# How to find the x and y Intercept of a Function

Posted 10 years ago
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 Bellow I have a simple script I have written where I attempt to fit a set of data points to a wave equation. At this point I would like to extract the period from this function. To do this I believe I would need to find the x-intercepts. As well as finding the x-intercepts I need to find the Y-Intercept for other reasons. How could I go about doing this? I have attempted the FindInstance[] command and have previously tried using findroot.... but it seems to only give a single solution. FindInstance also doesn't allow you to specifity a range so it gives random solutions that don't corrospnd to one another.(*Look Bellow for Data List*)xAxis = Union[data[[All, 1]]];(*Extract unique values of independent variable*)yMean = Mean@Cases[data, {#, _, c_} -> c] & /@ xAxis;(*Calculate the mean of the column 3 for each specific value of \column 1*)avg = Transpose[{xAxis, yMean}];ListPlotsol = FindFit[avg, a Sin[b x], {{a, 1}, {b, 3}}, x](*{a->1.2645,b->5.44369}*)f[x_] := a Sin[b x] /. solShow[ListPlot[Transpose[{data[[All, 1]], data[[All, 3]]}]], Plot[f, {x, -3, 3}, PlotStyle -> {Red, Thick}]]FindInstance[f == 0, x, Reals, 6](*1.2 a about amplitude an and By can chart checking Curve frequency \like looks see Sin that the this we with>3.*)data={{-3.02, -0.16, -1.36}, {-3.01, -0.16, -1.36}, {-3.01, -0.16, -1.28}, \{-3.01, -0.16, -1.28}, {-3.01, -0.16, -1.2}, {-3., -0.16, -1.2}, \{-3., -0.2, -1.2}, {-3., -0.2, -1.2}, {-3., -0.2, -1.2}, {-2.99, \-0.2, -1.04}, {-2.99, -0.2, -1.12}, {-2.99, -0.2, -1.12}, {-2.99, \-0.2, -1.04}, {-2.98, -0.2, -1.04}, {-2.98, -0.2, -1.04}, {-2.98, \-0.2, -0.96}, {-2.98, -0.24, -0.96}, {-2.97, -0.2, -0.88}, {-2.97, \-0.24, -0.88}, {-2.97, -0.24, -0.88}, {-2.97, -0.24, -0.88}, {-2.96, \-0.24, -0.96}, {-2.96, -0.24, -0.88}, {-2.96, -0.24, -0.72}, {-2.96, \-0.24, -0.72}, {-2.95, -0.24, -0.72}, {-2.95, -0.24, -0.72}, {-2.95, \-0.2, -0.72}, {-2.95, -0.24, -0.72}, {-2.94, -0.24, -0.72}, {-2.94, \-0.24, -0.72}, {-2.94, -0.24, -0.64}, {-2.94, -0.24, -0.64}, {-2.93, \-0.24, -0.56}, {-2.93, -0.24, -0.56}, {-2.93, -0.24, -0.56}, {-2.93, \-0.24, -0.56}, {-2.92, -0.24, -0.48}, {-2.92, -0.24, -0.4}, {-2.92, \-0.24, -0.4}, {-2.92, -0.24, -0.4}, {-2.91, -0.24, -0.4}, {-2.91, \-0.24, -0.4}, {-2.91, -0.24, -0.32}, {-2.91, -0.24, -0.4}, {-2.9, \-0.24, -0.32}, {-2.9, -0.24, -0.32}, {-2.9, -0.24, -0.24}, {-2.9, \-0.24, -0.24}, {-2.89, -0.24, -0.24}, {-2.89, -0.24, -0.32}, {-2.89, \-0.24, -0.08}, {-2.89, -0.28, -0.08}, {-2.88, -0.24, -0.08}, {-2.88, 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{-2.66, -0.08,   1.84}, {-2.65, -0.08, 1.84}, {-2.65, -0.08, 1.92}, {-2.65, -0.08,   1.92}, {-2.65, -0.08, 1.92}, {-2.64, -0.08, 1.92}, {-2.64, -0.08,   1.92}, {-2.64, -0.08, 1.92}, {-2.64, -0.08, 1.92}, {-2.63, -0.04,   2.}, {-2.63, -0.04, 2.}, {-2.63, -0.08, 2.}, {-2.63, -0.04,   2.}, {-2.63, -0.04, 2.}, {-2.62, -0.04, 2.}, {-2.62, -0.04,   2.