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Fourier Analysis of ZSL (ProShares UltraShort Silver)


ZSL (ProShares UltraShort Silver) appears to have interesting cyclic behaviour every 43 weeks (46.6761*sine), 28 weeks (45.4409*sine), and 39 weeks (42.5213*sine).

ZSL (ProShares UltraShort Silver) has an average price of 200.7 (topmost row, frequency = 0).



Click on the checkboxes shown on the right to see how the various frequencies contribute to the graph. Look for large magnitude coefficients (sine or cosine), as these are associated with frequencies which contribute most to the associated stock plot. If you find a large magnitude coefficient which dramatically changes the graph, look at the associated "Period" in weeks, as you may have found a significant recurring cycle for the stock of interest.

Right click on the graph above to see the menu of operations (download, full screen, etc.)

Fourier Analysis

Using data from 12/3/2008 to 1/17/2017 for ZSL (ProShares UltraShort Silver), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0200.7049   0 
1266.7361 127.3925 (1*2π)/425425 weeks
2139.2511 172.0081 (2*2π)/425213 weeks
373.01043 132.9077 (3*2π)/425142 weeks
462.32222 101.108 (4*2π)/425106 weeks
563.52256 94.42302 (5*2π)/42585 weeks
644.82718 96.15361 (6*2π)/42571 weeks
730.18311 83.18856 (7*2π)/42561 weeks
820.35673 64.5227 (8*2π)/42553 weeks
922.34622 51.74839 (9*2π)/42547 weeks
1022.36304 46.67611 (10*2π)/42543 weeks
1126.15864 42.52131 (11*2π)/42539 weeks
1225.1273 38.17649 (12*2π)/42535 weeks
1327.94849 37.11919 (13*2π)/42533 weeks
1431.63088 40.62882 (14*2π)/42530 weeks
1527.10837 45.44086 (15*2π)/42528 weeks
1619.63824 44.0017 (16*2π)/42527 weeks
1711.4046 37.41388 (17*2π)/42525 weeks
1815.61515 28.35939 (18*2π)/42524 weeks
1919.12316 26.30521 (19*2π)/42522 weeks
2020.36334 29.51766 (20*2π)/42521 weeks
2121.03834 28.44317 (21*2π)/42520 weeks
2222.15184 26.67948 (22*2π)/42519 weeks
2323.9021 27.57122 (23*2π)/42518 weeks
2422.96653 28.67704 (24*2π)/42518 weeks
2523.00988 30.04043 (25*2π)/42517 weeks
2623.55301 32.41906 (26*2π)/42516 weeks
2721.63114 36.29019 (27*2π)/42516 weeks
2816.85064 37.03829 (28*2π)/42515 weeks
2912.68804 38.04528 (29*2π)/42515 weeks
307.21356 36.6499 (30*2π)/42514 weeks
312.49883 31.83506 (31*2π)/42514 weeks
321.27295 27.55062 (32*2π)/42513 weeks
331.0789 23.22148 (33*2π)/42513 weeks
342.98464 21.06619 (34*2π)/42513 weeks
353.32444 19.26771 (35*2π)/42512 weeks
362.8955 17.02009 (36*2π)/42512 weeks
375.3308 13.40229 (37*2π)/42511 weeks
