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Fourier Analysis of ZSL (ProShares UltraShort Silver)


ZSL (ProShares UltraShort Silver) appears to have interesting cyclic behaviour every 64 weeks (58.0779*sine), 58 weeks (54.0165*sine), and 64 weeks (22.4654*cosine).

ZSL (ProShares UltraShort Silver) has an average price of 143.34 (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 2/22/2021 for ZSL (ProShares UltraShort Silver), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0143.3442   0 
1188.3126 64.50011 (1*2π)/639639 weeks
2152.3631 109.8343 (2*2π)/639320 weeks
389.61764 116.4901 (3*2π)/639213 weeks
459.42547 103.7236 (4*2π)/639160 weeks
545.255 79.37238 (5*2π)/639128 weeks
641.43285 68.83042 (6*2π)/639107 weeks
743.1279 61.59798 (7*2π)/63991 weeks
838.03308 64.58045 (8*2π)/63980 weeks
929.6575 65.79433 (9*2π)/63971 weeks
1022.46538 58.07789 (10*2π)/63964 weeks
1115.86959 54.01654 (11*2π)/63958 weeks
1213.84732 44.06656 (12*2π)/63953 weeks
1313.36061 37.96026 (13*2π)/63949 weeks
1416.35411 34.82832 (14*2π)/63946 weeks
1515.45354 31.21408 (15*2π)/63943 weeks
1616.4066 28.3149 (16*2π)/63940 weeks
1716.76472 28.59496 (17*2π)/63938 weeks
1815.93388 25.78741 (18*2π)/63936 weeks
1917.98228 26.34167 (19*2π)/63934 weeks
2020.09859 25.05026 (20*2π)/63932 weeks
2121.05624 26.95106 (21*2π)/63930 weeks
2219.21127 29.59094 (22*2π)/63929 weeks
2316.08186 31.07075 (23*2π)/63928 weeks
2412.90742 29.78404 (24*2π)/63927 weeks
259.1159 28.83941 (25*2π)/63926 weeks
268.03935 23.10406 (26*2π)/63925 weeks
2710.46095 19.30791 (27*2π)/63924 weeks
2811.96964 18.89101 (28*2π)/63923 weeks
2914.51179 17.89311 (29*2π)/63922 weeks
3013.84569 19.75838 (30*2π)/63921 weeks
3113.85845 18.47861 (31*2π)/63921 weeks
3213.3317 18.93349 (32*2π)/63920 weeks
3314.64468 18.09184 (33*2π)/63919 weeks
3415.13644 18.23686 (34*2π)/63919 weeks
3515.85909 19.5181 (35*2π)/63918 weeks
3615.27164 19.58056 (36*2π)/63918 weeks
3715.81292 20.3568 (37*2π)/63917 weeks
3815.90843 20.30456 (38*2π)/63917 weeks
3915.93011 21.50871 (39*2π)/63916 weeks
4015.36755 23.015 (40*2π)/63916 weeks
4113.47498 24.72866 (41*2π)/63916 weeks
4211.25186 24.65866 (42*2π)/63915 weeks
439.75057 25.36529 (43*2π)/63915 weeks
447.50491 25.36971 (44*2π)/63915 weeks
454.86472 24.55696 (45*2π)/63914 weeks
462.29716 23.29277 (46*2π)/63914 weeks
471.52848 20.70688 (47*2π)/63914 weeks
48.89713 19.03234 (48*2π)/63913 weeks
491.0298 17.1653 (49*2π)/63913 weeks
501.35326 14.80546 (50*2π)/63913 weeks
512.12659 14.25925 (51*2π)/63913 weeks
522.25394 13.3956 (52*2π)/63912 weeks
532.35879 12.71977 (53*2π)/63912 weeks
542.21727 11.59241 (54*2π)/63912 weeks
552.53965 9.47865 (55*2π)/63912 weeks
563.99555 8.88011 (56*2π)/63911 weeks
575.12267 8.79552 (57*2π)/63911 weeks
585.79765 8.48878 (58*2π)/63911 weeks
596.65319 8.85631 (59*2π)/63911 weeks
607.35063 8.76552 (60*2π)/63911 weeks
617.98547 9.3844 (61*2π)/63910 weeks
627.99306 9.63184 (62*2π)/63910 weeks
638.15254 9.89478 (63*2π)/63910 weeks
648.57624 11.15832 (64*2π)/63910 weeks
658.04947 11.03552 (65*2π)/63910 weeks
667.00678 11.32714 (66*2π)/63910 weeks
677.31507 11.76087 (67*2π)/63910 weeks
686.23221 10.74017 (68*2π)/6399 weeks
696.91685 11.30487 (69*2π)/6399 weeks
