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Fourier Analysis of ZSL (ProShares UltraShort Silver)


ZSL (ProShares UltraShort Silver) appears to have interesting cyclic behaviour every 59 weeks (58.6782*sine), 53 weeks (47.2377*sine), and 31 weeks (22.4202*cosine).

ZSL (ProShares UltraShort Silver) has an average price of 154.68 (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 2/24/2020 for ZSL (ProShares UltraShort Silver), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0154.6839   0 
1205.3699 73.2112 (1*2π)/587587 weeks
2156.7378 125.1766 (2*2π)/587294 weeks
390.13788 118.6575 (3*2π)/587196 weeks
454.64549 100.6349 (4*2π)/587147 weeks
547.85023 79.15186 (5*2π)/587117 weeks
644.41214 67.67954 (6*2π)/58798 weeks
744.9663 69.52965 (7*2π)/58784 weeks
836.78975 70.42261 (8*2π)/58773 weeks
924.90281 63.17435 (9*2π)/58765 weeks
1018.04364 58.67819 (10*2π)/58759 weeks
1114.48769 47.23773 (11*2π)/58753 weeks
1214.01369 40.19956 (12*2π)/58749 weeks
1316.84442 37.6207 (13*2π)/58745 weeks
1416.74376 33.46659 (14*2π)/58742 weeks
1518.86388 30.87642 (15*2π)/58739 weeks
1617.83091 30.4206 (16*2π)/58737 weeks
1720.09664 27.14427 (17*2π)/58735 weeks
1820.25607 26.26121 (18*2π)/58733 weeks
1922.42022 28.1101 (19*2π)/58731 weeks
2021.48676 31.55971 (20*2π)/58729 weeks
2118.21938 33.38413 (21*2π)/58728 weeks
2214.17225 32.02849 (22*2π)/58727 weeks
239.61941 30.68817 (23*2π)/58726 weeks
248.65456 24.12215 (24*2π)/58724 weeks
2511.88376 20.5656 (25*2π)/58723 weeks
2613.08451 19.70093 (26*2π)/58723 weeks
2716.13895 20.72062 (27*2π)/58722 weeks
2814.49068 20.761 (28*2π)/58721 weeks
2915.4252 20.77089 (29*2π)/58720 weeks
3015.46851 19.19603 (30*2π)/58720 weeks
3116.24309 19.61167 (31*2π)/58719 weeks
3217.34857 20.62976 (32*2π)/58718 weeks
3316.49207 21.02922 (33*2π)/58718 weeks
3417.00892 21.89116 (34*2π)/58717 weeks
3517.17777 22.07121 (35*2π)/58717 weeks
3617.11397 23.63827 (36*2π)/58716 weeks
3716.29671 25.63852 (37*2π)/58716 weeks
3813.57716 27.13066 (38*2π)/58715 weeks
3911.85681 26.9957 (39*2π)/58715 weeks
409.28868 27.5215 (40*2π)/58715 weeks
416.30121 27.21491 (41*2π)/58714 weeks
423.59362 25.91486 (42*2π)/58714 weeks
431.87692 22.63965 (43*2π)/58714 weeks
441.14248 20.6239 (44*2π)/58713 weeks
451.10114 18.36099 (45*2π)/58713 weeks
461.53619 15.71611 (46*2π)/58713 weeks
472.21516 15.1293 (47*2π)/58712 weeks
482.39448 14.12809 (48*2π)/58712 weeks
492.28041 13.29743 (49*2π)/58712 weeks
502.05526 11.78971 (50*2π)/58712 weeks
513.77614 9.84162 (51*2π)/58712 weeks
525.215 9.39245 (52*2π)/58711 weeks
535.98609 9.28014 (53*2π)/58711 weeks
547.20886 9.40978 (54*2π)/58711 weeks
557.85146 9.34421 (55*2π)/58711 weeks
568.65793 10.03362 (56*2π)/58710 weeks
578.70523 10.35968 (57*2π)/58710 weeks
588.97567 10.60128 (58*2π)/58710 weeks
598.84541 12.17821 (59*2π)/58710 weeks
608.67026 12.36266 (60*2π)/58710 weeks
617.9103 11.81233 (61*2π)/58710 weeks
626.83126 12.56852 (62*2π)/5879 weeks