387.78104 13.02401 (38*2π)/42511 weeks
399.78266 12.77512 (39*2π)/42511 weeks
4011.20019 12.92948 (40*2π)/42511 weeks
4111.92893 14.21885 (41*2π)/42510 weeks
4212.62687 14.65306 (42*2π)/42510 weeks
4311.86872 16.46931 (43*2π)/42510 weeks
4410.63333 16.67498 (44*2π)/42510 weeks
459.19393 17.04061 (45*2π)/4259 weeks
4610.06531 17.09594 (46*2π)/4259 weeks
479.07834 16.57632 (47*2π)/4259 weeks
488.47204 16.21998 (48*2π)/4259 weeks
497.87049 16.00836 (49*2π)/4259 weeks
505.91016 15.6987 (50*2π)/4259 weeks
514.03302 13.95217 (51*2π)/4258 weeks
524.40691 10.09696 (52*2π)/4258 weeks
536.0004 8.26362 (53*2π)/4258 weeks
549.06395 8.07071 (54*2π)/4258 weeks
5510.72746 8.96765 (55*2π)/4258 weeks
5610.89108 10.08883 (56*2π)/4258 weeks
579.55958 11.21091 (57*2π)/4257 weeks
588.22127 11.3761 (58*2π)/4257 weeks
598.04246 9.15253 (59*2π)/4257 weeks
6010.02872 7.33374 (60*2π)/4257 weeks
6111.49972 8.22714 (61*2π)/4257 weeks
6211.25599 9.5265 (62*2π)/4257 weeks
6311.29474 9.38994 (63*2π)/4257 weeks
6411.03349 10.08852 (64*2π)/4257 weeks
659.85612 9.60204 (65*2π)/4257 weeks
6610.61887 8.08797 (66*2π)/4256 weeks
6711.55952 8.28972 (67*2π)/4256 weeks
6812.68552 8.67182 (68*2π)/4256 weeks
6914.23096 9.8131 (69*2π)/4256 weeks
7014.88044 12.23906 (70*2π)/4256 weeks
7113.38303 14.34873 (71*2π)/4256 weeks
7210.11924 15.63326 (72*2π)/4256 weeks
737.63755 15.09303 (73*2π)/4256 weeks
745.7564 12.772 (74*2π)/4256 weeks
755.76267 10.05953 (75*2π)/4256 weeks
767.11588 8.8377 (76*2π)/4256 weeks
778.47265 9.7071 (77*2π)/4256 weeks
787.91687 10.25737 (78*2π)/4255 weeks
797.5421 9.821 (79*2π)/4255 weeks
807.87319 8.64501 (80*2π)/4255 weeks
818.48918 8.82058 (81*2π)/4255 weeks
828.94117 9.66312 (82*2π)/4255 weeks
837.36746 10.34918 (83*2π)/4255 weeks
845.8655 9.77739 (84*2π)/4255 weeks
854.57961 8.20833 (85*2π)/4255 weeks
865.3053 6.67094 (86*2π)/4255 weeks
876.9485 5.17622 (87*2π)/4255 weeks
887.6184 5.22023 (88*2π)/4255 weeks
898.38276 5.14721 (89*2π)/4255 weeks
909.41312 5.45458 (90*2π)/4255 weeks
9110.04881 6.37482 (91*2π)/4255 weeks
929.54614 7.24706 (92*2π)/4255 weeks
938.83364 7.75604 (93*2π)/4255 weeks
948.29311 7.46164 (94*2π)/4255 weeks
958.2217 6.9762 (95*2π)/4254 weeks
967.98517 6.44228 (96*2π)/4254 weeks
978.08909 6.54579 (97*2π)/4254 weeks
988.88206 6.16573 (98*2π)/4254 weeks
999.35641 6.31367 (99*2π)/4254 weeks
1008.87356 7.20205 (100*2π)/4254 weeks
1018.28757 7.89865 (101*2π)/4254 weeks
1027.32969 7.76843 (102*2π)/4254 weeks
1036.76524 6.93706 (103*2π)/4254 weeks
1047.0693 6.36011 (104*2π)/4254 weeks
1056.80458 6.55269 (105*2π)/4254 weeks
