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Fourier Analysis of SDOW (PROSHARES ULTRAPRO SHORT DOW30 PROSHARES ULTRAPRO SHORT DOW30)


SDOW (PROSHARES ULTRAPRO SHORT DOW30 PROSHARES ULTRAPRO SHORT DOW30) appears to have interesting cyclic behaviour every 38 weeks (33.4539*sine), 35 weeks (28.6805*sine), and 42 weeks (28.3938*sine).

SDOW (PROSHARES ULTRAPRO SHORT DOW30 PROSHARES ULTRAPRO SHORT DOW30) has an average price of 271.41 (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 2/11/2010 to 1/16/2018 for SDOW (PROSHARES ULTRAPRO SHORT DOW30 PROSHARES ULTRAPRO SHORT DOW30), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0271.4072   0 
1182.1802 233.9424 (1*2π)/415415 weeks
257.2365 162.4821 (2*2π)/415208 weeks
338.11147 119.6789 (3*2π)/415138 weeks
426.93035 97.18452 (4*2π)/415104 weeks
518.16109 81.8952 (5*2π)/41583 weeks
65.91056 83.33832 (6*2π)/41569 weeks
7-14.87107 66.27869 (7*2π)/41559 weeks
8-16.30268 36.70139 (8*2π)/41552 weeks
9-2.55714 27.96724 (9*2π)/41546 weeks
104.33443 28.39382 (10*2π)/41542 weeks
113.16428 33.45387 (11*2π)/41538 weeks
12-6.65784 28.68045 (12*2π)/41535 weeks
13-2.25837 12.67488 (13*2π)/41532 weeks
147.19367 13.76545 (14*2π)/41530 weeks
156.12061 17.28317 (15*2π)/41528 weeks
167.64792 17.1618 (16*2π)/41526 weeks
178.96011 15.85786 (17*2π)/41524 weeks
183.91193 17.75319 (18*2π)/41523 weeks
196.35177 11.99243 (19*2π)/41522 weeks
2013.67853 13.22219 (20*2π)/41521 weeks
219.6977 17.44916 (21*2π)/41520 weeks
224.89004 17.58173 (22*2π)/41519 weeks
234.9018 14.97057 (23*2π)/41518 weeks
248.10687 11.32157 (24*2π)/41517 weeks
259.2114 11.69834 (25*2π)/41517 weeks
269.35372 15.57076 (26*2π)/41516 weeks
276.39425 15.67127 (27*2π)/41515 weeks
286.23035 12.62517 (28*2π)/41515 weeks
297.98527 13.01393 (29*2π)/41514 weeks
309.37697 13.84043 (30*2π)/41514 weeks
318.97666 18.22283 (31*2π)/41513 weeks
323.30316 19.43854 (32*2π)/41513 weeks
33-1.4305 14.54932 (33*2π)/41513 weeks
341.62754 9.64245 (34*2π)/41512 weeks
353.97476 9.99332 (35*2π)/41512 weeks
364.23359 13.43572 (36*2π)/41512 weeks
372.1901 11.12647 (37*2π)/41511 weeks
381.83684 11.31026 (38*2π)/41511 weeks
39.72382 9.89282 (39*2π)/41511 weeks
402.53715 6.80279 (40*2π)/41510 weeks
414.07779 7.00618 (41*2π)/41510 weeks
425.21625 7.57467 (42*2π)/41510 weeks
435.61002 10.18291 (43*2π)/41510 weeks
444.54399 10.7644 (44*2π)/4159 weeks
451.99655 11.44278 (45*2π)/4159 weeks
46.2288 9.07005 (46*2π)/4159 weeks
471.23024 6.10281 (47*2π)/4159 weeks
483.67148 7.26102 (48*2π)/4159 weeks
493.04027 7.85965 (49*2π)/4158 weeks
50.96144 10.27951 (50*2π)/4158 weeks
51-2.19675 4.71018 (51*2π)/4158 weeks
522.58247 1.92985 (52*2π)/4158 weeks
534.49485 4.59679 (53*2π)/4158 weeks
544.24715 5.5859 (54*2π)/4158 weeks
552.47599 6.53168 (55*2π)/4158 weeks
561.75075 3.69741 (56*2π)/4157 weeks
