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Fourier Analysis of ZSL (ProShares UltraShort Silver ETF)


ZSL (ProShares UltraShort Silver ETF) appears to have interesting cyclic behaviour every 45 weeks (48.3987*sine), 28 weeks (43.1381*sine), and 41 weeks (41.87*sine).

ZSL (ProShares UltraShort Silver ETF) has an average price of 191.34 (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 7/10/2017 for ZSL (ProShares UltraShort Silver ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0191.3378   0 
1255.0614 114.8131 (1*2π)/450450 weeks
2142.2606 166.9237 (2*2π)/450225 weeks
376.22288 135.2062 (3*2π)/450150 weeks
462.08128 100.3385 (4*2π)/450113 weeks
562.2171 86.6371 (5*2π)/45090 weeks
650.39818 90.54043 (6*2π)/45075 weeks
731.82101 80.6447 (7*2π)/45064 weeks
818.76798 69.23414 (8*2π)/45056 weeks
918.00616 55.03442 (9*2π)/45050 weeks
1021.78423 48.39869 (10*2π)/45045 weeks
1122.21974 41.86996 (11*2π)/45041 weeks
1224.19167 40.88997 (12*2π)/45038 weeks
1325.74733 35.82601 (13*2π)/45035 weeks
1427.81878 34.70686 (14*2π)/45032 weeks
1529.743 39.2879 (15*2π)/45030 weeks
1624.89213 43.1381 (16*2π)/45028 weeks
1718.38919 41.39573 (17*2π)/45026 weeks
1810.83209 35.22516 (18*2π)/45025 weeks
1914.39833 26.86052 (19*2π)/45024 weeks
2017.42557 25.18337 (20*2π)/45023 weeks
2120.12257 27.98543 (21*2π)/45021 weeks
2220.15652 26.40841 (22*2π)/45020 weeks
2320.01366 24.96736 (23*2π)/45020 weeks
2421.58761 25.39889 (24*2π)/45019 weeks
2521.62683 27.59611 (25*2π)/45018 weeks
2622.12894 28.20674 (26*2π)/45017 weeks
2722.39972 29.098 (27*2π)/45017 weeks
2821.86519 32.01336 (28*2π)/45016 weeks
2918.3422 35.30517 (29*2π)/45016 weeks
3015.11542 35.42347 (30*2π)/45015 weeks
3110.66276 35.89451 (31*2π)/45015 weeks
325.79966 34.10418 (32*2π)/45014 weeks
332.40082 29.17442 (33*2π)/45014 weeks
341.24357 25.43946 (34*2π)/45013 weeks
351.13467 21.60026 (35*2π)/45013 weeks
362.8532 19.87675 (36*2π)/45013 weeks
373.19368 18.26621 (37*2π)/45012 weeks
382.87806 16.42641 (38*2π)/45012 weeks
394.49734 12.84245 (39*2π)/45012 weeks
407.00648 12.25959 (40*2π)/45011 weeks
418.60906 11.86014 (41*2π)/45011 weeks
429.80235 12.22191 (42*2π)/45011 weeks
4311.17157 13.26297 (43*2π)/45010 weeks
4411.3993 13.85907 (44*2π)/45010 weeks
4512.22724 15.36277 (45*2π)/45010 weeks
4611.22771 16.03267 (46*2π)/45010 weeks
4710.64692 15.81618 (47*2π)/45010 weeks
489.11558 14.73398 (48*2π)/4509 weeks
498.82942 15.8521 (49*2π)/4509 weeks
508.32203 15.49591 (50*2π)/4509 weeks
517.86788 15.22922 (51*2π)/4509 weeks
527.37997 15.10363 (52*2π)/4509 weeks
535.53751 14.6243 (53*2π)/4508 weeks