1066.58225 5.56423 (106*2π)/4254 weeks
1077.40762 4.8702 (107*2π)/4254 weeks
1087.93692 5.39653 (108*2π)/4254 weeks
1097.68555 5.48238 (109*2π)/4254 weeks
1107.87423 5.06508 (110*2π)/4254 weeks
1117.78295 5.36559 (111*2π)/4254 weeks
1127.98852 5.59646 (112*2π)/4254 weeks
1137.82471 5.94106 (113*2π)/4254 weeks
1147.21145 6.4119 (114*2π)/4254 weeks
1156.08179 6.12925 (115*2π)/4254 weeks
1165.32726 5.30602 (116*2π)/4254 weeks
1175.30196 3.77098 (117*2π)/4254 weeks
1185.7166 2.50204 (118*2π)/4254 weeks
1196.90411 2.30441 (119*2π)/4254 weeks
1207.86347 2.81936 (120*2π)/4254 weeks
1218.0514 3.07724 (121*2π)/4254 weeks
1227.69709 3.12461 (122*2π)/4253 weeks
1238.17138 2.45342 (123*2π)/4253 weeks
1249.17784 2.31157 (124*2π)/4253 weeks
1259.43983 3.5325 (125*2π)/4253 weeks
1268.81031 4.18145 (126*2π)/4253 weeks
1278.22792 3.95474 (127*2π)/4253 weeks
1288.40874 3.82916 (128*2π)/4253 weeks
1298.26515 3.9368 (129*2π)/4253 weeks
1307.77029 3.91611 (130*2π)/4253 weeks
1317.4898 3.70215 (131*2π)/4253 weeks
1327.09356 2.53789 (132*2π)/4253 weeks
1337.67382 1.61151 (133*2π)/4253 weeks
1348.95103 1.50949 (134*2π)/4253 weeks
1359.50773 1.81586 (135*2π)/4253 weeks
1369.95136 1.90085 (136*2π)/4253 weeks
13710.40224 2.23469 (137*2π)/4253 weeks
13811.09091 3.20304 (138*2π)/4253 weeks
13911.14036 4.01535 (139*2π)/4253 weeks
14010.06002 4.86191 (140*2π)/4253 weeks
1418.95156 4.58685 (141*2π)/4253 weeks
1428.77816 4.2214 (142*2π)/4253 weeks
1439.34338 4.08853 (143*2π)/4253 weeks
1449.19457 4.14419 (144*2π)/4253 weeks
1459.04741 4.62726 (145*2π)/4253 weeks
1468.52743 4.86929 (146*2π)/4253 weeks
1478.24941 4.49094 (147*2π)/4253 weeks
1488.15573 4.01937 (148*2π)/4253 weeks
1498.04457 3.85922 (149*2π)/4253 weeks
1508.4805 3.68561 (150*2π)/4253 weeks
1519.02968 3.96258 (151*2π)/4253 weeks
1528.70484 4.76842 (152*2π)/4253 weeks
1537.56095 4.9699 (153*2π)/4253 weeks
1546.71176 4.38131 (154*2π)/4253 weeks
1556.66925 3.25307 (155*2π)/4253 weeks
1567.08968 2.48544 (156*2π)/4253 weeks
1577.52098 2.54321 (157*2π)/4253 weeks
1587.91481 2.22363 (158*2π)/4253 weeks
1598.58094 2.1235 (159*2π)/4253 weeks
1609.2079 2.36162 (160*2π)/4253 weeks
1619.58755 3.056 (161*2π)/4253 weeks
1629.07928 3.95545 (162*2π)/4253 weeks
1638.12816 4.38939 (163*2π)/4253 weeks
1647.59091 4.06934 (164*2π)/4253 weeks
1657.79184 3.60674 (165*2π)/4253 weeks
1667.77837 3.50329 (166*2π)/4253 weeks
1677.84246 3.53287 (167*2π)/4253 weeks
1687.59484 4.19294 (168*2π)/4253 weeks
1696.59017 4.29481 (169*2π)/4253 weeks
1705.37146 3.25795 (170*2π)/4253 weeks