637.5517 11.57778 (63*2π)/5879 weeks
646.63214 12.16277 (64*2π)/5879 weeks
656.44529 12.00378 (65*2π)/5879 weeks
666.11181 11.73937 (66*2π)/5879 weeks
675.70929 11.71654 (67*2π)/5879 weeks
685.52653 11.83292 (68*2π)/5879 weeks
694.34422 11.44018 (69*2π)/5879 weeks
703.43071 10.75292 (70*2π)/5878 weeks
712.6394 8.99504 (71*2π)/5878 weeks
723.46625 7.05813 (72*2π)/5878 weeks
734.06966 6.24398 (73*2π)/5878 weeks
745.77306 5.55441 (74*2π)/5878 weeks
756.89167 6.09131 (75*2π)/5878 weeks
767.91468 6.4926 (76*2π)/5878 weeks
777.64771 7.05706 (77*2π)/5878 weeks
787.6524 8.20668 (78*2π)/5878 weeks
796.93255 8.12143 (79*2π)/5877 weeks
806.23601 8.38051 (80*2π)/5877 weeks
815.76462 6.88442 (81*2π)/5877 weeks
825.83113 5.99419 (82*2π)/5877 weeks
837.50473 5.44801 (83*2π)/5877 weeks
848.14418 5.76019 (84*2π)/5877 weeks
858.37111 6.70431 (85*2π)/5877 weeks
868.04288 6.99646 (86*2π)/5877 weeks
878.25119 6.84324 (87*2π)/5877 weeks
888.14194 7.20901 (88*2π)/5877 weeks
897.63297 7.4455 (89*2π)/5877 weeks
907.12277 6.80931 (90*2π)/5877 weeks
917.57239 6.00556 (91*2π)/5876 weeks
928.39397 6.09213 (92*2π)/5876 weeks
938.76632 5.85304 (93*2π)/5876 weeks
949.1397 6.30508 (94*2π)/5876 weeks
9510.22287 6.86054 (95*2π)/5876 weeks
9610.65042 7.72101 (96*2π)/5876 weeks
9710.51661 9.43324 (97*2π)/5876 weeks
989.77632 10.37087 (98*2π)/5876 weeks
998.25516 11.49167 (99*2π)/5876 weeks
1006.7904 11.10586 (100*2π)/5876 weeks
1015.33349 10.78236 (101*2π)/5876 weeks
1024.38633 9.47014 (102*2π)/5876 weeks
1033.96699 8.04752 (103*2π)/5876 weeks
1044.51069 6.88343 (104*2π)/5876 weeks
1055.19441 6.41553 (105*2π)/5876 weeks
1066.31308 6.74604 (106*2π)/5876 weeks
1076.07045 7.02307 (107*2π)/5875 weeks
1085.4362 7.29341 (108*2π)/5875 weeks
1095.5306 7.17287 (109*2π)/5875 weeks
1105.34198 6.34389 (110*2π)/5875 weeks
1115.81703 6.30299 (111*2π)/5875 weeks
1126.17321 6.42842 (112*2π)/5875 weeks
1136.40769 6.70075 (113*2π)/5875 weeks
1145.77683 7.61638 (114*2π)/5875 weeks
1155.13364 7.5613 (115*2π)/5875 weeks
1164.29147 7.0508 (116*2π)/5875 weeks
1173.52365 6.48512 (117*2π)/5875 weeks
1183.54772 5.14239 (118*2π)/5875 weeks
1193.79947 4.70096 (119*2π)/5875 weeks
1204.92879 3.67187 (120*2π)/5875 weeks
1215.24573 3.83805 (121*2π)/5875 weeks
1225.6705 3.80551 (122*2π)/5875 weeks
1236.10964 3.73552 (123*2π)/5875 weeks
1246.63843 3.79966 (124*2π)/5875 weeks
1256.96668 4.2242 (125*2π)/5875 weeks
1267.20505 4.92675 (126*2π)/5875 weeks
1276.88934 5.28907 (127*2π)/5875 weeks
1286.62973 5.63377 (128*2π)/5875 weeks
1296.15567 5.57562 (129*2π)/5875 weeks
1305.96329 5.44656 (130*2π)/5875 weeks
1315.93247 5.06535 (131*2π)/5874 weeks
1325.69412 5.04609 (132*2π)/5874 weeks
1335.9575 4.70921 (133*2π)/5874 weeks
1345.85012 4.83242 (134*2π)/5874 weeks
1356.29107 4.39551 (135*2π)/5874 weeks
1366.40934 4.65253 (136*2π)/5874 weeks
1376.94031 4.86649 (137*2π)/5874 weeks
1386.44268 5.30474 (138*2π)/5874 weeks
1396.45682 5.72438 (139*2π)/5874 weeks
1405.91516 5.66512 (140*2π)/5874 weeks