572.94553 1.15137 (57*2π)/4157 weeks
588.58015 1.36456 (58*2π)/4157 weeks
599.50356 6.29226 (59*2π)/4157 weeks
606.54367 8.9218 (60*2π)/4157 weeks
613.87687 7.7809 (61*2π)/4157 weeks
624.62204 5.66673 (62*2π)/4157 weeks
636.27072 7.68809 (63*2π)/4157 weeks
644.07657 9.39548 (64*2π)/4156 weeks
651.81651 8.10366 (65*2π)/4156 weeks
662.65152 6.89897 (66*2π)/4156 weeks
671.33707 6.72883 (67*2π)/4156 weeks
681.40355 5.88886 (68*2π)/4156 weeks
692.11463 5.59895 (69*2π)/4156 weeks
701.27427 5.62994 (70*2π)/4156 weeks
71.79058 3.58719 (71*2π)/4156 weeks
722.57655 2.53861 (72*2π)/4156 weeks
733.06004 3.74079 (73*2π)/4156 weeks
743.38511 3.73074 (74*2π)/4156 weeks
753.52483 3.96252 (75*2π)/4156 weeks
763.55598 3.12008 (76*2π)/4155 weeks
773.48308 4.07633 (77*2π)/4155 weeks
783.87071 3.73417 (78*2π)/4155 weeks
793.62923 3.68913 (79*2π)/4155 weeks
804.72858 2.94848 (80*2π)/4155 weeks
815.04392 4.83647 (81*2π)/4155 weeks
824.32685 5.54672 (82*2π)/4155 weeks
833.87389 4.6716 (83*2π)/4155 weeks
843.64139 5.5681 (84*2π)/4155 weeks
852.92133 5.96317 (85*2π)/4155 weeks
861.42215 5.1497 (86*2π)/4155 weeks
871.82775 3.57444 (87*2π)/4155 weeks
881.90097 3.42595 (88*2π)/4155 weeks
893.09482 3.54321 (89*2π)/4155 weeks
903.06979 4.32307 (90*2π)/4155 weeks
911.61406 3.4229 (91*2π)/4155 weeks
922.13287 3.33969 (92*2π)/4155 weeks
931.85461 2.78448 (93*2π)/4154 weeks
942.96905 2.56014 (94*2π)/4154 weeks
952.19812 2.90873 (95*2π)/4154 weeks
961.88704 2.48684 (96*2π)/4154 weeks
972.35606 1.82699 (97*2π)/4154 weeks
982.48928 1.58213 (98*2π)/4154 weeks
992.97903 .97208 (99*2π)/4154 weeks
1003.13114 .847 (100*2π)/4154 weeks
1014.23515 .89499 (101*2π)/4154 weeks
1025.83082 .92529 (102*2π)/4154 weeks
1035.62659 2.57885 (103*2π)/4154 weeks
1044.67651 3.73427 (104*2π)/4154 weeks
1054.03397 2.7878 (105*2π)/4154 weeks
1064.88495 1.70275 (106*2π)/4154 weeks
1076.02968 3.21319 (107*2π)/4154 weeks
1085.18542 5.03228 (108*2π)/4154 weeks
1094.01951 5.49159 (109*2π)/4154 weeks
1102.86658 4.2768 (110*2π)/4154 weeks
1112.87866 3.82704 (111*2π)/4154 weeks
1123.5165 4.3456 (112*2π)/4154 weeks
1132.15481 4.88531 (113*2π)/4154 weeks
114.93293 4.01776 (114*2π)/4154 weeks
1151.08668 2.38999 (115*2π)/4154 weeks
1162.27314 2.35461 (116*2π)/4154 weeks
1172.05698 3.09556 (117*2π)/4154 weeks
1181.18442 2.56705 (118*2π)/4154 weeks
119.20878 1.86409 (119*2π)/4153 weeks
1201.103 -.35841 (120*2π)/4153 weeks
1213.14211 -.12068 (121*2π)/4153 weeks
1223.73105 .68865 (122*2π)/4153 weeks
1233.37785 1.10534 (123*2π)/4153 weeks
1244.36001 .49939 (124*2π)/4153 weeks
1254.59613 2.43279 (125*2π)/4153 weeks
1262.92734 2.37047 (126*2π)/4153 weeks
1273.12202 1.68866 (127*2π)/4153 weeks
1283.32592 1.66249 (128*2π)/4153 weeks
1293.12611 1.86686 (129*2π)/4153 weeks
1303.64357 1.73247 (130*2π)/4153 weeks