706.09261 11.05212 (70*2π)/6399 weeks
715.80564 11.08523 (71*2π)/6399 weeks
725.60742 10.91222 (72*2π)/6399 weeks
735.26112 10.90584 (73*2π)/6399 weeks
745.1983 11.02317 (74*2π)/6399 weeks
754.20472 10.70195 (75*2π)/6399 weeks
763.50405 10.09044 (76*2π)/6398 weeks
772.61568 8.77335 (77*2π)/6398 weeks
782.7673 6.93889 (78*2π)/6398 weeks
793.66524 6.26082 (79*2π)/6398 weeks
804.50991 5.12183 (80*2π)/6398 weeks
815.81415 5.17205 (81*2π)/6398 weeks
826.35159 5.64384 (82*2π)/6398 weeks
837.21824 6.49471 (83*2π)/6398 weeks
847.14742 6.67141 (84*2π)/6398 weeks
856.9271 7.75022 (85*2π)/6398 weeks
866.42008 7.65419 (86*2π)/6397 weeks
875.972 7.88181 (87*2π)/6397 weeks
885.32336 6.59479 (88*2π)/6397 weeks
895.4794 5.94324 (89*2π)/6397 weeks
906.53977 4.8094 (90*2π)/6397 weeks
917.22587 5.25459 (91*2π)/6397 weeks
927.88726 5.77033 (92*2π)/6397 weeks
937.62689 6.26784 (93*2π)/6397 weeks
947.27778 6.29095 (94*2π)/6397 weeks
957.55691 6.4697 (95*2π)/6397 weeks
967.41366 6.76204 (96*2π)/6397 weeks
976.91554 6.92587 (97*2π)/6397 weeks
986.54738 6.37083 (98*2π)/6397 weeks
996.96354 5.69518 (99*2π)/6396 weeks
1007.76052 5.66468 (100*2π)/6396 weeks
1017.93894 5.55351 (101*2π)/6396 weeks
1028.59859 5.92962 (102*2π)/6396 weeks
1039.31176 5.80923 (103*2π)/6396 weeks
1049.62753 6.60902 (104*2π)/6396 weeks
10510.01129 7.65399 (105*2π)/6396 weeks
1069.26972 8.89166 (106*2π)/6396 weeks
1078.64305 9.85041 (107*2π)/6396 weeks
1087.05212 10.58204 (108*2π)/6396 weeks
1096.03097 10.29136 (109*2π)/6396 weeks
1104.78847 9.97973 (110*2π)/6396 weeks
1114.03603 8.8582 (111*2π)/6396 weeks
1123.64048 7.69706 (112*2π)/6396 weeks
1134.05386 6.63702 (113*2π)/6396 weeks
1144.73968 6.16269 (114*2π)/6396 weeks
1155.67212 5.86552 (115*2π)/6396 weeks
1165.65771 6.54088 (116*2π)/6396 weeks
1175.65759 6.7885 (117*2π)/6395 weeks
1185.1536 6.30729 (118*2π)/6395 weeks
1194.80665 6.39784 (119*2π)/6395 weeks
1205.03431 5.72087 (120*2π)/6395 weeks
1215.31952 5.77868 (121*2π)/6395 weeks
1225.61735 5.9671 (122*2π)/6395 weeks
1235.82884 6.21459 (123*2π)/6395 weeks
1245.38028 7.08572 (124*2π)/6395 weeks
1254.82987 7.00497 (125*2π)/6395 weeks
1264.03097 6.75182 (126*2π)/6395 weeks
1273.58062 6.39662 (127*2π)/6395 weeks
1283.18622 5.29832 (128*2π)/6395 weeks
1293.69048 4.5286 (129*2π)/6395 weeks
1303.63936 3.67809 (130*2π)/6395 weeks
1314.7746 3.63739 (131*2π)/6395 weeks
1324.99867 3.51877 (132*2π)/6395 weeks
1335.29303 3.5005 (133*2π)/6395 weeks
1345.66654 3.46782 (134*2π)/6395 weeks
1356.10943 3.54306 (135*2π)/6395 weeks
1366.38351 3.94847 (136*2π)/6395 weeks
1376.69552 4.52315 (137*2π)/6395 weeks
1386.46402 4.91417 (138*2π)/6395 weeks
1396.34642 5.13074 (139*2π)/6395 weeks
1405.9196 5.19923 (140*2π)/6395 weeks
1415.67501 4.98692 (141*2π)/6395 weeks
1425.39503 4.8071 (142*2π)/6395 weeks
1435.52336 4.6939 (143*2π)/6394 weeks
1445.25069 4.43046 (144*2π)/6394 weeks
1455.51622 4.32119 (145*2π)/6394 weeks
1465.30613 4.37519 (146*2π)/6394 weeks
1475.7837 4.08094 (147*2π)/6394 weeks
1485.89123 4.31837 (148*2π)/6394 weeks
1496.34216 4.38399 (149*2π)/6394 weeks
1506.00507 4.95529 (150*2π)/6394 weeks
1516.07473 5.04702 (151*2π)/6394 weeks
1525.46146 5.25222 (152*2π)/6394 weeks
1535.10022 5.35768 (153*2π)/6394 weeks
