/* Orion Sky Lawlor, olawlor@acm.org, 9/23/2000 Computes the Legendre Polynomial P upper (1) lower n at z; via the Pi lower n / Tau lower n recursion. The two are related by: P_n(z) = sin(acos(z)) * Pi_n (z) d P_n(z) /dz = Tau_n (z) */ #include #include #include class legendre { public: //Compute Pi and Tau of order n at z static void piTau(int n,double z,double *pi,double *tau); }; /*Compute Pi and Tau of order n at z using simple recurrence relation. */ void legendre::piTau(int n_stop,double z,double *pi,double *tau) { double p[4],d[4]; p[0]=0; d[0]=0; p[1]=1; d[1]=0; p[2]=3*z; d[2]=3; int n=2; if (n>=n_stop) n=n_stop; else while (n <@> ******** Program output: ******** <@> Psi0(-1.000)=0.000000e+00 tau=-0.000000e+00 <@> Psi0(-0.950)=0.000000e+00 tau=-0.000000e+00 <@> Psi0(-0.900)=0.000000e+00 tau=-0.000000e+00 <@> Psi0(-0.850)=0.000000e+00 tau=-0.000000e+00 <@> Psi0(-0.800)=0.000000e+00 tau=-0.000000e+00 <@> Psi0(-0.750)=0.000000e+00 tau=-0.000000e+00 <@> Psi0(-0.700)=0.000000e+00 tau=-0.000000e+00 <@> Psi0(-0.650)=0.000000e+00 tau=-0.000000e+00 <@> Psi0(-0.600)=0.000000e+00 tau=-0.000000e+00 <@> Psi0(-0.550)=0.000000e+00 tau=-0.000000e+00 <@> Psi0(-0.500)=0.000000e+00 tau=-0.000000e+00 <@> Psi0(-0.450)=0.000000e+00 tau=-0.000000e+00 <@> Psi0(-0.400)=0.000000e+00 tau=-0.000000e+00 <@> Psi0(-0.350)=0.000000e+00 tau=-0.000000e+00 <@> Psi0(-0.300)=0.000000e+00 tau=-0.000000e+00 <@> Psi0(-0.250)=0.000000e+00 tau=-0.000000e+00 <@> Psi0(-0.200)=0.000000e+00 tau=-0.000000e+00 <@> Psi0(-0.150)=0.000000e+00 tau=-0.000000e+00 <@> Psi0(-0.100)=0.000000e+00 tau=-0.000000e+00 <@> Psi0(-0.050)=0.000000e+00 tau=-0.000000e+00 <@> Psi0(0.000)=0.000000e+00 tau=0.000000e+00 <@> Psi0(0.050)=0.000000e+00 tau=0.000000e+00 <@> Psi0(0.100)=0.000000e+00 tau=0.000000e+00 <@> Psi0(0.150)=0.000000e+00 tau=0.000000e+00 <@> Psi0(0.200)=0.000000e+00 tau=0.000000e+00 <@> Psi0(0.250)=0.000000e+00 tau=0.000000e+00 <@> Psi0(0.300)=0.000000e+00 tau=0.000000e+00 <@> Psi0(0.350)=0.000000e+00 tau=0.000000e+00 <@> Psi0(0.400)=0.000000e+00 tau=0.000000e+00 <@> Psi0(0.450)=0.000000e+00 tau=0.000000e+00 <@> Psi0(0.500)=0.000000e+00 tau=0.000000e+00 <@> Psi0(0.550)=0.000000e+00 tau=0.000000e+00 <@> Psi0(0.600)=0.000000e+00 tau=0.000000e+00 <@> Psi0(0.650)=0.000000e+00 tau=0.000000e+00 <@> Psi0(0.700)=0.000000e+00 tau=0.000000e+00 <@> Psi0(0.750)=0.000000e+00 tau=0.000000e+00 <@> Psi0(0.800)=0.000000e+00 tau=0.000000e+00 <@> Psi0(0.850)=0.000000e+00 tau=0.000000e+00 <@> Psi0(0.900)=0.000000e+00 tau=0.000000e+00 <@> Psi0(0.950)=0.000000e+00 tau=0.000000e+00 <@> Psi1(-1.000)=1.000000e+00 tau=-1.000000e+00 <@> Psi1(-0.950)=1.000000e+00 tau=-9.500000e-01 <@> Psi1(-0.900)=1.000000e+00 tau=-9.000000e-01 <@> Psi1(-0.850)=1.000000e+00 tau=-8.500000e-01 <@> Psi1(-0.800)=1.000000e+00 tau=-8.000000e-01 <@> Psi1(-0.750)=1.000000e+00 tau=-7.500000e-01 <@> Psi1(-0.700)=1.000000e+00 tau=-7.000000e-01 <@> Psi1(-0.650)=1.000000e+00 tau=-6.500000e-01 <@> Psi1(-0.600)=1.000000e+00 tau=-6.000000e-01 <@> Psi1(-0.550)=1.000000e+00 tau=-5.500000e-01 <@> Psi1(-0.500)=1.000000e+00 tau=-5.000000e-01 <@> Psi1(-0.450)=1.000000e+00 tau=-4.500000e-01 <@> Psi1(-0.400)=1.000000e+00 tau=-4.000000e-01 <@> Psi1(-0.350)=1.000000e+00 tau=-3.500000e-01 <@> Psi1(-0.300)=1.000000e+00 tau=-3.000000e-01 <@> Psi1(-0.250)=1.000000e+00 tau=-2.500000e-01 <@> Psi1(-0.200)=1.000000e+00 tau=-2.000000e-01 <@> Psi1(-0.150)=1.000000e+00 tau=-1.500000e-01 <@> Psi1(-0.100)=1.000000e+00 tau=-1.000000e-01 <@> Psi1(-0.050)=1.000000e+00 tau=-5.000000e-02 <@> Psi1(0.000)=1.000000e+00 tau=3.191891e-16 <@> Psi1(0.050)=1.000000e+00 tau=5.000000e-02 <@> Psi1(0.100)=1.000000e+00 tau=1.000000e-01 <@> Psi1(0.150)=1.000000e+00 tau=1.500000e-01 <@> Psi1(0.200)=1.000000e+00 tau=2.000000e-01 <@> Psi1(0.250)=1.000000e+00 tau=2.500000e-01 <@> Psi1(0.300)=1.000000e+00 tau=3.000000e-01 <@> Psi1(0.350)=1.000000e+00 tau=3.500000e-01 <@> Psi1(0.400)=1.000000e+00 tau=4.000000e-01 <@> Psi1(0.450)=1.000000e+00 tau=4.500000e-01 <@> Psi1(0.500)=1.000000e+00 tau=5.000000e-01 <@> Psi1(0.550)=1.000000e+00 tau=5.500000e-01 <@> Psi1(0.600)=1.000000e+00 tau=6.000000e-01 <@> Psi1(0.650)=1.000000e+00 tau=6.500000e-01 <@> Psi1(0.700)=1.000000e+00 tau=7.000000e-01 <@> Psi1(0.750)=1.000000e+00 tau=7.500000e-01 <@> Psi1(0.800)=1.000000e+00 tau=8.000000e-01 <@> Psi1(0.850)=1.000000e+00 tau=8.500000e-01 <@> Psi1(0.900)=1.000000e+00 tau=9.000000e-01 <@> Psi1(0.950)=1.000000e+00 tau=9.500000e-01 <@> Psi2(-1.000)=-3.000000e+00 tau=3.000000e+00 <@> Psi2(-0.950)=-2.850000e+00 tau=2.415000e+00 <@> Psi2(-0.900)=-2.700000e+00 tau=1.860000e+00 <@> Psi2(-0.850)=-2.550000e+00 tau=1.335000e+00 <@> Psi2(-0.800)=-2.400000e+00 tau=8.400000e-01 <@> Psi2(-0.750)=-2.250000e+00 tau=3.750000e-01 <@> Psi2(-0.700)=-2.100000e+00 tau=-6.000000e-02 <@> Psi2(-0.650)=-1.950000e+00 tau=-4.650000e-01 <@> Psi2(-0.600)=-1.800000e+00 tau=-8.400000e-01 <@> Psi2(-0.550)=-1.650000e+00 tau=-1.185000e+00 <@> Psi2(-0.500)=-1.500000e+00 tau=-1.500000e+00 <@> Psi2(-0.450)=-1.350000e+00 tau=-1.785000e+00 <@> Psi2(-0.400)=-1.200000e+00 tau=-2.040000e+00 <@> Psi2(-0.350)=-1.050000e+00 tau=-2.265000e+00 <@> Psi2(-0.300)=-9.000000e-01 tau=-2.460000e+00 <@> Psi2(-0.250)=-7.500000e-01 tau=-2.625000e+00 <@> Psi2(-0.200)=-6.000000e-01 tau=-2.760000e+00 <@> Psi2(-0.150)=-4.500000e-01 tau=-2.865000e+00 <@> Psi2(-0.100)=-3.000000e-01 tau=-2.940000e+00 <@> Psi2(-0.050)=-1.500000e-01 tau=-2.985000e+00 <@> Psi2(0.000)=9.575674e-16 tau=-3.000000e+00 <@> Psi2(0.050)=1.500000e-01 tau=-2.985000e+00 <@> Psi2(0.100)=3.000000e-01 tau=-2.940000e+00 <@> Psi2(0.150)=4.500000e-01 tau=-2.865000e+00 <@> Psi2(0.200)=6.000000e-01 tau=-2.760000e+00 <@> Psi2(0.250)=7.500000e-01 tau=-2.625000e+00 <@> Psi2(0.300)=9.000000e-01 tau=-2.460000e+00 <@> Psi2(0.350)=1.050000e+00 tau=-2.265000e+00 <@> Psi2(0.400)=1.200000e+00 tau=-2.040000e+00 <@> Psi2(0.450)=1.350000e+00 tau=-1.785000e+00 <@> Psi2(0.500)=1.500000e+00 tau=-1.500000e+00 <@> Psi2(0.550)=1.650000e+00 tau=-1.185000e+00 <@> Psi2(0.600)=1.800000e+00 tau=-8.400000e-01 <@> Psi2(0.650)=1.950000e+00 tau=-4.650000e-01 <@> Psi2(0.700)=2.100000e+00 tau=-6.000000e-02 <@> Psi2(0.750)=2.250000e+00 tau=3.750000e-01 <@> Psi2(0.800)=2.400000e+00 tau=8.400000e-01 <@> Psi2(0.850)=2.550000e+00 tau=1.335000e+00 <@> Psi2(0.900)=2.700000e+00 tau=1.860000e+00 <@> Psi2(0.950)=2.850000e+00 tau=2.415000e+00 <@> Psi3(-1.000)=6.000000e+00 tau=-6.000000e+00 <@> Psi3(-0.950)=5.268750e+00 tau=-3.615937e+00 <@> Psi3(-0.900)=4.575000e+00 tau=-1.552500e+00 <@> Psi3(-0.850)=3.918750e+00 tau=2.071875e-01 <@> Psi3(-0.800)=3.300000e+00 tau=1.680000e+00 <@> Psi3(-0.750)=2.718750e+00 tau=2.882813e+00 <@> Psi3(-0.700)=2.175000e+00 tau=3.832500e+00 <@> Psi3(-0.650)=1.668750e+00 tau=4.545938e+00 <@> Psi3(-0.600)=1.200000e+00 tau=5.040000e+00 <@> Psi3(-0.550)=7.687500e-01 tau=5.331563e+00 <@> Psi3(-0.500)=3.750000e-01 tau=5.437500e+00 <@> Psi3(-0.450)=1.875000e-02 tau=5.374687e+00 <@> Psi3(-0.400)=-3.000000e-01 tau=5.160000e+00 <@> Psi3(-0.350)=-5.812500e-01 tau=4.810312e+00 <@> Psi3(-0.300)=-8.250000e-01 tau=4.342500e+00 <@> Psi3(-0.250)=-1.031250e+00 tau=3.773437e+00 <@> Psi3(-0.200)=-1.200000e+00 tau=3.120000e+00 <@> Psi3(-0.150)=-1.331250e+00 tau=2.399062e+00 <@> Psi3(-0.100)=-1.425000e+00 tau=1.627500e+00 <@> Psi3(-0.050)=-1.481250e+00 tau=8.221875e-01 <@> Psi3(0.000)=-1.500000e+00 tau=-5.266620e-15 <@> Psi3(0.050)=-1.481250e+00 tau=-8.221875e-01 <@> Psi3(0.100)=-1.425000e+00 tau=-1.627500e+00 <@> Psi3(0.150)=-1.331250e+00 tau=-2.399063e+00 <@> Psi3(0.200)=-1.200000e+00 tau=-3.120000e+00 <@> Psi3(0.250)=-1.031250e+00 tau=-3.773438e+00 <@> Psi3(0.300)=-8.250000e-01 tau=-4.342500e+00 <@> Psi3(0.350)=-5.812500e-01 tau=-4.810313e+00 <@> Psi3(0.400)=-3.000000e-01 tau=-5.160000e+00 <@> Psi3(0.450)=1.875000e-02 tau=-5.374688e+00 <@> Psi3(0.500)=3.750000e-01 tau=-5.437500e+00 <@> Psi3(0.550)=7.687500e-01 tau=-5.331562e+00 <@> Psi3(0.600)=1.200000e+00 tau=-5.040000e+00 <@> Psi3(0.650)=1.668750e+00 tau=-4.545937e+00 <@> Psi3(0.700)=2.175000e+00 tau=-3.832500e+00 <@> Psi3(0.750)=2.718750e+00 tau=-2.882812e+00 <@> Psi3(0.800)=3.300000e+00 tau=-1.680000e+00 <@> Psi3(0.850)=3.918750e+00 tau=-2.071875e-01 <@> Psi3(0.900)=4.575000e+00 tau=1.552500e+00 <@> Psi3(0.950)=5.268750e+00 tau=3.615938e+00 <@> Psi4(-1.000)=-1.000000e+01 tau=1.000000e+01 <@> Psi4(-0.950)=-7.879062e+00 tau=3.596687e+00 <@> Psi4(-0.900)=-6.007500e+00 tau=-1.248000e+00 <@> Psi4(-0.850)=-4.372187e+00 tau=-4.728313e+00 <@> Psi4(-0.800)=-2.960000e+00 tau=-7.028000e+00 <@> Psi4(-0.750)=-1.757812e+00 tau=-8.320313e+00 <@> Psi4(-0.700)=-7.525000e-01 tau=-8.768000e+00 <@> Psi4(-0.650)=6.906250e-02 tau=-8.523312e+00 <@> Psi4(-0.600)=7.200000e-01 tau=-7.728000e+00 <@> Psi4(-0.550)=1.213438e+00 tau=-6.513312e+00 <@> Psi4(-0.500)=1.562500e+00 tau=-5.000000e+00 <@> Psi4(-0.450)=1.780313e+00 tau=-3.298312e+00 <@> Psi4(-0.400)=1.880000e+00 tau=-1.508000e+00 <@> Psi4(-0.350)=1.874687e+00 tau=2.816875e-01 <@> Psi4(-0.300)=1.777500e+00 tau=1.992000e+00 <@> Psi4(-0.250)=1.601562e+00 tau=3.554688e+00 <@> Psi4(-0.200)=1.360000e+00 tau=4.912000e+00 <@> Psi4(-0.150)=1.065937e+00 tau=6.016688e+00 <@> Psi4(-0.100)=7.325000e-01 tau=6.832000e+00 <@> Psi4(-0.050)=3.728125e-01 tau=7.331688e+00 <@> Psi4(0.000)=-2.393918e-15 tau=7.500000e+00 <@> Psi4(0.050)=-3.728125e-01 tau=7.331687e+00 <@> Psi4(0.100)=-7.325000e-01 tau=6.832000e+00 <@> Psi4(0.150)=-1.065938e+00 tau=6.016687e+00 <@> Psi4(0.200)=-1.360000e+00 tau=4.912000e+00 <@> Psi4(0.250)=-1.601563e+00 tau=3.554687e+00 <@> Psi4(0.300)=-1.777500e+00 tau=1.992000e+00 <@> Psi4(0.350)=-1.874688e+00 tau=2.816875e-01 <@> Psi4(0.400)=-1.880000e+00 tau=-1.508000e+00 <@> Psi4(0.450)=-1.780312e+00 tau=-3.298313e+00 <@> Psi4(0.500)=-1.562500e+00 tau=-5.000000e+00 <@> Psi4(0.550)=-1.213437e+00 tau=-6.513313e+00 <@> Psi4(0.600)=-7.200000e-01 tau=-7.728000e+00 <@> Psi4(0.650)=-6.906250e-02 tau=-8.523313e+00 <@> Psi4(0.700)=7.525000e-01 tau=-8.768000e+00 <@> Psi4(0.750)=1.757813e+00 tau=-8.320312e+00 <@> Psi4(0.800)=2.960000e+00 tau=-7.028000e+00 <@> Psi4(0.850)=4.372188e+00 tau=-4.728312e+00 <@> Psi4(0.900)=6.007500e+00 tau=-1.248000e+00 <@> Psi4(0.950)=7.879063e+00 tau=3.596688e+00 <@> Psi5(-1.000)=1.500000e+01 tau=-1.500000e+01 <@> Psi5(-0.950)=1.025556e+01 tau=-1.439528e+00 <@> Psi5(-0.900)=6.446437e+00 tau=7.036031e+00 <@> Psi5(-0.850)=3.463371e+00 tau=1.151380e+01 <@> Psi5(-0.800)=1.203000e+00 tau=1.294800e+01 <@> Psi5(-0.750)=-4.321289e-01 tau=1.216736e+01 <@> Psi5(-0.700)=-1.533563e+00 tau=9.882469e+00 <@> Psi5(-0.650)=-2.186941e+00 tau=6.693185e+00 <@> Psi5(-0.600)=-2.472000e+00 tau=3.096000e+00 <@> Psi5(-0.550)=-2.462566e+00 tau=-5.085674e-01 <@> Psi5(-0.500)=-2.226562e+00 tau=-3.808594e+00 <@> Psi5(-0.450)=-1.826004e+00 tau=-6.573366e+00 <@> Psi5(-0.400)=-1.317000e+00 tau=-8.646000e+00 <@> Psi5(-0.350)=-7.497539e-01 tau=-9.936056e+00 <@> Psi5(-0.300)=-1.685625e-01 tau=-1.041216e+01 <@> Psi5(-0.250)=3.881836e-01 tau=-1.009460e+01 <@> Psi5(-0.200)=8.880000e-01 tau=-9.048000e+00 <@> Psi5(-0.150)=1.304309e+00 tau=-7.373856e+00 <@> Psi5(-0.100)=1.616438e+00 tau=-5.203219e+00 <@> Psi5(-0.050)=1.809621e+00 tau=-2.689280e+00 <@> Psi5(0.000)=1.875000e+00 tau=1.735591e-14 <@> Psi5(0.050)=1.809621e+00 tau=2.689280e+00 <@> Psi5(0.100)=1.616437e+00 tau=5.203219e+00 <@> Psi5(0.150)=1.304309e+00 tau=7.373856e+00 <@> Psi5(0.200)=8.880000e-01 tau=9.048000e+00 <@> Psi5(0.250)=3.881836e-01 tau=1.009460e+01 <@> Psi5(0.300)=-1.685625e-01 tau=1.041216e+01 <@> Psi5(0.350)=-7.497539e-01 tau=9.936056e+00 <@> Psi5(0.400)=-1.317000e+00 tau=8.646000e+00 <@> Psi5(0.450)=-1.826004e+00 tau=6.573366e+00 <@> Psi5(0.500)=-2.226563e+00 tau=3.808594e+00 <@> Psi5(0.550)=-2.462566e+00 tau=5.085674e-01 <@> Psi5(0.600)=-2.472000e+00 tau=-3.096000e+00 <@> Psi5(0.650)=-2.186941e+00 tau=-6.693185e+00 <@> Psi5(0.700)=-1.533562e+00 tau=-9.882469e+00 <@> Psi5(0.750)=-4.321289e-01 tau=-1.216736e+01 <@> Psi5(0.800)=1.203000e+00 tau=-1.294800e+01 <@> Psi5(0.850)=3.463371e+00 tau=-1.151380e+01 <@> Psi5(0.900)=6.446438e+00 tau=-7.036031e+00 <@> Psi5(0.950)=1.025556e+01 tau=1.439528e+00 <@> Psi6(-1.000)=-2.100000e+01 tau=2.100000e+01 <@> Psi6(-0.950)=-1.197924e+01 tau=-3.507228e+00 <@> Psi6(-0.900)=-5.554946e+00 tau=-1.512835e+01 <@> Psi6(-0.850)=-1.229879e+00 tau=-1.797122e+01 <@> Psi6(-0.800)=1.434720e+00 tau=-1.530766e+01 <@> Psi6(-0.750)=2.822388e+00 tau=-9.675842e+00 <@> Psi6(-0.700)=3.264686e+00 tau=-2.976745e+00 <@> Psi6(-0.650)=3.044451e+00 tau=3.435230e+00 <@> Psi6(-0.600)=2.399040e+00 tau=8.667456e+00 <@> Psi6(-0.550)=1.523580e+00 tau=1.221015e+01 <@> Psi6(-0.500)=5.742187e-01 tau=1.386328e+01 <@> Psi6(-0.450)=-3.286311e-01 tau=1.366933e+01 <@> Psi6(-0.400)=-1.097040e+00 tau=1.185190e+01 <@> Psi6(-0.350)=-1.672314e+00 tau=8.760138e+00 <@> Psi6(-0.300)=-2.021749e+00 tau=4.819085e+00 <@> Psi6(-0.250)=-2.135376e+00 tau=4.857788e-01 <@> Psi6(-0.200)=-2.022720e+00 tau=-3.788736e+00 <@> Psi6(-0.150)=-1.709547e+00 tau=-7.591568e+00 <@> Psi6(-0.100)=-1.234616e+00 tau=-1.057429e+01 <@> Psi6(-0.050)=-6.464333e-01 tau=-1.247342e+01 <@> Psi6(0.000)=4.189357e-15 tau=-1.312500e+01 <@> Psi6(0.050)=6.464333e-01 tau=-1.247342e+01 <@> Psi6(0.100)=1.234616e+00 tau=-1.057429e+01 <@> Psi6(0.150)=1.709547e+00 tau=-7.591568e+00 <@> Psi6(0.200)=2.022720e+00 tau=-3.788736e+00 <@> Psi6(0.250)=2.135376e+00 tau=4.857788e-01 <@> Psi6(0.300)=2.021749e+00 tau=4.819085e+00 <@> Psi6(0.350)=1.672314e+00 tau=8.760138e+00 <@> Psi6(0.400)=1.097040e+00 tau=1.185190e+01 <@> Psi6(0.450)=3.286311e-01 tau=1.366933e+01 <@> Psi6(0.500)=-5.742188e-01 tau=1.386328e+01 <@> Psi6(0.550)=-1.523580e+00 tau=1.221015e+01 <@> Psi6(0.600)=-2.399040e+00 tau=8.667456e+00 <@> Psi6(0.650)=-3.044451e+00 tau=3.435230e+00 <@> Psi6(0.700)=-3.264686e+00 tau=-2.976745e+00 <@> Psi6(0.750)=-2.822388e+00 tau=-9.675842e+00 <@> Psi6(0.800)=-1.434720e+00 tau=-1.530766e+01 <@> Psi6(0.850)=1.229879e+00 tau=-1.797122e+01 <@> Psi6(0.900)=5.554946e+00 tau=-1.512835e+01 <@> Psi6(0.950)=1.197924e+01 tau=-3.507228e+00 <@> Psi7(-1.000)=2.800000e+01 tau=-2.800000e+01 <@> Psi7(-0.950)=1.269246e+01 tau=1.142911e+01 <@> Psi7(-0.900)=3.311301e+00 tau=2.357837e+01 <@> Psi7(-0.850)=-1.775573e+00 tau=2.040369e+01 <@> Psi7(-0.800)=-3.890348e+00 tau=1.030819e+01 <@> Psi7(-0.750)=-4.082230e+00 tau=-1.147396e+00 <@> Psi7(-0.700)=-3.162285e+00 tau=-1.062230e+01 <@> Psi7(-0.650)=-1.736170e+00 tau=-1.645603e+01 <@> Psi7(-0.600)=-2.347520e-01 tau=-1.820636e+01 <@> Psi7(-0.550)=1.057394e+00 tau=-1.625961e+01 <@> Psi7(-0.500)=1.975586e+00 tau=-1.150830e+01 <@> Psi7(-0.450)=2.450753e+00 tau=-5.090824e+00 <@> Psi7(-0.400)=2.487268e+00 tau=1.811970e+00 <@> Psi7(-0.350)=2.142885e+00 tau=8.128448e+00 <@> Psi7(-0.300)=1.510793e+00 tau=1.300132e+01 <@> Psi7(-0.250)=7.037811e-01 tau=1.585139e+01 <@> Psi7(-0.200)=-1.594880e-01 tau=1.640504e+01 <@> Psi7(-0.150)=-9.660906e-01 tau=1.469077e+01 <@> Psi7(-0.100)=-1.618344e+00 tau=1.100977e+01 <@> Psi7(-0.050)=-2.041194e+00 tau=5.885885e+00 <@> Psi7(0.000)=-2.187500e+00 tau=-3.840244e-14 <@> Psi7(0.050)=-2.041194e+00 tau=-5.885885e+00 <@> Psi7(0.100)=-1.618344e+00 tau=-1.100977e+01 <@> Psi7(0.150)=-9.660906e-01 tau=-1.469077e+01 <@> Psi7(0.200)=-1.594880e-01 tau=-1.640504e+01 <@> Psi7(0.250)=7.037811e-01 tau=-1.585139e+01 <@> Psi7(0.300)=1.510793e+00 tau=-1.300132e+01 <@> Psi7(0.350)=2.142885e+00 tau=-8.128448e+00 <@> Psi7(0.400)=2.487268e+00 tau=-1.811970e+00 <@> Psi7(0.450)=2.450753e+00 tau=5.090824e+00 <@> Psi7(0.500)=1.975586e+00 tau=1.150830e+01 <@> Psi7(0.550)=1.057394e+00 tau=1.625961e+01 <@> Psi7(0.600)=-2.347520e-01 tau=1.820636e+01 <@> Psi7(0.650)=-1.736170e+00 tau=1.645603e+01 <@> Psi7(0.700)=-3.162285e+00 tau=1.062230e+01 <@> Psi7(0.750)=-4.082230e+00 tau=1.147396e+00 <@> Psi7(0.800)=-3.890348e+00 tau=-1.030819e+01 <@> Psi7(0.850)=-1.775573e+00 tau=-2.040369e+01 <@> Psi7(0.900)=3.311301e+00 tau=-2.357837e+01 <@> Psi7(0.950)=1.269246e+01 tau=-1.142911e+01 <@> Psi8(-1.000)=-3.600000e+01 tau=3.600000e+01 <@> Psi8(-0.950)=-1.214765e+01 tau=-2.190996e+01 <@> Psi8(-0.900)=-3.757134e-02 tau=-2.953120e+01 <@> Psi8(-0.850)=4.639655e+00 tau=-1.556950e+01 <@> Psi8(-0.800)=5.029488e+00 tau=2.824409e+00 <@> Psi8(-0.750)=3.335140e+00 tau=1.672923e+01 <@> Psi8(-0.700)=1.012357e+00 tau=2.279136e+01 <@> Psi8(-0.650)=-1.061135e+00 tau=2.114344e+01 <@> Psi8(-0.600)=-2.439936e+00 tau=1.382446e+01 <@> Psi8(-0.550)=-2.987449e+00 tau=3.628229e+00 <@> Psi8(-0.500)=-2.772949e+00 tau=-6.688477e+00 <@> Psi8(-0.450)=-1.987648e+00 tau=-1.490125e+01 <@> Psi8(-0.400)=-8.781840e-01 tau=-1.957522e+01 <@> Psi8(-0.350)=3.040530e-01 tau=-2.013731e+01 <@> Psi8(-0.300)=1.339346e+00 tau=-1.681157e+01 <@> Psi8(-0.250)=2.063404e+00 tau=-1.046084e+01 <@> Psi8(-0.200)=2.380032e+00 tau=-2.372659e+00 <@> Psi8(-0.150)=2.264297e+00 tau=5.977659e+00 <@> Psi8(-0.100)=1.757778e+00 tau=1.315887e+01 <@> Psi8(-0.050)=9.574803e-01 tau=1.798776e+01 <@> Psi8(0.000)=-6.284036e-15 tau=1.968750e+01 <@> Psi8(0.050)=-9.574803e-01 tau=1.798776e+01 <@> Psi8(0.100)=-1.757778e+00 tau=1.315887e+01 <@> Psi8(0.150)=-2.264297e+00 tau=5.977659e+00 <@> Psi8(0.200)=-2.380032e+00 tau=-2.372659e+00 <@> Psi8(0.250)=-2.063404e+00 tau=-1.046084e+01 <@> Psi8(0.300)=-1.339346e+00 tau=-1.681157e+01 <@> Psi8(0.350)=-3.040530e-01 tau=-2.013731e+01 <@> Psi8(0.400)=8.781840e-01 tau=-1.957522e+01 <@> Psi8(0.450)=1.987648e+00 tau=-1.490125e+01 <@> Psi8(0.500)=2.772949e+00 tau=-6.688477e+00 <@> Psi8(0.550)=2.987449e+00 tau=3.628229e+00 <@> Psi8(0.600)=2.439936e+00 tau=1.382446e+01 <@> Psi8(0.650)=1.061135e+00 tau=2.114344e+01 <@> Psi8(0.700)=-1.012357e+00 tau=2.279136e+01 <@> Psi8(0.750)=-3.335140e+00 tau=1.672923e+01 <@> Psi8(0.800)=-5.029488e+00 tau=2.824409e+00 <@> Psi8(0.850)=-4.639655e+00 tau=-1.556950e+01 <@> Psi8(0.900)=3.757134e-02 tau=-2.953120e+01 <@> Psi8(0.950)=1.214765e+01 tau=-2.190996e+01 <@> Psi9(-1.000)=4.500000e+01 tau=-4.500000e+01 <@> Psi9(-0.950)=1.024406e+01 tau=3.388982e+01 <@> Psi9(-0.900)=-3.653359e+00 tau=2.996792e+01 <@> Psi9(-0.850)=-6.382857e+00 tau=2.432310e+00 <@> Psi9(-0.800)=-4.173488e+00 tau=-2.024577e+01 <@> Psi9(-0.750)=-7.228714e-01 tau=-2.847202e+01 <@> Psi9(-0.700)=2.051689e+00 tau=-2.304921e+01 <@> Psi9(-0.650)=3.418885e+00 tau=-9.389124e+00 <@> Psi9(-0.600)=3.375014e+00 tau=6.174282e+00 <@> Psi9(-0.550)=2.302013e+00 tau=1.847953e+01 <@> Psi9(-0.500)=7.237244e-01 tau=2.447273e+01 <@> Psi9(-0.450)=-8.564091e-01 tau=2.334494e+01 <@> Psi9(-0.400)=-2.051720e+00 