}, {-2.62, -0.04, 2.08}, {-2.62, -0.04, 2.08}, {-2.61, -0.04,   2.08}, {-2.61, -0.04, 2.08}, {-2.61, -0.04, 2.16}, {-2.61, -0.04,   2.16}, {-2.6, -0.04, 2.16}, {-2.6, -0.04, 2.16}, {-2.6, -0.04,   2.16}, {-2.6, -0.04, 2.16}, {-2.59, -0.04, 2.16}, {-2.59, -0.04,   2.16}, {-2.59, -0.04, 2.16}, {-2.59, 0., 2.16}, {-2.58, -0.04,   2.24}, {-2.58, 0., 2.16}, {-2.58, -0.04, 2.16}, {-2.58, 0.,   2.16}, {-2.57, -0.04, 2.16}, {-2.57, -0.04, 2.16}, {-2.57, 0.,   2.24}, {-2.57, -0.04, 2.16}, {-2.56, -0.04, 2.24}, {-2.56, 0.,   2.24}, {-2.56, -0.04, 2.16}, {-2.55, 0., 2.24}, {-2.55, -0.04,   2.24}, {-2.55, 0., 2.24}, {-2.55, 0., 2.24}, {-2.54, 0.,   2.32}, 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-2.16}, {-1.72, -0.04, -2.24}, {-1.72, \-0.04, -2.24}, {-1.71, -0.08, -2.24}, {-1.71, -0.04, -2.24}, {-1.71, \-0.08, -2.16}, {-1.71, -0.08, -2.24}, {-1.7, -0.08, -2.24}, {-1.7, \-0.08, -2.16}, {-1.7, -0.08, -2.16}, {-1.7, -0.08, -2.08}, {-1.69, \-0.08, -2.08}, {-1.69, -0.08, -2.}, {-1.69, -0.08, -2.}, {-1.69, \-0.08, -2.}, {-1.68, -0.08, -2.}, {-1.68, -0.08, -2.}, {-1.68, -0.08, \-2.}, {-1.68, -0.08, -2.}, {-1.67, -0.08, -2.}, {-1.67, -0.08, -2.}, \{-1.67, -0.08, -2.}, {-1.67, -0.12, -1.92}, {-1.66, -0.08, -1.92}, \{-1.66, -0.08, -1.92}, {-1.66, -0.08, -1.92}, {-1.66, -0.08, -1.84}, \{-1.65, -0.08, -1.84}, {-1.65, -0.08, -1.92}, {-1.65, -0.08, -1.84}, \{-1.65, -0.08, -1.84}, {-1.64, -0.12, -1.84}, {-1.64, -0.08, -1.84}, \{-1.64, -0.08, -1.76}, {-1.64, -0.08, -1.84}, {-1.63, -0.12, -1.68}, \{-1.63, -0.12, -1.76}, {-1.63, -0.12, -1.68}, {-1.63, -0.12, -1.68}, \{-1.63, -0.12, -1.68}, {-1.62, -0.12, -1.68}, {-1.62, -0.12, -1.68}, \{-1.62, -0.12, -1.68}, {-1.62, -0.12, -1.6}, {-1.61, -0.12, -1.6}, \{-1.61, -0.12, -1.6}, {-1.61, -0.12, -1.52}, {-1.61, -0.12, -1.6}, \{-1.6, -0.12, -1.52}, {-1.6, -0.16, -1.52}, {-1.6, -0.12, -1.52}, \{-1.59, -0.16, -1.6}, {-1.59, -0.16, -1.44}, {-1.59, -0.16, -1.44}, \{-1.59, -0.12, -1.36}, {-1.58, -0.16, -1.36}, {-1.58, -0.16, -1.36}, \{-1.58, -0.16, -1.36}, {-1.58, -0.16, -1.28}, {-1.57, -0.16, -1.28}, \{-1.57, -0.16, -1.36}, {-1.57, -0.16, -1.28}, {-1.57, -0.16, -1.28}, \{-1.56, -0.2, -1.28}, {-1.56, -0.16, -1.2}, {-1.56, -0.2, -1.2}, \{-1.56, -0.2, -1.2}, {-1.55, -0.16, -1.2}, {-1.55, -0.16, -1.12}, \{-1.55, -0.2, -1.04}, {-1.55, -0.16, -1.12}, {-1.54, -0.2, -1.04}, \{-1.54, -0.2, -1.04}, {-1.54, -0.2, -1.04}, {-1.54, -0.2, -1.04}, \{-1.53, -0.2, -0.96}, {-1.53, -0.24, -0.96}, {-1.53, -0.24, -0.96}, \{-1.53, -0.2, -0.96}, {-1.52, -0.2, -0.96}, {-1.52, -0.2, -0.88}, \{-1.52, -0.24, -0.88}, {-1.52, -0.24, -0.8}, {-1.51, -0.24, -0.72}, \{-1.51, -0.24, -0.72}, {-1.51, -0.24, -0.72}, {-1.51, -0.24, -0.72}, \{-1.5, -0.24, -0.72}, {-1.5, -0.24, -0.72}, {-1.5, -0.24, -0.64}, \{-1.5, -0.24, -0.64}, {-1.5, -0.24, -0.64}, {-1.49, -0.24, -0.56}, \{-1.49, -0.24, -0.56}, {-1.49, -0.24, -0.56}, {-1.49, -0.24, -0.56}, \{-1.48, -0.24, -0.56}, {-1.48, -0.24, -0.4}, {-1.48, -0.24, -0.4}, \{-1.48, -0.24, -0.4}, {-1.47, -0.24, -0.4}, {-1.47, -0.24, -0.4}, \{-1.47, -0.24, -0.4}, {-1.46, -0.24, -0.4}, {-1.46, -0.24, -0.32}, \{-1.46, -0.24, -0.32}, {-1.46, -0.24, -0.24}, {-1.45, -0.24, -0.32}, \{-1.45, -0.24, -0.32}, {-1.45, -0.24, -0.24}, {-1.45, -0.24, -0.24}, \{-1.44, -0.24, -0.08}, {-1.44, -0.24, -0.08}, {-1.44, -0.24, -0.08}, \{-1.44, -0.24, -0.08}, {-1.43, -0.24, -0.08}, {-1.43, -0.24, -0.08}, \{-1.43, -0.24, -0.08}, {-1.43, -0.24, 0.