1544.79858 4.99061 (154*2π)/6394 weeks
1554.54904 4.53539 (155*2π)/6394 weeks
1564.69433 4.29779 (156*2π)/6394 weeks
1574.8353 4.25522 (157*2π)/6394 weeks
1584.45023 4.33723 (158*2π)/6394 weeks
1594.36869 3.90493 (159*2π)/6394 weeks
1604.52874 3.44976 (160*2π)/6394 weeks
1614.98596 3.27557 (161*2π)/6394 weeks
1625.24917 3.53739 (162*2π)/6394 weeks
1635.20332 3.80015 (163*2π)/6394 weeks
1645.19672 3.70892 (164*2π)/6394 weeks
1655.08477 3.42931 (165*2π)/6394 weeks
1665.37944 3.70205 (166*2π)/6394 weeks
1675.30916 3.62578 (167*2π)/6394 weeks
1685.42976 3.66587 (168*2π)/6394 weeks
1695.33947 3.80167 (169*2π)/6394 weeks
1705.21138 3.98151 (170*2π)/6394 weeks
1714.9856 4.24905 (171*2π)/6394 weeks
1724.53453 4.31752 (172*2π)/6394 weeks
1734.00996 4.08218 (173*2π)/6394 weeks
1743.70246 3.78637 (174*2π)/6394 weeks
1753.40272 3.23481 (175*2π)/6394 weeks
1763.61036 2.5774 (176*2π)/6394 weeks
1773.71489 2.12708 (177*2π)/6394 weeks
1784.48417 1.53057 (178*2π)/6394 weeks
1794.69787 1.44614 (179*2π)/6394 weeks
1805.27195 1.6888 (180*2π)/6394 weeks
1815.26075 1.87775 (181*2π)/6394 weeks
1825.36378 2.06623 (182*2π)/6394 weeks
1835.23788 2.16919 (183*2π)/6393 weeks
1845.14715 1.86775 (184*2π)/6393 weeks
1855.49931 1.59552 (185*2π)/6393 weeks
1865.71561 1.47692 (186*2π)/6393 weeks
1876.34982 2.01543 (187*2π)/6393 weeks
1886.33178 2.4451 (188*2π)/6393 weeks
1896.08449 2.82364 (189*2π)/6393 weeks
1905.80301 2.85556 (190*2π)/6393 weeks
1915.59421 2.64636 (191*2π)/6393 weeks
1925.68016 2.47179 (192*2π)/6393 weeks
1935.59476 2.57418 (193*2π)/6393 weeks
1945.57592 2.64223 (194*2π)/6393 weeks
1955.36445 2.61394 (195*2π)/6393 weeks
1965.08665 2.44624 (196*2π)/6393 weeks
1974.97007 2.49614 (197*2π)/6393 weeks
1984.64777 1.97436 (198*2π)/6393 weeks
1994.82776 1.53411 (199*2π)/6393 weeks
2005.16332 1.14234 (200*2π)/6393 weeks
2015.81233 .92129 (201*2π)/6393 weeks
2026.1004 1.11595 (202*2π)/6393 weeks
2036.37631 1.26021 (203*2π)/6393 weeks
2046.49802 1.28524 (204*2π)/6393 weeks
2056.83622 1.43747 (205*2π)/6393 weeks
2067.02474 1.49015 (206*2π)/6393 weeks
2077.42257 1.76749 (207*2π)/6393 weeks
2087.29173 2.2558 (208*2π)/6393 weeks
2097.35164 2.6322 (209*2π)/6393 weeks
2106.79976 3.31037 (210*2π)/6393 weeks
2116.52681 3.45894 (211*2π)/6393 weeks
2125.9743 3.10204 (212*2π)/6393 weeks
2135.98745 3.06128 (213*2π)/6393 weeks
2146.02351 2.71947 (214*2π)/6393 weeks
2156.3656 2.77291 (215*2π)/6393 weeks
2166.19119 2.80216 (216*2π)/6393 weeks
2176.29178 2.8384 (217*2π)/6393 weeks
2186.09933 3.08638 (218*2π)/6393 weeks
2195.9928 3.16991 (219*2π)/6393 weeks
2205.53522 3.06065 (220*2π)/6393 weeks
2215.52152 3.02188 (221*2π)/6393 weeks
2225.42057 2.75639 (222*2π)/6393 weeks
2235.47599 2.65742 (223*2π)/6393 weeks
2245.353 2.60161 (224*2π)/6393 weeks
2255.60004 2.43116 (225*2π)/6393 weeks
2265.70082 2.47986 (226*2π)/6393 weeks
2276.08325 2.6911 (227*2π)/6393 weeks
2285.97804 3.00371 (228*2π)/6393 weeks
2295.65753 3.34677 (229*2π)/6393 weeks
2305.13468 3.3369 (230*2π)/6393 weeks
2314.78422 3.07229 (231*2π)/6393 weeks
2324.40776 2.60004 (232*2π)/6393 weeks
2334.45668 2.10737 (233*2π)/6393 weeks
2344.50853 1.78981 (234*2π)/6393 weeks
2354.86241 1.62159 (235*2π)/6393 weeks
