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Fourier Analysis of SPXU (PROSHARES ULTRAPRO SHORT S&P500 PROSHARES ULTRAPRO SHORT S&P500)


SPXU (PROSHARES ULTRAPRO SHORT S&P500 PROSHARES ULTRAPRO SHORT S&P500) appears to have interesting cyclic behaviour every 44 weeks (40.7212*sine), 37 weeks (34.1774*sine), and 40 weeks (33.9114*sine).

SPXU (PROSHARES ULTRAPRO SHORT S&P500 PROSHARES ULTRAPRO SHORT S&P500) has an average price of 222.26 (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 11/6/2017 for SPXU (PROSHARES ULTRAPRO SHORT S&P500 PROSHARES ULTRAPRO SHORT S&P500), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0222.257   0 
1179.0998 208.3315 (1*2π)/438438 weeks
264.27103 139.9822 (2*2π)/438219 weeks
341.83665 106.3693 (3*2π)/438146 weeks
425.98854 84.46764 (4*2π)/438110 weeks
516.05916 63.40806 (5*2π)/43888 weeks
617.09163 41.16734 (6*2π)/43873 weeks
734.8264 37.85023 (7*2π)/43863 weeks
834.5064 54.52171 (8*2π)/43855 weeks
915.31798 54.43547 (9*2π)/43849 weeks
108.44008 40.72117 (10*2π)/43844 weeks
1112.01808 33.91137 (11*2π)/43840 weeks
1211.10313 34.17739 (12*2π)/43837 weeks
136.72294 27.35945 (13*2π)/43834 weeks
1415.6356 21.50383 (14*2π)/43831 weeks
1518.26884 27.50663 (15*2π)/43829 weeks
1615.26503 28.43955 (16*2π)/43827 weeks
1712.94538 29.71859 (17*2π)/43826 weeks
188.35394 29.40288 (18*2π)/43824 weeks
198.07049 24.09466 (19*2π)/43823 weeks
206.85266 25.38237 (20*2π)/43822 weeks
211.32987 20.86733 (21*2π)/43821 weeks
226.27392 14.47605 (22*2π)/43820 weeks
2310.73871 16.13012 (23*2π)/43819 weeks
2410.09692 16.9224 (24*2π)/43818 weeks
259.30018 15.21351 (25*2π)/43818 weeks
2612.39581 15.47491 (26*2π)/43817 weeks
2714.20563 19.0456 (27*2π)/43816 weeks
2810.6844 21.45792 (28*2π)/43816 weeks
298.44643 19.81386 (29*2π)/43815 weeks
307.87653 20.47197 (30*2π)/43815 weeks
315.45381 20.18232 (31*2π)/43814 weeks
321.99154 18.52478 (32*2π)/43814 weeks
331.92726 12.2276 (33*2π)/43813 weeks
347.07669 11.02327 (34*2π)/43813 weeks
358.01728 14.7475 (35*2π)/43813 weeks
365.14074 13.96212 (36*2π)/43812 weeks
376.06389 11.79956 (37*2π)/43812 weeks
388.60495 13.353 (38*2π)/43812 weeks
396.53991 13.68879 (39*2π)/43811 weeks
406.42145 13.57279 (40*2π)/43811 weeks
415.93433 12.79145 (41*2π)/43811 weeks
427.46191 12.23342 (42*2π)/43810 weeks
437.45497 13.75283 (43*2π)/43810 weeks
445.97766 14.82794 (44*2π)/43810 weeks
453.22566 14.09652 (45*2π)/43810 weeks
463.49362 11.64522 (46*2π)/43810 weeks
474.69447 10.38567 (47*2π)/4389 weeks
486.23309 11.56422 (48*2π)/4389 weeks
494.55575 12.83854 (49*2π)/4389 weeks
503.18917 10.64334 (50*2π)/4389 weeks
515.11726 10.10456 (51*2π)/4389 weeks
525.28243 11.10201 (52*2π)/4388 weeks
532.86845 11.9136 (53*2π)/4388 weeks
543.19136 7.54979 (54*2π)/4388 weeks
