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Fourier Analysis of SPXU (ProShares UltraPro Short S&P500)


SPXU (ProShares UltraPro Short S&P500) appears to have interesting cyclic behaviour every 41 weeks (37.1309*sine), 37 weeks (37.0491*sine), and 29 weeks (19.1557*cosine).

SPXU (ProShares UltraPro Short S&P500) has an average price of 239.14 (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 6/25/2009 to 3/20/2017 for SPXU (ProShares UltraPro Short S&P500), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0239.1363   0 
1175.8345 221.4938 (1*2π)/405405 weeks
264.9178 140.4491 (2*2π)/405203 weeks
339.71034 107.374 (3*2π)/405135 weeks
422.73812 83.63652 (4*2π)/405101 weeks
515.03742 59.33894 (5*2π)/40581 weeks
628.301 38.25325 (6*2π)/40568 weeks
741.71251 50.40733 (7*2π)/40558 weeks
823.01093 61.68395 (8*2π)/40551 weeks
99.13043 47.8096 (9*2π)/40545 weeks
1012.09741 37.13089 (10*2π)/40541 weeks
1112.51991 37.04907 (11*2π)/40537 weeks
127.26195 29.79232 (12*2π)/40534 weeks
1317.42853 23.43148 (13*2π)/40531 weeks
1419.15568 30.35874 (14*2π)/40529 weeks
1516.34817 30.96977 (15*2π)/40527 weeks
1612.95375 32.15091 (16*2π)/40525 weeks
177.11376 29.17716 (17*2π)/40524 weeks
189.21791 26.96003 (18*2π)/40523 weeks
194.1127 26.61065 (19*2π)/40521 weeks
204.39274 16.53387 (20*2π)/40520 weeks
2110.97066 15.9736 (21*2π)/40519 weeks
2210.78729 18.09975 (22*2π)/40518 weeks
239.72169 16.91117 (23*2π)/40518 weeks
2413.30284 16.60945 (24*2π)/40517 weeks
2515.26356 20.71801 (25*2π)/40516 weeks
2611.01646 23.1204 (26*2π)/40516 weeks
279.22318 21.20752 (27*2π)/40515 weeks
287.70215 22.16926 (28*2π)/40514 weeks
294.77494 21.5249 (29*2π)/40514 weeks
30.79704 17.17869 (30*2π)/40514 weeks
315.04597 11.56063 (31*2π)/40513 weeks
329.29421 14.32261 (32*2π)/40513 weeks
336.10512 16.03923 (33*2π)/40512 weeks
346.13579 13.19106 (34*2π)/40512 weeks
359.32222 13.72262 (35*2π)/40512 weeks
367.06551 14.85748 (36*2π)/40511 weeks
376.90507 14.6256 (37*2π)/40511 weeks
386.38171 13.6389 (38*2π)/40511 weeks
398.2291 13.58951 (39*2π)/40510 weeks
407.83075 15.32299 (40*2π)/40510 weeks
415.69706 16.23399 (41*2π)/40510 weeks
423.26359 13.66499 (42*2π)/40510 weeks
434.18489 11.76102 (43*2π)/4059 weeks
446.35227 11.52429 (44*2π)/4059 weeks
455.77945 13.73305 (45*2π)/4059 weeks
463.33269 12.31542 (46*2π)/4059 weeks
475.28479 10.6931 (47*2π)/4059 weeks
485.70773 11.86636 (48*2π)/4058 weeks
493.13391 12.87516 (49*2π)/4058 weeks
503.80475 7.94495 (50*2π)/4058 weeks
518.00791 9.93151 (51*2π)/4058 weeks
526.35684 12.60209 (52*2π)/4058 weeks
534.8317 12.22546 (53*2π)/4058 weeks
545.77446 11.54218 (54*2π)/4058 weeks
554.79726 14.37702 (55*2π)/4057 weeks
56-.39364 14.45553 (56*2π)/4057 weeks
