code: def index2poly(self, index):
          
  
          n = self._index2n(index)
  
          num_prev = n * (n + 1) / 2
          num = index + 1
          delta = int(num - num_prev - 1)
          if n % 2 == 0:
              if delta == 0:
                  m = delta
                  complex_bool = False
              elif delta % 2 == 0:
                  complex_bool = True
                  m = delta
              else:
                  complex_bool = False
                  m = delta + 1
          else:
              if delta % 2 == 0:
                  complex_bool = False
                  m = delta + 1
              else:
                  complex_bool = True
                  m = delta
          return n, m, complex_bool
docs: manages the convention from an iterative index to the specific polynomial n, m, (real/imaginary part)
  
          :param index: int, index of list
          :return: n, m bool