N, log(err) theta ~ 0, log(err) theta ~ pi/2, log(err) theta ~ pi 256, -13.6603, 0.576975, 1.99618 512, -13.2115, 0.392154, 2.4808 1024, -12.2524, 0.402099, 1.53426 2048, -12.2997, 0.876779, 1.82357 4096, -11.5949, 0.617393, 1.85418 8192, -11.2177, -0.0495326, 2.19589 16384, -11.2597, 1.02899, 2.43345 32768, -10.0855, 0.202046, 2.77032 65536, -9.99821, 0.408188, 2.83484 131072, -8.49087, 0.694223, 3.53864 262144, -8.82946, 0.599331, 3.48252 524288, -8.04363, 0.617189, 3.91063 1048576, -7.66483, 0.70864, 4.27771 2097152, -7.38818, 0.887405, 3.77672 4194304, -6.56794, 1.24452, 4.57043 8388608, -5.79699, 0.91462, 4.94472 16777216, -5.31444, 1.63695, 4.58285 33554432, -5.49517, 1.1116, 6.32326 67108864, -4.69461, 0.755833, 5.08611