1715.65005 1.88375 (171*2π)/4252 weeks
1726.72913 1.2513 (172*2π)/4252 weeks
1737.45399 1.6555 (173*2π)/4252 weeks
1747.47947 1.71457 (174*2π)/4252 weeks
1757.27579 1.55177 (175*2π)/4252 weeks
1767.42457 1.28868 (176*2π)/4252 weeks
1777.8776 .53118 (177*2π)/4252 weeks
1788.89661 .52581 (178*2π)/4252 weeks
1799.86922 1.21197 (179*2π)/4252 weeks
18010.09204 2.37044 (180*2π)/4252 weeks
18110.23229 3.17953 (181*2π)/4252 weeks
1829.64965 4.08843 (182*2π)/4252 weeks
1838.99941 4.82977 (183*2π)/4252 weeks
1847.78665 4.9601 (184*2π)/4252 weeks
1857.37303 4.73337 (185*2π)/4252 weeks
1866.88401 4.71629 (186*2π)/4252 weeks
1875.8013 4.64255 (187*2π)/4252 weeks
1885.33788 3.60486 (188*2π)/4252 weeks
1895.91051 3.01329 (189*2π)/4252 weeks
1906.14609 3.06821 (190*2π)/4252 weeks
1915.41811 3.44054 (191*2π)/4252 weeks
1924.72137 3.38379 (192*2π)/4252 weeks
1933.93005 2.52509 (193*2π)/4252 weeks
1943.9425 1.22143 (194*2π)/4252 weeks
1954.30968 .09521 (195*2π)/4252 weeks
1965.07972 -.14549 (196*2π)/4252 weeks
1975.69511 -.6728 (197*2π)/4252 weeks
1986.4646 -.43537 (198*2π)/4252 weeks
1996.84274 -.02325 (199*2π)/4252 weeks
2006.95988 .18787 (200*2π)/4252 weeks
2017.3218 .50166 (201*2π)/4252 weeks
2027.30302 1.12685 (202*2π)/4252 weeks
2036.66433 1.42162 (203*2π)/4252 weeks
2045.88794 .72121 (204*2π)/4252 weeks
2056.16293 -.15181 (205*2π)/4252 weeks
2067.32517 -.32203 (206*2π)/4252 weeks
2077.8159 1.11717 (207*2π)/4252 weeks
2086.88873 1.67373 (208*2π)/4252 weeks
2095.8891 1.65462 (209*2π)/4252 weeks
2105.36724 1.26146 (210*2π)/4252 weeks
2115.18216 .36931 (211*2π)/4252 weeks
2125.65822 -.00677 (212*2π)/4252 weeks
2135.65822 .00677 (213*2π)/4252 weeks
2145.18216 -.36931 (214*2π)/4252 weeks
2155.36724 -1.26146 (215*2π)/4252 weeks
2165.8891 -1.65462 (216*2π)/4252 weeks
2176.88873 -1.67373 (217*2π)/4252 weeks
2187.8159 -1.11717 (218*2π)/4252 weeks
2197.32517 .32203 (219*2π)/4252 weeks
2206.16293 .15181 (220*2π)/4252 weeks
2215.88794 -.72121 (221*2π)/4252 weeks
2226.66433 -1.42162 (222*2π)/4252 weeks
2237.30302 -1.12685 (223*2π)/4252 weeks
2247.3218 -.50166 (224*2π)/4252 weeks
2256.95988 -.18787 (225*2π)/4252 weeks
2266.84274 .02325 (226*2π)/4252 weeks
2276.4646 .43537 (227*2π)/4252 weeks
2285.69511 .6728 (228*2π)/4252 weeks
2295.07972 .14549 (229*2π)/4252 weeks
2304.30968 -.09521 (230*2π)/4252 weeks
2313.9425 -1.22143 (231*2π)/4252 weeks
2323.93005 -2.52509 (232*2π)/4252 weeks
2334.72137 -3.38379 (233*2π)/4252 weeks
2345.41811 -3.44054 (234*2π)/4252 weeks
2356.14609 -3.06821 (235*2π)/4252 weeks
2365.91051 -3.01329 (236*2π)/4252 weeks