57-1.80821 7.53691 (57*2π)/4057 weeks
583.39836 5.30247 (58*2π)/4057 weeks
595.04907 8.05929 (59*2π)/4057 weeks
604.24615 7.80504 (60*2π)/4057 weeks
616.4882 7.78833 (61*2π)/4057 weeks
625.91588 11.11966 (62*2π)/4057 weeks
632.8321 10.48775 (63*2π)/4056 weeks
643.2346 8.57094 (64*2π)/4056 weeks
653.52575 8.31464 (65*2π)/4056 weeks
664.19954 8.53275 (66*2π)/4056 weeks
674.36714 9.10189 (67*2π)/4056 weeks
684.49128 9.52116 (68*2π)/4056 weeks
693.59413 11.13925 (69*2π)/4056 weeks
70.74512 10.19402 (70*2π)/4056 weeks
711.24206 7.91683 (71*2π)/4056 weeks
721.5416 7.72787 (72*2π)/4056 weeks
731.54669 7.11388 (73*2π)/4056 weeks
741.76162 6.35934 (74*2π)/4055 weeks
752.44098 6.63059 (75*2π)/4055 weeks
762.56902 6.96518 (76*2π)/4055 weeks
772.1705 6.49226 (77*2π)/4055 weeks
782.58034 7.02938 (78*2π)/4055 weeks
791.21317 6.19169 (79*2π)/4055 weeks
801.81222 4.9691 (80*2π)/4055 weeks
812.4886 5.04822 (81*2π)/4055 weeks
823.48349 4.92613 (82*2π)/4055 weeks
834.01917 6.01033 (83*2π)/4055 weeks
842.50549 6.72371 (84*2π)/4055 weeks
851.89904 5.27957 (85*2π)/4055 weeks
862.40941 4.42496 (86*2π)/4055 weeks
873.56601 4.80318 (87*2π)/4055 weeks
883.25021 5.29225 (88*2π)/4055 weeks
893.97609 4.79983 (89*2π)/4055 weeks
904.2177 5.22332 (90*2π)/4055 weeks
914.71416 6.14622 (91*2π)/4054 weeks
923.75957 6.62435 (92*2π)/4054 weeks
933.67138 7.37517 (93*2π)/4054 weeks
942.54526 8.23105 (94*2π)/4054 weeks
95.98429 7.63922 (95*2π)/4054 weeks
96-.03894 6.5652 (96*2π)/4054 weeks
97-.06389 5.16316 (97*2π)/4054 weeks
98.60513 3.7363 (98*2π)/4054 weeks
991.95778 4.00419 (99*2π)/4054 weeks
1001.59032 5.85396 (100*2π)/4054 weeks
101-.20981 5.30252 (101*2π)/4054 weeks
102-.13906 3.28866 (102*2π)/4054 weeks
103.76381 3.38038 (103*2π)/4054 weeks
104-.71833 3.07133 (104*2π)/4054 weeks
105-.02355 .49762 (105*2π)/4054 weeks
1062.40608 .39948 (106*2π)/4054 weeks
1073.3675 2.15719 (107*2π)/4054 weeks
1082.82689 2.432 (108*2π)/4054 weeks
1093.08601 2.23333 (109*2π)/4054 weeks
1102.85252 3.46181 (110*2π)/4054 weeks
1111.10631 2.80393 (111*2π)/4054 weeks
1121.97112 .62493 (112*2π)/4054 weeks
1133.69438 1.28649 (113*2π)/4054 weeks
1143.55809 1.7032 (114*2π)/4054 weeks
1154.26686 1.46421 (115*2π)/4054 weeks
1165.46362 2.24475 (116*2π)/4053 weeks
1174.843 4.85392 (117*2π)/4053 weeks
1182.33283 4.48709 (118*2π)/4053 weeks
1192.16651 3.16427 (119*2π)/4053 weeks
1202.42632 2.9656 (120*2π)/4053 weeks
1212.55705 2.06188 (121*2π)/4053 weeks
1223.49899 2.98479 (122*2π)/4053 weeks
1232.42956 3.26045 (123*2π)/4053 weeks
1242.26468 2.81197 (124*2π)/4053 weeks
1252.12256 2.6124 (125*2π)/4053 weeks
1262.23881 2.22825 (126*2π)/4053 weeks
1271.96766 2.39502 (127*2π)/4053 weeks
1282.27354 1.68352 (128*2π)/4053 weeks
1292.62156 1.94302 (129*2π)/4053 weeks