}, {-1.42, -0.24,   0.08}, {-1.42, -0.24, 0.08}, {-1.42, -0.24, 0.08}, {-1.42, -0.24,   0.08}, {-1.41, -0.24, 0.08}, {-1.41, -0.24, 0.08}, {-1.41, -0.24,   0.16}, {-1.41, -0.24, 0.16}, {-1.4, -0.2, 0.24}, {-1.4, -0.24,   0.24}, {-1.4, -0.24, 0.24}, {-1.4, -0.24, 0.24}, {-1.39, -0.24,   0.32}, {-1.39, -0.24, 0.32}, {-1.39, -0.24, 0.32}, {-1.39, -0.2,   0.32}, {-1.38, -0.2, 0.4}, {-1.38, -0.2, 0.32}, {-1.38, -0.24,   0.56}, {-1.38, -0.24, 0.48}, {-1.38, -0.2, 0.56}, {-1.37, -0.2,   0.56}, {-1.37, -0.2, 0.56}, {-1.37, -0.24, 0.56}, {-1.37, -0.2,   0.64}, {-1.36, -0.2, 0.64}, {-1.36, -0.2, 0.72}, {-1.36, -0.2,   0.72}, {-1.36, -0.24, 0.72}, {-1.35, -0.16, 0.72}, {-1.35, -0.2,   0.72}, {-1.35, -0.16, 0.8}, {-1.35, -0.2, 0.88}, {-1.34, -0.16,   0.8}, {-1.34, -0.16, 0.88}, {-1.34, -0.16, 0.88}, {-1.33, -0.16,   0.88}, {-1.33, -0.16, 0.88}, {-1.33, -0.16, 0.88}, {-1.33, -0.16,   0.96}, {-1.32, -0.16, 0.96}, {-1.32, -0.16, 0.96}, {-1.32, -0.16,   1.04}, {-1.32, -0.16, 1.04}, {-1.31, -0.16, 0.96}, {-1.31, -0.16,   0.96}, {-1.31, -0.16, 1.12}, {-1.31, -0.16, 1.12}, {-1.3, -0.16,   1.12}, {-1.3, -0.16, 1.2}, {-1.3, -0.16, 1.2}, {-1.3, -0.16,   1.2}, {-1.29, -0.16, 1.2}, {-1.29, -0.12, 1.2}, {-1.29, -0.12,   1.28}, {-1.29, -0.12, 1.28}, {-1.28, -0.12, 1.28}, {-1.28, -0.12,   1.36}, {-1.28, -0.12, 1.36}, {-1.28, -0.12, 1.36}, {-1.27, -0.12,   1.36}, {-1.27, -0.12, 1.36}, {-1.27, -0.12, 1.44}, {-1.27, -0.12,   1.52}, {-1.26, -0.12, 1.52}, {-1.26, -0.12, 1.52}, {-1.26, -0.12,   1.52}, {-1.26, -0.12, 1.52}, {-1.25, -0.08, 1.52}, {-1.25, -0.08,   1.52}, {-1.25, -0.08, 1.6}, {-1.25, -0.08, 1.6}, {-1.25, -0.08,   1.6}, {-1.24, -0.08, 1.6}, {-1.24, -0.08, 1.68}, {-1.24, -0.08,   1.68}, {-1.24, -0.08, 1.68}, {-1.23, -0.08, 1.68}, {-1.23, -0.08,   1.6}, {-1.23, -0.08, 1.76}, {-1.23, -0.08, 1.76}, {-1.22, -0.08,   1.76}, {-1.22, -0.08, 1.84}, {-1.22, -0.08, 1.84}, {-1.21, -0.08,   1.84}, {-1.21, -0.08, 1.84}, {-1.21, -0.08, 1.84}, {-1.21, -0.08,   1.84}, {-1.2, -0.08, 1.84}, {-1.2, -0.08, 1.84}, {-1.2, -0.08,   1.92}, {-1.2, -0.08, 1.92}, {-1.19, -0.08, 1.92}, {-1.19, -0.04,   1.92}, {-1.19, -0.08, 2.}, {-1.19, -0.08, 2.}, {-1.18, -0.04,   2.}, {-1.18, -0.08, 2.}, {-1.18, -0.04, 2.}, {-1.18, -0.04,   2.}, {-1.17, -0.04, 2.}, {-1.17, -0.04, 2.}, {-1.17, -0.04,   2.}, {-1.17, -0.04, 2.08}, {-1.16, -0.04, 2.08}, {-1.16, -0.04,   2.08}, {-1.16, -0.04, 2.16}, {-1.16, -0.04, 2.08}, {-1.15, -0.04,   2.16}, {-1.15, -0.04, 2.16}, {-1.15, -0.04, 2.16}, {-1.15, -0.04,   2.16}, {-1.14, -0.04, 2.16}, {-1.14, -0.04, 2.16}, {-1.14, -0.04,   2.16}, {-1.14, 0., 2.16}, {-1.13, -0.04, 2.16}, {-1.13, -0.04,   2.16}, {-1.13, -0.04, 2.16}, {-1.13, -0.04, 2.16}, {-1.13, -0.04,   2.16}, {-1.12, -0.04, 2.16}, {-1.12, 0., 2.16}, {-1.12, 0.,   2.16}, {-1.12, -0.04, 2.16}, {-1.11, -0.04, 2.16}, {-1.11, -0.04,   2.16}, {-1.11, 0., 2.24}, {-1.11, 0., 2.16}, {-1.1, 0.,   2.16}, {-1.1, 0., 2.24}, {-1.1, 0., 2.24}, {-1.1, -0.04,   2.24}, {-1.09, -0.04, 2.24}, {-1.09, -0.04, 