557.21401 8.60918 (55*2π)/4388 weeks
566.38095 11.50862 (56*2π)/4388 weeks
574.80316 11.52713 (57*2π)/4388 weeks
584.60069 10.48564 (58*2π)/4388 weeks
595.42697 12.23883 (59*2π)/4387 weeks
602.59493 14.06777 (60*2π)/4387 weeks
61-2.12654 11.12083 (61*2π)/4387 weeks
62-.24981 5.52263 (62*2π)/4387 weeks
634.1108 5.47754 (63*2π)/4387 weeks
644.46461 7.71268 (64*2π)/4387 weeks
654.01566 7.11735 (65*2π)/4387 weeks
666.08002 7.30309 (66*2π)/4387 weeks
675.62726 10.20383 (67*2π)/4387 weeks
682.82642 9.99602 (68*2π)/4386 weeks
692.73414 8.08567 (69*2π)/4386 weeks
703.19541 7.97237 (70*2π)/4386 weeks
713.88783 7.79917 (71*2π)/4386 weeks
724.17545 8.11324 (72*2π)/4386 weeks
734.02752 8.44354 (73*2π)/4386 weeks
744.11147 9.31138 (74*2π)/4386 weeks
752.29231 10.46233 (75*2π)/4386 weeks
76.39778 8.66141 (76*2π)/4386 weeks
771.31491 7.32892 (77*2π)/4386 weeks
781.41691 7.1399 (78*2π)/4386 weeks
791.44854 6.5815 (79*2π)/4386 weeks
801.59417 5.92807 (80*2π)/4385 weeks
812.27336 6.15772 (81*2π)/4385 weeks
822.474 6.36023 (82*2π)/4385 weeks
831.96914 6.20553 (83*2π)/4385 weeks
842.49478 6.09403 (84*2π)/4385 weeks
851.35066 6.45669 (85*2π)/4385 weeks
861.31956 5.14023 (86*2π)/4385 weeks
872.26027 4.58642 (87*2π)/4385 weeks
882.51824 4.40553 (88*2π)/4385 weeks
893.40346 4.76262 (89*2π)/4385 weeks
903.57074 5.93631 (90*2π)/4385 weeks
912.11566 6.12308 (91*2π)/4385 weeks
921.8137 4.83015 (92*2π)/4385 weeks
932.22377 4.11764 (93*2π)/4385 weeks
943.29305 4.40962 (94*2π)/4385 weeks
953.1713 4.94852 (95*2π)/4385 weeks
963.43958 4.28572 (96*2π)/4385 weeks
973.77785 4.791 (97*2π)/4385 weeks
984.24604 5.20016 (98*2π)/4384 weeks
993.82395 6.32624 (99*2π)/4384 weeks
1003.6945 6.30461 (100*2π)/4384 weeks
1013.16846 7.06229 (101*2π)/4384 weeks
1021.74271 7.54911 (102*2π)/4384 weeks
103.64861 6.89542 (103*2π)/4384 weeks
104-.13709 5.84619 (104*2π)/4384 weeks
105-.05254 4.71185 (105*2π)/4384 weeks
106.58902 3.45236 (106*2π)/4384 weeks
1071.72663 3.6682 (107*2π)/4384 weeks
1081.76242 5.29716 (108*2π)/4384 weeks
109.13644 5.13379 (109*2π)/4384 weeks
110-.50217 3.42803 (110*2π)/4384 weeks
111.4806 2.93865 (111*2π)/4384 weeks
112.06249 3.56489 (112*2π)/4384 weeks
113-.70817 1.72908 (113*2π)/4384 weeks
1141.14041 .12925 (114*2π)/4384 weeks
1152.89956 .67157 (115*2π)/4384 weeks
1162.86788 2.17208 (116*2π)/4384 weeks
1172.5632 2.24546 (117*2π)/4384 weeks
1182.96252 2.13612 (118*2π)/4384 weeks
1192.59571 3.22634 (119*2π)/4384 weeks
1201.07694 2.6811 (120*2π)/4384 weeks
1211.59292 .70894 (121*2π)/4384 weeks
1223.33221 .93562 (122*2π)/4384 weeks
1233.32617 1.58061 (123*2π)/4384 weeks
1243.57181 1.29989 (124*2π)/4384 weeks
1254.46693 1.62244 (125*2π)/4384 weeks
1265.26758 3.35743 (126*2π)/4383 weeks
1273.30483 4.82296 (127*2π)/4383 weeks
1281.9395 3.62762 (128*2π)/4383 weeks
