HW #10

Due: 11/20/2023

Note: If you have not registered on the web, your hw paper is NOT graded.

Submission Instructions: (Important! If you do not follow them, your paper is not graded.)

Template (word file)
One page for each problem (a total of 2 pages). 50 % Penalty if not followed.
Make a single PDF file. File name: hw_10_doe_john.pdf.
Email the PDF file to me5331exam@gmail.com with the subject line: Doe, John, HW#10

1. Remove noise from the signal below and plot the original signal less noise.

(MATLAB/Octave users)

y=[6.28345, 3.22246, 5.39914, 3.60865, 3.65644, 4.9384, 6.71493, 4.66608, 4.95818, 4.87514, 3.65405, 5.58718, 4.40297, 3.56216, 4.26301, 7.17059, 3.8773, 3.65189, 2.62594, 6.38777, 5.10231, 4.97363, 4.92931, 6.88091, 4.02733, 4.91927, 5.35723, 5.22676, 4.93593, 3.10154, 3.80014, 4.06031, 4.0938, 2.32529, 2.33921, 2.54891, 1.34026, 2.67622, 0.942549, 4.21709, 2.67793, 1.7866, 3.44514, 0.0870244, -0.296949, -0.0974269, 3.39252, -0.730539, 1.95505, 2.28344, 0.691118, 1.63496, 3.37392, -0.796132, 3.18227, 2.27203, 2.54027, 1.34103, -0.0650801, 2.77979, 0.714989, -0.835475, 0.531536, 1.98343, -0.335429, 1.24667, 0.81676, 1.38371, 0.667464, 2.42286, 1.00915, -0.0767671, 2.68488, -0.8332, 2.4854, 1.54572, 1.3195, 4.73976, 0.990827, 1.99647, 3.02067, 2.3319, 2.73444, 1.29938, 4.91075, 1.16644, 1.53354, 4.70443, 3.47393, 3.30089, 3.79532, 2.69182, 4.33596, 1.89338, 3.20495, 2.26482, 4.02946, 4.99474, 2.44974, 2.19765, 3.03248, 2.99834, 5.27905, 4.484, 1.15131, 4.72466, 4.10129, 4.63075, 2.25385, 3.92437, 4.09418, 3.91403, 1.342, 1.18493, 2.21738, 2.8371, 1.28084, 4.20303, 3.24356, 3.70767, 2.99487, 1.75703, 2.94221, 3.75199, 1.57677, 2.51171, 5.17309, 1.45874, 3.7486, 2.98649, 4.31283, 3.06652, 2.98886, 1.06716, 3.79495, 2.95823, 3.86032, 2.09225, 2.44123, 2.30055, 4.37755, 3.12176, 3.90007, 1.82306, 2.71626, 4.70279, 2.9145, 1.78829, 5.05247, 5.75262, 4.72955, 5.63518, 4.70264, 2.93391, 5.29481, 5.67629, 3.21819, 3.58788, 6.99283, 6.66301, 6.87711, 1.91899, 5.12603, 3.32968, 5.6337, 3.56705, 3.56726, 3.27185, 5.77811, 7.05581, 6.19436, 1.93323, 6.78286, 5.59857, 5.15317, 5.77036, 5.11903, 3.79379, 5.02595, 3.97256, 4.76766, 4.2986, 5.9101, 3.75019, 4.45336, 3.41256, 2.3897, 4.65437, 4.19994, 1.80178, 1.92235, 2.58043, 1.8049, 0.727705, 2.23352, 3.20678, 1.99824, -0.100039, -0.398669, 1.0254, 1.06878, 0.779708, 0.592887, 1.63836, 0.022458, 2.04382, 0.924611, 1.87949, -0.219661, 2.75017, 2.97187, 0.445748, 0.558413, 0.162202, 2.50927, 1.02211, 2.84669, 3.30699, 0.326872, 3.81569, 0.825398, 1.34227, 2.13528, 3.29024, -0.0106859, 3.46575, 1.8493, 2.85042, 1.55254, 2.14178, 3.87732, 2.93549, 3.72309, 2.3297, 0.492662, 2.01528, 3.55222, 3.57302, 2.80209, 3.99803, 2.50128, 3.18386, 2.12652, 3.82451, 3.95133, 1.21219, 3.24286, 4.94487, 3.599, 3.23689, 0.814642, 3.30503, 4.32353, 2.1707, 2.38114, 2.56006];

(Mathematica users)

y={6.28345, 3.22246, 5.39914, 3.60865, 3.65644, 4.9384, 6.71493, 4.66608, 4.95818, 4.87514, 3.65405, 5.58718, 4.40297, 3.56216, 4.26301, 7.17059, 3.8773, 3.65189, 2.62594, 6.38777, 5.10231, 4.97363, 4.92931, 6.88091, 4.02733, 4.91927, 5.35723, 5.22676, 4.93593, 3.10154, 3.80014, 4.06031, 4.0938, 2.32529, 2.33921, 2.54891, 1.34026, 2.67622, 0.942549, 4.21709, 2.67793, 1.7866, 3.44514, 0.0870244, -0.296949, -0.0974269, 3.39252, -0.730539, 1.95505, 2.28344, 0.691118, 1.63496, 3.37392, -0.796132, 3.18227, 2.27203, 2.54027, 1.34103, -0.0650801, 2.77979, 0.714989, -0.835475, 0.531536, 1.98343, -0.335429, 1.24667, 0.81676, 1.38371, 0.667464, 2.42286, 1.00915, -0.0767671, 2.68488, -0.8332, 2.4854, 1.54572, 1.3195, 4.73976, 0.990827, 1.99647, 3.02067, 2.3319, 2.73444, 1.29938, 4.91075, 1.16644, 1.53354, 4.70443, 3.47393, 3.30089, 3.79532, 2.69182, 4.33596, 1.89338, 3.20495, 2.26482, 4.02946, 4.99474, 2.44974, 2.19765, 3.03248, 2.99834, 5.27905, 4.484, 1.15131, 4.72466, 4.10129, 4.63075, 2.25385, 3.92437, 4.09418, 3.91403, 1.342, 1.18493, 2.21738, 2.8371, 1.28084, 4.20303, 3.24356, 3.70767, 2.99487, 1.75703, 2.94221, 3.75199, 1.57677, 2.51171, 5.17309, 1.45874, 3.7486, 2.98649, 4.31283, 3.06652, 2.98886, 1.06716, 3.79495, 2.95823, 3.86032, 2.09225, 2.44123, 2.30055, 4.37755, 3.12176, 3.90007, 1.82306, 2.71626, 4.70279, 2.9145, 1.78829, 5.05247, 5.75262, 4.72955, 5.63518, 4.70264, 2.93391, 5.29481, 5.67629, 3.21819, 3.58788, 6.99283, 6.66301, 6.87711, 1.91899, 5.12603, 3.32968, 5.6337, 3.56705, 3.56726, 3.27185, 5.77811, 7.05581, 6.19436, 1.93323, 6.78286, 5.59857, 5.15317, 5.77036, 5.11903, 3.79379, 5.02595, 3.97256, 4.76766, 4.2986, 5.9101, 3.75019, 4.45336, 3.41256, 2.3897, 4.65437, 4.19994, 1.80178, 1.92235, 2.58043, 1.8049, 0.727705, 2.23352, 3.20678, 1.99824, -0.100039, -0.398669, 1.0254, 1.06878, 0.779708, 0.592887, 1.63836, 0.022458, 2.04382, 0.924611, 1.87949, -0.219661, 2.75017, 2.97187, 0.445748, 0.558413, 0.162202, 2.50927, 1.02211, 2.84669, 3.30699, 0.326872, 3.81569, 0.825398, 1.34227, 2.13528, 3.29024, -0.0106859, 3.46575, 1.8493, 2.85042, 1.55254, 2.14178, 3.87732, 2.93549, 3.72309, 2.3297, 0.492662, 2.01528, 3.55222, 3.57302, 2.80209, 3.99803, 2.50128, 3.18386, 2.12652, 3.82451, 3.95133, 1.21219, 3.24286, 4.94487, 3.599, 3.23689, 0.814642, 3.30503, 4.32353, 2.1707, 2.38114, 2.56006};

Describe how you can get the result. Listing your code is accepted.