2.24}, {-1.09, 0.,   2.24}, {-1.08, 0., 2.24}, {-1.08, 0., 2.24}, {-1.08, 0.,   2.24}, {-1.08, 0., 2.24}, {-1.07, 0., 2.24}, {-1.07, 0.,   2.24}, {-1.07, 0., 2.24}, {-1.07, 0., 2.24}, {-1.06, 0.,   2.24}, {-1.06, 0., 2.24}, {-1.06, 0., 2.24}, {-1.06, 0.,   2.24}, {-1.05, 0., 2.24}, {-1.05, 0., 2.24}, {-1.05, 0.,   2.24}, {-1.05, 0., 2.24}, {-1.04, 0., 2.24}, {-1.04, 0.,   2.24}, {-1.04, 0., 2.24}, {-1.04, 0., 2.24}, {-1.03, 0.,   2.24}, {-1.03, 0., 2.24}, {-1.03, 0., 2.16}, {-1.03, 0.,   2.24}, {-1.02, 0., 2.16}, {-1.02, 0., 2.16}, {-1.02, 0.,   2.16}, {-1.02, 0., 2.16}, {-1.01, 0., 2.16}, {-1.01, 0.04,   2.16}, {-1.01, 0., 2.16}, {-1.01, 0.04, 2.16}, {-1., 0.04,   2.16}, {-1., 0.04, 2.16}, {-1., 0.04, 2.16}, {-0.998, 0.,   2.16}, {-0.995, 0., 2.16}, {-0.993, 0.04, 2.16}, {-0.99, 0.04,   2.16}, {-0.987, 0.04, 2.16}, {-0.985, 0.04, 2.16}, {-0.982, 0.04,   2.16}, {-0.98, 0.04, 2.08}, {-0.977, 0.04, 2.}, {-0.975, 0.04,   2.08}, {-0.972, 0.04, 2.}, {-0.97, 0.04, 2.}, {-0.967, 0.04,   2.}, {-0.965, 0.04, 2.}, {-0.962, 0.04, 2.}, {-0.96, 0.04,   2.}, {-0.957, 0.04, 2.}, {-0.955, 0.04, 2.}, {-0.952, 0.04,   2.}, {-0.95, 0.04, 1.92}, {-0.947, 0.04, 1.92}, {-0.945, 0.04,   2.}, {-0.942, 0.04, 1.92}, {-0.94, 0.04, 1.84}, {-0.938, 0.08,   1.84}, {-0.935, 0.04, 1.84}, {-0.933, 0.08, 1.84}, {-0.93, 0.04,   1.84}, {-0.927, 0.08, 1.84}, {-0.925, 0.08, 1.84}, {-0.922, 0.08,   1.84}, {-0.92, 0.08, 1.68}, {-0.917, 0.08, 1.84}, {-0.915, 0.08,   1.84}, {-0.912, 0.08, 1.68}, {-0.91, 0.08, 1.6}, {-0.907, 0.08,   1.68}, {-0.905, 0.08, 1.6}, {-0.902, 0.08, 1.68}, {-0.9, 0.08,   1.6}, {-0.897, 0.08, 1.6}, {-0.895, 0.08, 1.6}, {-0.892, 0.08,   1.52}, {-0.89, 0.08, 1.52}, {-0.887, 0.08, 1.52}, {-0.885, 0.08,   1.52}, {-0.882, 0.08, 1.52}, {-0.88, 0.08, 1.52}, {-0.877, 0.08,   1.52}, {-0.875, 0.08, 1.44}, {-0.873, 0.12, 1.44}, {-0.87, 0.08,   1.36}, {-0.868, 0.12, 1.36}, {-0.865, 0.12, 1.36}, {-0.862, 0.12,   1.36}, {-0.86, 0.12, 1.36}, {-0.857, 0.16, 1.28}, {-0.855, 0.12,   1.28}, {-0.852, 0.12, 1.28}, {-0.85, 0.12, 1.2}, {-0.847, 0.16,   1.2}, {-0.845, 0.16, 1.2}, {-0.842, 0.16, 1.2}, {-0.84, 0.12,   1.2}, {-0.837, 0.16, 1.2}, {-0.835, 0.16, 1.2}, {-0.832, 0.16,   1.04}, {-0.83, 0.16, 1.04}, {-0.827, 0.16, 0.96}, {-0.825, 0.16,   0.96}, {-0.822, 0.16, 1.04}, {-0.82, 0.16, 1.04}, {-0.817, 0.16,   1.04}, {-0.815, 0.16, 0.96}, {-0.813, 0.16, 0.96}, {-0.81, 0.2,   0.88}, {-0.808, 0.16, 0.88}, {-0.805, 0.16, 0.88}, {-0.803, 0.2,   0.88}, {-0.8, 0.2, 0.88}, {-0.797, 0.16, 0.8}, {-0.795, 0.2,   0.8}, {-0.792, 0.2, 0.72}, {-0.79, 0.2, 0.72}, {-0.787, 0.2,   0.72}, {-0.785, 0.2, 0.72}, {-0.782, 0.2, 0.64}, {-0.78, 0.2,   0.64}, {-0.777, 0.2, 0.64}, {-0.775, 0.2, 0.64}, {-0.772, 0.2,   0.56}, {-0.77, 0.2, 0.56}, {-0.767, 0.2, 0.56}, {-0.765, 0.2,   0.56}, {-0.762, 0.2, 0.56}, {-0.76, 0.2, 0.56}, {-0.757, 0.2,   0.32}, {-0.755, 0.2, 0.32}, {-0.752, 0.2, 0.4}, {-0.75, 0.2,   0.32}, {-0.748, 0.2, 0.32}, {-0.745, 0.2, 0.32}, {-0.743, 0.2,   0.24}, {-0.74, 0.2, 0.24}, {-0.738, 0.2, 0.24}, {-0.735, 0.2,   0.24}, {-0.732, 0.2, 0.16}, {-0.73, 0.2, 0.16}, {-0.727, 0.2,   0.16}, {-0.725, 0.2, 0.08}, {-0.722, 0.2, 0.08}, {-0.72, 0.24,   0.08}, {-0.717, 0.2, 0.08}, {-0.715, 0.2, 0.