1292.13288 2.78666 (129*2π)/4383 weeks
1302.15731 2.72262 (130*2π)/4383 weeks
1312.58317 1.87606 (131*2π)/4383 weeks
1323.22435 2.84308 (132*2π)/4383 weeks
1332.27234 3.03429 (133*2π)/4383 weeks
1342.1062 2.63083 (134*2π)/4383 weeks
1352.00657 2.47882 (135*2π)/4383 weeks
1361.99295 2.13186 (136*2π)/4383 weeks
1372.10212 2.29576 (137*2π)/4383 weeks
1381.85695 1.66092 (138*2π)/4383 weeks
1392.34585 1.60307 (139*2π)/4383 weeks
1402.25947 1.89885 (140*2π)/4383 weeks
1412.07622 1.74849 (141*2π)/4383 weeks
1422.15397 1.19025 (142*2π)/4383 weeks
1432.60975 1.35478 (143*2π)/4383 weeks
1442.31319 1.59932 (144*2π)/4383 weeks
1452.269 1.04678 (145*2π)/4383 weeks
1462.93772 1.26199 (146*2π)/4383 weeks
1472.32389 1.38704 (147*2π)/4383 weeks
1482.75972 .75537 (148*2π)/4383 weeks
1493.4542 1.70558 (149*2π)/4383 weeks
1502.52186 2.24108 (150*2π)/4383 weeks
1511.70318 1.59212 (151*2π)/4383 weeks
1522.17818 1.14228 (152*2π)/4383 weeks
1532.05569 1.61792 (153*2π)/4383 weeks
154.65051 1.01486 (154*2π)/4383 weeks
1551.11384 -1.22798 (155*2π)/4383 weeks
1563.71958 -1.15721 (156*2π)/4383 weeks
1573.59525 .48362 (157*2π)/4383 weeks
1582.86011 .20959 (158*2π)/4383 weeks
1593.46013 -.43206 (159*2π)/4383 weeks
1604.64928 .96713 (160*2π)/4383 weeks
1612.54602 2.19923 (161*2π)/4383 weeks
1621.39446 -.16703 (162*2π)/4383 weeks
1633.41363 -1.28719 (163*2π)/4383 weeks
1644.32919 -.27772 (164*2π)/4383 weeks
1654.13125 .67354 (165*2π)/4383 weeks
1663.81757 .47385 (166*2π)/4383 weeks
1674.22495 .70816 (167*2π)/4383 weeks
1683.93054 1.72115 (168*2π)/4383 weeks
1692.58594 1.56324 (169*2π)/4383 weeks
1702.03852 .10201 (170*2π)/4383 weeks
1713.32529 -.28198 (171*2π)/4383 weeks
1723.3589 .03904 (172*2π)/4383 weeks
1733.23625 -.3425 (173*2π)/4383 weeks
1743.88665 -.64974 (174*2π)/4383 weeks
1754.74883 -.35339 (175*2π)/4383 weeks
1765.16037 .49177 (176*2π)/4382 weeks
1774.67393 1.80208 (177*2π)/4382 weeks
1783.20094 1.82501 (178*2π)/4382 weeks
1792.85633 .62329 (179*2π)/4382 weeks
1803.72642 .57943 (180*2π)/4382 weeks
1812.87654 1.08428 (181*2π)/4382 weeks
1822.35917 -.15544 (182*2π)/4382 weeks
1833.58176 -.72818 (183*2π)/4382 weeks
1844.33476 -.1088 (184*2π)/4382 weeks
1853.80954 .22868 (185*2π)/4382 weeks
1863.81735 -.07248 (186*2π)/4382 weeks
1874.26826 -.01023 (187*2π)/4382 weeks
1884.35198 .43073 (188*2π)/4382 weeks
1893.80183 .78563 (189*2π)/4382 weeks
1903.36472 -.17899 (190*2π)/4382 weeks
1914.9208 -.03952 (191*2π)/4382 weeks
1924.14905 1.14382 (192*2π)/4382 weeks
1933.49126 .04815 (193*2π)/4382 weeks
1944.70645 -.06768 (194*2π)/4382 weeks
1954.86229 1.06119 (195*2π)/4382 weeks
1963.87026 1.35155 (196*2π)/4382 weeks
1973.24297 .62791 (197*2π)/4382 weeks
1984.36752 .26712 (198*2π)/4382 weeks
1994.47061 1.07806 (199*2π)/4382 weeks