tau=1.616803e+01 <@> Psi9(-0.350)=-2.636885e+00 tau=5.265657e+00 <@> Psi9(-0.300)=-2.553475e+00 tau=-6.499077e+00 <@> Psi9(-0.250)=-1.887937e+00 tau=-1.638618e+01 <@> Psi9(-0.200)=-8.320896e-01 tau=-2.230256e+01 <@> Psi9(-0.150)=3.651073e-01 tau=-2.313586e+01 <@> Psi9(-0.100)=1.447109e+00 tau=-1.888018e+01 <@> Psi9(-0.050)=2.194611e+00 tau=-1.056238e+01 <@> Psi9(0.000)=2.460938e+00 tau=6.990990e-14 <@> Psi9(0.050)=2.194611e+00 tau=1.056238e+01 <@> Psi9(0.100)=1.447109e+00 tau=1.888018e+01 <@> Psi9(0.150)=3.651073e-01 tau=2.313586e+01 <@> Psi9(0.200)=-8.320896e-01 tau=2.230256e+01 <@> Psi9(0.250)=-1.887937e+00 tau=1.638618e+01 <@> Psi9(0.300)=-2.553475e+00 tau=6.499077e+00 <@> Psi9(0.350)=-2.636885e+00 tau=-5.265657e+00 <@> Psi9(0.400)=-2.051720e+00 tau=-1.616803e+01 <@> Psi9(0.450)=-8.564091e-01 tau=-2.334494e+01 <@> Psi9(0.500)=7.237244e-01 tau=-2.447273e+01 <@> Psi9(0.550)=2.302013e+00 tau=-1.847953e+01 <@> Psi9(0.600)=3.375014e+00 tau=-6.174282e+00 <@> Psi9(0.650)=3.418885e+00 tau=9.389124e+00 <@> Psi9(0.700)=2.051689e+00 tau=2.304921e+01 <@> Psi9(0.750)=-7.228714e-01 tau=2.847202e+01 <@> Psi9(0.800)=-4.173488e+00 tau=2.024577e+01 <@> Psi9(0.850)=-6.382857e+00 tau=-2.432310e+00 <@> Psi9(0.900)=-3.653359e+00 tau=-2.996792e+01 <@> Psi9(0.950)=1.024406e+01 tau=-3.388982e+01 <@> Psi10(-1.000)=-5.500000e+01 tau=5.500000e+01 <@> Psi10(-0.950)=-7.047636e+00 tau=-4.573209e+01 <@> Psi10(-0.900)=6.983128e+00 tau=-2.266120e+01 <@> Psi10(-0.850)=6.298510e+00 tau=1.667409e+01 <@> Psi10(-0.800)=1.460238e+00 tau=3.422647e+01 <@> Psi10(-0.750)=-2.561165e+00 tau=2.716032e+01 <@> Psi10(-0.700)=-4.156782e+00 tau=6.528890e+00 <@> Psi10(-0.650)=-3.512431e+00 tau=-1.477694e+01 <@> Psi10(-0.600)=-1.563978e+00 tau=-2.774129e+01 <@> Psi10(-0.550)=6.464954e-01 tau=-2.887787e+01 <@> Psi10(-0.500)=2.317123e+00 tau=-1.954659e+01 <@> Psi10(-0.450)=3.022086e+00 tau=-4.178888e+00 <@> Psi10(-0.400)=2.708324e+00 tau=1.173563e+01 <@> Psi10(-0.350)=1.610528e+00 tau=2.336888e+01 <@> Psi10(-0.300)=1.290387e-01 tau=2.770111e+01 <@> Psi10(-0.250)=-1.296260e+00 tau=2.400796e+01 <@> Psi10(-0.200)=-2.293153e+00 tau=1.373929e+01 <@> Psi10(-0.150)=-2.631503e+00 tau=-6.892626e-02 <@> Psi10(-0.100)=-2.258587e+00 tau=-1.365961e+01 <@> Psi10(-0.050)=-1.295520e+00 tau=-2.349296e+01 <@> Psi10(0.000)=8.640549e-15 tau=-2.707031e+01 <@> Psi10(0.050)=1.295520e+00 tau=-2.349296e+01 <@> Psi10(0.100)=2.258587e+00 tau=-1.365961e+01 <@> Psi10(0.150)=2.631503e+00 tau=-6.892626e-02 <@> Psi10(0.200)=2.293153e+00 tau=1.373929e+01 <@> Psi10(0.250)=1.296260e+00 tau=2.400796e+01 <@> Psi10(0.300)=-1.290387e-01 tau=2.770111e+01 <@> Psi10(0.350)=-1.610528e+00 tau=2.336888e+01 <@> Psi10(0.400)=-2.708324e+00 tau=1.173563e+01 <@> Psi10(0.450)=-3.022086e+00 tau=-4.178888e+00 <@> Psi10(0.500)=-2.317123e+00 tau=-1.954659e+01 <@> Psi10(0.550)=-6.464954e-01 tau=-2.887787e+01 <@> Psi10(0.600)=1.563978e+00 tau=-2.774129e+01 <@> Psi10(0.650)=3.512431e+00 tau=-1.477694e+01 <@> Psi10(0.700)=4.156782e+00 tau=6.528890e+00 <@> Psi10(0.750)=2.561165e+00 tau=2.716032e+01 <@> Psi10(0.800)=-1.460238e+00 tau=3.422647e+01 <@> Psi10(0.850)=-6.298510e+00 tau=1.667409e+01 <@> Psi10(0.900)=-6.983128e+00 tau=-2.266120e+01 <@> Psi10(0.950)=7.047636e+00 tau=-4.573209e+01 <@> Psi11(-1.000)=6.600000e+01 tau=-6.600000e+01 <@> Psi11(-0.950)=2.791571e+00 tau=5.539972e+01 <@> Psi11(-0.900)=-9.179417e+00 tau=7.078693e+00 <@> Psi11(-0.850)=-4.221698e+00 tau=-3.610924e+01 <@> Psi11(-0.800)=2.137638e+00 tau=-3.633406e+01 <@> Psi11(-0.750)=4.828993e+00 tau=-9.105216e+00 <@> Psi11(-0.700)=3.853611e+00 tau=2.020858e+01 <@> Psi11(-0.650)=1.033694e+00 tau=3.475825e+01 <@> Psi11(-0.600)=-1.741903e+00 