}, {-0.712, 0.2,   0.}, {-0.71, 0.2, 0.}, {-0.707, 0.2, 0.}, {-0.705,   0.2, -0.08}, {-0.702, 0.2, -0.08}, {-0.7, 0.2, -0.08}, {-0.697,   0.2, -0.24}, {-0.695, 0.2, -0.24}, {-0.692, 0.2, -0.16}, {-0.69,   0.2, -0.24}, {-0.688, 0.2, -0.24}, {-0.685, 0.2, -0.24}, {-0.683,   0.2, -0.32}, {-0.68, 0.24, -0.4}, {-0.678, 0.2, -0.4}, {-0.675,   0.2, -0.32}, {-0.673, 0.2, -0.4}, {-0.67, 0.16, -0.4}, {-0.667,   0.2, -0.4}, {-0.665, 0.2, -0.4}, {-0.662, 0.2, -0.48}, {-0.66,   0.16, -0.48}, {-0.657, 0.16, -0.56}, {-0.655, 0.16, -0.56}, {-0.652,   0.16, -0.56}, {-0.65, 0.2, -0.56}, {-0.647, 0.16, -0.56}, {-0.645,   0.2, -0.64}, {-0.642, 0.2, -0.56}, {-0.64, 0.16, -0.72}, {-0.637,   0.16, -0.72}, {-0.635, 0.16, -0.72}, {-0.632, 0.16, -0.72}, {-0.63,   0.16, -0.72}, {-0.627, 0.16, -0.72}, {-0.625, 0.16, -0.8}, {-0.623,   0.16, -0.8}, {-0.62, 0.16, -0.88}, {-0.618, 0.16, -0.96}, {-0.615,   0.16, -0.88}, {-0.613, 0.16, -0.96}, {-0.61, 0.16, -0.96}, {-0.607,   0.16, -0.96}, {-0.605, 0.16, -1.04}, {-0.602, 0.16, -1.04}, {-0.6,   0.12, -1.04}, {-0.597, 0.16, -1.04}, {-0.595, 0.12, -1.04}, {-0.592,   0.12, -1.12}, {-0.59, 0.12, -1.04}, {-0.587, 0.12, -1.12}, {-0.585,   0.12, -1.2}, {-0.582, 0.12, -1.2}, {-0.58, 0.12, -1.2}, {-0.577,   0.12, -1.2}, {-0.575, 0.12, -1.2}, {-0.572, 0.08, -1.28}, {-0.57,   0.08, -1.28}, {-0.567, 0.12, -1.28}, {-0.565, 0.12, -1.36}, {-0.563,   0.08, -1.36}, {-0.56, 0.08, -1.36}, {-0.558, 0.08, -1.36}, {-0.555,   0.08, -1.36}, {-0.553, 0.08, -1.36}, {-0.55, 0.08, -1.36}, {-0.548,   0.08, -1.44}, {-0.545, 0.08, -1.52}, {-0.542, 0.08, -1.52}, {-0.54,   0.08, -1.6}, {-0.537, 0.08, -1.52}, {-0.535, 0.08, -1.52}, {-0.532,   0.08, -1.6}, {-0.53, 0.08, -1.6}, {-0.527, 0.08, -1.6}, {-0.525,   0.08, -1.6}, {-0.522, 0.08, -1.6}, {-0.52, 0.08, -1.68}, {-0.517,   0.04, -1.68}, {-0.515, 0.08, -1.68}, {-0.512, 0.04, -1.68}, {-0.51,   0.08, -1.68}, {-0.507, 0.04, -1.76}, {-0.505, 0.04, -1.68}, {-0.502,   0.04, -1.76}, {-0.5, 0.04, -1.84}, {-0.498, 0.04, -1.84}, {-0.495,   0.08, -1.76}, {-0.492, 0.04, -1.84}, {-0.49, 0.04, -1.84}, {-0.487,   0.04, -1.84}, {-0.485, 0.04, -1.84}, {-0.482, 0.04, -1.92}, {-0.48,   0.04, -1.92}, {-0.477, 0.04, -1.92}, {-0.475, 0.04, -1.92}, {-0.472,   0.04, -1.92}, {-0.47, 0.04, -1.92}, {-0.468, 0.04, -2.}, {-0.465,   0.04, -2.}, {-0.462, 0.04, -2.}, {-0.46, 0.04, -2.}, {-0.457,   0.04, -2.}, {-0.455, 0.04, -2.}, {-0.452, 0.04, -2.}, {-0.45,   0.04, -2.}, {-0.447, 0., -2.}, {-0.445, 0.04, -2.}, {-0.442,   0.04, -2.}, {-0.44, 0., -2.08}, {-0.438, 0., -2.16}, {-0.435,   0., -2.}, {-0.433, 0., -2.16}, {-0.43, 0., -2.16}, {-0.427,   0., -2.24}, {-0.425, 0., -2.24}, {-0.422, 0.04, -2.16}, {-0.42,   0., -2.16}, {-0.417, 0., -2.24}, {-0.415, 0., -2.16}, {-0.412,   0., -2.16}, {-0.41, 0., -2.16}, {-0.407, 0., -2.24}, {-0.405,   0., -2.16}, {-0.403, 0., -2.16}, {-0.4, 0., -2.16}, {-0.397,   0., -2.16}, {-0.395, 0., -2.24}, {-0.392, 0., -2.24}, {-0.39,   0., -2.24}, {-0.387, 0., -2.24}, {-0.385, 0., -2.24}, {-0.382,   0., -2.24}, {-0.38, 0., -2.24}, {-0.377, 0., -2.32}, {-0.375,   