Folk tradition gives the basilisk a gaze that turns others to stillness, and dreams of it are read as a look, a judgement or a fear that freezes you. It points to what you cannot bring yourself to face directly.
Does the traditional reading fit your dream, or did it mean something else to you?
My Cosmic Code has a private dream journal. Write a dream down and the app picks out the symbols in it, shows what dream books say about them and, over time, which words recur across your entries. The journal is stored on your device only.