1312.72521 2.12658 (131*2π)/4153 weeks
1322.58584 1.5002 (132*2π)/4153 weeks
1333.01298 1.25244 (133*2π)/4153 weeks
1343.33707 1.15541 (134*2π)/4153 weeks
1353.24424 1.74735 (135*2π)/4153 weeks
1362.70639 1.56116 (136*2π)/4153 weeks
1372.72274 .76447 (137*2π)/4153 weeks
1383.83099 .77737 (138*2π)/4153 weeks
1393.2091 1.97522 (139*2π)/4153 weeks
1402.36883 1.11562 (140*2π)/4153 weeks
1413.26702 -.11407 (141*2π)/4153 weeks
1424.12182 .59774 (142*2π)/4153 weeks
1434.06151 1.60759 (143*2π)/4153 weeks
1443.03521 1.18111 (144*2π)/4153 weeks
1452.88085 .19694 (145*2π)/4153 weeks
1464.72579 -.53553 (146*2π)/4153 weeks
1476.31857 1.13474 (147*2π)/4153 weeks
1484.76781 3.66331 (148*2π)/4153 weeks
1492.76313 2.84173 (149*2π)/4153 weeks
1502.69019 1.39067 (150*2π)/4153 weeks
1514.15221 .43965 (151*2π)/4153 weeks
1525.3042 2.60479 (152*2π)/4153 weeks
1533.11449 4.46368 (153*2π)/4153 weeks
1541.02541 3.13384 (154*2π)/4153 weeks
1551.40412 1.33342 (155*2π)/4153 weeks
1561.84768 .62897 (156*2π)/4153 weeks
1572.57227 .93768 (157*2π)/4153 weeks
1582.29102 1.43155 (158*2π)/4153 weeks
1591.31738 1.24055 (159*2π)/4153 weeks
1601.34051 -.21869 (160*2π)/4153 weeks
1612.43605 -1.32382 (161*2π)/4153 weeks
1623.7795 -.09911 (162*2π)/4153 weeks
1633.31789 .51712 (163*2π)/4153 weeks
1642.67708 .1828 (164*2π)/4153 weeks
1652.57752 -.1272 (165*2π)/4153 weeks
1662.98236 -.74674 (166*2π)/4153 weeks
1673.46328 -1.11796 (167*2π)/4152 weeks
1684.66911 -.78515 (168*2π)/4152 weeks
1695.05164 .34799 (169*2π)/4152 weeks
1704.15315 1.42381 (170*2π)/4152 weeks
1712.74206 .3076 (171*2π)/4152 weeks
1723.62689 -.81075 (172*2π)/4152 weeks
1735.22577 .10717 (173*2π)/4152 weeks
1744.93098 1.20723 (174*2π)/4152 weeks
1753.47771 1.39964 (175*2π)/4152 weeks
1763.34914 .70628 (176*2π)/4152 weeks
1773.64184 .42594 (177*2π)/4152 weeks
1783.92548 .48773 (178*2π)/4152 weeks
1794.1895 1.04129 (179*2π)/4152 weeks
1803.23197 1.74831 (180*2π)/4152 weeks
1812.47503 -.10103 (181*2π)/4152 weeks
1824.17332 -.50759 (182*2π)/4152 weeks
1834.82765 1.21483 (183*2π)/4152 weeks
1843.30656 1.82192 (184*2π)/4152 weeks
1852.27415 .97113 (185*2π)/4152 weeks
1862.53254 .04083 (186*2π)/4152 weeks
1873.7669 -1.18824 (187*2π)/4152 weeks
1884.53015 .33964 (188*2π)/4152 weeks
1894.3402 .86327 (189*2π)/4152 weeks
1903.62662 .91078 (190*2π)/4152 weeks
1913.8347 .93157 (191*2π)/4152 weeks
1923.52119 .8062 (192*2π)/4152 weeks
1934.0955 1.65721 (193*2π)/4152 weeks
1942.75299 2.51804 (194*2π)/4152 weeks
1951.23955 1.73285 (195*2π)/4152 weeks
196.98074 .01624 (196*2π)/4152 weeks
1971.41228 -.59415 (197*2π)/4152 weeks
1981.44939 -1.08437 (198*2π)/4152 weeks
1992.75764 -1.59009 (199*2π)/4152 weeks
2002.72203 -1.4706 (200*2π)/4152 weeks
2012.50769 -1.97565 (201*2π)/4152 weeks
2023.98566 -2.54841 (202*2π)/4152 weeks
2035.21205 -2.17589 (203*2π)/4152 weeks