0., -2.32}, {-0.373, 0., -2.24}, {-0.37, 0., -2.24}, {-0.367,   0., -2.32}, {-0.365, 0., -2.24}, {-0.362, 0., -2.32}, {-0.36,   0., -2.32}, {-0.357, -0.04, -2.32}, {-0.355, -0.04, -2.32}, {-0.352,   0., -2.24}, {-0.35,   0., -2.32}, {-0.347, -0.04, -2.32}, {-0.345, -0.04, -2.32}, {-0.343,   0., -2.32}, {-0.34,   0., -2.32}, {-0.338, -0.04, -2.32}, {-0.335, -0.04, -2.32}, {-0.332,   0., -2.32}, {-0.33, -0.04, -2.24}, {-0.327, -0.04, -2.24}, {-0.325,   0., -2.32}, {-0.322, -0.04, -2.24}, {-0.32, -0.04, -2.24}, \{-0.317, -0.04, -2.32}, {-0.315, -0.04, -2.24}, {-0.313, -0.04, \-2.32}, {-0.31, -0.04, -2.24}, {-0.308, -0.04, -2.24}, {-0.305, \-0.04, -2.24}, {-0.302, -0.04, -2.24}, {-0.3, -0.04, -2.24}, {-0.297, \-0.08, -2.16}, {-0.295, -0.04, -2.16}, {-0.292, -0.04, -2.16}, \{-0.29, -0.04, -2.16}, {-0.287, -0.08, -2.16}, {-0.285, -0.04, \-2.16}, {-0.282, -0.04, -2.16}, {-0.28, -0.04, -2.24}, {-0.278, \-0.08, -2.16}, {-0.275, -0.08, -2.16}, {-0.273, -0.08, -2.16}, \{-0.27, -0.08, -2.24}, {-0.267, -0.08, -2.24}, {-0.265, -0.04, \-2.24}, {-0.262, -0.08, -2.08}, {-0.26, 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{-0.153, -0.12, \-1.52}, {-0.15, -0.16, -1.44}, {-0.147, -0.16, -1.44}, {-0.145, \-0.16, -1.44}, {-0.142, -0.16, -1.36}, {-0.14, -0.16, -1.36}, \{-0.138, -0.16, -1.36}, {-0.135, -0.16, -1.36}, {-0.132, -0.16, \-1.36}, {-0.13, -0.16, -1.28}, {-0.127, -0.16, -1.36}, {-0.125, \-0.16, -1.28}, {-0.122, -0.16, -1.2}, {-0.12, -0.16, -1.2}, {-0.117, \-0.16, -1.2}, {-0.115, -0.16, -1.2}, {-0.112, -0.16, -1.2}, {-0.11, \-0.2, -1.2}, {-0.107, -0.16, -1.04}, {-0.105, -0.2, -1.04}, {-0.102, \-0.2, -1.12}, {-0.1, -0.2, -1.04}, {-0.0975, -0.2, -1.04}, {-0.095, \-0.2, -0.96}, {-0.0925, -0.2, -0.96}, {-0.09, -0.2, -0.96}, {-0.0875, \-0.2, -0.96}, {-0.085, -0.24, -0.88}, {-0.0825, -0.24, -0.88}, \{-0.08, -0.2, -0.96}, {-0.0775, -0.2, -0.88}, {-0.075, -0.24, -0.88}, \{-0.0725, -0.24, -0.8}, {-0.07, -0.24, -0.72}, {-0.0675, -0.24, \-0.72}, {-0.065, -0.24, -0.72}, {-0.0625, -0.24, -0.72}, {-0.06, \-0.24, -0.72}, {-0.0575, -0.24, -0.64}, {-0.055, -0.24, -0.64}, \{-0.0525, -0.24, -0.64}, {-0.05, -0.24, 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1.36}, {0.172, -0.12,   1.36}, {0.175, -0.12, 1.44}, {0.177, -0.12, 1.44}, {0.18, -0.08,   1.52}, {0.182, -0.08, 1.52}, {0.185, -0.08, 1.52}, {0.188, -0.08,   1.52}, {0.19, -0.08, 1.52}, {0.192, -0.08, 1.52}, {0.195, -0.08,   1.6}, {0.197, -0.08, 1.6}, {0.2, -0.08, 1.68}, {0.203, -0.08,   1.6}, {0.205, -0.08, 1.68}, {0.207, -0.08, 1.6}, {0.21, -0.08,   1.6}, {0.212, -0.08, 1.68}, {0.215, -0.08, 1.68}, {0.218, -0.08,   1.76}, {0.22, -0.08, 1.84}, {0.222, -0.08, 1.84}, {0.225, -0.08,   1.84}, {0.227, -0.08, 1.84}, {0.23, -0.08, 1.84}, {0.233, -0.08,   1.84}, {0.235, -0.08, 1.84}, {0.237, -0.08, 1.84}, {0.24, -0.08,   1.84}, {0.242, -0.08, 1.92}, {0.245, -0.08, 1.92}, {0.247, -0.04,   1.92}, {0.25, -0.08, 2.}, {0.252, -0.08, 1.92}, {0.255, -0.04,   2.}, {0.257, -0.08, 2.}, {0.26, -0.08, 2.}, {0.262, -0.04,   2.}, {0.265, -0.04, 2.}, {0.267, -0.04, 2.}, {0.27, -0.04,   2.}, {0.273, -0.08, 2.}, {0.275, -0.04, 2.}, {0.278, -0.04,   2.