1302.31798 1.92222 (130*2π)/4053 weeks
1312.12396 1.47227 (131*2π)/4053 weeks
1322.74774 1.3675 (132*2π)/4053 weeks
1332.5874 1.7592 (133*2π)/4053 weeks
1342.40677 1.18142 (134*2π)/4053 weeks
1353.17232 1.36148 (135*2π)/4053 weeks
1362.49232 1.42647 (136*2π)/4053 weeks
1373.19428 .80907 (137*2π)/4053 weeks
1383.52368 2.13315 (138*2π)/4053 weeks
1392.35387 2.35882 (139*2π)/4053 weeks
1401.98368 1.29407 (140*2π)/4053 weeks
1412.42884 1.41375 (141*2π)/4053 weeks
1421.34317 1.7565 (142*2π)/4053 weeks
143.65843 -.51286 (143*2π)/4053 weeks
1443.3791 -1.76614 (144*2π)/4053 weeks
1454.0576 .34161 (145*2π)/4053 weeks
1463.08931 .31313 (146*2π)/4053 weeks
1473.69747 -.46319 (147*2π)/4053 weeks
1484.97831 1.1992 (148*2π)/4053 weeks
1492.31724 2.19291 (149*2π)/4053 weeks
1501.80224 -.75014 (150*2π)/4053 weeks
1514.21644 -1.05183 (151*2π)/4053 weeks
1524.80498 .12722 (152*2π)/4053 weeks
1534.13847 .69149 (153*2π)/4053 weeks
1544.37295 .51793 (154*2π)/4053 weeks
1554.59075 1.40301 (155*2π)/4053 weeks
1563.12671 1.88418 (156*2π)/4053 weeks
1572.09941 .53906 (157*2π)/4053 weeks
1583.47998 -.40418 (158*2π)/4053 weeks
1593.62262 .03405 (159*2π)/4053 weeks
1603.50342 -.40141 (160*2π)/4053 weeks
1614.28815 -.71719 (161*2π)/4053 weeks
1625.24686 -.20966 (162*2π)/4053 weeks
1635.62338 .91028 (163*2π)/4052 weeks
1644.46704 2.16493 (164*2π)/4052 weeks
1653.01589 1.40611 (165*2π)/4052 weeks
1663.56629 .32705 (166*2π)/4052 weeks
1673.62552 1.2505 (167*2π)/4052 weeks
1682.51329 .39382 (168*2π)/4052 weeks
1693.60171 -.84977 (169*2π)/4052 weeks
1704.62888 -.31267 (170*2π)/4052 weeks
1714.12206 .26922 (171*2π)/4052 weeks
1724.12005 -.08174 (172*2π)/4052 weeks
1734.63492 .0335 (173*2π)/4052 weeks
1744.66961 .57008 (174*2π)/4052 weeks
1753.86393 .74375 (175*2π)/4052 weeks
1764.13703 -.64113 (176*2π)/4052 weeks
1775.24476 .73097 (177*2π)/4052 weeks
1783.7521 .8525 (178*2π)/4052 weeks
1794.54771 -.32465 (179*2π)/4052 weeks
1805.36693 .7221 (180*2π)/4052 weeks
1814.40047 1.54363 (181*2π)/4052 weeks
1823.53511 .94413 (182*2π)/4052 weeks
1834.63034 .20065 (183*2π)/4052 weeks
1844.82776 1.15869 (184*2π)/4052 weeks
1854.06185 1.78605 (185*2π)/4052 weeks
1863.42863 1.57102 (186*2π)/4052 weeks
1872.90848 .94633 (187*2π)/4052 weeks
1882.77665 .93978 (188*2π)/4052 weeks
1892.3366 -.48704 (189*2π)/4052 weeks
1904.14047 -1.26043 (190*2π)/4052 weeks
1915.08619 .34215 (191*2π)/4052 weeks
1924.07405 1.18871 (192*2π)/4052 weeks
1933.26441 1.13155 (193*2π)/4052 weeks
1942.30559 .00002 (194*2π)/4052 weeks
1952.90742 -.79615 (195*2π)/4052 weeks
1963.23992 -1.2468 (196*2π)/4052 weeks
1974.78596 -1.83937 (197*2π)/4052 weeks
1986.02174 -.48031 (198*2π)/4052 weeks
1995.29258 1.03631 (199*2π)/4052 weeks
