On the zeros of certain modular functions for the normalizers of   congruence subgroups of low levels I
  We research the location of the zeros of the Eisenstein series and the modular functions from the Hecke type Faber polynomials associated with the normalizers of congruence subgroups which are of genus zero and of level at most twelve.   In Part I, we will consider the general theory of modular functions for the normalizers. 
Junichi Shigezumi