543.82807 13.04321 (54*2π)/4508 weeks
554.03413 9.53932 (55*2π)/4508 weeks
565.45292 7.95999 (56*2π)/4508 weeks
578.28443 7.2737 (57*2π)/4508 weeks
589.72767 7.8952 (58*2π)/4508 weeks
599.95076 9.22272 (59*2π)/4508 weeks
609.56926 10.76059 (60*2π)/4508 weeks
618.81081 10.71562 (61*2π)/4507 weeks
627.2996 9.07971 (62*2π)/4507 weeks
637.74514 7.3092 (63*2π)/4507 weeks
6410.01208 7.41064 (64*2π)/4507 weeks
6510.99802 8.52519 (65*2π)/4507 weeks
6610.41058 9.02569 (66*2π)/4507 weeks
6710.74918 9.15086 (67*2π)/4507 weeks
6810.25429 9.67306 (68*2π)/4507 weeks
699.30397 8.81643 (69*2π)/4507 weeks
7010.26765 7.60825 (70*2π)/4506 weeks
7110.97892 7.79641 (71*2π)/4506 weeks
7211.98956 8.21217 (72*2π)/4506 weeks
7313.44819 9.18897 (73*2π)/4506 weeks
7414.16729 11.17765 (74*2π)/4506 weeks
7512.84953 13.19904 (75*2π)/4506 weeks
7610.33247 14.9248 (76*2π)/4506 weeks
778.10524 14.42793 (77*2π)/4506 weeks
785.85428 12.77431 (78*2π)/4506 weeks
795.17725 10.45148 (79*2π)/4506 weeks
806.30144 8.75391 (80*2π)/4506 weeks
817.90909 8.25731 (81*2π)/4506 weeks
827.91032 9.17125 (82*2π)/4505 weeks
837.10187 9.16424 (83*2π)/4505 weeks
846.63741 8.80732 (84*2π)/4505 weeks
857.4862 8.22116 (85*2π)/4505 weeks
868.00041 8.47019 (86*2π)/4505 weeks
878.29267 9.50298 (87*2π)/4505 weeks
886.8469 9.78778 (88*2π)/4505 weeks
895.50756 9.16626 (89*2π)/4505 weeks
904.34002 7.73375 (90*2π)/4505 weeks
915.06162 6.33265 (91*2π)/4505 weeks
926.35436 4.74736 (92*2π)/4505 weeks
937.02255 4.90367 (93*2π)/4505 weeks
947.7042 4.83123 (94*2π)/4505 weeks
958.59211 4.91335 (95*2π)/4505 weeks
969.24862 5.58644 (96*2π)/4505 weeks
979.14659 6.69641 (97*2π)/4505 weeks
988.75207 7.18067 (98*2π)/4505 weeks
997.97201 7.11102 (99*2π)/4505 weeks
1007.55941 6.78182 (100*2π)/4505 weeks
1017.55922 6.65063 (101*2π)/4504 weeks
1027.81198 6.05654 (102*2π)/4504 weeks
1037.58336 5.87269 (103*2π)/4504 weeks
1048.35205 5.99713 (104*2π)/4504 weeks
1058.97866 6.23375 (105*2π)/4504 weeks
1068.40481 6.78162 (106*2π)/4504 weeks
1077.73985 7.42107 (107*2π)/4504 weeks
1086.88032 7.32122 (108*2π)/4504 weeks
1096.36051 6.60677 (109*2π)/4504 weeks
1106.61475 6.03409 (110*2π)/4504 weeks
1116.58849 6.22491 (111*2π)/4504 weeks
1126.17131 5.4196 (112*2π)/4504 weeks
1136.66585 4.60285 (113*2π)/4504 weeks
1147.42201 4.84079 (114*2π)/4504 weeks
1157.23585 5.17459 (115*2π)/4504 weeks
1167.04849 4.9837 (116*2π)/4504 weeks
1177.50683 5.18628 (117*2π)/4504 weeks
1187.52483 5.09506 (118*2π)/4504 weeks
1197.51353 5.42418 (119*2π)/4504 weeks
1207.30921 5.77286 (120*2π)/4504 weeks
1216.53916 6.08316 (121*2π)/4504 weeks
1225.58696 5.60097 (122*2π)/4504 weeks