}, {0.28, -0.04, 2.08}, {0.282, -0.04, 2.08}, {0.285, 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1.6}, {0.53, 0.08, 1.6}, {0.532, 0.08, 1.68}, {0.535, 0.08,   1.6}, {0.537, 0.08, 1.68}, {0.54, 0.08, 1.68}, {0.542, 0.08,   1.6}, {0.545, 0.08, 1.52}, {0.548, 0.08, 1.6}, {0.55, 0.08,   1.52}, {0.553, 0.08, 1.52}, {0.555, 0.12, 1.52}, {0.558, 0.08,   1.52}, {0.56, 0.12, 1.52}, {0.563, 0.12, 1.52}, {0.565, 0.12,   1.44}, {0.567, 0.12, 1.44}, {0.57, 0.12, 1.36}, {0.572, 0.12,   1.36}, {0.575, 0.12, 1.36}, {0.577, 0.12, 1.36}, {0.58, 0.12,   1.36}, {0.582, 0.16, 1.28}, {0.585, 0.12, 1.28}, {0.587, 0.12,   1.2}, {0.59, 0.16, 1.2}, {0.592, 0.16, 1.2}, {0.595, 0.16,   1.2}, {0.597, 0.16, 1.2}, {0.6, 0.16, 1.2}, {0.602, 0.16,   1.2}, {0.605, 0.16, 1.2}, {0.607, 0.12, 1.04}, {0.61, 0.16,   1.04}, {0.613, 0.16, 0.96}, {0.615, 0.16, 1.04}, {0.618, 0.16,   1.04}, {0.62, 0.16, 0.96}, {0.623, 0.16, 0.96}, {0.625, 0.16,   0.88}, {0.627, 0.16, 0.96}, {0.63, 0.16, 0.88}, {0.632, 0.2,   0.88}, {0.635, 0.16, 0.88}, {0.637, 0.16, 0.88}, {0.64, 0.16,   0.8}, {0.642, 0.2, 0.8}, {0.645, 0.2, 0.72}, {0.647, 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0.08, -1.36}, {0.885, 0.08, -1.36}, {0.887, 0.08, -1.36}, {0.89,   0.08, -1.36}, {0.892, 0.08, -1.36}, {0.895, 0.08, -1.44}, {0.897,   0.08, -1.44}, {0.9, 0.08, -1.6}, {0.902, 0.08, -1.52}, {0.905,   0.08, -1.52}, {0.907, 0.08, -1.52}, {0.91, 0.08, -1.6}, {0.912,   0.08, -1.6}, {0.915, 0.08, -1.68}, {0.917, 0.08, -1.6}, {0.92,   0.08, -1.68}, {0.922, 0.08, -1.68}, {0.925, 0.08, -1.68}, {0.927,   0.08, -1.68}, {0.93, 0.08, -1.68}, {0.933, 0.04, -1.68}, {0.935,   0.04, -1.68}, {0.938, 0.08, -1.76}, {0.94, 0.04, -1.76}, {0.942,   0.04, -1.76}, {0.945, 0.04, -1.84}, {0.947, 0.04, -1.84}, {0.95,   0.04, -1.84}, {0.952, 0.04, -1.84}, {0.955, 0.04, -1.84}, {0.957,   0.04, -1.84}, {0.96, 0.04, -1.92}, {0.962, 0.04, -1.92}, {0.965,   0.04, -1.92}, {0.967, 0.04, -1.92}, {0.97, 0.04, -2.}, {0.972,   0.04, -2.}, {0.975, 0.04, -2.}, {0.977, 0.04, -2.}, {0.98,   0.04, -2.}, {0.982, 0.04, -2.}, {0.985, 0., -2.}, {0.987,   0.04, -2.}, {0.99, 0.04, -2.}, {0.993, 0.04, -2.}, {0.995,   0.04, -2.}, 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1.2}, {1.58, -0.12, 1.2}, {1.59, -0.12, 1.2}, {1.59, -0.12,   1.2}, {1.59, -0.12, 1.2}, {1.59, -0.12, 1.2}, {1.6, -0.12,   1.28}, {1.6, -0.12, 1.28}, {1.6, -0.12, 1.36}, {1.61, -0.12,   1.36}, {1.61, -0.12, 1.36}, {1.61, -0.12, 1.36}, {1.61, -0.12,   1.36}, {1.62, -0.12, 1.36}, {1.62, -0.12, 1.44}, {1.62, -0.12,   1.52}, {1.62, -0.08, 1.52}, {1.63, -0.08, 1.44}, {1.63, -0.08,   1.52}, {1.63, -0.08, 1.52}, {1.63, -0.08, 1.52}, {1.63, -0.08,   1.52}, {1.64, -0.08, 1.52}, {1.64, -0.12, 1.6}, {1.64, -0.08,   1.6}, {1.64, -0.08, 1.6}, {1.65, -0.08, 1.6}, {1.65, -0.08,   1.6}, {1.65, -0.08, 1.68}, {1.65, -0.08, 1.68}, {1.66, -0.08,   1.6}, {1.66, -0.08, 1.76}, {1.66, -0.08, 1.76}, {1.66, -0.08,   1.68}, {1.67, -0.08, 1.76}, {1.67, -0.08, 1.84}, {1.67, -0.08,   1.84}, {1.67, -0.08, 1.84}, {1.68, -0.08, 1.84}, {1.68, -0.08,   1.84}, {1.68, -0.08, 1.84}, {1.68, -0.08, 1.84}, {1.69, -0.04,   1.84}, {1.69, -0.04, 1.92}, {1.69, -0.04, 1.92}, {1.69, -0.08,   1.92}, {1.7, -0.08, 2.