2. Monthly sunspots activities data from January, 1749 to September, 2016 (268 years = 3213 months) are given below. source

Source:https://solarscience.msfc.nasa.gov/SunspotCycle.shtml

For MATLAB/Octave users:

x=[96.7,104.3,116.7,92.8,141.7,139.2,158,110.5,126.5,125.8,264.3,142,122.2,126.5,148.7,147.2,150,166.7,142.3,171.7,152,109.5,105.5,125.7,116.7,72.5,75.5,94,101.2,84.5,110.5,99.7,39.2,38.7,47.5,73.3,58.3,83.3,118.3,98.8,99.5,66,130.7,48.8,45.2,77.7,62.7,66.7,73.3,53.3,76.2,63.3,60,52.8,36.7,65,46.7,41.7,33.3,11.2,0,5,2.8,22.8,34.5,44.5,31.3,20.5,13.7,40.2,22,7,17,18.7,11.3,10.8,0,0,14.3,5.3,29.7,39.5,11.3,33.3,20.8,11.8,9,15.7,20.8,21.5,6,10.7,19.7,23.8,28.3,15.7,23.5,35.3,43.7,50,63.5,21.3,41.7,85.5,66.2,54.2,107.8,55.8,62.7,86.7,81.7,120.5,77.3,75,73.3,64.5,104.2,62.8,71.7,71.7,80.5,73.3,78,78.3,81.7,83.3,85,118.8,128.7,99.5,77.2,95,112.2,99.2,124.5,97.2,120,80.5,110,126,102.2,84.3,99.5,101.7,116.7,151.7,134.5,119.5,178.7,165.5,156.8,151.8,167.8,147.8,149.5,76.7,73,121.3,76.2,100.3,66.5,128.5,56.3,112.8,114.2,115.5,129.7,128.7,94.2,53.2,57,54.8,54.5,59.7,90.3,44.2,113.5,77.2,101.5,102.3,99.5,99.5,67,57.3,73.8,50,50,50,47,46.7,43.3,42.8,40,43.3,41.7,36.7,33.7,33.3,45,49.5,26.7,23.3,23.3,21.7,20,18.3,61,10,44.7,5,5.5,6.7,7.2,8.3,9.5,32,45.7,50,71.7,54.8,49.7,55.5,36.5,68,71.2,73.5,91.2,88.8,89.2,110.2,77.2,71.2,129.5,129,87.7,111.3,124.7,129.7,151,186.3,123.2,107,107.2,161.2,122.7,157.3,197.7,200.5,248,263.7,246.8,186.7,173.3,237.5,133.5,85,116.8,138.8,183,210.5,174,172.7,220.3,170.5,60,77,77.8,108.2,254.5,199.2,112.8,97.5,169,150,166.2,159.5,168.2,151.3,51.8,153.7,63.3,95,128.8,93.7,84.2,131,102.2,106.7,91,48.3,85.3,54.8,68.5,47.3,46.2,21.2,48.8,43.8,68.2,72,78,109,92.8,73,85.5,47.5,29.2,11,13.2,23.3,29.5,20.3,7.3,0,19.3,18.7,6.5,20.5,1.7,13.2,5.3,9.3,25.2,13.2,36.2,19.3,10.5,36.3,18.7,31.7,1.7,40.3,26.7,50,58.3,66.7,75,60.8,65,159.2,133.8,134.5,158.3,186.7,193.7,177.5,243.3,262.2,295.5,182.2,223.3,241.7,398.2,286,255,233.3,286.2,260.5,250.5,175,191.2,276.2,196.7,241.7,233.3,189.5,238.3,186.7,185,206.7,190,183.3,116.7,163.3,163.3,158.3,178.7,146.7,143.3,143.3,156.2,128.3,100,97.8,164.5,124.5,88.3,113.8,174.5,162.8,122.5,110,85,45.5,111.7,58.7,90,62.5,61.7,68.3,90.5,63.3,61.7,73.3,56.7,38.7,52.5,50,46.7,64.5,44.5,47.2,38.3,42,53.7,33.3,30,13.3,25,17.5,21.7,13.3,18.3,16.7,10,15,10,16.7,16.7,13.3,28.3,23.3,10.8,13.3,15,26.2,34.5,43.8,60.5,33.3,53.3,78.7,67,45.5,62,79.3,79.5,142.3,153.8,98.3,138.3,149.5,185.8,187.2,193.3,187.8,224.5,176.7,145.7,212,224.7,165.3,213.3,228.7,262.2,261.7,235.8,290,230,215.3,238.8,180.8,188.3,257,235.8,226.7,235,236.7,157.8,215.8,190,208.8,200,205.5,205.8,200,195,171.7,186.7,149.5,223.3,225.8,171.7,212.5,160.5,156.7,155,151.7,115.5,145,128.8,140.5,136.7,123.3,121.2,103.3,123.3,128.7,122.8,107,118.3,71.7,110.8,102.8,111.7,110,96.7,106.7,105,126.2,103.3,101.7,76.3,100,98.3,98.3,95,93.3,93.3,91.7,92.5,88.3,87.2,85,83.3,48.8,40,78.3,73.3,76.2,75,73.3,63.3,47.3,92.8,69.2,68.3,66.7,18.5,47.5,112.3,85.7,35.7,66.5,21,31,51.7,28.5,21.5,42.8,22.5,32.5,41.7,30,36.7,39.7,26.2,52.8,35,11.2,44.8,2.5,30.7,18.3,14,8.5,24,7,6.7,6.7,12.2,18.5,7.2,10,9.5,11.5,9.7,5,3.3,6.7,20.7,1.8,0,0,0,5,4,2.5,20.8,16.5,2.7,21,36.2,14,13.7,17.7,3.5,0,0,7.7,4.5,14.3,11.5,15.5,23.2,0,8.3,39.5,35,32.5,19.2,20.5,17.5,66.8,45,48.3,50,51.7,53.3,52,58.3,64.5,55.8,54.3,66.3,80.3,79.7,78.3,68,70,73.3,76.7,80,83.3,86.3,64.2,57.5,83.3,83.3,84.7,49.2,41.7,73.8,60,80.5,56.8,75.5,90.5,85,80,75.5,80.5,80,84.3,55.7,58,49.7,71.8,88.3,103.8,101.7,100,101.7,73.5,85.7,62.5,65,67.5,62.7,71.2,74,49,68.3,63.8,65,49.3,54.5,46.2,44,42.7,50,43.8,40,45,41.7,40,20,20.3,16,39.7,16.7,20,21.2,20,9.5,13.3,4.3,0,0,7.5,0,20.5,22.5,22.5,11.2,13.3,19.5,7.8,17.5,20.5,12,15.3,1.5,4.2,3.3,12.8,0.5,0.3,0.7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,11,0,4,10.2,1.3,1.8,18.8,3.2,1.2,0,1.7,2.2,0.8,26,8.7,6.5,13.2,16.8,0,17.2,3.2,27.7,9.2,18.7,30.5,14,25.5,46.3,27.8,23.8,37,20,9.5,39.7,9.7,24.8,30.8,3.8,13.5,32.2,24.2,33.5,32,53.7,43.7,52.7,16.3,93.2,59.2,78.7,52.5,55.8,62,108.3,43.8,114.7,122