for about a hundred years!! ;-))