1234.90197 4.78865 (123*2π)/4504 weeks
1245.07469 3.45939 (124*2π)/4504 weeks
1255.4877 2.25794 (125*2π)/4504 weeks
1266.50161 2.14982 (126*2π)/4504 weeks
1277.42362 2.60937 (127*2π)/4504 weeks
1287.59101 2.81991 (128*2π)/4504 weeks
1297.33114 2.98056 (129*2π)/4503 weeks
1307.50074 2.2898 (130*2π)/4503 weeks
1318.16333 2.07342 (131*2π)/4503 weeks
1328.94697 3.08681 (132*2π)/4503 weeks
1338.63539 3.86299 (133*2π)/4503 weeks
1347.99191 3.9199 (134*2π)/4503 weeks
1357.86564 3.49736 (135*2π)/4503 weeks
1367.85187 3.62566 (136*2π)/4503 weeks
1377.64146 3.75465 (137*2π)/4503 weeks
1387.20209 3.51288 (138*2π)/4503 weeks
1396.73578 3.35768 (139*2π)/4503 weeks
1406.77592 2.22295 (140*2π)/4503 weeks
1417.40177 1.40065 (141*2π)/4503 weeks
1428.49366 1.50169 (142*2π)/4503 weeks
1438.98515 1.75893 (143*2π)/4503 weeks
1449.38998 1.80526 (144*2π)/4503 weeks
1459.77494 2.11033 (145*2π)/4503 weeks
14610.47614 2.87507 (146*2π)/4503 weeks
14710.42867 3.54393 (147*2π)/4503 weeks
1489.61468 4.60528 (148*2π)/4503 weeks
1498.61417 4.71159 (149*2π)/4503 weeks
1508.48511 4.21958 (150*2π)/4503 weeks
1518.67443 3.66253 (151*2π)/4503 weeks
1528.66337 4.02967 (152*2π)/4503 weeks
1538.84635 4.18667 (153*2π)/4503 weeks
1548.49758 4.40663 (154*2π)/4503 weeks
1557.82771 4.31381 (155*2π)/4503 weeks
1567.6091 4.10945 (156*2π)/4503 weeks
1577.72792 3.79193 (157*2π)/4503 weeks
1587.61767 3.4891 (158*2π)/4503 weeks
1597.99247 3.47934 (159*2π)/4503 weeks
1608.50815 3.88244 (160*2π)/4503 weeks
1618.17246 4.57273 (161*2π)/4503 weeks
1627.13536 4.71445 (162*2π)/4503 weeks
1636.38379 4.20643 (163*2π)/4503 weeks
1646.26471 3.15523 (164*2π)/4503 weeks
1656.55791 2.4566 (165*2π)/4503 weeks
1667.14001 2.42219 (166*2π)/4503 weeks
1677.36213 2.08946 (167*2π)/4503 weeks
1687.81595 1.8834 (168*2π)/4503 weeks
1698.30045 2.06527 (169*2π)/4503 weeks
1708.76696 2.64686 (170*2π)/4503 weeks
1718.89662 3.61723 (171*2π)/4503 weeks
1728.41639 4.1274 (172*2π)/4503 weeks
1737.54435 3.94565 (173*2π)/4503 weeks
1747.0658 3.51757 (174*2π)/4503 weeks
1757.2737 3.45019 (175*2π)/4503 weeks
1767.34353 3.37987 (176*2π)/4503 weeks
1777.46729 3.43289 (177*2π)/4503 weeks
1787.08907 4.02439 (178*2π)/4503 weeks
1796.16856 4.06224 (179*2π)/4503 weeks
1805.07442 3.09271 (180*2π)/4503 weeks
1815.31293 1.87143 (181*2π)/4502 weeks
1826.27467 1.21082 (182*2π)/4502 weeks
1837.05681 1.45143 (183*2π)/4502 weeks
1847.02143 1.56423 (184*2π)/4502 weeks
1856.8657 1.60111 (185*2π)/4502 weeks
1866.99913 1.2941 (186*2π)/4502 weeks
1877.06325 .80253 (187*2π)/4502 weeks
1887.99715 .51741 (188*2π)/4502 weeks
1898.97467 .77119 (189*2π)/4502 weeks