.8,98,73.8,72.7,64.7,38.7,79.7,94,63.5,49.8,60.7,96.5,160.3,44,35.3,66.7,83.3,75,61.2,42.7,48.2,47.3,58.1,37.4,42.4,57.5,88.5,60.8,46.8,52.6,43.4,52.8,18.3,43,54.7,34.6,6.3,33.7,32.6,58.3,52.5,43.5,24.8,45.9,41.8,50.9,32,44.4,7.5,32.3,48.9,17.9,34.1,43.1,8.6,14.9,13.2,15.1,36,7,9.5,15.2,2.8,3,4.3,8,7.3,31.4,7.3,0.4,0,1.5,26.9,21.7,2.4,9.3,13.2,3.4,0,0.6,0,0,0,0,1,0,0,0,0.8,0,0,0,0,34,36,18,0,32.3,4.6,0,0,2.3,34.3,42,0,1.4,8.4,25.9,37.4,6.2,25.8,25.6,51.5,42.8,26.2,26,19.6,36.7,29.4,30.2,61.3,40,53.9,61.7,87.5,66,31.6,84.4,65.8,113.6,57.7,79,96.3,76.7,93.8,94.4,70.4,89.4,82.6,93.5,80.4,76.8,88,107.3,108.5,101.9,148.6,163.4,90.4,127.3,83.9,91.1,95,78.1,71.6,82.3,120.6,158.4,112.3,123.2,151.5,129.3,88,95.3,112.7,94.1,87,120.1,141,177.3,110.5,108.4,73.2,84.6,103.4,140.6,135.4,136.8,79,83.6,155.8,90.9,63.4,55.6,75.4,91.6,63.2,77.1,72.5,48.3,51.5,92.6,91.9,44.8,68.9,44.5,23.3,14.8,13.7,35.2,23.8,45.8,18.7,24.9,19.6,4.6,21.5,1.7,11.6,9.5,19.3,12.5,9.8,16.6,8.2,30.1,6.5,2.4,14.8,13.1,14.4,6.6,19.2,41.3,50.9,57.5,12.4,40.7,32.7,102.4,72.6,55.2,99.6,98.5,168,158.6,166.7,129.3,147.6,179.4,163.7,238,185.7,207.9,194.6,179.6,158.5,228.9,201.5,343.8,313.4,292.6,224.3,230.3,186.1,263.4,271.2,223.5,160.4,206.2,178.4,216.1,241.5,141.3,234.5,211.1,229.4,157.6,180.4,131.3,122.7,151.5,129.2,132.9,175.9,170.8,129.5,102.9,89.6,91.2,141.3,218.8,221.1,151.5,114.7,106.2,135.4,146.1,112.9,109.8,115.4,80.9,101,96.4,123.3,91.7,90.4,89.5,40.1,49.9,49.6,66.9,112.4,92.8,51.4,65.4,60.9,47.4,32.9,64.8,34,36.8,36.2,44.9,41.4,34.2,21,44.4,30.6,63.5,67.5,29.3,22.2,5.9,13.9,15.8,35.1,17.6,15.9,19.6,6.9,8.9,31.7,21.2,15.7,24.5,22.5,34.6,19.2,6.2,35.2,39.7,11.6,35.9,17.9,36,42.8,72.8,72.1,95,79.7,51.8,51,53.9,49.3,67.8,65.7,99.5,64.6,84.9,106.5,115.5,99.9,108.4,77.5,91.3,178.6,93.4,100.6,109.1,104.4,74.9,143,74.6,125.7,142.2,87.1,234.3,268.2,300.6,231.5,182.6,265.2,186.4,181.2,178.6,170.5,214.9,232,220.9,167.3,220.6,191,265.8,298.3,250.3,182.7,194.7,153.2,154.2,148.2,128.6,178,135.7,188.2,184.3,148.2,169.8,156.8,83.8,117,133,74.3,117,163.7,134.9,104.1,115.9,143.5,200.1,122.8,107.3,118.9,120,68.6,109,128.9,118.7,96.8,135.5,129.9,126.2,116.2,124.3,104.3,89,80,75.3,71.2,127.9,103.1,86.1,77.9,81.5,71.6,90.4,65.9,76,87.2,95.8,63.7,80.5,54.7,44.5,29.3,38,39.4,50.3,45.6,40.1,35.5,30.1,42.6,24.1,53.5,41.1,23.4,21.6,33,8.4,17.3,10,0.7,5.9,0,18.3,7.9,5.8,1,9.3,0.7,12.4,0,9.8,8.8,11.3,8.4,8.5,14.7,13.7,26,14.2,10,21.1,54.2,30.5,42.2,32,80.6,77.1,59.6,70.7,74.2,66.3,109.2,72.8,78.6,84.5,107.7,104.9,152.2,173.2,98.6,127,159,166.4,171.5,162.9,172.8,165.2,180.7,203,200.9,217.8,184.6,153.9,156.6,167.9,188,135.7,203.5,206.3,221.9,190.5,175.2,171.1,186,181.7,118.5,147.5,192,187.1,107.8,167.5,148.2,156.7,151.9,127.7,102,152.8,119.9,122.4,82.7,102.1,122.4,159.7,139.5,118.7,126.4,79.8,96,77.6,91.8,107.7,126,77.1,102.1,77.6,62,91.3,41.7,75.7,71.6,78.1,109.7,89.5,125.9,68.1,77.1,109.9,103.8,104.1,54.2,64.4,109.3,54.3,92.5,74.6,75,55.9,65.6,63.8,50.8,71.8,41,32.5,46.7,24.3,60,72.9,46.6,33.5,24.6,31.4,17.6,24.2,13.9,26.8,17.2,2.9,0,1.4,17.4,9.7,5.5,2.8,9.5,9.1,18.7,25.5,18.1,47.9,25.9,26.3,44,61.1,44.5,51.8,48.3,57.3,78.7,102.8,98.7,112.8,101.6,99.9,88,68.4,173.4,180.7,98.8,132.7,134.5,99,130.2,174.1,129,191.7,262.7,266.9,293.6,226.3,220.9,256.5,226.8,244.3,246,216.7,147.2,209,238.7,270.9,242.6,152.9,171.8,183.7,133.9,148.5,175.7,150.8,132.7,200.3,147.5,170.4,179.5,183.3,176,155,191.1,171.2,186.8,139.9,144.6,178.4,164,127.1,80,74.8,111.7,113.8,78.7,78.6,92.5,82,101.4,107.1,77.5,53.5,74.6,63.8,113.2,102.3,46.8,57.4,48.2,48.8,24.4,35.9,56.4,48.6,19.2,39.9,20.9,24.4,4,21.3,29.6,16.5,23.9,25.1,51.1,3.9,8.5,2.7,25.5,14.8,16.6,23.9,16.6,13.6,40.6,14.5,19.9,26.3,36.1,23.6,10,10.5,28.1,11.2,23.6,3.5,5.5,11,13.1,0.2,9.9,10.7,0.2,0,8.8,1.9,6.8,0.9,1.6,0.9,0,10.4,4,8,12.6,17.9,10.1,20.4,21.9,12.2,40.1,45.4,32.1,32.4,39.1,56.9,36.5,80.3,110.1,71.7,51.1,49.4,60.6,88.6,85.8,86.1,72.5,100.8,128.2,97.3,88.6,107.3,91.5,78.8,75,115.9,111.5,159.6,106.9,75.4,75.7,67.5,96.1,98.6,140.6,69.7,101,78.2,71.3,136.8,52.5,127.2,134.4,76.6,87.8,139.6,140