1415.26271 5.52944 (141*2π)/5874 weeks
1424.94588 5.1963 (142*2π)/5874 weeks
1435.06631 4.71929 (143*2π)/5874 weeks
1445.22116 4.57949 (144*2π)/5874 weeks
1454.95065 4.76627 (145*2π)/5874 weeks
1464.78102 4.23484 (146*2π)/5874 weeks
1474.95821 3.69259 (147*2π)/5874 weeks
1485.50687 3.51317 (148*2π)/5874 weeks
1495.74229 3.80563 (149*2π)/5874 weeks
1505.5495 4.00158 (150*2π)/5874 weeks
1515.50447 4.00227 (151*2π)/5874 weeks
1525.81803 3.68347 (152*2π)/5874 weeks
1535.67631 3.91667 (153*2π)/5874 weeks
1545.77136 3.89017 (154*2π)/5874 weeks
1555.75874 4.11764 (155*2π)/5874 weeks
1565.67416 4.31756 (156*2π)/5874 weeks
1575.46746 4.59215 (157*2π)/5874 weeks
1584.94238 4.66952 (158*2π)/5874 weeks
1594.34429 4.35415 (159*2π)/5874 weeks
1603.95131 3.96232 (160*2π)/5874 weeks
1613.6517 3.19338 (161*2π)/5874 weeks
1623.92639 2.58568 (162*2π)/5874 weeks
1634.10846 1.81271 (163*2π)/5874 weeks
1644.88944 1.84615 (164*2π)/5874 weeks
1655.56979 1.69179 (165*2π)/5874 weeks
1665.71228 2.08836 (166*2π)/5874 weeks
1675.87099 2.21879 (167*2π)/5874 weeks
1685.75615 2.35724 (168*2π)/5873 weeks
1695.61665 2.03175 (169*2π)/5873 weeks
1706.04041 1.72971 (170*2π)/5873 weeks
1716.40577 1.52868 (171*2π)/5873 weeks
1726.90411 2.25613 (172*2π)/5873 weeks
1736.84362 2.73717 (173*2π)/5873 weeks
1746.42775 3.00614 (174*2π)/5873 weeks
1756.06996 2.96382 (175*2π)/5873 weeks
1766.01643 2.71179 (176*2π)/5873 weeks
1776.10553 2.82355 (177*2π)/5873 weeks
1786.07731 2.82582 (178*2π)/5873 weeks
1795.8359 2.84732 (179*2π)/5873 weeks
1805.53391 2.6866 (180*2π)/5873 weeks
1815.39971 2.69746 (181*2π)/5873 weeks
1825.08935 2.03112 (182*2π)/5873 weeks
1835.30421 1.50776 (183*2π)/5873 weeks
1845.73671 1.05474 (184*2π)/5873 weeks
1856.48613 1.10192 (185*2π)/5873 weeks
1866.7844 1.21453 (186*2π)/5873 weeks
1876.96336 1.39043 (187*2π)/5873 weeks
1887.31843 1.40575 (188*2π)/5873 weeks
1897.49632 1.57561 (189*2π)/5873 weeks
1907.95418 1.81729 (190*2π)/5873 weeks
1917.92764 2.46163 (191*2π)/5873 weeks
1928.02641 2.87615 (192*2π)/5873 weeks
1937.3641 3.54373 (193*2π)/5873 weeks
1946.95019 3.7501 (194*2π)/5873 weeks
1956.57477 3.19702 (195*2π)/5873 weeks
1966.3863 3.08664 (196*2π)/5873 weeks
1976.62404 2.79233 (197*2π)/5873 weeks
1986.66956 3.11803 (198*2π)/5873 weeks
1996.70505 3.05884 (199*2π)/5873 weeks
2006.688 3.37445 (200*2π)/5873 weeks
2016.52306 3.41817 (201*2π)/5873 weeks
2026.02439 3.4175 (202*2π)/5873 weeks
2036.01498 3.30646 (203*2π)/5873 weeks
2045.91352 2.99851 (204*2π)/5873 weeks
2055.99235 2.89506 (205*2π)/5873 weeks
2065.86851 2.69449 (206*2π)/5873 weeks
2076.17234 2.63474 (207*2π)/5873 weeks
2086.35818 2.57919 (208*2π)/5873 weeks
2096.48101 3.09318 (209*2π)/5873 weeks
2106.29815 3.49967 (210*2π)/5873 weeks
2115.70435 3.66003 (211*2π)/5873 weeks
2125.21684 3.38758 (212*2π)/5873 weeks
2134.76435 2.94554 (213*2π)/5873 weeks
2144.82294 2.34572 (214*2π)/5873 weeks
2154.935 1.94594 (215*2π)/5873 weeks
2165.36692 1.75369 (216*2π)/5873 weeks