2044.89947 -.96679 (204*2π)/4152 weeks
2054.75698 -.31908 (205*2π)/4152 weeks
2064.81307 -1.0536 (206*2π)/4152 weeks
2075.89682 -.97201 (207*2π)/4152 weeks
2085.89682 .97201 (208*2π)/4152 weeks
2094.81307 1.0536 (209*2π)/4152 weeks
2104.75698 .31908 (210*2π)/4152 weeks
2114.89947 .96679 (211*2π)/4152 weeks
2125.21205 2.17589 (212*2π)/4152 weeks
2133.98566 2.54841 (213*2π)/4152 weeks
2142.50769 1.97565 (214*2π)/4152 weeks
2152.72203 1.4706 (215*2π)/4152 weeks
2162.75764 1.59009 (216*2π)/4152 weeks
2171.44939 1.08437 (217*2π)/4152 weeks
2181.41228 .59415 (218*2π)/4152 weeks
219.98074 -.01624 (219*2π)/4152 weeks
2201.23955 -1.73285 (220*2π)/4152 weeks
2212.75299 -2.51804 (221*2π)/4152 weeks
2224.0955 -1.65721 (222*2π)/4152 weeks
2233.52119 -.8062 (223*2π)/4152 weeks
2243.8347 -.93157 (224*2π)/4152 weeks
2253.62662 -.91078 (225*2π)/4152 weeks
2264.3402 -.86327 (226*2π)/4152 weeks
2274.53015 -.33964 (227*2π)/4152 weeks
2283.7669 1.18824 (228*2π)/4152 weeks
2292.53254 -.04083 (229*2π)/4152 weeks
2302.27415 -.97113 (230*2π)/4152 weeks
2313.30656 -1.82192 (231*2π)/4152 weeks
2324.82765 -1.21483 (232*2π)/4152 weeks
2334.17332 .50759 (233*2π)/4152 weeks
2342.47503 .10103 (234*2π)/4152 weeks
2353.23197 -1.74831 (235*2π)/4152 weeks
2364.1895 -1.04129 (236*2π)/4152 weeks
2373.92548 -.48773 (237*2π)/4152 weeks
2383.64184 -.42594 (238*2π)/4152 weeks
2393.34914 -.70628 (239*2π)/4152 weeks
2403.47771 -1.39964 (240*2π)/4152 weeks
2414.93098 -1.20723 (241*2π)/4152 weeks
2425.22577 -.10717 (242*2π)/4152 weeks
2433.62689 .81075 (243*2π)/4152 weeks
2442.74206 -.3076 (244*2π)/4152 weeks
2454.15315 -1.42381 (245*2π)/4152 weeks
2465.05164 -.34799 (246*2π)/4152 weeks
2474.66911 .78515 (247*2π)/4152 weeks
2483.46328 1.11796 (248*2π)/4152 weeks
2492.98236 .74674 (249*2π)/4152 weeks
2502.57752 .1272 (250*2π)/4152 weeks
2512.67708 -.1828 (251*2π)/4152 weeks
2523.31789 -.51712 (252*2π)/4152 weeks
2533.7795 .09911 (253*2π)/4152 weeks
2542.43605 1.32382 (254*2π)/4152 weeks
2551.34051 .21869 (255*2π)/4152 weeks
2561.31738 -1.24055 (256*2π)/4152 weeks
2572.29102 -1.43155 (257*2π)/4152 weeks
2582.57227 -.93768 (258*2π)/4152 weeks
2591.84768 -.62897 (259*2π)/4152 weeks
2601.40412 -1.33342 (260*2π)/4152 weeks
2611.02541 -3.13384 (261*2π)/4152 weeks
2623.11449 -4.46368 (262*2π)/4152 weeks
2635.3042 -2.60479 (263*2π)/4152 weeks
2644.15221 -.43965 (264*2π)/4152 weeks
2652.69019 -1.39067 (265*2π)/4152 weeks
2662.76313 -2.84173 (266*2π)/4152 weeks
2674.76781 -3.66331 (267*2π)/4152 weeks
2686.31857 -1.13474 (268*2π)/4152 weeks
2694.72579 .53553 (269*2π)/4152 weeks
2702.88085 -.19694 (270*2π)/4152 weeks
2713.03521 -1.18111 (271*2π)/4152 weeks
2724.06151 -1.60759 (272*2π)/4152 weeks
2734.12182 -.59774 (273*2π)/4152 weeks
2743.26702 .11407 (274*2π)/4152 weeks
2752.36883 -1.11562 (275*2π)/4152 weeks