.8,126.5,152.6,144.8,145.8,126.9,110.9,85.3,88.5,93.1,103.1,79.6,60.9,78.6,71.4,119.7,82.9,91.7,121.6,139.5,110.9,83.5,66,64.5,51.6,36.3,49.8,43.2,95.5,72.9,51.2,45.3,50.4,28.1,35.7,14.4,0.6,21.7,17,22,7.1,11.6,33.4,26.1,38.9,35.7,12.4,11,11.5,34.5,21.2,11.8,13.1,8.5,11.7,11.8,5,4.6,14.6,3.4,17.9,11.1,1.3,14.2,11.1,7.3,4,10.8,15.8,34.3,10.9,3.4,0.3,11.2,8.8,1.1,8.5,2.7,7.9,2.2,19.3,14.2,28.6,18.6,15.9,13.1,22.5,36.9,17.2,34.2,68.5,80.4,98,55.1,89.7,86,69.8,54.3,115.2,126.1,83.3,116,132.7,127.3,127.6,169,104.7,117.5,108.9,131,125,121.6,109.5,146.8,141.3,149.8,147.6,215.4,129.9,133.3,125.2,156.4,138.6,141,87.1,136,168.7,164.8,176.7,117.1,110,125.7,94.3,100.1,105.4,112,101.6,128.2,112.5,119.1,79.7,114.9,96.1,113.2,78.6,117.9,48.4,95.7,86.5,73,46.1,81.7,75.2,45.4,102.2,47.9,63.3,71,67.6,49,48.7,51.7,33.3,18.9,46.1,36.4,80.4,23.9,14,55.5,50.4,60.7,63.9,24.2,43,37.1,15,52.3,58.1,57.1,51.6,21.1,32.4,15.3,30.3,23.6,12.9,34.1,22.5,4.9,14,21.7,13,17.6,15.7,22.8,14.4,26.8,25.3,20.1,13.9,7.1,13.9,21.6,7.5,0.5,0.4,4,7.4,0,17,9.7,1.2,1.7,0.9,6.3,6.4,0,9.3,0,20.7,0,4.7,2.4,1.5,3.8,12.6,27.2,17.2,1.8,13.9,28.4,22.5,43.5,24.3,27.2,46.4,48,18.5,64.8,74.2,76.2,52.6,40.8,61.9,71.6,65.7,69.8,84.3,97.1,50.2,90.4,63.4,91.1,91.2,143,94.3,65.5,79.9,81.6,121.6,98.1,91.8,131.2,178.7,92.5,75.8,52.3,107.4,92.2,96.2,105.3,172.7,79.6,93.5,29.7,64.8,108,127.4,180.3,101.1,87.6,71.4,67.2,82.9,90.5,141.7,109.1,102.5,78.9,65.4,56.6,47.9,96.1,68,80.2,65.8,150.9,144.9,53.9,75.9,65.9,94.6,77.6,110.5,53.7,60,37.8,59.6,38.5,64.7,97.4,93,90.2,44,52.5,35.7,14.1,36.9,20.5,23.5,19.3,43.7,63.9,8.3,9.6,5.6,15,13,27.6,15.1,3.7,5.9,6.7,6.7,4.5,7,3.7,0.4,0,8.2,7.6,7.4,6.9,4.9,0.5,15.9,7.6,1.9,10.6,3.8,4.8,0.8,1.6,0,0,2.9,0.4,2,5.2,1.2,6.3,4.7,4.4,5.3,28.9,8.7,19.1,9.1,12.9,21.2,13.7,27.3,37.3,38.5,70.4,64.8,68.9,55.1,114.7,119.4,116,82.4,89.1,70.9,57.5,75.5,92.4,111.7,119.8,124,112.9,89.3,58.6,75.1,84.5,109.5,88.3,124.5,119.9,158,124.6,190.2,191.4,199.7,257.7,215.6,120.3,160.7,215.5,160,108.7,120.4,134.1,127.9,99,179.5,169.6,133.2,141.7,139,98.5,80.2,132.5,110.9,86.3,146.9,185.3,107.8,115.1,91.1,88,69.9,58,85.3,89.8,116.9,24.7,55.4,64.6,45.7,31.9,60.5,82.7,45.3,49.8,52.5,47.1,44.5,54,37,56.2,69.7,38,29.6,30.3,29.6,33.9,19.7,43.9,91.3,18.3,13.4,9.8,18.3,10.9,7.8,10.4,12.2,29,7.5,2.5,5.5,10.2,5.3,15.3,5.9,0.8,22.1,19.5,16.7,4.6,0.8,8.5,3,18.9,34.6,40,46.9,32.1,41.9,42.6,37.5,27.5,9.1,38.6,30,53,71.4,79.1,64.2,63.3,100.3,115.3,97.6,164.4,119.7,116.4,104.2,64.2,107,122.4,87.2,102.7,101.4,119.3,100.8,132.4,136,155.1,116.1,155.8,131.9,98.5,91.6,89.6,114.1,105.2,112.1,75.3,139.2,122.4,142.4,134.3,128.3,152.4,163.4,139.6,149.6,102.3,83.9,98.3,114.8,104.7,83.8,87.9,97,119.9,117.1,109.6,57.3,90.1,135.1,179.9,108.8,83.1,58.4,63.7,61.4,48,36.5,41.5,53.5,57.2,59.4,43,24.4,71.8,50.1,52,40.8,25.5,29,21.6,31.7,16.6,31.2,29.7,20.1,17.6,18.8,18.7,29.7,36.9,16,11.3,6.6,14.8,13.7,18.5,20.4,36.9,16.8,4.9,5.3,8.7,4.7,0.4,8.5,5,1,0.4,5.7,12.9,7.2,18.8,32.9,11.2,15.3,13.9,6.7,9.5,14.5,25.7,31.1,34.1,38.5,20.4,45.4,76.2,56.5,50.2,70.1,88.7,107,102.5,104.7,123.9,128.4,124.8,90.9,116.7,87.2,145,126.7,148.2,192.3,205.6,220.9,214.1,139.7,182.2,194.4,217.1,241.8,229.5,167.9,208.2,123.9,147.9,164,198.6,144.2,168.4,212.3,162.6,275.6,192.8,149.3,165.3,203.6,154.7,133.9,129,107.8,181.9,197.3,168.3,162.6,176.3,187.7,146.9,113.7,70.2,84.1,99.1,138.9,101.1,90.6,139.8,112.5,175.9,110.8,91.5,97.4,113.8,76.1,74.3,77.5,54.6,49,99.6,111.4,100.1,109.8,77.2,64,56.2,59.5,87.9,90.4,101.2,41.8,18.9,29.6,33.7,28.7,32,51.3,37.6,20.7,48.1,45.7,43.5,23.6,12.7,22,32.3,16.7,13,17,31.4,6.1,0.8,18.3,0.4,4.1,8.2,8.5,27.9,23.7,28.1,17.9,47.4,30.8,21.2,35.9,53.4,51,60.2,71,43.1,58.1,114.5,76.6,45.7,79.3,143.8,127.7,126.1,141.6,122.6,193.7,178.7,157.4,170.5,206.3,202.9,163.7,188.9,183.8,212.1,285,232.1,223.5,267.4,239.9,231.7,181.3,164.9,153.6,122,134.3,268.5,246.4,237.5,201.4,223.7,202.9,192.9,135.6,195.3,168.6,258,223,208.1,150.4,172.4,178.3,175.3,205.8,186.3,203.2,166.6,143.9,134.3,155.4,160.6,150.5,118.3,128.9,120.6,72.7,87,77.7,76.7,85,84.8,79.3,131.7,153.7,142.