2003.82974 1.65468 (200*2π)/4382 weeks
2013.25167 1.46916 (201*2π)/4382 weeks
2022.69875 1.06912 (202*2π)/4382 weeks
2032.83019 .84418 (203*2π)/4382 weeks
2042.07942 .17344 (204*2π)/4382 weeks
2052.94894 -1.18339 (205*2π)/4382 weeks
2064.54298 -.61718 (206*2π)/4382 weeks
2074.35526 .8361 (207*2π)/4382 weeks
2083.46265 1.10903 (208*2π)/4382 weeks
2092.73003 1.04693 (209*2π)/4382 weeks
2102.25671 -.22992 (210*2π)/4382 weeks
2112.75607 -.78328 (211*2π)/4382 weeks
2123.01451 -1.17905 (212*2π)/4382 weeks
2134.35294 -1.73201 (213*2π)/4382 weeks
2145.49433 -.67697 (214*2π)/4382 weeks
2155.06787 .82764 (215*2π)/4382 weeks
2164.01223 1.32154 (216*2π)/4382 weeks
2173.7713 1.02209 (217*2π)/4382 weeks
2182.8959 1.22299 (218*2π)/4382 weeks
2191.89707   (219*2π)/4382 weeks
2202.8959 -1.22299 (220*2π)/4382 weeks
2213.7713 -1.02209 (221*2π)/4382 weeks
2224.01223 -1.32154 (222*2π)/4382 weeks
2235.06787 -.82764 (223*2π)/4382 weeks
2245.49433 .67697 (224*2π)/4382 weeks
2254.35294 1.73201 (225*2π)/4382 weeks
2263.01451 1.17905 (226*2π)/4382 weeks
2272.75607 .78328 (227*2π)/4382 weeks
2282.25671 .22992 (228*2π)/4382 weeks
2292.73003 -1.04693 (229*2π)/4382 weeks
2303.46265 -1.10903 (230*2π)/4382 weeks
2314.35526 -.8361 (231*2π)/4382 weeks
2324.54298 .61718 (232*2π)/4382 weeks
2332.94894 1.18339 (233*2π)/4382 weeks
2342.07942 -.17344 (234*2π)/4382 weeks
2352.83019 -.84418 (235*2π)/4382 weeks
2362.69875 -1.06912 (236*2π)/4382 weeks
2373.25167 -1.46916 (237*2π)/4382 weeks
2383.82974 -1.65468 (238*2π)/4382 weeks
2394.47061 -1.07806 (239*2π)/4382 weeks
2404.36752 -.26712 (240*2π)/4382 weeks
2413.24297 -.62791 (241*2π)/4382 weeks
2423.87026 -1.35155 (242*2π)/4382 weeks
2434.86229 -1.06119 (243*2π)/4382 weeks
2444.70645 .06768 (244*2π)/4382 weeks
2453.49126 -.04815 (245*2π)/4382 weeks
2464.14905 -1.14382 (246*2π)/4382 weeks
2474.9208 .03952 (247*2π)/4382 weeks
2483.36472 .17899 (248*2π)/4382 weeks
2493.80183 -.78563 (249*2π)/4382 weeks
2504.35198 -.43073 (250*2π)/4382 weeks
2514.26826 .01023 (251*2π)/4382 weeks
2523.81735 .07248 (252*2π)/4382 weeks
2533.80954 -.22868 (253*2π)/4382 weeks
2544.33476 .1088 (254*2π)/4382 weeks
2553.58176 .72818 (255*2π)/4382 weeks
2562.35917 .15544 (256*2π)/4382 weeks
2572.87654 -1.08428 (257*2π)/4382 weeks
2583.72642 -.57943 (258*2π)/4382 weeks
2592.85633 -.62329 (259*2π)/4382 weeks
2603.20094 -1.82501 (260*2π)/4382 weeks
2614.67393 -1.80208 (261*2π)/4382 weeks
2625.16037 -.49177 (262*2π)/4382 weeks
2634.74883 .35339 (263*2π)/4382 weeks
2643.88665 .64974 (264*2π)/4382 weeks
2653.23625 .3425 (265*2π)/4382 weeks
2663.3589 -.03904 (266*2π)/4382 weeks
2673.32529 .28198 (267*2π)/4382 weeks
2682.03852 -.10201 (268*2π)/4382 weeks
2692.58594 -1.56324 (269*2π)/4382 weeks
2703.93054 -1.72115 (270*2π)/4382 weeks