2004.02534 1.18804 (200*2π)/4052 weeks
2013.80405 1.30258 (201*2π)/4052 weeks
2022.46302 .99365 (202*2π)/4052 weeks
2032.46302 -.99365 (203*2π)/4052 weeks
2043.80405 -1.30258 (204*2π)/4052 weeks
2054.02534 -1.18804 (205*2π)/4052 weeks
2065.29258 -1.03631 (206*2π)/4052 weeks
2076.02174 .48031 (207*2π)/4052 weeks
2084.78596 1.83937 (208*2π)/4052 weeks
2093.23992 1.2468 (209*2π)/4052 weeks
2102.90742 .79615 (210*2π)/4052 weeks
2112.30559 -.00002 (211*2π)/4052 weeks
2123.26441 -1.13155 (212*2π)/4052 weeks
2134.07405 -1.18871 (213*2π)/4052 weeks
2145.08619 -.34215 (214*2π)/4052 weeks
2154.14047 1.26043 (215*2π)/4052 weeks
2162.3366 .48704 (216*2π)/4052 weeks
2172.77665 -.93978 (217*2π)/4052 weeks
2182.90848 -.94633 (218*2π)/4052 weeks
2193.42863 -1.57102 (219*2π)/4052 weeks
2204.06185 -1.78605 (220*2π)/4052 weeks
2214.82776 -1.15869 (221*2π)/4052 weeks
2224.63034 -.20065 (222*2π)/4052 weeks
2233.53511 -.94413 (223*2π)/4052 weeks
2244.40047 -1.54363 (224*2π)/4052 weeks
2255.36693 -.7221 (225*2π)/4052 weeks
2264.54771 .32465 (226*2π)/4052 weeks
2273.7521 -.8525 (227*2π)/4052 weeks
2285.24476 -.73097 (228*2π)/4052 weeks
2294.13703 .64113 (229*2π)/4052 weeks
2303.86393 -.74375 (230*2π)/4052 weeks
2314.66961 -.57008 (231*2π)/4052 weeks
2324.63492 -.0335 (232*2π)/4052 weeks
2334.12005 .08174 (233*2π)/4052 weeks
2344.12206 -.26922 (234*2π)/4052 weeks
2354.62888 .31267 (235*2π)/4052 weeks
2363.60171 .84977 (236*2π)/4052 weeks
2372.51329 -.39382 (237*2π)/4052 weeks
2383.62552 -1.2505 (238*2π)/4052 weeks
2393.56629 -.32705 (239*2π)/4052 weeks
2403.01589 -1.40611 (240*2π)/4052 weeks
2414.46704 -2.16493 (241*2π)/4052 weeks
2425.62338 -.91028 (242*2π)/4052 weeks
2435.24686 .20966 (243*2π)/4052 weeks
2444.28815 .71719 (244*2π)/4052 weeks
2453.50342 .40141 (245*2π)/4052 weeks
2463.62262 -.03405 (246*2π)/4052 weeks
2473.47998 .40418 (247*2π)/4052 weeks
2482.09941 -.53906 (248*2π)/4052 weeks
2493.12671 -1.88418 (249*2π)/4052 weeks
2504.59075 -1.40301 (250*2π)/4052 weeks
2514.37295 -.51793 (251*2π)/4052 weeks
2524.13847 -.69149 (252*2π)/4052 weeks
2534.80498 -.12722 (253*2π)/4052 weeks
2544.21644 1.05183 (254*2π)/4052 weeks
2551.80224 .75014 (255*2π)/4052 weeks
2562.31724 -2.19291 (256*2π)/4052 weeks
2574.97831 -1.1992 (257*2π)/4052 weeks
2583.69747 .46319 (258*2π)/4052 weeks
2593.08931 -.31313 (259*2π)/4052 weeks
2604.0576 -.34161 (260*2π)/4052 weeks
2613.3791 1.76614 (261*2π)/4052 weeks
262.65843 .51286 (262*2π)/4052 weeks
2631.34317 -1.7565 (263*2π)/4052 weeks
2642.42884 -1.41375 (264*2π)/4052 weeks
2651.98368 -1.29407 (265*2π)/4052 weeks
2662.35387 -2.35882 (266*2π)/4052 weeks
2673.52368 -2.13315 (267*2π)/4052 weeks
2683.19428 -.80907 (268*2π)/4052 weeks
2692.49232 -1.42647 (269*2π)/4052 weeks
