#      energy          pdf          cdf
      5.55906    0.0182402        0.005
      5.83318    0.0310083       0.0135
       6.1073     0.098497       0.0405
      6.38142     0.202466        0.096
      6.65554     0.271779       0.1705
      6.92966     0.357508       0.2685
      7.20378     0.483365        0.401
       7.4779     0.481541        0.533
      7.75202     0.465125       0.6605
      8.02614     0.328323       0.7505
      8.30026     0.279075        0.827
      8.57438     0.193346         0.88
       8.8485     0.144097       0.9195
      9.12262     0.122209        0.953
      9.39674    0.0601926       0.9695
      9.67086    0.0437764       0.9815
      9.94498    0.0218882       0.9875
      10.2191    0.0200642        0.993
      10.4932    0.0145921        0.997
      10.7673   0.00364804        0.998
      11.0415   0.00182402       0.9985
      11.3156            0       0.9985
      11.5897   0.00364804       0.9995
      11.8638            0       0.9995
      12.1379   0.00182402            1