2175.42592 1.80641 (217*2π)/5873 weeks
2185.69176 1.59793 (218*2π)/5873 weeks
2195.90138 1.45176 (219*2π)/5873 weeks
2206.25121 1.63922 (220*2π)/5873 weeks
2216.69074 1.74426 (221*2π)/5873 weeks
2226.8206 2.05912 (222*2π)/5873 weeks
2236.89035 2.7146 (223*2π)/5873 weeks
2246.57388 2.91965 (224*2π)/5873 weeks
2255.94545 3.21855 (225*2π)/5873 weeks
2265.7146 3.03458 (226*2π)/5873 weeks
2275.42204 2.69388 (227*2π)/5873 weeks
2285.63904 2.65015 (228*2π)/5873 weeks
2295.60354 2.54099 (229*2π)/5873 weeks
2305.61122 2.60515 (230*2π)/5873 weeks
2315.7796 2.67854 (231*2π)/5873 weeks
2325.56025 3.01504 (232*2π)/5873 weeks
2335.02369 3.11711 (233*2π)/5873 weeks
2344.37507 2.98512 (234*2π)/5873 weeks
2353.88117 2.15266 (235*2π)/5872 weeks
2364.05501 1.50697 (236*2π)/5872 weeks
2374.60116 .94372 (237*2π)/5872 weeks
2385.10365 .87541 (238*2π)/5872 weeks
2395.40674 1.21522 (239*2π)/5872 weeks
2405.39416 1.17675 (240*2π)/5872 weeks
2415.30822 1.27346 (241*2π)/5872 weeks
2425.29372 1.06437 (242*2π)/5872 weeks
2435.38372 .95121 (243*2π)/5872 weeks
2445.44803 .56813 (244*2π)/5872 weeks
2456.02513 .37136 (245*2π)/5872 weeks
2466.53849 .40728 (246*2π)/5872 weeks
2477.07016 .80759 (247*2π)/5872 weeks
2487.43443 1.36853 (248*2π)/5872 weeks
2497.30584 1.78157 (249*2π)/5872 weeks
2507.40392 2.28892 (250*2π)/5872 weeks
2517.10228 2.84526 (251*2π)/5872 weeks
2526.83649 3.17953 (252*2π)/5872 weeks
2536.37499 3.57849 (253*2π)/5872 weeks
2545.72774 3.64464 (254*2π)/5872 weeks
2555.48378 3.39015 (255*2π)/5872 weeks
2565.1995 3.3818 (256*2π)/5872 weeks
2574.94509 3.40303 (257*2π)/5872 weeks
2584.38016 3.45971 (258*2π)/5872 weeks
2593.92739 2.93136 (259*2π)/5872 weeks
2603.84732 2.42444 (260*2π)/5872 weeks
2614.30052 2.20294 (261*2π)/5872 weeks
2624.33856 2.13068 (262*2π)/5872 weeks
2634.3489 2.51823 (263*2π)/5872 weeks
2643.88292 2.46477 (264*2π)/5872 weeks
2653.56685 2.50946 (265*2π)/5872 weeks
2663.09219 2.07446 (266*2π)/5872 weeks
2672.71298 1.47802 (267*2π)/5872 weeks
2682.84977 .84616 (268*2π)/5872 weeks
2692.9219 .28244 (269*2π)/5872 weeks
2703.51206 -.04591 (270*2π)/5872 weeks
2713.72333 -.17605 (271*2π)/5872 weeks
2724.02006 -.45878 (272*2π)/5872 weeks
2734.55918 -.28995 (273*2π)/5872 weeks
2744.9199 -.19373 (274*2π)/5872 weeks
2755.00322 -.0117 (275*2π)/5872 weeks
2765.06174 .13456 (276*2π)/5872 weeks
2775.24859 .16219 (277*2π)/5872 weeks
2785.33536 .44543 (278*2π)/5872 weeks
2795.33752 .79711 (279*2π)/5872 weeks
2804.97565 .90691 (280*2π)/5872 weeks
2814.42864 .93391 (281*2π)/5872 weeks
2824.29065 .39361 (282*2π)/5872 weeks
2834.38848 -.09492 (283*2π)/5872 weeks
2844.89963 -.2963 (284*2π)/5872 weeks
2855.61163 .04507 (285*2π)/5872 weeks
2865.63007 .88071 (286*2π)/5872 weeks
2875.09196 1.17224 (287*2π)/5872 weeks
2884.66085 1.33144 (288*2π)/5872 weeks
2894.18309 1.06856 (289*2π)/5872 weeks
2903.92681 .92811 (290*2π)/5872 weeks
2913.74812 .39194 (291*2π)/5872 weeks
2923.81964 -.00782 (292*2π)/5872 weeks