2364.99227 1.73922 (236*2π)/6393 weeks
2375.14483 1.52595 (237*2π)/6393 weeks
2385.33168 1.49361 (238*2π)/6393 weeks
2395.75675 1.45218 (239*2π)/6393 weeks
2405.92001 1.47458 (240*2π)/6393 weeks
2416.2321 1.80578 (241*2π)/6393 weeks
2426.42127 2.03582 (242*2π)/6393 weeks
2436.26675 2.60299 (243*2π)/6393 weeks
2446.07784 2.74724 (244*2π)/6393 weeks
2455.4535 2.91928 (245*2π)/6393 weeks
2465.26253 2.79038 (246*2π)/6393 weeks
2474.98148 2.54946 (247*2π)/6393 weeks
2485.21134 2.43604 (248*2π)/6393 weeks
2495.14026 2.39417 (249*2π)/6393 weeks
2505.22343 2.42152 (250*2π)/6393 weeks
2515.25305 2.37287 (251*2π)/6393 weeks
2525.2717 2.68238 (252*2π)/6393 weeks
2534.98085 2.92207 (253*2π)/6393 weeks
2544.54856 2.88235 (254*2π)/6393 weeks
2553.93442 2.60826 (255*2π)/6393 weeks
2563.65502 1.794 (256*2π)/6392 weeks
2573.76166 1.2797 (257*2π)/6392 weeks
2584.22851 .8338 (258*2π)/6392 weeks
2594.62964 .7918 (259*2π)/6392 weeks
2604.95685 1.07592 (260*2π)/6392 weeks
2614.87861 1.12609 (261*2π)/6392 weeks
2624.93502 1.26508 (262*2π)/6392 weeks
2634.87278 1.14138 (263*2π)/6392 weeks
2644.98927 .98238 (264*2π)/6392 weeks
2655.00639 .83124 (265*2π)/6392 weeks
2665.27267 .41368 (266*2π)/6392 weeks
2675.74655 .35189 (267*2π)/6392 weeks
2686.20173 .38074 (268*2π)/6392 weeks
2696.57665 .74593 (269*2π)/6392 weeks
2706.85918 1.2433 (270*2π)/6392 weeks
2716.70813 1.59802 (271*2π)/6392 weeks
2726.79186 2.02328 (272*2π)/6392 weeks
2736.59534 2.57011 (273*2π)/6392 weeks
2746.35772 2.86066 (274*2π)/6392 weeks
2756.08776 3.22592 (275*2π)/6392 weeks
2765.59514 3.41826 (276*2π)/6392 weeks
2775.12644 3.2406 (277*2π)/6392 weeks
2785.02742 3.19278 (278*2π)/6392 weeks
2794.81788 3.12723 (279*2π)/6392 weeks
2804.58304 3.13977 (280*2π)/6392 weeks
2814.01426 3.09413 (281*2π)/6392 weeks
2823.65084 2.62069 (282*2π)/6392 weeks
2833.56526 2.20907 (283*2π)/6392 weeks
2843.95337 1.95455 (284*2π)/6392 weeks
2853.92722 1.94696 (285*2π)/6392 weeks
2864.07946 2.19799 (286*2π)/6392 weeks
2873.66742 2.35676 (287*2π)/6392 weeks
2883.49425 2.28178 (288*2π)/6392 weeks
2892.98865 2.17816 (289*2π)/6392 weeks
2902.72573 1.82653 (290*2π)/6392 weeks
2912.57414 1.16998 (291*2π)/6392 weeks
2922.72932 .70764 (292*2π)/6392 weeks
2932.83265 .13185 (293*2π)/6392 weeks
2943.31038 -.0754 (294*2π)/6392 weeks
2953.45785 -.20082 (295*2π)/6392 weeks
2963.67138 -.42044 (296*2π)/6392 weeks
2974.1983 -.33565 (297*2π)/6392 weeks
2984.43772 -.30574 (298*2π)/6392 weeks
2994.53428 -.0639 (299*2π)/6392 weeks
3004.6229 .0794 (300*2π)/6392 weeks
3014.65963 .1253 (301*2π)/6392 weeks
3024.86797 .31126 (302*2π)/6392 weeks
3034.90915 .54117 (303*2π)/6392 weeks
3044.82241 .90802 (304*2π)/6392 weeks
3054.6051 .93492 (305*2π)/6392 weeks
3064.09696 .84021 (306*2π)/6392 weeks
3074.01075 .36465 (307*2π)/6392 weeks
3084.05411 -.05418 (308*2π)/6392 weeks
3094.47053 -.23907 (309*2π)/6392 weeks
3105.09443 -.09694 (310*2π)/6392 weeks
3115.30704 .57553 (311*2π)/6392 weeks
3124.87313 1.05401 (312*2π)/6392 weeks
3134.5502 1.16935 (313*2π)/6392 weeks
3144.06777 1.18524 (314*2π)/6392 weeks
3153.84758 .92343 (315*2π)/6392 weeks
3163.52754 .76202 (316*2π)/6392 weeks
3173.52175 .32483 (317*2π)/6392 weeks
3183.62525 -.04125 (318*2π)/6392 weeks