1909.63182 1.62776 (190*2π)/4502 weeks
1919.53317 2.40275 (191*2π)/4502 weeks
1929.53252 3.38628 (192*2π)/4502 weeks
1938.99267 4.01589 (193*2π)/4502 weeks
1948.26286 4.67782 (194*2π)/4502 weeks
1957.22179 4.58237 (195*2π)/4502 weeks
1966.88633 4.47778 (196*2π)/4502 weeks
1976.46294 4.47631 (197*2π)/4502 weeks
1985.47266 4.39765 (198*2π)/4502 weeks
1995.05374 3.47353 (199*2π)/4502 weeks
2005.54326 2.81173 (200*2π)/4502 weeks
2015.7096 2.81036 (201*2π)/4502 weeks
2025.27153 3.36016 (202*2π)/4502 weeks
2034.77903 3.26334 (203*2π)/4502 weeks
2043.93792 2.67007 (204*2π)/4502 weeks
2053.53543 1.52837 (205*2π)/4502 weeks
2063.72809 .67513 (206*2π)/4502 weeks
2074.58658 -.03913 (207*2π)/4502 weeks
2084.96348 -.28865 (208*2π)/4502 weeks
2095.83344 -.56448 (209*2π)/4502 weeks
2106.35378 -.33085 (210*2π)/4502 weeks
2116.53642 .00181 (211*2π)/4502 weeks
2126.6346 .12984 (212*2π)/4502 weeks
2136.90902 .52839 (213*2π)/4502 weeks
2146.82203 1.13053 (214*2π)/4502 weeks
2156.24941 1.35258 (215*2π)/4502 weeks
2165.56855 .66896 (216*2π)/4502 weeks
2175.77718 -.11542 (217*2π)/4502 weeks
2186.76632 -.36362 (218*2π)/4502 weeks
2197.46898 .80206 (219*2π)/4502 weeks
2206.64109 1.53859 (220*2π)/4502 weeks
2215.83516 1.72474 (221*2π)/4502 weeks
2225.33471 1.28561 (222*2π)/4502 weeks
2234.85183 .59813 (223*2π)/4502 weeks
2245.08715 -.0462 (224*2π)/4502 weeks
2255.27847   (225*2π)/4502 weeks
2265.08715 .0462 (226*2π)/4502 weeks
2274.85183 -.59813 (227*2π)/4502 weeks
2285.33471 -1.28561 (228*2π)/4502 weeks
2295.83516 -1.72474 (229*2π)/4502 weeks
2306.64109 -1.53859 (230*2π)/4502 weeks
2317.46898 -.80206 (231*2π)/4502 weeks
2326.76632 .36362 (232*2π)/4502 weeks
2335.77718 .11542 (233*2π)/4502 weeks
2345.56855 -.66896 (234*2π)/4502 weeks
2356.24941 -1.35258 (235*2π)/4502 weeks
2366.82203 -1.13053 (236*2π)/4502 weeks
2376.90902 -.52839 (237*2π)/4502 weeks
2386.6346 -.12984 (238*2π)/4502 weeks
2396.53642 -.00181 (239*2π)/4502 weeks
2406.35378 .33085 (240*2π)/4502 weeks
2415.83344 .56448 (241*2π)/4502 weeks
2424.96348 .28865 (242*2π)/4502 weeks
2434.58658 .03913 (243*2π)/4502 weeks
2443.72809 -.67513 (244*2π)/4502 weeks
2453.53543 -1.52837 (245*2π)/4502 weeks
2463.93792 -2.67007 (246*2π)/4502 weeks
2474.77903 -3.26334 (247*2π)/4502 weeks
2485.27153 -3.36016 (248*2π)/4502 weeks
2495.7096 -2.81036 (249*2π)/4502 weeks
2505.54326 -2.81173 (250*2π)/4502 weeks
2515.05374 -3.47353 (251*2π)/4502 weeks
2525.47266 -4.39765 (252*2π)/4502 weeks
2536.46294 -4.47631 (253*2π)/4502 weeks
2546.88633 -4.47778 (254*2π)/4502 weeks
2557.22179 -4.58237 (255*2π)/4502 weeks
2568.26286 -4.67782 (256*2π)/4502 weeks