4,87.2,86.5,117.7,73.3,74.2,65,57.9,32.4,31.5,41.7,33.6,52,56.1,77.8,40.4,34.2,31.8,48.9,37.9,5.9,14.7,39.6,18.3,31.5,12.7,33.6,28,12.3,2.5,3.9,0.4,0.8,15.8,2.7,1.2,0.4,7.3,12.6,2.3,10.5,13.4,11.3,33.4,29.9,7.3,16.4,41.3,45.2,38.2,58,60.8,83,126.3,108.8,104.1,175.6,167.7,156.7,193.4,165.1,182.7,240.2,245.4,219.9,285,272,233.7,184.5,222.8,248,233,284.3,265.1,223.7,334,359.4,298.6,339,286.7,233.6,270,277.6,248.2,242.9,271,283.5,285.1,256.9,215.6,265.7,307.7,202.6,263,231.3,243.6,238.9,211.9,282.6,205.6,157.7,175.6,177.1,207.2,149.9,144.6,172.7,169.3,156,172.4,190,180.1,117.3,126.9,121.2,82.1,65.4,75.2,86.9,72.3,109.5,99.3,79.2,90.1,53.7,46.5,56.9,55.1,71.7,64.9,65.9,61.9,59.6,31.4,31.5,72.7,56.1,38.8,33.2,28.7,35.2,24.8,41.7,61.1,51.2,28.7,47.5,55.2,50.1,33.7,21.6,22.6,25.3,24.1,12.9,14.3,13.5,4.8,13.8,7,9.2,11.1,22.1,25.4,20.8,17.5,10.2,34.5,23.3,17.3,13.3,24.5,29.1,22.8,24.7,40.3,35.3,36.4,69,64.2,67.7,80.2,72.6,71.1,81.2,81,99.8,157,132.6,158.3,98.4,122.5,95.4,129.5,151.8,108.7,125,133.6,179,172.5,158.5,130.5,115,180,156.2,136.2,154.8,166,152.5,121.7,155.5,147.8,170.5,192.3,151.1,169.9,150.1,137.1,138.8,129.3,135.4,132.4,138.6,157.9,180.8,145.7,155.1,180.5,151.3,159.3,131.7,140.8,122.6,134.8,118.2,129.2,111.8,85.9,101.6,81.5,70.7,114.7,87,71.3,73.4,89.5,116.5,87,125.3,113.5,89.6,113.9,124.7,108.3,108.9,90.7,86.9,59.2,64.3,61.8,60.9,65.4,81.8,60.3,56.1,33.2,36.6,84.1,43.7,34.3,33.3,39.4,37.3,30.9,57.5,56.3,51.5,79.1,47.9,57.2,67.2,35.9,29.6,27.3,16.7,16.9,7.7,13.1,16.7,40.4,56.7,20.3,13.6,27.9,11.6,11.9,6.4,31.5,27.3,18.2,17.9,2.9,24.1,20,29.7,7.9,22.3,23.8,33.3,13,19,27,54.9,30.6,43,62.4,62.1,41.6,61.4,73.7,132.6,108.4,141.2,117.1,134.6,99.7,82.4,195.7,177.1,138.5,173.9,235.9,194.7,195.3,143.7,190.3,211.7,225.7,201.4,266.9,263.6,259.5,249.6,226.1,219.4,178.7,232.2,254.7,222.7,192.9,191.7,219.6,233.3,209.5,246.9,156.6,189.9,196.6,225.3,194.7,131.6,205.3,242.5,245.3,216.2,186,195.4,149.8,230.9,221.1,170.3,119.3,163.7,139.4,161.9,167.4,134.3,127.5,169,115.5,73.1,88.7,109.6,132.5,131.5,108.9,96,69.9,72.5,45.7,45.6,74.8,110.2,116.7,90.4,96.9,65.1,55.7,35,22.6,12.6,26.5,21.4,17.8,20.7,16.9,20.4,32.4,28.3,39.9,10.1,4.3,22,17.9,15.8,2.8,27.9,13.8,22.4,16.1,0.6,18.1,9.9,5.1,40.1,15.4,5.8,9.8,3.4,17.4,46,39.1,18.8,38.2,47.9,42.2,63.4,48.8,29.1,70.5,45.4,91.2,108.8,74.2,124.3,131.4,139.4,142.7,156.5,156.8,231.2,210.1,208.7,170.4,166.3,195.4,284.5,180.5,232,225.1,212.2,238.2,211.4,227.4,171.8,191.7,189.7,175.2,153.3,191.1,252.1,169.1,199.4,178.8,197.1,195.3,240.3,197,197.6,166.9,224.7,240.2,240.8,168.9,197.1,159.5,212.6,198.3,230.7,151,142.2,94.3,98.5,114.2,91.9,94,133.4,129.6,122,81.4,127.8,102.4,94.4,78.8,69.6,80.4,62.5,31.2,71.1,48.2,68.4,84.9,54.9,47.5,27.4,29.8,39.7,50.6,34.3,40.5,67.1,29.5,32.2,32.6,45.8,46.3,21.6,19.4,22.5,20.4,18.2,15.7,30.6,14,14.9,13.3,7.7,12.6,6.8,7.6,16.5,11.8,19.7,3,0.7,24.9,14,7.4,11,12.1,23,25.4,20.8,12.9,35.7,59.7,32.8,50.4,55.5,44.5,50.2,82,70.6,74,90.5,96.7,121.1,132,78.5,97.3,119.2,86,98,103.5,93.6,149.6,207.2,173.5,142.3,106.3,168.7,188.3,116.8,133.1,165.7,217.7,191.5,165.9,188,244.3,180.5,156,141.6,158.1,143.3,142.6,121.5,165.8,161.7,142.1,202.9,123,161.5,238.2,194.1,176.6,213.4,184.6,170.2,147.1,186.9,187.5,128.8,161,175.6,187.9,151.2,147.2,135.3,133.5,75.7,100.7,97.9,86.8,118.7,128.3,115.4,78.5,97.8,82.9,72.2,60.6,74.6,74.8,59.2,72.8,66.5,83.8,69.7,48.8,74.2,70.1,28.9,48.1,43.5,39.6,38.7,61.9,56.8,62.4,60.5,37.2,13.2,27.5,59.3,20.9,5.7,17.3,50.3,37.2,24.5,22.2,20.8,23.7,14.9,35.7,22.3,29.3,18.4,7.2,5.4,19.5,21.3,15.1,9.8,4,1.5,2.8,17.3,4.1,2.9,15.5,3.6,4.6,5.2,0.6,0.3,1.2,4.2,6.6,1,1.3,1.2,0.6,1.2,2.9,6.3,5.5,0,7.1,7.7,6.9,16.3,19.5,28.5,24,10.4,13.9,18.8,25.2,29.6,36.4,33.6,34.4,24.5,27.3,48.3,78.6,76.1,58.2,56.1,64.5,65.8,120.1,125.7,139.1,109.3,94.4,47.8,86.6,85.9,96.5,92,100.1,94.8,93.7,76.5,87.6,56.8,96.1,60.9,78.3,107.3,120.2,76.7,86.2,91.8,54.5,114.4,113.9,124.2,117,146.1,128.7,112.5,112.5,102.9,100.2,106.9,130,90,103.6,112.9,93,66.7,54.5,75.3,88.8,66.5,65.8,64.4,78.6,63.6,62.2,58,57,56.4,54.1,38,52.1,20.9,32.5,50.7,44.7];

