a = np.array([2.000040,
3.980832,
7.387186,
12.908319,
21.413612,
33.952858,
51.746601,
76.167656,
108.715561,
150.986023,
204.637451,
271.356506,
352.824493,
450.685791,
566.519226,
701.813354,
857.945801,
1036.166504,
1237.585449,
1463.163940,
1713.709595,
1989.874390,
2292.155518,
2620.898438,
2976.302246,
3358.425781,
3767.196045,
4202.416504,
4663.776367,
5150.859863,
5663.156250,
6199.839355,
6759.727051,
7341.469727,
7942.926270,
8564.624023,
9208.305664,
9873.560547,
10558.881836,
11262.484375,
11982.662109,
12713.897461,
13453.225586,
14192.009766,
14922.685547,
15638.053711,
16329.560547,
16990.623047,
17613.281250,
18191.029297,
18716.968750,
19184.544922,
19587.513672,
19919.796875,
20175.394531,
20348.916016,
20434.158203,
20426.218750,
20319.011719,
20107.031250,
19785.357422,
19348.775391,
18798.822266,
18141.296875,
17385.595703,
16544.585938,
15633.566406,
14665.645508,
13653.219727,
12608.383789,
11543.166992,
10471.310547,
9405.222656,
8356.252930,
7335.164551,
6353.920898,
5422.802734,
4550.215820,
3743.464355,
3010.146973,
2356.202637,
1784.854614,
1297.656128,
895.193542,
576.314148,
336.772369,
162.043427,
54.208336,
6.575628,
0.003160,
0.000000])

b = np.array([0.000000,
0.000000,
0.000000,
0.000000,
0.000000,
0.000000,
0.000000,
0.000000,
0.000000,
0.000000,
0.000000,
0.000000,
0.000000,
0.000000,
0.000000,
0.000000,
0.000000,
0.000000,
0.000000,
0.000000,
0.000000,
0.000000,
0.000000,
0.000000,
0.000000,
0.000000,
0.000000,
0.000000,
0.000000,
0.000000,
0.000000,
0.000000,
0.000000,
0.000000,
0.000014,
0.000055,
0.000131,
0.000279,
0.000548,
0.001000,
0.001701,
0.002765,
0.004267,
0.006322,
0.009035,
0.012508,
0.016860,
0.022189,
0.028610,
0.036227,
0.045146,
0.055474,
0.067316,
0.080777,
0.095964,
0.112979,
0.131935,
0.152934,
0.176091,
0.201520,
0.229315,
0.259554,
0.291993,
0.326329,
0.362203,
0.399205,
0.436906,
0.475016,
0.513280,
0.551458,
0.589317,
0.626559,
0.662934,
0.698224,
0.732224,
0.764679,
0.795385,
0.824185,
0.850950,
0.875518,
0.897767,
0.917651,
0.935157,
0.950274,
0.963007,
0.973466,
0.982238,
0.989153,
0.994204,
0.997630,
1.000000])