2578.99267 -4.01589 (257*2π)/4502 weeks
2589.53252 -3.38628 (258*2π)/4502 weeks
2599.53317 -2.40275 (259*2π)/4502 weeks
2609.63182 -1.62776 (260*2π)/4502 weeks
2618.97467 -.77119 (261*2π)/4502 weeks
2627.99715 -.51741 (262*2π)/4502 weeks
2637.06325 -.80253 (263*2π)/4502 weeks
2646.99913 -1.2941 (264*2π)/4502 weeks
2656.8657 -1.60111 (265*2π)/4502 weeks
2667.02143 -1.56423 (266*2π)/4502 weeks
2677.05681 -1.45143 (267*2π)/4502 weeks
2686.27467 -1.21082 (268*2π)/4502 weeks
2695.31293 -1.87143 (269*2π)/4502 weeks
2705.07442 -3.09271 (270*2π)/4502 weeks
2716.16856 -4.06224 (271*2π)/4502 weeks
2727.08907 -4.02439 (272*2π)/4502 weeks
2737.46729 -3.43289 (273*2π)/4502 weeks
2747.34353 -3.37987 (274*2π)/4502 weeks
2757.2737 -3.45019 (275*2π)/4502 weeks
2767.0658 -3.51757 (276*2π)/4502 weeks
2777.54435 -3.94565 (277*2π)/4502 weeks
2788.41639 -4.1274 (278*2π)/4502 weeks
2798.89662 -3.61723 (279*2π)/4502 weeks
2808.76696 -2.64686 (280*2π)/4502 weeks
2818.30045 -2.06527 (281*2π)/4502 weeks
2827.81595 -1.8834 (282*2π)/4502 weeks
2837.36213 -2.08946 (283*2π)/4502 weeks
2847.14001 -2.42219 (284*2π)/4502 weeks
2856.55791 -2.4566 (285*2π)/4502 weeks
2866.26471 -3.15523 (286*2π)/4502 weeks
2876.38379 -4.20643 (287*2π)/4502 weeks
2887.13536 -4.71445 (288*2π)/4502 weeks
2898.17246 -4.57273 (289*2π)/4502 weeks
2908.50815 -3.88244 (290*2π)/4502 weeks
2917.99247 -3.47934 (291*2π)/4502 weeks
2927.61767 -3.4891 (292*2π)/4502 weeks
2937.72792 -3.79193 (293*2π)/4502 weeks
2947.6091 -4.10945 (294*2π)/4502 weeks
2957.82771 -4.31381 (295*2π)/4502 weeks
2968.49758 -4.40663 (296*2π)/4502 weeks
2978.84635 -4.18667 (297*2π)/4502 weeks
2988.66337 -4.02967 (298*2π)/4502 weeks
2998.67443 -3.66253 (299*2π)/4502 weeks
3008.48511 -4.21958 (300*2π)/4502 weeks
3018.61417 -4.71159 (301*2π)/4501 weeks
3029.61468 -4.60528 (302*2π)/4501 weeks
30310.42867 -3.54393 (303*2π)/4501 weeks
30410.47614 -2.87507 (304*2π)/4501 weeks
3059.77494 -2.11033 (305*2π)/4501 weeks
3069.38998 -1.80526 (306*2π)/4501 weeks
3078.98515 -1.75893 (307*2π)/4501 weeks
3088.49366 -1.50169 (308*2π)/4501 weeks
3097.40177 -1.40065 (309*2π)/4501 weeks
3106.77592 -2.22295 (310*2π)/4501 weeks
3116.73578 -3.35768 (311*2π)/4501 weeks
3127.20209 -3.51288 (312*2π)/4501 weeks
3137.64146 -3.75465 (313*2π)/4501 weeks
3147.85187 -3.62566 (314*2π)/4501 weeks
3157.86564 -3.49736 (315*2π)/4501 weeks
3167.99191 -3.9199 (316*2π)/4501 weeks
3178.63539 -3.86299 (317*2π)/4501 weeks
3188.94697 -3.08681 (318*2π)/4501 weeks
3198.16333 -2.07342 (319*2π)/4501 weeks
3207.50074 -2.2898 (320*2π)/4501 weeks
3217.33114 -2.98056 (321*2π)/4501 weeks