2375.33788 -3.60486 (237*2π)/4252 weeks
2385.8013 -4.64255 (238*2π)/4252 weeks
2396.88401 -4.71629 (239*2π)/4252 weeks
2407.37303 -4.73337 (240*2π)/4252 weeks
2417.78665 -4.9601 (241*2π)/4252 weeks
2428.99941 -4.82977 (242*2π)/4252 weeks
2439.64965 -4.08843 (243*2π)/4252 weeks
24410.23229 -3.17953 (244*2π)/4252 weeks
24510.09204 -2.37044 (245*2π)/4252 weeks
2469.86922 -1.21197 (246*2π)/4252 weeks
2478.89661 -.52581 (247*2π)/4252 weeks
2487.8776 -.53118 (248*2π)/4252 weeks
2497.42457 -1.28868 (249*2π)/4252 weeks
2507.27579 -1.55177 (250*2π)/4252 weeks
2517.47947 -1.71457 (251*2π)/4252 weeks
2527.45399 -1.6555 (252*2π)/4252 weeks
2536.72913 -1.2513 (253*2π)/4252 weeks
2545.65005 -1.88375 (254*2π)/4252 weeks
2555.37146 -3.25795 (255*2π)/4252 weeks
2566.59017 -4.29481 (256*2π)/4252 weeks
2577.59484 -4.19294 (257*2π)/4252 weeks
2587.84246 -3.53287 (258*2π)/4252 weeks
2597.77837 -3.50329 (259*2π)/4252 weeks
2607.79184 -3.60674 (260*2π)/4252 weeks
2617.59091 -4.06934 (261*2π)/4252 weeks
2628.12816 -4.38939 (262*2π)/4252 weeks
2639.07928 -3.95545 (263*2π)/4252 weeks
2649.58755 -3.056 (264*2π)/4252 weeks
2659.2079 -2.36162 (265*2π)/4252 weeks
2668.58094 -2.1235 (266*2π)/4252 weeks
2677.91481 -2.22363 (267*2π)/4252 weeks
2687.52098 -2.54321 (268*2π)/4252 weeks
2697.08968 -2.48544 (269*2π)/4252 weeks
2706.66925 -3.25307 (270*2π)/4252 weeks
2716.71176 -4.38131 (271*2π)/4252 weeks
2727.56095 -4.9699 (272*2π)/4252 weeks
2738.70484 -4.76842 (273*2π)/4252 weeks
2749.02968 -3.96258 (274*2π)/4252 weeks
2758.4805 -3.68561 (275*2π)/4252 weeks
2768.04457 -3.85922 (276*2π)/4252 weeks
2778.15573 -4.01937 (277*2π)/4252 weeks
2788.24941 -4.49094 (278*2π)/4252 weeks
2798.52743 -4.86929 (279*2π)/4252 weeks
2809.04741 -4.62726 (280*2π)/4252 weeks
2819.19457 -4.14419 (281*2π)/4252 weeks
2829.34338 -4.08853 (282*2π)/4252 weeks
2838.77816 -4.2214 (283*2π)/4252 weeks
2848.95156 -4.58685 (284*2π)/4251 weeks
28510.06002 -4.86191 (285*2π)/4251 weeks
28611.14036 -4.01535 (286*2π)/4251 weeks
28711.09091 -3.20304 (287*2π)/4251 weeks
28810.40224 -2.23469 (288*2π)/4251 weeks
2899.95136 -1.90085 (289*2π)/4251 weeks
2909.50773 -1.81586 (290*2π)/4251 weeks
2918.95103 -1.50949 (291*2π)/4251 weeks
2927.67382 -1.61151 (292*2π)/4251 weeks
2937.09356 -2.53789 (293*2π)/4251 weeks
2947.4898 -3.70215 (294*2π)/4251 weeks
2957.77029 -3.91611 (295*2π)/4251 weeks
2968.26515 -3.9368 (296*2π)/4251 weeks
2978.40874 -3.82916 (297*2π)/4251 weeks
2988.22792 -3.95474 (298*2π)/4251 weeks
2998.81031 -4.18145 (299*2π)/4251 weeks