(For Mathematica users)

x={96.7,104.3,116.7,92.8,141.7,139.2,158,110.5,126.5,125.8,264.3,142,122.2,126.5,148.7,147.2,150,166.7,142.3,171.7,152,109.5,105.5,125.7,116.7,72.5,75.5,94,101.2,84.5,110.5,99.7,39.2,38.7,47.5,73.3,58.3,83.3,118.3,98.8,99.5,66,130.7,48.8,45.2,77.7,62.7,66.7,73.3,53.3,76.2,63.3,60,52.8,36.7,65,46.7,41.7,33.3,11.2,0,5,2.8,22.8,34.5,44.5,31.3,20.5,13.7,40.2,22,7,17,18.7,11.3,10.8,0,0,14.3,5.3,29.7,39.5,11.3,33.3,20.8,11.8,9,15.7,20.8,21.5,6,10.7,19.7,23.8,28.3,15.7,23.5,35.3,43.7,50,63.5,21.3,41.7,85.5,66.2,54.2,107.8,55.8,62.7,86.7,81.7,120.5,77.3,75,73.3,64.5,104.2,62.8,71.7,71.7,80.5,73.3,78,78.3,81.7,83.3,85,118.8,128.7,99.5,77.2,95,112.2,99.2,124.5,97.2,120,80.5,110,126,102.2,84.3,99.5,101.7,116.7,151.7,134.5,119.5,178.7,165.5,156.8,151.8,167.8,147.8,149.5,76.7,73,121.3,76.2,100.3,66.5,128.5,56.3,112.8,114.2,115.5,129.7,128.7,94.2,53.2,57,54.8,54.5,59.7,90.3,44.2,113.5,77.2,101.5,102.3,99.5,99.5,67,57.3,73.8,50,50,50,47,46.7,43.3,42.8,40,43.3,41.7,36.7,33.7,33.3,45,49.5,26.7,23.3,23.3,21.7,20,18.3,61,10,44.7,5,5.5,6.7,7.2,8.3,9.5,32,45.7,50,71.7,54.8,49.7,55.5,36.5,68,71.2,73.5,91.2,88.8,89.2,110.2,77.2,71.2,129.5,129,87.7,111.3,124.7,129.7,151,186.3,123.2,107,107.2,161.2,122.7,157.3,197.7,200.5,248,263.7,246.8,186.7,173.3,237.5,133.5,85,116.8,138.8,183,210.5,174,172.7,220.3,170.5,60,77,77.8,108.2,254.5,199.2,112.8,97.5,169,150,166.2,159.5,168.2,151.3,51.8,153.7,63.3,95,128.8,93.7,84.2,131,102.2,106.7,91,48.3,85.3,54.8,68.5,47.3,46.2,21.2,48.8,43.8,68.2,72,78,109,92.8,73,85.5,47.5,29.2,11,13.2,23.3,29.5,20.3,7.3,0,19.3,18.7,6.5,20.5,1.7,13.2,5.3,9.3,25.2,13.2,36.2,19.3,10.5,36.3,18.7,31.7,1.7,40.3,26.7,50,58.3,66.7,75,60.8,65,159.2,133.8,134.5,158.3,186.7,193.7,177.5,243.3,262.2,295.5,182.2,223.3,241.7,398.2,286,255,233.3,286.2,260.5,250.5,175,191.2,276.2,196.7,241.7,233.3,189.5,238.3,186.7,185,206.7,190,183.3,116.7,163.3,163.3,158.3,178.7,146.7,143.3,143.3,156.2,128.3,100,97.8,164.5,124.5,88.3,113.8,174.5,162.8,122.5,110,85,45.5,111.7,58.7,90,62.5,61.7,68.3,90.5,63.3,61.7,73.3,56.7,38.7,52.5,50,46.7,64.5,44.5,47.2,38.3,42,53.7,33.3,30,13.3,25,17.5,21.7,13.3,18.3,16.7,10,15,10,16.7,16.7,13.3,28.3,23.3,10.8,13.3,15,26.2,34.5,43.8,60.5,33.3,53.3,78.7,67,45.5,62,79.3,79.5,142.3,153.8,98.3,138.3,149.5,185.8,187.2,193.3,187.8,224.5,176.7,145.7,212,224.7,165.3,213.3,228.7,262.2,261.7,235.8,290,230,215.3,238.8,180.8,188.3,257,235.8,226.7,235,236.7,157.8,215.8,190,208.8,200,205.5,205.8,200,195,171.7,186.7,149.5,223.3,225.8,171.7,212.5,160.5,156.7,155,151.7,115.5,145,128.8,140.5,136.7,123.3,121.2,103.3,123.3,128.7,122.8,107,118.3,71.7,110.8,102.8,111.7,110,96.7,106.7,105,126.2,103.3,101.7,76.3,100,98.3,98.3,95,93.3,93.3,91.7,92.5,88.3,87.2,85,83.3,48.8,40,78.3,73.3,76.2,75,73.3,63.3,47.3,92.8,69.2,68.3,66.7,18.5,47.5,112.3,85.7,35.7,66.5,21,31,51.7,28.5,21.5,42.8,22.5,32.5,41.7,30,36.7,39.7,26.2,52.8,35,11.2,44.8,2.5,30.7,18.3,14,8.5,24,7,6.7,6.7,12.2,18.5,7.2,10,9.5,11.5,9.7,5,3.3,6.7,20.7,1.8,0,0,0,5,4,2.5,20.8,16.5,2.7,21,36.2,14,13.7,17.7,3.5,0,0,7.7,4.5,14.3,11.5,15.5,23.2,0,8.3,39.5,35,32.5,19.2,20.5,17.5,66.8,45,48.3,50,51.7,53.3,52,58.3,64.5,55.8,54.3,66.3,80.3,79.7,78.3,68,70,73.3,76.7,80,83.3,86.3,64.2,57.5,83.3,83.3,84.7,49.2,41.7,73.8,60,80.5,56.8,75.5,90.5,85,80,75.5,80.5,80,84.3,55.7,58,49.7,71.8,88.3,103.8,101.7,100,101.7,73.5,85.7,62.5,65,67.5,62.7,71.2,74,49,68.3,63.8,65,49.3,54.5,46.2,44,42.7,50,43.8,40,45,41.7,40,20,20.3,16,39.7,16.7,20,21.2,20,9.5,13.3,4.3,0,0,7.5,0,20.5,22.5,22.5,11.2,13.3,19.5,7.8,17.5,20.5,12,15.3,1.5,4.2,3.3,12.8,0.5,0.3,0.7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,11,0,4,10.2,1.3,1.8,18.8,3.2,1.2,0,1.7,2.2,0.8,26,8.7,6.5,13.2,16.8,0,17.2,3.2,27.7,9.2,18.7,30.5,14,25.5,46.3,27.8,23.8,37,20,9.5,39.7,9.7,24.8,30.8,3.8,13.5,32.2,24.2,33.5,32,53.7,43.7,52.7,16.3,93.2,59.2,78.7,52.5,55.8,62,108.3,43.8,114.7,122.8,98,73.8,72.7,64.7,38.7,79.7,94,63.5,49.8,60.7,96.5,160.3,44,35.3,66.7,83.3,75,61.2,42.7,48.2,47.3,58.1,37.4,42.4,57.5,88.5,60.8,46.8,52.6,43.4,52.8,18.3,43,54.7,34.6,6.3,33.7,32.6,58.3,52.5,43.5,24.8,45.9,41.8,50.9,32,44.4,7.5,32.3,48.9,17.9,34.1,43.1,8.6,14.9,13.2,15.1,36,7,9.5,15.2,2.8,3,4.3,8,7.3,31.4,7.3,0.4,0,1.5,26.9,21.7,2.4,9.3,13.2,3.4,0,0.6,0,0,0,0,1,0,0,0,0.8,0,0,0,0,34,36,18,0,32.3,4.6,0,0,2.3,34.3,42,0,1.4,8.4,25.9,37.4,6.2,25.8,25.6,51.5,42.8,26.2,26,19.6,36.7,29.4,30.2,61.3,40,53.9,61.7,87.5,66,31.6,84.4,65.8,113.6,57.7,79,96.3,76.7,93.8,94.4,70.4,89.4,82.6,93.5,80.4,76.8,88,107.3,108.5,101.9,148.6,163.4,90.4,127.3,83.9,91.1,95,78.1,71.6,82.3,120.6,158.4,112.3,123.2,151.5,129.3,88,95.3,112.7,94.1,87,120.1,141,177.3,110.5,108.4,73.2,84.6,103.4,140.6,135.4,136.8,79,83.6,155.8,90.9,63.4,55.6,75.4,91.6,63.2,77.1,72.5,48.3,51.5,92.6,91.9,44.8,68.9,44.5,23.3,14.8,13.7,35.2,23.8,45.8,18.7,24.9,19.6,4.6,21.5,1.7,11.6,9.5,19.3,12.5,9.8,16.6,8.2,30.1,6.5,2.4,14.8,13.1,14.4,6.6,19.2,41.3,50.9,57.5,12.4,40.7,32.7,102.4,72.6,55.2,99.6,98.5,168,158.6,166.7,129.3,147.6,179.4,163.7,238,185.7,207.9,194.6,179.6,158.5,228.9,201.5,343.8,313.4,292.6,224.3,230.3,186.1,263.4,271.2,223.5,160.4,206.2,178.4,216.1,241.5,141.3,234.5,211.1,229.4,157.6,180.4,131.3,122.7,151.5,129.2,132.9,175.9,170.8,129.5,102.9,89.6,91.2,141.3,218.8,221.1,151.5,114.7,106.2,135.4,146.1,112.9,109.8,115.4,80.9,101,96.4,123.3,91.7,90.4,89.5,40.1,49.9,49.6,66.9,112.4,92.8,51.4,65.4,60.9,47.4,32.9,64.8,34,