3193.78538 .00605 (319*2π)/6392 weeks
3203.78538 -.00605 (320*2π)/6392 weeks
3213.62525 .04125 (321*2π)/6392 weeks
3223.52175 -.32483 (322*2π)/6392 weeks
3233.52754 -.76202 (323*2π)/6392 weeks
3243.84758 -.92343 (324*2π)/6392 weeks
3254.06777 -1.18524 (325*2π)/6392 weeks
3264.5502 -1.16935 (326*2π)/6392 weeks
3274.87313 -1.05401 (327*2π)/6392 weeks
3285.30704 -.57553 (328*2π)/6392 weeks
3295.09443 .09694 (329*2π)/6392 weeks
3304.47053 .23907 (330*2π)/6392 weeks
3314.05411 .05418 (331*2π)/6392 weeks
3324.01075 -.36465 (332*2π)/6392 weeks
3334.09696 -.84021 (333*2π)/6392 weeks
3344.6051 -.93492 (334*2π)/6392 weeks
3354.82241 -.90802 (335*2π)/6392 weeks
3364.90915 -.54117 (336*2π)/6392 weeks
3374.86797 -.31126 (337*2π)/6392 weeks
3384.65963 -.1253 (338*2π)/6392 weeks
3394.6229 -.0794 (339*2π)/6392 weeks
3404.53428 .0639 (340*2π)/6392 weeks
3414.43772 .30574 (341*2π)/6392 weeks
3424.1983 .33565 (342*2π)/6392 weeks
3433.67138 .42044 (343*2π)/6392 weeks
3443.45785 .20082 (344*2π)/6392 weeks
3453.31038 .0754 (345*2π)/6392 weeks
3462.83265 -.13185 (346*2π)/6392 weeks
3472.72932 -.70764 (347*2π)/6392 weeks
3482.57414 -1.16998 (348*2π)/6392 weeks
3492.72573 -1.82653 (349*2π)/6392 weeks
3502.98865 -2.17816 (350*2π)/6392 weeks
3513.49425 -2.28178 (351*2π)/6392 weeks
3523.66742 -2.35676 (352*2π)/6392 weeks
3534.07946 -2.19799 (353*2π)/6392 weeks
3543.92722 -1.94696 (354*2π)/6392 weeks
3553.95337 -1.95455 (355*2π)/6392 weeks
3563.56526 -2.20907 (356*2π)/6392 weeks
3573.65084 -2.62069 (357*2π)/6392 weeks
3584.01426 -3.09413 (358*2π)/6392 weeks
3594.58304 -3.13977 (359*2π)/6392 weeks
3604.81788 -3.12723 (360*2π)/6392 weeks
3615.02742 -3.19278 (361*2π)/6392 weeks
3625.12644 -3.2406 (362*2π)/6392 weeks
3635.59514 -3.41826 (363*2π)/6392 weeks
3646.08776 -3.22592 (364*2π)/6392 weeks
3656.35772 -2.86066 (365*2π)/6392 weeks
3666.59534 -2.57011 (366*2π)/6392 weeks
3676.79186 -2.02328 (367*2π)/6392 weeks
3686.70813 -1.59802 (368*2π)/6392 weeks
3696.85918 -1.2433 (369*2π)/6392 weeks
3706.57665 -.74593 (370*2π)/6392 weeks
3716.20173 -.38074 (371*2π)/6392 weeks
3725.74655 -.35189 (372*2π)/6392 weeks
3735.27267 -.41368 (373*2π)/6392 weeks
3745.00639 -.83124 (374*2π)/6392 weeks
3754.98927 -.98238 (375*2π)/6392 weeks
3764.87278 -1.14138 (376*2π)/6392 weeks
3774.93502 -1.26508 (377*2π)/6392 weeks
3784.87861 -1.12609 (378*2π)/6392 weeks
3794.95685 -1.07592 (379*2π)/6392 weeks
3804.62964 -.7918 (380*2π)/6392 weeks
3814.22851 -.8338 (381*2π)/6392 weeks
3823.76166 -1.2797 (382*2π)/6392 weeks
3833.65502 -1.794 (383*2π)/6392 weeks
3843.93442 -2.60826 (384*2π)/6392 weeks
3854.54856 -2.88235 (385*2π)/6392 weeks
3864.98085 -2.92207 (386*2π)/6392 weeks
3875.2717 -2.68238 (387*2π)/6392 weeks
3885.25305 -2.37287 (388*2π)/6392 weeks
3895.22343 -2.42152 (389*2π)/6392 weeks
3905.14026 -2.39417 (390*2π)/6392 weeks
3915.21134 -2.43604 (391*2π)/6392 weeks
3924.98148 -2.54946 (392*2π)/6392 weeks
3935.26253 -2.79038 (393*2π)/6392 weeks
3945.4535 -2.91928 (394*2π)/6392 weeks
3956.07784 -2.74724 (395*2π)/6392 weeks
3966.26675 -2.60299 (396*2π)/6392 weeks
3976.42127 -2.03582 (397*2π)/6392 weeks
3986.2321 -1.80578 (398*2π)/6392 weeks
3995.92001 -1.47458 (399*2π)/6392 weeks
4005.75675 -1.45218 (400*2π)/6392 weeks