tau=3.026430e+01 <@> Psi11(-0.550)=-3.278916e+00 tau=1.207950e+01 <@> Psi11(-0.500)=-3.229076e+00 tau=-1.004556e+01 <@> Psi11(-0.450)=-1.913822e+00 tau=-2.679162e+01 <@> Psi11(-0.400)=-1.809975e-02 tau=-3.242024e+01 <@> Psi11(-0.350)=1.716835e+00 tau=-2.593615e+01 <@> Psi11(-0.300)=2.727528e+00 tau=-1.054931e+01 <@> Psi11(-0.250)=2.757267e+00 tau=7.972634e+00 <@> Psi11(-0.200)=1.878423e+00 tau=2.338531e+01 <@> Psi11(-0.150)=4.273053e-01 tau=3.087298e+01 <@> Psi11(-0.100)=-1.117516e+00 tau=2.833232e+01 <@> Psi11(-0.050)=-2.278043e+00 tau=1.679917e+01 <@> Psi11(0.000)=-2.707031e+00 tau=-1.131912e-13 <@> Psi11(0.050)=-2.278043e+00 tau=-1.679917e+01 <@> Psi11(0.100)=-1.117516e+00 tau=-2.833232e+01 <@> Psi11(0.150)=4.273053e-01 tau=-3.087298e+01 <@> Psi11(0.200)=1.878423e+00 tau=-2.338531e+01 <@> Psi11(0.250)=2.757267e+00 tau=-7.972634e+00 <@> Psi11(0.300)=2.727528e+00 tau=1.054931e+01 <@> Psi11(0.350)=1.716835e+00 tau=2.593615e+01 <@> Psi11(0.400)=-1.809975e-02 tau=3.242024e+01 <@> Psi11(0.450)=-1.913822e+00 tau=2.679162e+01 <@> Psi11(0.500)=-3.229076e+00 tau=1.004556e+01 <@> Psi11(0.550)=-3.278916e+00 tau=-1.207950e+01 <@> Psi11(0.600)=-1.741903e+00 tau=-3.026430e+01 <@> Psi11(0.650)=1.033694e+00 tau=-3.475825e+01 <@> Psi11(0.700)=3.853611e+00 tau=-2.020858e+01 <@> Psi11(0.750)=4.828993e+00 tau=9.105216e+00 <@> Psi11(0.800)=2.137638e+00 tau=3.633406e+01 <@> Psi11(0.850)=-4.221698e+00 tau=3.610924e+01 <@> Psi11(0.900)=-9.179417e+00 tau=-7.078693e+00 <@> Psi11(0.950)=2.791571e+00 tau=-5.539972e+01 <@> Psi12(-1.000)=-7.800000e+01 tau=7.800000e+01 <@> Psi12(-0.950)=2.143255e+00 tau=-6.072353e+01 <@> Psi12(-0.900)=9.656036e+00 tau=1.504723e+01 <@> Psi12(-0.850)=6.320073e-01 tau=4.843561e+01 <@> Psi12(-0.800)=-5.168671e+00 tau=2.182996e+01 <@> Psi12(-0.750)=-4.778741e+00 tau=-1.976824e+01 <@> Psi12(-0.700)=-1.105614e+00 tau=-4.080978e+01 <@> Psi12(-0.650)=2.426858e+00 tau=-3.236752e+01 <@> Psi12(-0.600)=3.891455e+00 tau=-5.373733e+00 <@> Psi12(-0.550)=3.065486e+00 tau=2.239370e+01 <@> Psi12(-0.500)=8.480816e-01 tau=3.688950e+01 <@> Psi12(-0.450)=-1.496089e+00 tau=3.295856e+01 <@> Psi12(-0.400)=-2.939397e+00 tau=1.434440e+01 <@> Psi12(-0.350)=-3.013351e+00 tau=-9.662782e+00 <@> Psi12(-0.300)=-1.851674e+00 tau=-2.879184e+01 <@> Psi12(-0.250)=-2.719713e-02 tau=-3.576288e+01 <@> Psi12(-0.200)=1.716099e+00 tau=-2.853814e+01 <@> Psi12(-0.150)=2.736712e+00 tau=-1.048105e+01 <@> Psi12(-0.100)=2.697576e+00 tau=1.129062e+01 <@> Psi12(-0.050)=1.651454e+00 tau=2.862368e+01 <@> Psi12(0.000)=-1.123271e-14 tau=3.519141e+01 <@> Psi12(0.050)=-1.651454e+00 tau=2.862368e+01 <@> Psi12(0.100)=-2.697576e+00 tau=1.129062e+01 <@> Psi12(0.150)=-2.736712e+00 tau=-1.048105e+01 <@> Psi12(0.200)=-1.716099e+00 tau=-2.853814e+01 <@> Psi12(0.250)=2.719713e-02 tau=-3.576288e+01 <@> Psi12(0.300)=1.851674e+00 tau=-2.879184e+01 <@> Psi12(0.350)=3.013351e+00 tau=-9.662782e+00 <@> Psi12(0.400)=2.939397e+00 tau=1.434440e+01 <@> Psi12(0.450)=1.496089e+00 tau=3.295856e+01 <@> Psi12(0.500)=-8.480816e-01 tau=3.688950e+01 <@> Psi12(0.550)=-3.065486e+00 tau=2.239370e+01 <@> Psi12(0.600)=-3.891455e+00 tau=-5.373733e+00 <@> Psi12(0.650)=-2.426858e+00 tau=-3.236752e+01 <@> Psi12(0.700)=1.105614e+00 tau=-4.080978e+01 <@> Psi12(0.750)=4.778741e+00 tau=-1.976824e+01 <@> Psi12(0.800)=5.168671e+00 tau=2.182996e+01 <@> Psi12(0.850)=-6.320073e-01 tau=4.843561e+01 <@> Psi12(0.900)=-9.656036e+00 tau=1.504723e+01 <@> Psi12(0.950)=-2.143255e+00 tau=-6.072353e+01 <@> Psi13(-1.000)=9.100000e+01 tau=-9.100000e+01 <@> Psi13(-0.950)=-7.266061e+00 tau=5.973028e+01 <@> Psi13(-0.900)=-8.160699e+00 tau=-3.970432e+01 <@> Psi13(-0.850)=3.454327e+00 tau=-4.701842e+01 <@> Psi13(-0.800)=6.298678e+00 