}, {1.7, -0.04, 1.92}, {1.7, -0.08,   2.}, {1.7, -0.04, 2.}, {1.71, -0.08, 2.}, {1.71, -0.04,   2.}, {1.71, -0.04, 2.}, {1.71, -0.04, 2.}, {1.72, -0.04,   2.}, {1.72, -0.04, 2.}, {1.72, -0.08, 2.}, {1.72, -0.04,   2.08}, {1.73, 0., 2.08}, {1.73, -0.04, 2.}, {1.73, -0.04,   2.08}, {1.74, -0.04, 2.08}, {1.74, 0., 2.08}, {1.74, -0.04,   2.08}, {1.74, -0.04, 2.16}, {1.75, -0.04, 2.}, {1.75, -0.04,   2.16}, {1.75, -0.04, 2.16}, {1.75, 0., 2.16}, {1.75, 0.,   2.16}, {1.76, 0., 2.16}, {1.76, -0.04, 2.16}, {1.76, -0.04,   2.16}, {1.76, -0.04, 2.16}, {1.77, 0., 2.16}, {1.77, 0.,   2.16}, {1.77, 0., 2.16}, {1.77, -0.04, 2.16}, {1.78, 0.,   2.16}, {1.78, -0.04, 2.16}, {1.78, 0., 2.16}, {1.78, 0.,   2.16}, {1.79, 0., 2.16}, {1.79, 0., 2.16}, {1.79, 0., 2.24}, {1.79,   0., 2.16}, {1.8, 0., 2.24}, {1.8, 0., 2.16}, {1.8, 0., 2.16}, {1.8,   0., 2.16}, {1.81, 0., 2.16}, {1.81, 0., 2.16}, {1.81, -0.04,   2.16}, {1.81, 0., 2.16}, {1.82, 0., 2.16}, {1.82, 0., 2.16}, {1.82,   0., 2.16}, {1.82, 0., 2.16}, {1.83, 0., 2.16}, {1.83, 0.,   2.16}, {1.83, 0., 2.16}, {1.83, 0., 2.16}, {1.84, 0., 2.16}, {1.84,   0., 2.16}, {1.84, 0., 2.16}, {1.84, 0., 2.16}, {1.85, 0.,   2.16}, {1.85, 0., 2.16}, {1.85, 0., 2.16}, {1.85, 0., 2.16}, {1.86,   0., 2.16}, {1.86, 0., 2.16}, {1.86, 0., 2.16}, {1.87, 0.,   2.16}, {1.87, 0., 2.16}, {1.87, 0., 2.16}, {1.87, 0.04,   2.16}, {1.88, 0., 2.16}, {1.88, 0.04, 2.08}, {1.88, 0.04,   2.16}, {1.88, 0.04, 2.16}, {1.88, 0., 2.08}, {1.89, 0.04,   2.08}, {1.89, 0.04, 2.08}, {1.89, 0.04, 2.16}, {1.89, 0.04,   2.08}, {1.9, 0.04, 2.}, {1.9, 0.04, 2.}, {1.9, 0.04, 2.}, {1.9,   0.04, 2.}, {1.91, 0.04, 2.}, {1.91, 0.04, 2.}, {1.91, 0.04,   2.}, {1.91, 0.04, 2.}, {1.92, 0.04, 2.}, {1.92, 0.04, 2.}, {1.92,   0.04, 2.}, {1.92, 0.04, 1.84}, {1.93, 0.04, 1.92}, {1.93, 0.04,   1.92}, {1.93, 0.04, 1.92}, {1.93, 0.08, 1.84}, {1.94, 0.08,   1.92}, {1.94, 0.04, 1.84}, {1.94, 0.04, 1.84}, {1.94, 0.08,   1.84}, {1.95, 0.08, 1.84}, {1.95, 0.04, 1.84}, {1.95, 0.08,   1.84}, {1.95, 0.08, 1.84}, {1.96, 0.08, 1.76}, {1.96, 0.08,   1.68}, {1.96, 0.08, 1.76}, {1.96, 0.08, 1.76}, {1.97, 0.08,   1.76}, {1.97, 0.08, 1.68}, {1.97, 0.08, 1.6}, {1.97, 0.08,   1.68}, {1.98, 0.08, 1.68}, {1.98, 0.08, 1.68}, {1.98, 0.08,   1.6}, {1.99, 0.08, 1.6}, {1.99, 0.08, 1.52}, {1.99, 0.08,   1.52}, {1.99, 0.08, 1.52}, {2., 0.08, 1.52}, {2., 0.12, 1.52}, {2.,   0.08, 1.52}, {2., 0.12, 1.44}, {2., 0.12, 1.44}, {2.01, 0.08,   1.36}, {2.01, 0.12, 1.36}, {2.01, 0.08, 1.36}, {2.01, 0.12,   1.36}, {2.02, 0.12, 1.36}, {2.02, 0.12, 1.36}, {2.02, 0.12,   1.36}, {2.02, 0.12, 1.28}, {2.03, 0.16, 1.28}, {2.03, 0.12,   1.28}, {2.03, 0.16, 1.2}, {2.03, 0.16, 1.2}, {2.04, 0.16,   1.2}, {2.04, 0.16, 1.2}, {2.04, 0.16, 1.2}, {2.04, 0.16,   1.2}, {2.05, 0.16, 1.12}, {2.05, 0.12, 1.12}, {2.05, 0.16,   0.96}, {2.06, 0.16, 0.96}, {2.06, 0.16, 1.04}, {2.06, 0.16,   0.96}, {2.06, 0.2, 1.04}, {2.07, 0.16, 0.96}, {2.07, 0.16,   0.96}, {2.07, 0.16, 0.88}, {2.07, 0.16, 0.88}, {2.08, 0.16,   0.88}, {2.08, 0.16, 0.88}, {2.08, 0.16, 0.8}, 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