2763.2091 -1.97522 (276*2π)/4152 weeks
2773.83099 -.77737 (277*2π)/4151 weeks
2782.72274 -.76447 (278*2π)/4151 weeks
2792.70639 -1.56116 (279*2π)/4151 weeks
2803.24424 -1.74735 (280*2π)/4151 weeks
2813.33707 -1.15541 (281*2π)/4151 weeks
2823.01298 -1.25244 (282*2π)/4151 weeks
2832.58584 -1.5002 (283*2π)/4151 weeks
2842.72521 -2.12658 (284*2π)/4151 weeks
2853.64357 -1.73247 (285*2π)/4151 weeks
2863.12611 -1.86686 (286*2π)/4151 weeks
2873.32592 -1.66249 (287*2π)/4151 weeks
2883.12202 -1.68866 (288*2π)/4151 weeks
2892.92734 -2.37047 (289*2π)/4151 weeks
2904.59613 -2.43279 (290*2π)/4151 weeks
2914.36001 -.49939 (291*2π)/4151 weeks
2923.37785 -1.10534 (292*2π)/4151 weeks
2933.73105 -.68865 (293*2π)/4151 weeks
2943.14211 .12068 (294*2π)/4151 weeks
2951.103 .35841 (295*2π)/4151 weeks
296.20878 -1.86409 (296*2π)/4151 weeks
2971.18442 -2.56705 (297*2π)/4151 weeks
2982.05698 -3.09556 (298*2π)/4151 weeks
2992.27314 -2.35461 (299*2π)/4151 weeks
3001.08668 -2.38999 (300*2π)/4151 weeks
301.93293 -4.01776 (301*2π)/4151 weeks
3022.15481 -4.88531 (302*2π)/4151 weeks
3033.5165 -4.3456 (303*2π)/4151 weeks
3042.87866 -3.82704 (304*2π)/4151 weeks
3052.86658 -4.2768 (305*2π)/4151 weeks
3064.01951 -5.49159 (306*2π)/4151 weeks
3075.18542 -5.03228 (307*2π)/4151 weeks
3086.02968 -3.21319 (308*2π)/4151 weeks
3094.88495 -1.70275 (309*2π)/4151 weeks
3104.03397 -2.7878 (310*2π)/4151 weeks
3114.67651 -3.73427 (311*2π)/4151 weeks
3125.62659 -2.57885 (312*2π)/4151 weeks
3135.83082 -.92529 (313*2π)/4151 weeks
3144.23515 -.89499 (314*2π)/4151 weeks
3153.13114 -.847 (315*2π)/4151 weeks
3162.97903 -.97208 (316*2π)/4151 weeks
3172.48928 -1.58213 (317*2π)/4151 weeks
3182.35606 -1.82699 (318*2π)/4151 weeks
3191.88704 -2.48684 (319*2π)/4151 weeks
3202.19812 -2.90873 (320*2π)/4151 weeks
3212.96905 -2.56014 (321*2π)/4151 weeks
3221.85461 -2.78448 (322*2π)/4151 weeks
3232.13287 -3.33969 (323*2π)/4151 weeks
3241.61406 -3.4229 (324*2π)/4151 weeks
3253.06979 -4.32307 (325*2π)/4151 weeks
3263.09482 -3.54321 (326*2π)/4151 weeks
3271.90097 -3.42595 (327*2π)/4151 weeks
3281.82775 -3.57444 (328*2π)/4151 weeks
3291.42215 -5.1497 (329*2π)/4151 weeks
3302.92133 -5.96317 (330*2π)/4151 weeks
3313.64139 -5.5681 (331*2π)/4151 weeks
3323.87389 -4.6716 (332*2π)/4151 weeks
3334.32685 -5.54672 (333*2π)/4151 weeks
3345.04392 -4.83647 (334*2π)/4151 weeks
3354.72858 -2.94848 (335*2π)/4151 weeks
3363.62923 -3.68913 (336*2π)/4151 weeks
3373.87071 -3.73417 (337*2π)/4151 weeks
3383.48308 -4.07633 (338*2π)/4151 weeks
3393.55598 -3.12008 (339*2π)/4151 weeks
3403.52483 -3.96252 (340*2π)/4151 weeks
3413.38511 -3.73074 (341*2π)/4151 weeks
3423.06004 -3.74079 (342*2π)/4151 weeks
3432.57655 -2.53861 (343*2π)/4151 weeks
344.79058 -3.58719 (344*2π)/4151 weeks
3451.27427 -5.62994 (345*2π)/4151 weeks