3227.59101 -2.81991 (322*2π)/4501 weeks
3237.42362 -2.60937 (323*2π)/4501 weeks
3246.50161 -2.14982 (324*2π)/4501 weeks
3255.4877 -2.25794 (325*2π)/4501 weeks
3265.07469 -3.45939 (326*2π)/4501 weeks
3274.90197 -4.78865 (327*2π)/4501 weeks
3285.58696 -5.60097 (328*2π)/4501 weeks
3296.53916 -6.08316 (329*2π)/4501 weeks
3307.30921 -5.77286 (330*2π)/4501 weeks
3317.51353 -5.42418 (331*2π)/4501 weeks
3327.52483 -5.09506 (332*2π)/4501 weeks
3337.50683 -5.18628 (333*2π)/4501 weeks
3347.04849 -4.9837 (334*2π)/4501 weeks
3357.23585 -5.17459 (335*2π)/4501 weeks
3367.42201 -4.84079 (336*2π)/4501 weeks
3376.66585 -4.60285 (337*2π)/4501 weeks
3386.17131 -5.4196 (338*2π)/4501 weeks
3396.58849 -6.22491 (339*2π)/4501 weeks
3406.61475 -6.03409 (340*2π)/4501 weeks
3416.36051 -6.60677 (341*2π)/4501 weeks
3426.88032 -7.32122 (342*2π)/4501 weeks
3437.73985 -7.42107 (343*2π)/4501 weeks
3448.40481 -6.78162 (344*2π)/4501 weeks
3458.97866 -6.23375 (345*2π)/4501 weeks
3468.35205 -5.99713 (346*2π)/4501 weeks
3477.58336 -5.87269 (347*2π)/4501 weeks
3487.81198 -6.05654 (348*2π)/4501 weeks
3497.55922 -6.65063 (349*2π)/4501 weeks
3507.55941 -6.78182 (350*2π)/4501 weeks
3517.97201 -7.11102 (351*2π)/4501 weeks
3528.75207 -7.18067 (352*2π)/4501 weeks
3539.14659 -6.69641 (353*2π)/4501 weeks
3549.24862 -5.58644 (354*2π)/4501 weeks
3558.59211 -4.91335 (355*2π)/4501 weeks
3567.7042 -4.83123 (356*2π)/4501 weeks
3577.02255 -4.90367 (357*2π)/4501 weeks
3586.35436 -4.74736 (358*2π)/4501 weeks
3595.06162 -6.33265 (359*2π)/4501 weeks
3604.34002 -7.73375 (360*2π)/4501 weeks
3615.50756 -9.16626 (361*2π)/4501 weeks
3626.8469 -9.78778 (362*2π)/4501 weeks
3638.29267 -9.50298 (363*2π)/4501 weeks
3648.00041 -8.47019 (364*2π)/4501 weeks
3657.4862 -8.22116 (365*2π)/4501 weeks
3666.63741 -8.80732 (366*2π)/4501 weeks
3677.10187 -9.16424 (367*2π)/4501 weeks
3687.91032 -9.17125 (368*2π)/4501 weeks
3697.90909 -8.25731 (369*2π)/4501 weeks
3706.30144 -8.75391 (370*2π)/4501 weeks
3715.17725 -10.45148 (371*2π)/4501 weeks
3725.85428 -12.77431 (372*2π)/4501 weeks
3738.10524 -14.42793 (373*2π)/4501 weeks
37410.33247 -14.9248 (374*2π)/4501 weeks
37512.84953 -13.19904 (375*2π)/4501 weeks
37614.16729 -11.17765 (376*2π)/4501 weeks
37713.44819 -9.18897 (377*2π)/4501 weeks
37811.98956 -8.21217 (378*2π)/4501 weeks
37910.97892 -7.79641 (379*2π)/4501 weeks
38010.26765 -7.60825 (380*2π)/4501 weeks
3819.30397 -8.81643 (381*2π)/4501 weeks
38210.25429 -9.67306 (382*2π)/4501 weeks
38310.74918 -9.15086 (383*2π)/4501 weeks
38410.41058 -9.02569 (384*2π)/4501 weeks
38510.99802 -8.52519 (385*2π)/4501 weeks
38610.01208 -7.41064 (386*2π)/4501 weeks