2934.05992 .00867 (293*2π)/5872 weeks
2944.05992 -.00867 (294*2π)/5872 weeks
2953.81964 .00782 (295*2π)/5872 weeks
2963.74812 -.39194 (296*2π)/5872 weeks
2973.92681 -.92811 (297*2π)/5872 weeks
2984.18309 -1.06856 (298*2π)/5872 weeks
2994.66085 -1.33144 (299*2π)/5872 weeks
3005.09196 -1.17224 (300*2π)/5872 weeks
3015.63007 -.88071 (301*2π)/5872 weeks
3025.61163 -.04507 (302*2π)/5872 weeks
3034.89963 .2963 (303*2π)/5872 weeks
3044.38848 .09492 (304*2π)/5872 weeks
3054.29065 -.39361 (305*2π)/5872 weeks
3064.42864 -.93391 (306*2π)/5872 weeks
3074.97565 -.90691 (307*2π)/5872 weeks
3085.33752 -.79711 (308*2π)/5872 weeks
3095.33536 -.44543 (309*2π)/5872 weeks
3105.24859 -.16219 (310*2π)/5872 weeks
3115.06174 -.13456 (311*2π)/5872 weeks
3125.00322 .0117 (312*2π)/5872 weeks
3134.9199 .19373 (313*2π)/5872 weeks
3144.55918 .28995 (314*2π)/5872 weeks
3154.02006 .45878 (315*2π)/5872 weeks
3163.72333 .17605 (316*2π)/5872 weeks
3173.51206 .04591 (317*2π)/5872 weeks
3182.9219 -.28244 (318*2π)/5872 weeks
3192.84977 -.84616 (319*2π)/5872 weeks
3202.71298 -1.47802 (320*2π)/5872 weeks
3213.09219 -2.07446 (321*2π)/5872 weeks
3223.56685 -2.50946 (322*2π)/5872 weeks
3233.88292 -2.46477 (323*2π)/5872 weeks
3244.3489 -2.51823 (324*2π)/5872 weeks
3254.33856 -2.13068 (325*2π)/5872 weeks
3264.30052 -2.20294 (326*2π)/5872 weeks
3273.84732 -2.42444 (327*2π)/5872 weeks
3283.92739 -2.93136 (328*2π)/5872 weeks
3294.38016 -3.45971 (329*2π)/5872 weeks
3304.94509 -3.40303 (330*2π)/5872 weeks
3315.1995 -3.3818 (331*2π)/5872 weeks
3325.48378 -3.39015 (332*2π)/5872 weeks
3335.72774 -3.64464 (333*2π)/5872 weeks
3346.37499 -3.57849 (334*2π)/5872 weeks
3356.83649 -3.17953 (335*2π)/5872 weeks
3367.10228 -2.84526 (336*2π)/5872 weeks
3377.40392 -2.28892 (337*2π)/5872 weeks
3387.30584 -1.78157 (338*2π)/5872 weeks
3397.43443 -1.36853 (339*2π)/5872 weeks
3407.07016 -.80759 (340*2π)/5872 weeks
3416.53849 -.40728 (341*2π)/5872 weeks
3426.02513 -.37136 (342*2π)/5872 weeks
3435.44803 -.56813 (343*2π)/5872 weeks
3445.38372 -.95121 (344*2π)/5872 weeks
3455.29372 -1.06437 (345*2π)/5872 weeks
3465.30822 -1.27346 (346*2π)/5872 weeks
3475.39416 -1.17675 (347*2π)/5872 weeks
3485.40674 -1.21522 (348*2π)/5872 weeks
3495.10365 -.87541 (349*2π)/5872 weeks
3504.60116 -.94372 (350*2π)/5872 weeks
3514.05501 -1.50697 (351*2π)/5872 weeks
3523.88117 -2.15266 (352*2π)/5872 weeks
3534.37507 -2.98512 (353*2π)/5872 weeks
3545.02369 -3.11711 (354*2π)/5872 weeks
3555.56025 -3.01504 (355*2π)/5872 weeks
3565.7796 -2.67854 (356*2π)/5872 weeks
3575.61122 -2.60515 (357*2π)/5872 weeks
3585.60354 -2.54099 (358*2π)/5872 weeks
3595.63904 -2.65015 (359*2π)/5872 weeks
3605.42204 -2.69388 (360*2π)/5872 weeks
3615.7146 -3.03458 (361*2π)/5872 weeks
3625.94545 -3.21855 (362*2π)/5872 weeks
3636.57388 -2.91965 (363*2π)/5872 weeks
3646.89035 -2.7146 (364*2π)/5872 weeks
3656.8206 -2.05912 (365*2π)/5872 weeks
3666.69074 -1.74426 (366*2π)/5872 weeks
3676.25121 -1.63922 (367*2π)/5872 weeks