4015.33168 -1.49361 (401*2π)/6392 weeks
4025.14483 -1.52595 (402*2π)/6392 weeks
4034.99227 -1.73922 (403*2π)/6392 weeks
4044.86241 -1.62159 (404*2π)/6392 weeks
4054.50853 -1.78981 (405*2π)/6392 weeks
4064.45668 -2.10737 (406*2π)/6392 weeks
4074.40776 -2.60004 (407*2π)/6392 weeks
4084.78422 -3.07229 (408*2π)/6392 weeks
4095.13468 -3.3369 (409*2π)/6392 weeks
4105.65753 -3.34677 (410*2π)/6392 weeks
4115.97804 -3.00371 (411*2π)/6392 weeks
4126.08325 -2.6911 (412*2π)/6392 weeks
4135.70082 -2.47986 (413*2π)/6392 weeks
4145.60004 -2.43116 (414*2π)/6392 weeks
4155.353 -2.60161 (415*2π)/6392 weeks
4165.47599 -2.65742 (416*2π)/6392 weeks
4175.42057 -2.75639 (417*2π)/6392 weeks
4185.52152 -3.02188 (418*2π)/6392 weeks
4195.53522 -3.06065 (419*2π)/6392 weeks
4205.9928 -3.16991 (420*2π)/6392 weeks
4216.09933 -3.08638 (421*2π)/6392 weeks
4226.29178 -2.8384 (422*2π)/6392 weeks
4236.19119 -2.80216 (423*2π)/6392 weeks
4246.3656 -2.77291 (424*2π)/6392 weeks
4256.02351 -2.71947 (425*2π)/6392 weeks
4265.98745 -3.06128 (426*2π)/6392 weeks
4275.9743 -3.10204 (427*2π)/6391 weeks
4286.52681 -3.45894 (428*2π)/6391 weeks
4296.79976 -3.31037 (429*2π)/6391 weeks
4307.35164 -2.6322 (430*2π)/6391 weeks
4317.29173 -2.2558 (431*2π)/6391 weeks
4327.42257 -1.76749 (432*2π)/6391 weeks
4337.02474 -1.49015 (433*2π)/6391 weeks
4346.83622 -1.43747 (434*2π)/6391 weeks
4356.49802 -1.28524 (435*2π)/6391 weeks
4366.37631 -1.26021 (436*2π)/6391 weeks
4376.1004 -1.11595 (437*2π)/6391 weeks
4385.81233 -.92129 (438*2π)/6391 weeks
4395.16332 -1.14234 (439*2π)/6391 weeks
4404.82776 -1.53411 (440*2π)/6391 weeks
4414.64777 -1.97436 (441*2π)/6391 weeks
4424.97007 -2.49614 (442*2π)/6391 weeks
4435.08665 -2.44624 (443*2π)/6391 weeks
4445.36445 -2.61394 (444*2π)/6391 weeks
4455.57592 -2.64223 (445*2π)/6391 weeks
4465.59476 -2.57418 (446*2π)/6391 weeks
4475.68016 -2.47179 (447*2π)/6391 weeks
4485.59421 -2.64636 (448*2π)/6391 weeks
4495.80301 -2.85556 (449*2π)/6391 weeks
4506.08449 -2.82364 (450*2π)/6391 weeks
4516.33178 -2.4451 (451*2π)/6391 weeks
4526.34982 -2.01543 (452*2π)/6391 weeks
4535.71561 -1.47692 (453*2π)/6391 weeks
4545.49931 -1.59552 (454*2π)/6391 weeks
4555.14715 -1.86775 (455*2π)/6391 weeks
4565.23788 -2.16919 (456*2π)/6391 weeks
4575.36378 -2.06623 (457*2π)/6391 weeks
4585.26075 -1.87775 (458*2π)/6391 weeks
4595.27195 -1.6888 (459*2π)/6391 weeks
4604.69787 -1.44614 (460*2π)/6391 weeks
4614.48417 -1.53057 (461*2π)/6391 weeks
4623.71489 -2.12708 (462*2π)/6391 weeks
4633.61036 -2.5774 (463*2π)/6391 weeks
4643.40272 -3.23481 (464*2π)/6391 weeks
4653.70246 -3.78637 (465*2π)/6391 weeks
4664.00996 -4.08218 (466*2π)/6391 weeks
4674.53453 -4.31752 (467*2π)/6391 weeks
4684.9856 -4.24905 (468*2π)/6391 weeks
4695.21138 -3.98151 (469*2π)/6391 weeks
4705.33947 -3.80167 (470*2π)/6391 weeks
4715.42976 -3.66587 (471*2π)/6391 weeks
4725.30916 -3.62578 (472*2π)/6391 weeks
4735.37944 -3.70205 (473*2π)/6391 weeks
4745.08477 -3.42931 (474*2π)/6391 weeks
4755.19672 -3.70892 (475*2π)/6391 weeks
4765.20332 -3.80015 (476*2π)/6391 weeks
4775.24917 -3.53739 (477*2π)/6391 weeks
4784.98596 -3.27557 (478*2π)/6391 weeks
4794.52874 -3.44976 (479*2π)/6391 weeks
4804.36869 -3.90493 (480*2π)/6391 weeks