3009.43983 -3.5325 (300*2π)/4251 weeks
3019.17784 -2.31157 (301*2π)/4251 weeks
3028.17138 -2.45342 (302*2π)/4251 weeks
3037.69709 -3.12461 (303*2π)/4251 weeks
3048.0514 -3.07724 (304*2π)/4251 weeks
3057.86347 -2.81936 (305*2π)/4251 weeks
3066.90411 -2.30441 (306*2π)/4251 weeks
3075.7166 -2.50204 (307*2π)/4251 weeks
3085.30196 -3.77098 (308*2π)/4251 weeks
3095.32726 -5.30602 (309*2π)/4251 weeks
3106.08179 -6.12925 (310*2π)/4251 weeks
3117.21145 -6.4119 (311*2π)/4251 weeks
3127.82471 -5.94106 (312*2π)/4251 weeks
3137.98852 -5.59646 (313*2π)/4251 weeks
3147.78295 -5.36559 (314*2π)/4251 weeks
3157.87423 -5.06508 (315*2π)/4251 weeks
3167.68555 -5.48238 (316*2π)/4251 weeks
3177.93692 -5.39653 (317*2π)/4251 weeks
3187.40762 -4.8702 (318*2π)/4251 weeks
3196.58225 -5.56423 (319*2π)/4251 weeks
3206.80458 -6.55269 (320*2π)/4251 weeks
3217.0693 -6.36011 (321*2π)/4251 weeks
3226.76524 -6.93706 (322*2π)/4251 weeks
3237.32969 -7.76843 (323*2π)/4251 weeks
3248.28757 -7.89865 (324*2π)/4251 weeks
3258.87356 -7.20205 (325*2π)/4251 weeks
3269.35641 -6.31367 (326*2π)/4251 weeks
3278.88206 -6.16573 (327*2π)/4251 weeks
3288.08909 -6.54579 (328*2π)/4251 weeks
3297.98517 -6.44228 (329*2π)/4251 weeks
3308.2217 -6.9762 (330*2π)/4251 weeks
3318.29311 -7.46164 (331*2π)/4251 weeks
3328.83364 -7.75604 (332*2π)/4251 weeks
3339.54614 -7.24706 (333*2π)/4251 weeks
33410.04881 -6.37482 (334*2π)/4251 weeks
3359.41312 -5.45458 (335*2π)/4251 weeks
3368.38276 -5.14721 (336*2π)/4251 weeks
3377.6184 -5.22023 (337*2π)/4251 weeks
3386.9485 -5.17622 (338*2π)/4251 weeks
3395.3053 -6.67094 (339*2π)/4251 weeks
3404.57961 -8.20833 (340*2π)/4251 weeks
3415.8655 -9.77739 (341*2π)/4251 weeks
3427.36746 -10.34918 (342*2π)/4251 weeks
3438.94117 -9.66312 (343*2π)/4251 weeks
3448.48918 -8.82058 (344*2π)/4251 weeks
3457.87319 -8.64501 (345*2π)/4251 weeks
3467.5421 -9.821 (346*2π)/4251 weeks
3477.91687 -10.25737 (347*2π)/4251 weeks
3488.47265 -9.7071 (348*2π)/4251 weeks
3497.11588 -8.8377 (349*2π)/4251 weeks
3505.76267 -10.05953 (350*2π)/4251 weeks
3515.7564 -12.772 (351*2π)/4251 weeks
3527.63755 -15.09303 (352*2π)/4251 weeks
35310.11924 -15.63326 (353*2π)/4251 weeks
35413.38303 -14.34873 (354*2π)/4251 weeks
35514.88044 -12.23906 (355*2π)/4251 weeks
35614.23096 -9.8131 (356*2π)/4251 weeks
35712.68552 -8.67182 (357*2π)/4251 weeks
35811.55952 -8.28972 (358*2π)/4251 weeks
35910.61887 -8.08797 (359*2π)/4251 weeks
3609.85612 -9.60204 (360*2π)/4251 weeks
36111.03349 -10.08852 (361*2π)/4251 weeks
36211.29474 -9.38994 (362*2π)/4251 weeks
36311.25599 -9.5265 (363*2π)/4251 weeks