2703.17232 -1.36148 (270*2π)/4052 weeks
2712.40677 -1.18142 (271*2π)/4051 weeks
2722.5874 -1.7592 (272*2π)/4051 weeks
2732.74774 -1.3675 (273*2π)/4051 weeks
2742.12396 -1.47227 (274*2π)/4051 weeks
2752.31798 -1.92222 (275*2π)/4051 weeks
2762.62156 -1.94302 (276*2π)/4051 weeks
2772.27354 -1.68352 (277*2π)/4051 weeks
2781.96766 -2.39502 (278*2π)/4051 weeks
2792.23881 -2.22825 (279*2π)/4051 weeks
2802.12256 -2.6124 (280*2π)/4051 weeks
2812.26468 -2.81197 (281*2π)/4051 weeks
2822.42956 -3.26045 (282*2π)/4051 weeks
2833.49899 -2.98479 (283*2π)/4051 weeks
2842.55705 -2.06188 (284*2π)/4051 weeks
2852.42632 -2.9656 (285*2π)/4051 weeks
2862.16651 -3.16427 (286*2π)/4051 weeks
2872.33283 -4.48709 (287*2π)/4051 weeks
2884.843 -4.85392 (288*2π)/4051 weeks
2895.46362 -2.24475 (289*2π)/4051 weeks
2904.26686 -1.46421 (290*2π)/4051 weeks
2913.55809 -1.7032 (291*2π)/4051 weeks
2923.69438 -1.28649 (292*2π)/4051 weeks
2931.97112 -.62493 (293*2π)/4051 weeks
2941.10631 -2.80393 (294*2π)/4051 weeks
2952.85252 -3.46181 (295*2π)/4051 weeks
2963.08601 -2.23333 (296*2π)/4051 weeks
2972.82689 -2.432 (297*2π)/4051 weeks
2983.3675 -2.15719 (298*2π)/4051 weeks
2992.40608 -.39948 (299*2π)/4051 weeks
300-.02355 -.49762 (300*2π)/4051 weeks
301-.71833 -3.07133 (301*2π)/4051 weeks
302.76381 -3.38038 (302*2π)/4051 weeks
303-.13906 -3.28866 (303*2π)/4051 weeks
304-.20981 -5.30252 (304*2π)/4051 weeks
3051.59032 -5.85396 (305*2π)/4051 weeks
3061.95778 -4.00419 (306*2π)/4051 weeks
307.60513 -3.7363 (307*2π)/4051 weeks
308-.06389 -5.16316 (308*2π)/4051 weeks
309-.03894 -6.5652 (309*2π)/4051 weeks
310.98429 -7.63922 (310*2π)/4051 weeks
3112.54526 -8.23105 (311*2π)/4051 weeks
3123.67138 -7.37517 (312*2π)/4051 weeks
3133.75957 -6.62435 (313*2π)/4051 weeks
3144.71416 -6.14622 (314*2π)/4051 weeks
3154.2177 -5.22332 (315*2π)/4051 weeks
3163.97609 -4.79983 (316*2π)/4051 weeks
3173.25021 -5.29225 (317*2π)/4051 weeks
3183.56601 -4.80318 (318*2π)/4051 weeks
3192.40941 -4.42496 (319*2π)/4051 weeks
3201.89904 -5.27957 (320*2π)/4051 weeks
3212.50549 -6.72371 (321*2π)/4051 weeks
3224.01917 -6.01033 (322*2π)/4051 weeks
3233.48349 -4.92613 (323*2π)/4051 weeks
3242.4886 -5.04822 (324*2π)/4051 weeks
3251.81222 -4.9691 (325*2π)/4051 weeks
3261.21317 -6.19169 (326*2π)/4051 weeks
3272.58034 -7.02938 (327*2π)/4051 weeks
3282.1705 -6.49226 (328*2π)/4051 weeks
3292.56902 -6.96518 (329*2π)/4051 weeks
3302.44098 -6.63059 (330*2π)/4051 weeks
3311.76162 -6.35934 (331*2π)/4051 weeks
3321.54669 -7.11388 (332*2π)/4051 weeks
3331.5416 -7.72787 (333*2π)/4051 weeks
3341.24206 -7.91683 (334*2π)/4051 weeks
335.74512 -10.19402 (335*2π)/4051 weeks
3363.59413 -11.13925 (336*2π)/4051 weeks
3374.49128 -9.52116 (337*2π)/4051 weeks
3384.36714 -9.10189 (338*2π)/4051 weeks