36.8,36.2,44.9,41.4,34.2,21,44.4,30.6,63.5,67.5,29.3,22.2,5.9,13.9,15.8,35.1,17.6,15.9,19.6,6.9,8.9,31.7,21.2,15.7,24.5,22.5,34.6,19.2,6.2,35.2,39.7,11.6,35.9,17.9,36,42.8,72.8,72.1,95,79.7,51.8,51,53.9,49.3,67.8,65.7,99.5,64.6,84.9,106.5,115.5,99.9,108.4,77.5,91.3,178.6,93.4,100.6,109.1,104.4,74.9,143,74.6,125.7,142.2,87.1,234.3,268.2,300.6,231.5,182.6,265.2,186.4,181.2,178.6,170.5,214.9,232,220.9,167.3,220.6,191,265.8,298.3,250.3,182.7,194.7,153.2,154.2,148.2,128.6,178,135.7,188.2,184.3,148.2,169.8,156.8,83.8,117,133,74.3,117,163.7,134.9,104.1,115.9,143.5,200.1,122.8,107.3,118.9,120,68.6,109,128.9,118.7,96.8,135.5,129.9,126.2,116.2,124.3,104.3,89,80,75.3,71.2,127.9,103.1,86.1,77.9,81.5,71.6,90.4,65.9,76,87.2,95.8,63.7,80.5,54.7,44.5,29.3,38,39.4,50.3,45.6,40.1,35.5,30.1,42.6,24.1,53.5,41.1,23.4,21.6,33,8.4,17.3,10,0.7,5.9,0,18.3,7.9,5.8,1,9.3,0.7,12.4,0,9.8,8.8,11.3,8.4,8.5,14.7,13.7,26,14.2,10,21.1,54.2,30.5,42.2,32,80.6,77.1,59.6,70.7,74.2,66.3,109.2,72.8,78.6,84.5,107.7,104.9,152.2,173.2,98.6,127,159,166.4,171.5,162.9,172.8,165.2,180.7,203,200.9,217.8,184.6,153.9,156.6,167.9,188,135.7,203.5,206.3,221.9,190.5,175.2,171.1,186,181.7,118.5,147.5,192,187.1,107.8,167.5,148.2,156.7,151.9,127.7,102,152.8,119.9,122.4,82.7,102.1,122.4,159.7,139.5,118.7,126.4,79.8,96,77.6,91.8,107.7,126,77.1,102.1,77.6,62,91.3,41.7,75.7,71.6,78.1,109.7,89.5,125.9,68.1,77.1,109.9,103.8,104.1,54.2,64.4,109.3,54.3,92.5,74.6,75,55.9,65.6,63.8,50.8,71.8,41,32.5,46.7,24.3,60,72.9,46.6,33.5,24.6,31.4,17.6,24.2,13.9,26.8,17.2,2.9,0,1.4,17.4,9.7,5.5,2.8,9.5,9.1,18.7,25.5,18.1,47.9,25.9,26.3,44,61.1,44.5,51.8,48.3,57.3,78.7,102.8,98.7,112.8,101.6,99.9,88,68.4,173.4,180.7,98.8,132.7,134.5,99,130.2,174.1,129,191.7,262.7,266.9,293.6,226.3,220.9,256.5,226.8,244.3,246,216.7,147.2,209,238.7,270.9,242.6,152.9,171.8,183.7,133.9,148.5,175.7,150.8,132.7,200.3,147.5,170.4,179.5,183.3,176,155,191.1,171.2,186.8,139.9,144.6,178.4,164,127.1,80,74.8,111.7,113.8,78.7,78.6,92.5,82,101.4,107.1,77.5,53.5,74.6,63.8,113.2,102.3,46.8,57.4,48.2,48.8,24.4,35.9,56.4,48.6,19.2,39.9,20.9,24.4,4,21.3,29.6,16.5,23.9,25.1,51.1,3.9,8.5,2.7,25.5,14.8,16.6,23.9,16.6,13.6,40.6,14.5,19.9,26.3,36.1,23.6,10,10.5,28.1,11.2,23.6,3.5,5.5,11,13.1,0.2,9.9,10.7,0.2,0,8.8,1.9,6.8,0.9,1.6,0.9,0,10.4,4,8,12.6,17.9,10.1,20.4,21.9,12.2,40.1,45.4,32.1,32.4,39.1,56.9,36.5,80.3,110.1,71.7,51.1,49.4,60.6,88.6,85.8,86.1,72.5,100.8,128.2,97.3,88.6,107.3,91.5,78.8,75,115.9,111.5,159.6,106.9,75.4,75.7,67.5,96.1,98.6,140.6,69.7,101,78.2,71.3,136.8,52.5,127.2,134.4,76.6,87.8,139.6,140.8,126.5,152.6,144.8,145.8,126.9,110.9,85.3,88.5,93.1,103.1,79.6,60.9,78.6,71.4,119.7,82.9,91.7,121.6,139.5,110.9,83.5,66,64.5,51.6,36.3,49.8,43.2,95.5,72.9,51.2,45.3,50.4,28.1,35.7,14.4,0.6,21.7,17,22,7.1,11.6,33.4,26.1,38.9,35.7,12.4,11,11.5,34.5,21.2,11.8,13.1,8.5,11.7,11.8,5,4.6,14.6,3.4,17.9,11.1,1.3,14.2,11.1,7.3,4,10.8,15.8,34.3,10.9,3.4,0.3,11.2,8.8,1.1,8.5,2.7,7.9,2.2,19.3,14.2,28.6,18.6,15.9,13.1,22.5,36.9,17.2,34.2,68.5,80.4,98,55.1,89.7,86,69.8,54.3,115.2,126.1,83.3,116,132.7,127.3,127.6,169,104.7,117.5,108.9,131,125,121.6,109.5,146.8,141.3,149.8,147.6,215.4,129.9,133.3,125.2,156.4,138.6,141,87.1,136,168.7,164.8,176.7,117.1,110,125.7,94.3,100.1,105.4,112,101.6,128.2,112.5,119.1,79.7,114.9,96.1,113.2,78.6,117.9,48.4,95.7,86.5,73,46.1,81.7,75.2,45.4,102.2,47.9,63.3,71,67.6,49,48.7,51.7,33.3,18.9,46.1,36.4,80.4,23.9,14,55.5,50.4,60.7,63.9,24.2,43,37.1,15,52.3,58.1,57.1,51.6,21.1,32.4,15.3,30.3,23.6,12.9,34.1,22.5,4.9,14,21.7,13,17.6,15.7,22.8,14.4,26.8,25.3,20.1,13.9,7.1,13.9,21.6,7.5,0.5,0.4,4,7.4,0,17,9.7,1.2,1.7,0.9,6.3,6.4,0,9.3,0,20.7,0,4.7,2.4,1.5,3.8,12.6,27.2,17.2,1.8,13.9,28.4,22.5,43.5,24.3,27.2,46.4,48,18.5,64.8,74.2,76.2,52.6,40.8,61.9,71.6,65.7,69.8,84.3,97.1,50.2,90.4,63.4,91.1,91.2,143,94.3,65.5,79.9,81.6,121.6,98.1,91.8,131.2,178.7,92.5,75.8,52.3,107.4,92.2,96.2,105.3,172.7,79.6,93.5,29.7,64.8,108,127.4,180.3,101.1,87.6,71.4,67.2,82.9,90.5,141.7,109.1,102.5,78.9,65.4,56.6,47.9,96.1,68,80.2,65.8,150.9,144.9,53.9,75.9,65.9,94.6,77.6,110.5,53.7,60,37.8,59.6,38.5,64.7,97.4,93,90.2,44,52.5,35.7,14.1,36.9,20.5,23.5,19.3,43.7,63.9,8.3,9.6,5.6,15,13,27.6,15.1,3.7,5.9,6.7,6.7,4.5,7,3.7,0.4,0,8.2,7.6,7.4,6.9,4.9,0.5,15.9,7.6,1.9,10.6,3.8,4.8,0.8,1.6,0,0,2.9,0.4,2,5.2,1.2,6.3,4.7,4.4,5.3,28.9,8.7,19.1,9.1,12.9,21.2,13.7,27.3,37.3,38.5,70.4,64.8,68.9,55.1,114.7,119.4,116,82.4,89.1,70.9,57.5,75.5,92.4,111.7,119.8,124,112.9,89.3,58.6,75.1,84.5,109.5,88.3,124.5,119.9,158,124.6,190.2,191.4,199.7,257.7,215.6,120.3,160.7,215.5,160,108.7,120.4,134.1,127.9,99,179.5,169.6,133.2,141.7,139,98.5,80.2,132.5,110.9,86.3,146.9,185.3,107.8,115.1,91.1,88,69.9,58,85.3,89.8,116.9,24.7,55.4,64.6,45.7,31.9,60.5,82.7,45.3,49.8,52.5,47.1,44.5,54,37,56.2,69.7,38,29.6,30.3,29.6,33.9,19.7,43.9,91.3,18.3,13.4,9.8,18.3,10.9,7.8,10.4,12.2,29,7.5,2.5,5.5,10.2,5.3,15.3,5.9,0.8,22.1,19.5,16.7,4.6,0.8,8.5,3,18.9,34.6,40,46.9,32.1,41.9,42.6,37.5,27.5,9.1,38.6,30,53,71.4,79.1,64.2,63.3,100.3,115.3,97.6,164.4,119.7,116.4,104.2,64.2,107,122.4,87.2,102.7,101.4,119.3,100.8,132.4,136,155.1,116.1,155.8,131.9,98.5,91.6,89.6,114.1,105.2,112.1,75.3,139.2,122.4,142.4,134.3,128.3,152.4,163.4,139.6,149.6,102.3,83.9,98.3,114.8,104.7,83.8,87.9,97,119.9,117.1,109.6,57.3,90.1,135.1,179.9,108.8,83.1,58.4,63.7,61.4,48,36.5,41.5,53.5,57.2,59.4,43,24.4,71.8,50.1,52,40.8,25.5,29,21.6,31.7,16.6,31