3685.90138 -1.45176 (368*2π)/5872 weeks
3695.69176 -1.59793 (369*2π)/5872 weeks
3705.42592 -1.80641 (370*2π)/5872 weeks
3715.36692 -1.75369 (371*2π)/5872 weeks
3724.935 -1.94594 (372*2π)/5872 weeks
3734.82294 -2.34572 (373*2π)/5872 weeks
3744.76435 -2.94554 (374*2π)/5872 weeks
3755.21684 -3.38758 (375*2π)/5872 weeks
3765.70435 -3.66003 (376*2π)/5872 weeks
3776.29815 -3.49967 (377*2π)/5872 weeks
3786.48101 -3.09318 (378*2π)/5872 weeks
3796.35818 -2.57919 (379*2π)/5872 weeks
3806.17234 -2.63474 (380*2π)/5872 weeks
3815.86851 -2.69449 (381*2π)/5872 weeks
3825.99235 -2.89506 (382*2π)/5872 weeks
3835.91352 -2.99851 (383*2π)/5872 weeks
3846.01498 -3.30646 (384*2π)/5872 weeks
3856.02439 -3.4175 (385*2π)/5872 weeks
3866.52306 -3.41817 (386*2π)/5872 weeks
3876.688 -3.37445 (387*2π)/5872 weeks
3886.70505 -3.05884 (388*2π)/5872 weeks
3896.66956 -3.11803 (389*2π)/5872 weeks
3906.62404 -2.79233 (390*2π)/5872 weeks
3916.3863 -3.08664 (391*2π)/5872 weeks
3926.57477 -3.19702 (392*2π)/5871 weeks
3936.95019 -3.7501 (393*2π)/5871 weeks
3947.3641 -3.54373 (394*2π)/5871 weeks
3958.02641 -2.87615 (395*2π)/5871 weeks
3967.92764 -2.46163 (396*2π)/5871 weeks
3977.95418 -1.81729 (397*2π)/5871 weeks
3987.49632 -1.57561 (398*2π)/5871 weeks
3997.31843 -1.40575 (399*2π)/5871 weeks
4006.96336 -1.39043 (400*2π)/5871 weeks
4016.7844 -1.21453 (401*2π)/5871 weeks
4026.48613 -1.10192 (402*2π)/5871 weeks
4035.73671 -1.05474 (403*2π)/5871 weeks
4045.30421 -1.50776 (404*2π)/5871 weeks
4055.08935 -2.03112 (405*2π)/5871 weeks
4065.39971 -2.69746 (406*2π)/5871 weeks
4075.53391 -2.6866 (407*2π)/5871 weeks
4085.8359 -2.84732 (408*2π)/5871 weeks
4096.07731 -2.82582 (409*2π)/5871 weeks
4106.10553 -2.82355 (410*2π)/5871 weeks
4116.01643 -2.71179 (411*2π)/5871 weeks
4126.06996 -2.96382 (412*2π)/5871 weeks
4136.42775 -3.00614 (413*2π)/5871 weeks
4146.84362 -2.73717 (414*2π)/5871 weeks
4156.90411 -2.25613 (415*2π)/5871 weeks
4166.40577 -1.52868 (416*2π)/5871 weeks
4176.04041 -1.72971 (417*2π)/5871 weeks
4185.61665 -2.03175 (418*2π)/5871 weeks
4195.75615 -2.35724 (419*2π)/5871 weeks
4205.87099 -2.21879 (420*2π)/5871 weeks
4215.71228 -2.08836 (421*2π)/5871 weeks
4225.56979 -1.69179 (422*2π)/5871 weeks
4234.88944 -1.84615 (423*2π)/5871 weeks
4244.10846 -1.81271 (424*2π)/5871 weeks
4253.92639 -2.58568 (425*2π)/5871 weeks
4263.6517 -3.19338 (426*2π)/5871 weeks
4273.95131 -3.96232 (427*2π)/5871 weeks
4284.34429 -4.35415 (428*2π)/5871 weeks
4294.94238 -4.66952 (429*2π)/5871 weeks
4305.46746 -4.59215 (430*2π)/5871 weeks
4315.67416 -4.31756 (431*2π)/5871 weeks
4325.75874 -4.11764 (432*2π)/5871 weeks
4335.77136 -3.89017 (433*2π)/5871 weeks
4345.67631 -3.91667 (434*2π)/5871 weeks
4355.81803 -3.68347 (435*2π)/5871 weeks
4365.50447 -4.00227 (436*2π)/5871 weeks
4375.5495 -4.00158 (437*2π)/5871 weeks
4385.74229 -3.80563 (438*2π)/5871 weeks
4395.50687 -3.51317 (439*2π)/5871 weeks
4404.95821 -3.69259 (440*2π)/5871 weeks
4414.78102 -4.23484 (441*2π)/5871 weeks