tau=6.855146e+00 <@> Psi13(-0.750)=2.235374e+00 tau=4.510748e+01 <@> Psi13(-0.700)=-2.562391e+00 tau=3.879636e+01 <@> Psi13(-0.650)=-4.406206e+00 tau=3.256427e+00 <@> Psi13(-0.600)=-2.977257e+00 tau=-3.125777e+01 <@> Psi13(-0.550)=3.962322e-02 tau=-4.320011e+01 <@> Psi13(-0.500)=2.614748e+00 tau=-2.886900e+01 <@> Psi13(-0.450)=3.475890e+00 tau=6.112915e-01 <@> Psi13(-0.400)=2.469105e+00 tau=2.831221e+01 <@> Psi13(-0.350)=3.373304e-01 tau=4.065206e+01 <@> Psi13(-0.300)=-1.797526e+00 tau=3.293378e+01 <@> Psi13(-0.250)=-2.972874e+00 tau=1.004260e+01 <@> Psi13(-0.200)=-2.750000e+00 tau=-1.687539e+01 <@> Psi13(-0.150)=-1.318137e+00 tau=-3.574360e+01 <@> Psi13(-0.100)=6.486476e-01 tau=-3.860930e+01 <@> Psi13(-0.050)=2.295853e+00 tau=-2.461266e+01 <@> Psi13(0.000)=2.932617e+00 tau=1.694268e-13 <@> Psi13(0.050)=2.295853e+00 tau=2.461266e+01 <@> Psi13(0.100)=6.486476e-01 tau=3.860930e+01 <@> Psi13(0.150)=-1.318137e+00 tau=3.574360e+01 <@> Psi13(0.200)=-2.750000e+00 tau=1.687539e+01 <@> Psi13(0.250)=-2.972874e+00 tau=-1.004260e+01 <@> Psi13(0.300)=-1.797526e+00 tau=-3.293378e+01 <@> Psi13(0.350)=3.373304e-01 tau=-4.065206e+01 <@> Psi13(0.400)=2.469105e+00 tau=-2.831221e+01 <@> Psi13(0.450)=3.475890e+00 tau=-6.112915e-01 <@> Psi13(0.500)=2.614748e+00 tau=2.886900e+01 <@> Psi13(0.550)=3.962322e-02 tau=4.320011e+01 <@> Psi13(0.600)=-2.977257e+00 tau=3.125777e+01 <@> Psi13(0.650)=-4.406206e+00 tau=-3.256427e+00 <@> Psi13(0.700)=-2.562391e+00 tau=-3.879636e+01 <@> Psi13(0.750)=2.235374e+00 tau=-4.510748e+01 <@> Psi13(0.800)=6.298678e+00 tau=-6.855146e+00 <@> Psi13(0.850)=3.454327e+00 tau=4.701842e+01 <@> Psi13(0.900)=-8.160699e+00 tau=3.970432e+01 <@> Psi13(0.950)=-7.266061e+00 tau=-5.973028e+01 <@> Psi14(-1.000)=-1.050000e+02 tau=1.050000e+02 <@> Psi14(-0.950)=1.202838e+01 tau=-5.098649e+01 <@> Psi14(-0.900)=4.855422e+00 tau=6.123217e+01 <@> Psi14(-0.850)=-6.778839e+00 tau=2.885328e+01 <@> Psi14(-0.800)=-4.899234e+00 tau=-3.960874e+01 <@> Psi14(-0.750)=1.664312e+00 tau=-5.100589e+01 <@> Psi14(-0.700)=4.915984e+00 tau=-9.740775e+00 <@> Psi14(-0.650)=3.334838e+00 tau=3.574606e+01 <@> Psi14(-0.600)=-4.806776e-01 tau=4.869654e+01 <@> Psi14(-0.550)=-3.346555e+00 tau=2.517412e+01 <@> Psi14(-0.500)=-3.628634e+00 tau=-1.382078e+01 <@> Psi14(-0.450)=-1.637448e+00 tau=-4.182244e+01 <@> Psi14(-0.400)=1.114247e+00 tau=-4.327637e+01 <@> Psi14(-0.350)=2.999934e+00 tau=-1.975963e+01 <@> Psi14(-0.300)=3.114107e+00 tau=1.388364e+01 <@> Psi14(-0.250)=1.572897e+00 tau=3.908798e+01 <@> Psi14(-0.200)=-7.057996e-01 tau=4.322623e+01 <@> Psi14(-0.150)=-2.536578e+00 tau=2.509886e+01 <@> Psi14(-0.100)=-3.039801e+00 tau=-5.473993e+00 <@> Psi14(-0.050)=-2.016905e+00 tau=-3.302597e+01 <@> Psi14(0.000)=1.404089e-14 tau=-4.398926e+01 <@> Psi14(0.050)=2.016905e+00 tau=-3.302597e+01 <@> Psi14(0.100)=3.039801e+00 tau=-5.473993e+00 <@> Psi14(0.150)=2.536578e+00 tau=2.509886e+01 <@> Psi14(0.200)=7.057996e-01 tau=4.322623e+01 <@> Psi14(0.250)=-1.572897e+00 tau=3.908798e+01 <@> Psi14(0.300)=-3.114107e+00 tau=1.388364e+01 <@> Psi14(0.350)=-2.999934e+00 tau=-1.975963e+01 <@> Psi14(0.400)=-1.114247e+00 tau=-4.327637e+01 <@> Psi14(0.450)=1.637448e+00 tau=-4.182244e+01 <@> Psi14(0.500)=3.628634e+00 tau=-1.382078e+01 <@> Psi14(0.550)=3.346555e+00 tau=2.517412e+01 <@> Psi14(0.600)=4.806776e-01 tau=4.869654e+01 <@> Psi14(0.650)=-3.334838e+00 tau=3.574606e+01 <@> Psi14(0.700)=-4.915984e+00 tau=-9.740775e+00 <@> Psi14(0.750)=-1.664312e+00 tau=-5.100589e+01 <@> Psi14(0.800)=4.899234e+00 tau=-3.960874e+01 <@> Psi14(0.850)=6.778839e+00 tau=2.885328e+01 <@> Psi14(0.900)=-4.855422e+00 tau=6.123217e+01 <@> Psi14(0.950)=-1.202838e+01 tau=-5.098649e+01 <@> */