.2,29.7,20.1,17.6,18.8,18.7,29.7,36.9,16,11.3,6.6,14.8,13.7,18.5,20.4,36.9,16.8,4.9,5.3,8.7,4.7,0.4,8.5,5,1,0.4,5.7,12.9,7.2,18.8,32.9,11.2,15.3,13.9,6.7,9.5,14.5,25.7,31.1,34.1,38.5,20.4,45.4,76.2,56.5,50.2,70.1,88.7,107,102.5,104.7,123.9,128.4,124.8,90.9,116.7,87.2,145,126.7,148.2,192.3,205.6,220.9,214.1,139.7,182.2,194.4,217.1,241.8,229.5,167.9,208.2,123.9,147.9,164,198.6,144.2,168.4,212.3,162.6,275.6,192.8,149.3,165.3,203.6,154.7,133.9,129,107.8,181.9,197.3,168.3,162.6,176.3,187.7,146.9,113.7,70.2,84.1,99.1,138.9,101.1,90.6,139.8,112.5,175.9,110.8,91.5,97.4,113.8,76.1,74.3,77.5,54.6,49,99.6,111.4,100.1,109.8,77.2,64,56.2,59.5,87.9,90.4,101.2,41.8,18.9,29.6,33.7,28.7,32,51.3,37.6,20.7,48.1,45.7,43.5,23.6,12.7,22,32.3,16.7,13,17,31.4,6.1,0.8,18.3,0.4,4.1,8.2,8.5,27.9,23.7,28.1,17.9,47.4,30.8,21.2,35.9,53.4,51,60.2,71,43.1,58.1,114.5,76.6,45.7,79.3,143.8,127.7,126.1,141.6,122.6,193.7,178.7,157.4,170.5,206.3,202.9,163.7,188.9,183.8,212.1,285,232.1,223.5,267.4,239.9,231.7,181.3,164.9,153.6,122,134.3,268.5,246.4,237.5,201.4,223.7,202.9,192.9,135.6,195.3,168.6,258,223,208.1,150.4,172.4,178.3,175.3,205.8,186.3,203.2,166.6,143.9,134.3,155.4,160.6,150.5,118.3,128.9,120.6,72.7,87,77.7,76.7,85,84.8,79.3,131.7,153.7,142.4,87.2,86.5,117.7,73.3,74.2,65,57.9,32.4,31.5,41.7,33.6,52,56.1,77.8,40.4,34.2,31.8,48.9,37.9,5.9,14.7,39.6,18.3,31.5,12.7,33.6,28,12.3,2.5,3.9,0.4,0.8,15.8,2.7,1.2,0.4,7.3,12.6,2.3,10.5,13.4,11.3,33.4,29.9,7.3,16.4,41.3,45.2,38.2,58,60.8,83,126.3,108.8,104.1,175.6,167.7,156.7,193.4,165.1,182.7,240.2,245.4,219.9,285,272,233.7,184.5,222.8,248,233,284.3,265.1,223.7,334,359.4,298.6,339,286.7,233.6,270,277.6,248.2,242.9,271,283.5,285.1,256.9,215.6,265.7,307.7,202.6,263,231.3,243.6,238.9,211.9,282.6,205.6,157.7,175.6,177.1,207.2,149.9,144.6,172.7,169.3,156,172.4,190,180.1,117.3,126.9,121.2,82.1,65.4,75.2,86.9,72.3,109.5,99.3,79.2,90.1,53.7,46.5,56.9,55.1,71.7,64.9,65.9,61.9,59.6,31.4,31.5,72.7,56.1,38.8,33.2,28.7,35.2,24.8,41.7,61.1,51.2,28.7,47.5,55.2,50.1,33.7,21.6,22.6,25.3,24.1,12.9,14.3,13.5,4.8,13.8,7,9.2,11.1,22.1,25.4,20.8,17.5,10.2,34.5,23.3,17.3,13.3,24.5,29.1,22.8,24.7,40.3,35.3,36.4,69,64.2,67.7,80.2,72.6,71.1,81.2,81,99.8,157,132.6,158.3,98.4,122.5,95.4,129.5,151.8,108.7,125,133.6,179,172.5,158.5,130.5,115,180,156.2,136.2,154.8,166,152.5,121.7,155.5,147.8,170.5,192.3,151.1,169.9,150.1,137.1,138.8,129.3,135.4,132.4,138.6,157.9,180.8,145.7,155.1,180.5,151.3,159.3,131.7,140.8,122.6,134.8,118.2,129.2,111.8,85.9,101.6,81.5,70.7,114.7,87,71.3,73.4,89.5,116.5,87,125.3,113.5,89.6,113.9,124.7,108.3,108.9,90.7,86.9,59.2,64.3,61.8,60.9,65.4,81.8,60.3,56.1,33.2,36.6,84.1,43.7,34.3,33.3,39.4,37.3,30.9,57.5,56.3,51.5,79.1,47.9,57.2,67.2,35.9,29.6,27.3,16.7,16.9,7.7,13.1,16.7,40.4,56.7,20.3,13.6,27.9,11.6,11.9,6.4,31.5,27.3,18.2,17.9,2.9,24.1,20,29.7,7.9,22.3,23.8,33.3,13,19,27,54.9,30.6,43,62.4,62.1,41.6,61.4,73.7,132.6,108.4,141.2,117.1,134.6,99.7,82.4,195.7,177.1,138.5,173.9,235.9,194.7,195.3,143.7,190.3,211.7,225.7,201.4,266.9,263.6,259.5,249.6,226.1,219.4,178.7,232.2,254.7,222.7,192.9,191.7,219.6,233.3,209.5,246.9,156.6,189.9,196.6,225.3,194.7,131.6,205.3,242.5,245.3,216.2,186,195.4,149.8,230.9,221.1,170.3,119.3,163.7,139.4,161.9,167.4,134.3,127.5,169,115.5,73.1,88.7,109.6,132.5,131.5,108.9,96,69.9,72.5,45.7,45.6,74.8,110.2,116.7,90.4,96.9,65.1,55.7,35,22.6,12.6,26.5,21.4,17.8,20.7,16.9,20.4,32.4,28.3,39.9,10.1,4.3,22,17.9,15.8,2.8,27.9,13.8,22.4,16.1,0.6,18.1,9.9,5.1,40.1,15.4,5.8,9.8,3.4,17.4,46,39.1,18.8,38.2,47.9,42.2,63.4,48.8,29.1,70.5,45.4,91.2,108.8,74.2,124.3,131.4,139.4,142.7,156.5,156.8,231.2,210.1,208.7,170.4,166.3,195.4,284.5,180.5,232,225.1,212.2,238.2,211.4,227.4,171.8,191.7,189.7,175.2,153.3,191.1,252.1,169.1,199.4,178.8,197.1,195.3,240.3,197,197.6,166.9,224.7,240.2,240.8,168.9,197.1,159.5,212.6,198.3,230.7,151,142.2,94.3,98.5,114.2,91.9,94,133.4,129.6,122,81.4,127.8,102.4,94.4,78.8,69.6,80.4,62.5,31.2,71.1,48.2,68.4,84.9,54.9,47.5,27.4,29.8,39.7,50.6,34.3,40.5,67.1,29.5,32.2,32.6,45.8,46.3,21.6,19.4,22.5,20.4,18.2,15.7,30.6,14,14.9,13.3,7.7,12.6,6.8,7.6,16.5,11.8,19.7,3,0.7,24.9,14,7.4,11,12.1,23,25.4,20.8,12.9,35.7,59.7,32.8,50.4,55.5,44.5,50.2,82,70.6,74,90.5,96.7,121.1,132,78.5,97.3,119.2,86,98,103.5,93.6,149.6,207.2,173.5,142.3,106.3,168.7,188.3,116.8,133.1,165.7,217.7,191.5,165.9,188,244.3,180.5,156,141.6,158.1,143.3,142.6,121.5,165.8,161.7,142.1,202.9,123,161.5,238.2,194.1,176.6,213.4,184.6,170.2,147.1,186.9,187.5,128.8,161,175.6,187.9,151.2,147.2,135.3,133.5,75.7,100.7,97.9,86.8,118.7,128.3,115.4,78.5,97.8,82.9,72.2,60.6,74.6,74.8,59.2,72.8,66.5,83.8,69.7,48.8,74.2,70.1,28.9,48.1,43.5,39.6,38.7,61.9,56.8,62.4,60.5,37.2,13.2,27.5,59.3,20.9,5.7,17.3,50.3,37.2,24.5,22.2,20.8,23.7,14.9,35.7,22.3,29.3,18.4,7.2,5.4,19.5,21.3,15.1,9.8,4,1.5,2.8,17.3,4.1,2.9,15.5,3.6,4.6,5.2,0.6,0.3,1.2,4.2,6.6,1,1.3,1.2,0.6,1.2,2.9,6.3,5.5,0,7.1,7.7,6.9,16.3,19.5,28.5,24,10.4,13.9,18.8,25.2,29.6,36.4,33.6,34.4,24.5,27.3,48.3,78.6,76.1,58.2,56.1,64.5,65.8,120.1,125.7,139.1,109.3,94.4,47.8,86.6,85.9,96.5,92,100.1,94.8,93.7,76.5,87.6,56.8,96.1,60.9,78.3,107.3,120.2,76.7,86.2,91.8,54.5,114.4,113.9,124.2,117,146.1,128.7,112.5,112.5,102.9,100.2,106.9,130,90,103.6,112.9,93,66.7,54.5,75.3,88.8,66.5,65.8,64.4,78.6,63.6,62.2,58,57,56.4,54.1,38,52.1,20.9,32.5,50.7,44.7};

From these data points, estimate the cycle (in years) of sunspot activities.