4814.45023 -4.33723 (481*2π)/6391 weeks
4824.8353 -4.25522 (482*2π)/6391 weeks
4834.69433 -4.29779 (483*2π)/6391 weeks
4844.54904 -4.53539 (484*2π)/6391 weeks
4854.79858 -4.99061 (485*2π)/6391 weeks
4865.10022 -5.35768 (486*2π)/6391 weeks
4875.46146 -5.25222 (487*2π)/6391 weeks
4886.07473 -5.04702 (488*2π)/6391 weeks
4896.00507 -4.95529 (489*2π)/6391 weeks
4906.34216 -4.38399 (490*2π)/6391 weeks
4915.89123 -4.31837 (491*2π)/6391 weeks
4925.7837 -4.08094 (492*2π)/6391 weeks
4935.30613 -4.37519 (493*2π)/6391 weeks
4945.51622 -4.32119 (494*2π)/6391 weeks
4955.25069 -4.43046 (495*2π)/6391 weeks
4965.52336 -4.6939 (496*2π)/6391 weeks
4975.39503 -4.8071 (497*2π)/6391 weeks
4985.67501 -4.98692 (498*2π)/6391 weeks
4995.9196 -5.19923 (499*2π)/6391 weeks
5006.34642 -5.13074 (500*2π)/6391 weeks
5016.46402 -4.91417 (501*2π)/6391 weeks
5026.69552 -4.52315 (502*2π)/6391 weeks
5036.38351 -3.94847 (503*2π)/6391 weeks
5046.10943 -3.54306 (504*2π)/6391 weeks
5055.66654 -3.46782 (505*2π)/6391 weeks
5065.29303 -3.5005 (506*2π)/6391 weeks
5074.99867 -3.51877 (507*2π)/6391 weeks
5084.7746 -3.63739 (508*2π)/6391 weeks
5093.63936 -3.67809 (509*2π)/6391 weeks
5103.69048 -4.5286 (510*2π)/6391 weeks
5113.18622 -5.29832 (511*2π)/6391 weeks
5123.58062 -6.39662 (512*2π)/6391 weeks
5134.03097 -6.75182 (513*2π)/6391 weeks
5144.82987 -7.00497 (514*2π)/6391 weeks
5155.38028 -7.08572 (515*2π)/6391 weeks
5165.82884 -6.21459 (516*2π)/6391 weeks
5175.61735 -5.9671 (517*2π)/6391 weeks
5185.31952 -5.77868 (518*2π)/6391 weeks
5195.03431 -5.72087 (519*2π)/6391 weeks
5204.80665 -6.39784 (520*2π)/6391 weeks
5215.1536 -6.30729 (521*2π)/6391 weeks
5225.65759 -6.7885 (522*2π)/6391 weeks
5235.65771 -6.54088 (523*2π)/6391 weeks
5245.67212 -5.86552 (524*2π)/6391 weeks
5254.73968 -6.16269 (525*2π)/6391 weeks
5264.05386 -6.63702 (526*2π)/6391 weeks
5273.64048 -7.69706 (527*2π)/6391 weeks
5284.03603 -8.8582 (528*2π)/6391 weeks
5294.78847 -9.97973 (529*2π)/6391 weeks
5306.03097 -10.29136 (530*2π)/6391 weeks
5317.05212 -10.58204 (531*2π)/6391 weeks
5328.64305 -9.85041 (532*2π)/6391 weeks
5339.26972 -8.89166 (533*2π)/6391 weeks
53410.01129 -7.65399 (534*2π)/6391 weeks
5359.62753 -6.60902 (535*2π)/6391 weeks
5369.31176 -5.80923 (536*2π)/6391 weeks
5378.59859 -5.92962 (537*2π)/6391 weeks
5387.93894 -5.55351 (538*2π)/6391 weeks
5397.76052 -5.66468 (539*2π)/6391 weeks
5406.96354 -5.69518 (540*2π)/6391 weeks
5416.54738 -6.37083 (541*2π)/6391 weeks
5426.91554 -6.92587 (542*2π)/6391 weeks
5437.41366 -6.76204 (543*2π)/6391 weeks
5447.55691 -6.4697 (544*2π)/6391 weeks
5457.27778 -6.29095 (545*2π)/6391 weeks
5467.62689 -6.26784 (546*2π)/6391 weeks
5477.88726 -5.77033 (547*2π)/6391 weeks
5487.22587 -5.25459 (548*2π)/6391 weeks
5496.53977 -4.8094 (549*2π)/6391 weeks
5505.4794 -5.94324 (550*2π)/6391 weeks
5515.32336 -6.59479 (551*2π)/6391 weeks
5525.972 -7.88181 (552*2π)/6391 weeks
5536.42008 -7.65419 (553*2π)/6391 weeks
5546.9271 -7.75022 (554*2π)/6391 weeks
5557.14742 -6.67141 (555*2π)/6391 weeks
5567.21824 -6.49471 (556*2π)/6391 weeks
5576.35159 -5.64384 (557*2π)/6391 weeks
5585.81415 -5.17205 (558*2π)/6391 weeks
5594.50991 -5.12183 (559*2π)/6391 weeks
5603.66524 -6.26082 (560*2π)/6391 weeks
5612.7673 -6.93889 (561*2π)/6391 weeks