4424.95065 -4.76627 (442*2π)/5871 weeks
4435.22116 -4.57949 (443*2π)/5871 weeks
4445.06631 -4.71929 (444*2π)/5871 weeks
4454.94588 -5.1963 (445*2π)/5871 weeks
4465.26271 -5.52944 (446*2π)/5871 weeks
4475.91516 -5.66512 (447*2π)/5871 weeks
4486.45682 -5.72438 (448*2π)/5871 weeks
4496.44268 -5.30474 (449*2π)/5871 weeks
4506.94031 -4.86649 (450*2π)/5871 weeks
4516.40934 -4.65253 (451*2π)/5871 weeks
4526.29107 -4.39551 (452*2π)/5871 weeks
4535.85012 -4.83242 (453*2π)/5871 weeks
4545.9575 -4.70921 (454*2π)/5871 weeks
4555.69412 -5.04609 (455*2π)/5871 weeks
4565.93247 -5.06535 (456*2π)/5871 weeks
4575.96329 -5.44656 (457*2π)/5871 weeks
4586.15567 -5.57562 (458*2π)/5871 weeks
4596.62973 -5.63377 (459*2π)/5871 weeks
4606.88934 -5.28907 (460*2π)/5871 weeks
4617.20505 -4.92675 (461*2π)/5871 weeks
4626.96668 -4.2242 (462*2π)/5871 weeks
4636.63843 -3.79966 (463*2π)/5871 weeks
4646.10964 -3.73552 (464*2π)/5871 weeks
4655.6705 -3.80551 (465*2π)/5871 weeks
4665.24573 -3.83805 (466*2π)/5871 weeks
4674.92879 -3.67187 (467*2π)/5871 weeks
4683.79947 -4.70096 (468*2π)/5871 weeks
4693.54772 -5.14239 (469*2π)/5871 weeks
4703.52365 -6.48512 (470*2π)/5871 weeks
4714.29147 -7.0508 (471*2π)/5871 weeks
4725.13364 -7.5613 (472*2π)/5871 weeks
4735.77683 -7.61638 (473*2π)/5871 weeks
4746.40769 -6.70075 (474*2π)/5871 weeks
4756.17321 -6.42842 (475*2π)/5871 weeks
4765.81703 -6.30299 (476*2π)/5871 weeks
4775.34198 -6.34389 (477*2π)/5871 weeks
4785.5306 -7.17287 (478*2π)/5871 weeks
4795.4362 -7.29341 (479*2π)/5871 weeks
4806.07045 -7.02307 (480*2π)/5871 weeks
4816.31308 -6.74604 (481*2π)/5871 weeks
4825.19441 -6.41553 (482*2π)/5871 weeks
4834.51069 -6.88343 (483*2π)/5871 weeks
4843.96699 -8.04752 (484*2π)/5871 weeks
4854.38633 -9.47014 (485*2π)/5871 weeks
4865.33349 -10.78236 (486*2π)/5871 weeks
4876.7904 -11.10586 (487*2π)/5871 weeks
4888.25516 -11.49167 (488*2π)/5871 weeks
4899.77632 -10.37087 (489*2π)/5871 weeks
49010.51661 -9.43324 (490*2π)/5871 weeks
49110.65042 -7.72101 (491*2π)/5871 weeks
49210.22287 -6.86054 (492*2π)/5871 weeks
4939.1397 -6.30508 (493*2π)/5871 weeks
4948.76632 -5.85304 (494*2π)/5871 weeks
4958.39397 -6.09213 (495*2π)/5871 weeks
4967.57239 -6.00556 (496*2π)/5871 weeks
4977.12277 -6.80931 (497*2π)/5871 weeks
4987.63297 -7.4455 (498*2π)/5871 weeks
4998.14194 -7.20901 (499*2π)/5871 weeks
5008.25119 -6.84324 (500*2π)/5871 weeks
5018.04288 -6.99646 (501*2π)/5871 weeks
5028.37111 -6.70431 (502*2π)/5871 weeks
5038.14418 -5.76019 (503*2π)/5871 weeks
5047.50473 -5.44801 (504*2π)/5871 weeks
5055.83113 -5.99419 (505*2π)/5871 weeks
5065.76462 -6.88442 (506*2π)/5871 weeks
5076.23601 -8.38051 (507*2π)/5871 weeks
5086.93255 -8.12143 (508*2π)/5871 weeks
5097.6524 -8.20668 (509*2π)/5871 weeks
5107.64771 -7.05706 (510*2π)/5871 weeks
5117.91468 -6.4926 (511*2π)/5871 weeks
5126.89167 -6.09131 (512*2π)/5871 weeks
5135.77306 -5.55441 (513*2π)/5871 weeks
5144.06966 -6.24398 (514*2π)/5871 weeks
5153.46625 -7.05813 (515*2π)/5871 weeks