36411.49972 -8.22714 (364*2π)/4251 weeks
36510.02872 -7.33374 (365*2π)/4251 weeks
3668.04246 -9.15253 (366*2π)/4251 weeks
3678.22127 -11.3761 (367*2π)/4251 weeks
3689.55958 -11.21091 (368*2π)/4251 weeks
36910.89108 -10.08883 (369*2π)/4251 weeks
37010.72746 -8.96765 (370*2π)/4251 weeks
3719.06395 -8.07071 (371*2π)/4251 weeks
3726.0004 -8.26362 (372*2π)/4251 weeks
3734.40691 -10.09696 (373*2π)/4251 weeks
3744.03302 -13.95217 (374*2π)/4251 weeks
3755.91016 -15.6987 (375*2π)/4251 weeks
3767.87049 -16.00836 (376*2π)/4251 weeks
3778.47204 -16.21998 (377*2π)/4251 weeks
3789.07834 -16.57632 (378*2π)/4251 weeks
37910.06531 -17.09594 (379*2π)/4251 weeks
3809.19393 -17.04061 (380*2π)/4251 weeks
38110.63333 -16.67498 (381*2π)/4251 weeks
38211.86872 -16.46931 (382*2π)/4251 weeks
38312.62687 -14.65306 (383*2π)/4251 weeks
38411.92893 -14.21885 (384*2π)/4251 weeks
38511.20019 -12.92948 (385*2π)/4251 weeks
3869.78266 -12.77512 (386*2π)/4251 weeks
3877.78104 -13.02401 (387*2π)/4251 weeks
3885.3308 -13.40229 (388*2π)/4251 weeks
3892.8955 -17.02009 (389*2π)/4251 weeks
3903.32444 -19.26771 (390*2π)/4251 weeks
3912.98464 -21.06619 (391*2π)/4251 weeks
3921.0789 -23.22148 (392*2π)/4251 weeks
3931.27295 -27.55062 (393*2π)/4251 weeks
3942.49883 -31.83506 (394*2π)/4251 weeks
3957.21356 -36.6499 (395*2π)/4251 weeks
39612.68804 -38.04528 (396*2π)/4251 weeks
39716.85064 -37.03829 (397*2π)/4251 weeks
39821.63114 -36.29019 (398*2π)/4251 weeks
39923.55301 -32.41906 (399*2π)/4251 weeks
40023.00988 -30.04043 (400*2π)/4251 weeks
40122.96653 -28.67704 (401*2π)/4251 weeks
40223.9021 -27.57122 (402*2π)/4251 weeks
40322.15184 -26.67948 (403*2π)/4251 weeks
40421.03834 -28.44317 (404*2π)/4251 weeks
40520.36334 -29.51766 (405*2π)/4251 weeks
40619.12316 -26.30521 (406*2π)/4251 weeks
40715.61515 -28.35939 (407*2π)/4251 weeks
40811.4046 -37.41388 (408*2π)/4251 weeks
40919.63824 -44.0017 (409*2π)/4251 weeks
41027.10837 -45.44086 (410*2π)/4251 weeks
41131.63088 -40.62882 (411*2π)/4251 weeks
41227.94849 -37.11919 (412*2π)/4251 weeks
41325.1273 -38.17649 (413*2π)/4251 weeks
41426.15864 -42.52131 (414*2π)/4251 weeks
41522.36304 -46.67611 (415*2π)/4251 weeks
41622.34622 -51.74839 (416*2π)/4251 weeks
41720.35673 -64.5227 (417*2π)/4251 weeks
41830.18311 -83.18856 (418*2π)/4251 weeks
41944.82718 -96.15361 (419*2π)/4251 weeks
42063.52256 -94.42302 (420*2π)/4251 weeks
42162.32222 -101.108 (421*2π)/4251 weeks
42273.01043 -132.9077 (422*2π)/4251 weeks
423139.2511 -172.0081 (423*2π)/4251 weeks

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