3877.74514 -7.3092 (387*2π)/4501 weeks
3887.2996 -9.07971 (388*2π)/4501 weeks
3898.81081 -10.71562 (389*2π)/4501 weeks
3909.56926 -10.76059 (390*2π)/4501 weeks
3919.95076 -9.22272 (391*2π)/4501 weeks
3929.72767 -7.8952 (392*2π)/4501 weeks
3938.28443 -7.2737 (393*2π)/4501 weeks
3945.45292 -7.95999 (394*2π)/4501 weeks
3954.03413 -9.53932 (395*2π)/4501 weeks
3963.82807 -13.04321 (396*2π)/4501 weeks
3975.53751 -14.6243 (397*2π)/4501 weeks
3987.37997 -15.10363 (398*2π)/4501 weeks
3997.86788 -15.22922 (399*2π)/4501 weeks
4008.32203 -15.49591 (400*2π)/4501 weeks
4018.82942 -15.8521 (401*2π)/4501 weeks
4029.11558 -14.73398 (402*2π)/4501 weeks
40310.64692 -15.81618 (403*2π)/4501 weeks
40411.22771 -16.03267 (404*2π)/4501 weeks
40512.22724 -15.36277 (405*2π)/4501 weeks
40611.3993 -13.85907 (406*2π)/4501 weeks
40711.17157 -13.26297 (407*2π)/4501 weeks
4089.80235 -12.22191 (408*2π)/4501 weeks
4098.60906 -11.86014 (409*2π)/4501 weeks
4107.00648 -12.25959 (410*2π)/4501 weeks
4114.49734 -12.84245 (411*2π)/4501 weeks
4122.87806 -16.42641 (412*2π)/4501 weeks
4133.19368 -18.26621 (413*2π)/4501 weeks
4142.8532 -19.87675 (414*2π)/4501 weeks
4151.13467 -21.60026 (415*2π)/4501 weeks
4161.24357 -25.43946 (416*2π)/4501 weeks
4172.40082 -29.17442 (417*2π)/4501 weeks
4185.79966 -34.10418 (418*2π)/4501 weeks
41910.66276 -35.89451 (419*2π)/4501 weeks
42015.11542 -35.42347 (420*2π)/4501 weeks
42118.3422 -35.30517 (421*2π)/4501 weeks
42221.86519 -32.01336 (422*2π)/4501 weeks
42322.39972 -29.098 (423*2π)/4501 weeks
42422.12894 -28.20674 (424*2π)/4501 weeks
42521.62683 -27.59611 (425*2π)/4501 weeks
42621.58761 -25.39889 (426*2π)/4501 weeks
42720.01366 -24.96736 (427*2π)/4501 weeks
42820.15652 -26.40841 (428*2π)/4501 weeks
42920.12257 -27.98543 (429*2π)/4501 weeks
43017.42557 -25.18337 (430*2π)/4501 weeks
43114.39833 -26.86052 (431*2π)/4501 weeks
43210.83209 -35.22516 (432*2π)/4501 weeks
43318.38919 -41.39573 (433*2π)/4501 weeks
43424.89213 -43.1381 (434*2π)/4501 weeks
43529.743 -39.2879 (435*2π)/4501 weeks
43627.81878 -34.70686 (436*2π)/4501 weeks
43725.74733 -35.82601 (437*2π)/4501 weeks
43824.19167 -40.88997 (438*2π)/4501 weeks
43922.21974 -41.86996 (439*2π)/4501 weeks
44021.78423 -48.39869 (440*2π)/4501 weeks
44118.00616 -55.03442 (441*2π)/4501 weeks
44218.76798 -69.23414 (442*2π)/4501 weeks
44331.82101 -80.6447 (443*2π)/4501 weeks
44450.39818 -90.54043 (444*2π)/4501 weeks
44562.2171 -86.6371 (445*2π)/4501 weeks
44662.08128 -100.3385 (446*2π)/4501 weeks
44776.22288 -135.2062 (447*2π)/4501 weeks
448142.2606 -166.9237 (448*2π)/4501 weeks



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