5162.6394 -8.99504 (516*2π)/5871 weeks
5173.43071 -10.75292 (517*2π)/5871 weeks
5184.34422 -11.44018 (518*2π)/5871 weeks
5195.52653 -11.83292 (519*2π)/5871 weeks
5205.70929 -11.71654 (520*2π)/5871 weeks
5216.11181 -11.73937 (521*2π)/5871 weeks
5226.44529 -12.00378 (522*2π)/5871 weeks
5236.63214 -12.16277 (523*2π)/5871 weeks
5247.5517 -11.57778 (524*2π)/5871 weeks
5256.83126 -12.56852 (525*2π)/5871 weeks
5267.9103 -11.81233 (526*2π)/5871 weeks
5278.67026 -12.36266 (527*2π)/5871 weeks
5288.84541 -12.17821 (528*2π)/5871 weeks
5298.97567 -10.60128 (529*2π)/5871 weeks
5308.70523 -10.35968 (530*2π)/5871 weeks
5318.65793 -10.03362 (531*2π)/5871 weeks
5327.85146 -9.34421 (532*2π)/5871 weeks
5337.20886 -9.40978 (533*2π)/5871 weeks
5345.98609 -9.28014 (534*2π)/5871 weeks
5355.215 -9.39245 (535*2π)/5871 weeks
5363.77614 -9.84162 (536*2π)/5871 weeks
5372.05526 -11.78971 (537*2π)/5871 weeks
5382.28041 -13.29743 (538*2π)/5871 weeks
5392.39448 -14.12809 (539*2π)/5871 weeks
5402.21516 -15.1293 (540*2π)/5871 weeks
5411.53619 -15.71611 (541*2π)/5871 weeks
5421.10114 -18.36099 (542*2π)/5871 weeks
5431.14248 -20.6239 (543*2π)/5871 weeks
5441.87692 -22.63965 (544*2π)/5871 weeks
5453.59362 -25.91486 (545*2π)/5871 weeks
5466.30121 -27.21491 (546*2π)/5871 weeks
5479.28868 -27.5215 (547*2π)/5871 weeks
54811.85681 -26.9957 (548*2π)/5871 weeks
54913.57716 -27.13066 (549*2π)/5871 weeks
55016.29671 -25.63852 (550*2π)/5871 weeks
55117.11397 -23.63827 (551*2π)/5871 weeks
55217.17777 -22.07121 (552*2π)/5871 weeks
55317.00892 -21.89116 (553*2π)/5871 weeks
55416.49207 -21.02922 (554*2π)/5871 weeks
55517.34857 -20.62976 (555*2π)/5871 weeks
55616.24309 -19.61167 (556*2π)/5871 weeks
55715.46851 -19.19603 (557*2π)/5871 weeks
55815.4252 -20.77089 (558*2π)/5871 weeks
55914.49068 -20.761 (559*2π)/5871 weeks
56016.13895 -20.72062 (560*2π)/5871 weeks
56113.08451 -19.70093 (561*2π)/5871 weeks
56211.88376 -20.5656 (562*2π)/5871 weeks
5638.65456 -24.12215 (563*2π)/5871 weeks
5649.61941 -30.68817 (564*2π)/5871 weeks
56514.17225 -32.02849 (565*2π)/5871 weeks
56618.21938 -33.38413 (566*2π)/5871 weeks
56721.48676 -31.55971 (567*2π)/5871 weeks
56822.42022 -28.1101 (568*2π)/5871 weeks
56920.25607 -26.26121 (569*2π)/5871 weeks
57020.09664 -27.14427 (570*2π)/5871 weeks
57117.83091 -30.4206 (571*2π)/5871 weeks
57218.86388 -30.87642 (572*2π)/5871 weeks
57316.74376 -33.46659 (573*2π)/5871 weeks
57416.84442 -37.6207 (574*2π)/5871 weeks
57514.01369 -40.19956 (575*2π)/5871 weeks
57614.48769 -47.23773 (576*2π)/5871 weeks
57718.04364 -58.67819 (577*2π)/5871 weeks
57824.90281 -63.17435 (578*2π)/5871 weeks
57936.78975 -70.42261 (579*2π)/5871 weeks
58044.9663 -69.52965 (580*2π)/5871 weeks
58144.41214 -67.67954 (581*2π)/5871 weeks
58247.85023 -79.15186 (582*2π)/5871 weeks
58354.64549 -100.6349 (583*2π)/5871 weeks
58490.13788 -118.6575 (584*2π)/5871 weeks
585156.7378 -125.1766 (585*2π)/5871 weeks



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