3394.19954 -8.53275 (339*2π)/4051 weeks
3403.52575 -8.31464 (340*2π)/4051 weeks
3413.2346 -8.57094 (341*2π)/4051 weeks
3422.8321 -10.48775 (342*2π)/4051 weeks
3435.91588 -11.11966 (343*2π)/4051 weeks
3446.4882 -7.78833 (344*2π)/4051 weeks
3454.24615 -7.80504 (345*2π)/4051 weeks
3465.04907 -8.05929 (346*2π)/4051 weeks
3473.39836 -5.30247 (347*2π)/4051 weeks
348-1.80821 -7.53691 (348*2π)/4051 weeks
349-.39364 -14.45553 (349*2π)/4051 weeks
3504.79726 -14.37702 (350*2π)/4051 weeks
3515.77446 -11.54218 (351*2π)/4051 weeks
3524.8317 -12.22546 (352*2π)/4051 weeks
3536.35684 -12.60209 (353*2π)/4051 weeks
3548.00791 -9.93151 (354*2π)/4051 weeks
3553.80475 -7.94495 (355*2π)/4051 weeks
3563.13391 -12.87516 (356*2π)/4051 weeks
3575.70773 -11.86636 (357*2π)/4051 weeks
3585.28479 -10.6931 (358*2π)/4051 weeks
3593.33269 -12.31542 (359*2π)/4051 weeks
3605.77945 -13.73305 (360*2π)/4051 weeks
3616.35227 -11.52429 (361*2π)/4051 weeks
3624.18489 -11.76102 (362*2π)/4051 weeks
3633.26359 -13.66499 (363*2π)/4051 weeks
3645.69706 -16.23399 (364*2π)/4051 weeks
3657.83075 -15.32299 (365*2π)/4051 weeks
3668.2291 -13.58951 (366*2π)/4051 weeks
3676.38171 -13.6389 (367*2π)/4051 weeks
3686.90507 -14.6256 (368*2π)/4051 weeks
3697.06551 -14.85748 (369*2π)/4051 weeks
3709.32222 -13.72262 (370*2π)/4051 weeks
3716.13579 -13.19106 (371*2π)/4051 weeks
3726.10512 -16.03923 (372*2π)/4051 weeks
3739.29421 -14.32261 (373*2π)/4051 weeks
3745.04597 -11.56063 (374*2π)/4051 weeks
375.79704 -17.17869 (375*2π)/4051 weeks
3764.77494 -21.5249 (376*2π)/4051 weeks
3777.70215 -22.16926 (377*2π)/4051 weeks
3789.22318 -21.20752 (378*2π)/4051 weeks
37911.01646 -23.1204 (379*2π)/4051 weeks
38015.26356 -20.71801 (380*2π)/4051 weeks
38113.30284 -16.60945 (381*2π)/4051 weeks
3829.72169 -16.91117 (382*2π)/4051 weeks
38310.78729 -18.09975 (383*2π)/4051 weeks
38410.97066 -15.9736 (384*2π)/4051 weeks
3854.39274 -16.53387 (385*2π)/4051 weeks
3864.1127 -26.61065 (386*2π)/4051 weeks
3879.21791 -26.96003 (387*2π)/4051 weeks
3887.11376 -29.17716 (388*2π)/4051 weeks
38912.95375 -32.15091 (389*2π)/4051 weeks
39016.34817 -30.96977 (390*2π)/4051 weeks
39119.15568 -30.35874 (391*2π)/4051 weeks
39217.42853 -23.43148 (392*2π)/4051 weeks
3937.26195 -29.79232 (393*2π)/4051 weeks
39412.51991 -37.04907 (394*2π)/4051 weeks
39512.09741 -37.13089 (395*2π)/4051 weeks
3969.13043 -47.8096 (396*2π)/4051 weeks
39723.01093 -61.68395 (397*2π)/4051 weeks
39841.71251 -50.40733 (398*2π)/4051 weeks
39928.301 -38.25325 (399*2π)/4051 weeks
40015.03742 -59.33894 (400*2π)/4051 weeks
40122.73812 -83.63652 (401*2π)/4051 weeks
40239.71034 -107.374 (402*2π)/4051 weeks
40364.9178 -140.4491 (403*2π)/4051 weeks

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