3462.11463 -5.59895 (346*2π)/4151 weeks
3471.40355 -5.88886 (347*2π)/4151 weeks
3481.33707 -6.72883 (348*2π)/4151 weeks
3492.65152 -6.89897 (349*2π)/4151 weeks
3501.81651 -8.10366 (350*2π)/4151 weeks
3514.07657 -9.39548 (351*2π)/4151 weeks
3526.27072 -7.68809 (352*2π)/4151 weeks
3534.62204 -5.66673 (353*2π)/4151 weeks
3543.87687 -7.7809 (354*2π)/4151 weeks
3556.54367 -8.9218 (355*2π)/4151 weeks
3569.50356 -6.29226 (356*2π)/4151 weeks
3578.58015 -1.36456 (357*2π)/4151 weeks
3582.94553 -1.15137 (358*2π)/4151 weeks
3591.75075 -3.69741 (359*2π)/4151 weeks
3602.47599 -6.53168 (360*2π)/4151 weeks
3614.24715 -5.5859 (361*2π)/4151 weeks
3624.49485 -4.59679 (362*2π)/4151 weeks
3632.58247 -1.92985 (363*2π)/4151 weeks
364-2.19675 -4.71018 (364*2π)/4151 weeks
365.96144 -10.27951 (365*2π)/4151 weeks
3663.04027 -7.85965 (366*2π)/4151 weeks
3673.67148 -7.26102 (367*2π)/4151 weeks
3681.23024 -6.10281 (368*2π)/4151 weeks
369.2288 -9.07005 (369*2π)/4151 weeks
3701.99655 -11.44278 (370*2π)/4151 weeks
3714.54399 -10.7644 (371*2π)/4151 weeks
3725.61002 -10.18291 (372*2π)/4151 weeks
3735.21625 -7.57467 (373*2π)/4151 weeks
3744.07779 -7.00618 (374*2π)/4151 weeks
3752.53715 -6.80279 (375*2π)/4151 weeks
376.72382 -9.89282 (376*2π)/4151 weeks
3771.83684 -11.31026 (377*2π)/4151 weeks
3782.1901 -11.12647 (378*2π)/4151 weeks
3794.23359 -13.43572 (379*2π)/4151 weeks
3803.97476 -9.99332 (380*2π)/4151 weeks
3811.62754 -9.64245 (381*2π)/4151 weeks
382-1.4305 -14.54932 (382*2π)/4151 weeks
3833.30316 -19.43854 (383*2π)/4151 weeks
3848.97666 -18.22283 (384*2π)/4151 weeks
3859.37697 -13.84043 (385*2π)/4151 weeks
3867.98527 -13.01393 (386*2π)/4151 weeks
3876.23035 -12.62517 (387*2π)/4151 weeks
3886.39425 -15.67127 (388*2π)/4151 weeks
3899.35372 -15.57076 (389*2π)/4151 weeks
3909.2114 -11.69834 (390*2π)/4151 weeks
3918.10687 -11.32157 (391*2π)/4151 weeks
3924.9018 -14.97057 (392*2π)/4151 weeks
3934.89004 -17.58173 (393*2π)/4151 weeks
3949.6977 -17.44916 (394*2π)/4151 weeks
39513.67853 -13.22219 (395*2π)/4151 weeks
3966.35177 -11.99243 (396*2π)/4151 weeks
3973.91193 -17.75319 (397*2π)/4151 weeks
3988.96011 -15.85786 (398*2π)/4151 weeks
3997.64792 -17.1618 (399*2π)/4151 weeks
4006.12061 -17.28317 (400*2π)/4151 weeks
4017.19367 -13.76545 (401*2π)/4151 weeks
402-2.25837 -12.67488 (402*2π)/4151 weeks
403-6.65784 -28.68045 (403*2π)/4151 weeks
4043.16428 -33.45387 (404*2π)/4151 weeks
4054.33443 -28.39382 (405*2π)/4151 weeks
406-2.55714 -27.96724 (406*2π)/4151 weeks
407-16.30268 -36.70139 (407*2π)/4151 weeks
408-14.87107 -66.27869 (408*2π)/4151 weeks
4095.91056 -83.33832 (409*2π)/4151 weeks
41018.16109 -81.8952 (410*2π)/4151 weeks
41126.93035 -97.18452 (411*2π)/4151 weeks
41238.11147 -119.6789 (412*2π)/4151 weeks
41357.2365 -162.4821 (413*2π)/4151 weeks



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