5622.61568 -8.77335 (562*2π)/6391 weeks
5633.50405 -10.09044 (563*2π)/6391 weeks
5644.20472 -10.70195 (564*2π)/6391 weeks
5655.1983 -11.02317 (565*2π)/6391 weeks
5665.26112 -10.90584 (566*2π)/6391 weeks
5675.60742 -10.91222 (567*2π)/6391 weeks
5685.80564 -11.08523 (568*2π)/6391 weeks
5696.09261 -11.05212 (569*2π)/6391 weeks
5706.91685 -11.30487 (570*2π)/6391 weeks
5716.23221 -10.74017 (571*2π)/6391 weeks
5727.31507 -11.76087 (572*2π)/6391 weeks
5737.00678 -11.32714 (573*2π)/6391 weeks
5748.04947 -11.03552 (574*2π)/6391 weeks
5758.57624 -11.15832 (575*2π)/6391 weeks
5768.15254 -9.89478 (576*2π)/6391 weeks
5777.99306 -9.63184 (577*2π)/6391 weeks
5787.98547 -9.3844 (578*2π)/6391 weeks
5797.35063 -8.76552 (579*2π)/6391 weeks
5806.65319 -8.85631 (580*2π)/6391 weeks
5815.79765 -8.48878 (581*2π)/6391 weeks
5825.12267 -8.79552 (582*2π)/6391 weeks
5833.99555 -8.88011 (583*2π)/6391 weeks
5842.53965 -9.47865 (584*2π)/6391 weeks
5852.21727 -11.59241 (585*2π)/6391 weeks
5862.35879 -12.71977 (586*2π)/6391 weeks
5872.25394 -13.3956 (587*2π)/6391 weeks
5882.12659 -14.25925 (588*2π)/6391 weeks
5891.35326 -14.80546 (589*2π)/6391 weeks
5901.0298 -17.1653 (590*2π)/6391 weeks
591.89713 -19.03234 (591*2π)/6391 weeks
5921.52848 -20.70688 (592*2π)/6391 weeks
5932.29716 -23.29277 (593*2π)/6391 weeks
5944.86472 -24.55696 (594*2π)/6391 weeks
5957.50491 -25.36971 (595*2π)/6391 weeks
5969.75057 -25.36529 (596*2π)/6391 weeks
59711.25186 -24.65866 (597*2π)/6391 weeks
59813.47498 -24.72866 (598*2π)/6391 weeks
59915.36755 -23.015 (599*2π)/6391 weeks
60015.93011 -21.50871 (600*2π)/6391 weeks
60115.90843 -20.30456 (601*2π)/6391 weeks
60215.81292 -20.3568 (602*2π)/6391 weeks
60315.27164 -19.58056 (603*2π)/6391 weeks
60415.85909 -19.5181 (604*2π)/6391 weeks
60515.13644 -18.23686 (605*2π)/6391 weeks
60614.64468 -18.09184 (606*2π)/6391 weeks
60713.3317 -18.93349 (607*2π)/6391 weeks
60813.85845 -18.47861 (608*2π)/6391 weeks
60913.84569 -19.75838 (609*2π)/6391 weeks
61014.51179 -17.89311 (610*2π)/6391 weeks
61111.96964 -18.89101 (611*2π)/6391 weeks
61210.46095 -19.30791 (612*2π)/6391 weeks
6138.03935 -23.10406 (613*2π)/6391 weeks
6149.1159 -28.83941 (614*2π)/6391 weeks
61512.90742 -29.78404 (615*2π)/6391 weeks
61616.08186 -31.07075 (616*2π)/6391 weeks
61719.21127 -29.59094 (617*2π)/6391 weeks
61821.05624 -26.95106 (618*2π)/6391 weeks
61920.09859 -25.05026 (619*2π)/6391 weeks
62017.98228 -26.34167 (620*2π)/6391 weeks
62115.93388 -25.78741 (621*2π)/6391 weeks
62216.76472 -28.59496 (622*2π)/6391 weeks
62316.4066 -28.3149 (623*2π)/6391 weeks
62415.45354 -31.21408 (624*2π)/6391 weeks
62516.35411 -34.82832 (625*2π)/6391 weeks
62613.36061 -37.96026 (626*2π)/6391 weeks
62713.84732 -44.06656 (627*2π)/6391 weeks
62815.86959 -54.01654 (628*2π)/6391 weeks
62922.46538 -58.07789 (629*2π)/6391 weeks
63029.6575 -65.79433 (630*2π)/6391 weeks
63138.03308 -64.58045 (631*2π)/6391 weeks
63243.1279 -61.59798 (632*2π)/6391 weeks
63341.43285 -68.83042 (633*2π)/6391 weeks
63445.255 -79.37238 (634*2π)/6391 weeks
63559.42547 -103.7236 (635*2π)/6391 weeks
63689.61764 -116.4901 (636*2π)/6391 weeks
637152.3631 -109.8343 (637*2π)/6391 weeks



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