Implementation
const List<double> MAGIC = [0.0,1.0,1.2246469E-16,-1.0
,0.8660254,-0.5,-0.8660254,6.123234E-17
,-1.8369701E-16,0.95105654,0.309017,0.58778524
,-0.809017,-0.58778524,-0.95105654,0.5
,0.777146,0.6293204,0.9781476,-0.20791169
,0.4539905,-0.8910065,-0.40673664,-0.9135454
,-0.9659258,-0.25881904,-0.052335955,0.9986295
,0.70710677,-0.70710677,0.64278764,0.76604444
,0.9848077,0.17364818,0.34202015,-0.9396926
,-0.34202015,-0.9848077,-0.64278764,0.809017
,-0.309017,0.52991927,0.8480481,0.89879405
,0.43837115,0.9945219,-0.104528464,0.7880108
,-0.6156615,-0.9781476,-0.6946584,-0.7193398
,-0.9702957,-0.2419219,-0.1391731,0.99026805
,0.8910065,0.98768836,0.15643446,-0.15643446
,-0.98768836,-0.4539905,0.42261827,0.9063078
,0.9659258,0.25881904,-0.17364818,0.81915206
,-0.57357645,0.087155744,-0.9961947,0.40673664
,0.9135454,0.7431448,0.6691306,0.20791169
,-0.9945219,-0.7431448,0.37460658,0.92718387
,0.6946584,0.7193398,0.99939084,0.034899496
,0.9396926,-0.6691306,-0.89879405,0.06975647
,-0.9975641,-0.76604444,-0.88294756,-0.46947157
,-0.9612617,0.27563736,-0.7880108,0.6156615
,0.35836795,0.9335804,0.104528464,0.54463905
,-0.83867055,-0.777146,-0.6293204,-0.9986295
,0.052335955,0.2923717,0.9563047,0.5591929
,0.82903755,0.9961947,0.8746197,-0.4848096
,-0.12186934,-0.99254614,-0.656059,-0.7547096
,-0.8480481,-0.52991927,-0.99939084,-0.94551855
,0.32556817,-0.60181504,0.7986355,0.9612617
,-0.37460658,-0.82903755,0.2419219,0.9702957
,0.46947157,0.88294756,-0.034899496,-0.27563736
,-0.06975647,0.22495106,0.97437006,0.9998477
,-0.017452406,0.60181504,-0.7986355,0.190809
,-0.98162717,-0.92050487,-0.39073113,-0.8746197
,0.4848096,0.98162717,0.83867055,0.57357645
,0.8571673,-0.5150381,-0.9563047,-0.2923717
,0.7547096,-0.32556817,0.94551855,0.1391731
,-0.92718387,0.12186934,0.99254614,0.656059
,0.7313537,-0.6819984,-0.9063078,-0.42261827
,-0.190809,-0.8571673,0.5150381,-0.087155744
,-0.81915206,0.9975641,-0.43837115,-0.5591929
,-0.99026805,-0.35836795,-0.54463905,-0.9335804];
