Numerical results for seven cases in the first group shown in Table 1. The diagram of each case consists of four panels: the electron distribution (upper left), the corresponding synchrotron flux density F_ν from electrons (upper right), the spectral energy distribution νF_ν (lower left), and light curves at three bands and the evolution of E_p (lower right). Notably, in the electron distribution, orange dashed lines are the standard fast-cooling pattern, i.e., , and gray dashed lines present the expected cooling pattern, i.e., . In the flux density, three vertical lines are given corresponding to three different frequencies of 300 keV, 10 keV, and 1 keV respectively. The peak energy E_p is derived from the peak point of νF_ν.