2714.22495 -.70816 (271*2π)/4382 weeks
2723.81757 -.47385 (272*2π)/4382 weeks
2734.13125 -.67354 (273*2π)/4382 weeks
2744.32919 .27772 (274*2π)/4382 weeks
2753.41363 1.28719 (275*2π)/4382 weeks
2761.39446 .16703 (276*2π)/4382 weeks
2772.54602 -2.19923 (277*2π)/4382 weeks
2784.64928 -.96713 (278*2π)/4382 weeks
2793.46013 .43206 (279*2π)/4382 weeks
2802.86011 -.20959 (280*2π)/4382 weeks
2813.59525 -.48362 (281*2π)/4382 weeks
2823.71958 1.15721 (282*2π)/4382 weeks
2831.11384 1.22798 (283*2π)/4382 weeks
284.65051 -1.01486 (284*2π)/4382 weeks
2852.05569 -1.61792 (285*2π)/4382 weeks
2862.17818 -1.14228 (286*2π)/4382 weeks
2871.70318 -1.59212 (287*2π)/4382 weeks
2882.52186 -2.24108 (288*2π)/4382 weeks
2893.4542 -1.70558 (289*2π)/4382 weeks
2902.75972 -.75537 (290*2π)/4382 weeks
2912.32389 -1.38704 (291*2π)/4382 weeks
2922.93772 -1.26199 (292*2π)/4382 weeks
2932.269 -1.04678 (293*2π)/4381 weeks
2942.31319 -1.59932 (294*2π)/4381 weeks
2952.60975 -1.35478 (295*2π)/4381 weeks
2962.15397 -1.19025 (296*2π)/4381 weeks
2972.07622 -1.74849 (297*2π)/4381 weeks
2982.25947 -1.89885 (298*2π)/4381 weeks
2992.34585 -1.60307 (299*2π)/4381 weeks
3001.85695 -1.66092 (300*2π)/4381 weeks
3012.10212 -2.29576 (301*2π)/4381 weeks
3021.99295 -2.13186 (302*2π)/4381 weeks
3032.00657 -2.47882 (303*2π)/4381 weeks
3042.1062 -2.63083 (304*2π)/4381 weeks
3052.27234 -3.03429 (305*2π)/4381 weeks
3063.22435 -2.84308 (306*2π)/4381 weeks
3072.58317 -1.87606 (307*2π)/4381 weeks
3082.15731 -2.72262 (308*2π)/4381 weeks
3092.13288 -2.78666 (309*2π)/4381 weeks
3101.9395 -3.62762 (310*2π)/4381 weeks
3113.30483 -4.82296 (311*2π)/4381 weeks
3125.26758 -3.35743 (312*2π)/4381 weeks
3134.46693 -1.62244 (313*2π)/4381 weeks
3143.57181 -1.29989 (314*2π)/4381 weeks
3153.32617 -1.58061 (315*2π)/4381 weeks
3163.33221 -.93562 (316*2π)/4381 weeks
3171.59292 -.70894 (317*2π)/4381 weeks
3181.07694 -2.6811 (318*2π)/4381 weeks
3192.59571 -3.22634 (319*2π)/4381 weeks
3202.96252 -2.13612 (320*2π)/4381 weeks
3212.5632 -2.24546 (321*2π)/4381 weeks
3222.86788 -2.17208 (322*2π)/4381 weeks
3232.89956 -.67157 (323*2π)/4381 weeks
3241.14041 -.12925 (324*2π)/4381 weeks
325-.70817 -1.72908 (325*2π)/4381 weeks
326.06249 -3.56489 (326*2π)/4381 weeks
327.4806 -2.93865 (327*2π)/4381 weeks
328-.50217 -3.42803 (328*2π)/4381 weeks
329.13644 -5.13379 (329*2π)/4381 weeks
3301.76242 -5.29716 (330*2π)/4381 weeks
3311.72663 -3.6682 (331*2π)/4381 weeks
332.58902 -3.45236 (332*2π)/4381 weeks
333-.05254 -4.71185 (333*2π)/4381 weeks
334-.13709 -5.84619 (334*2π)/4381 weeks
335.64861 -6.89542 (335*2π)/4381 weeks
3361.74271 -7.54911 (336*2π)/4381 weeks
3373.16846 -7.06229 (337*2π)/4381 weeks
3383.6945 -6.30461 (338*2π)/4381 weeks
3393.82395 -6.32624 (339*2π)/4381 weeks
3404.24604 -5.20016 (340*2π)/4381 weeks
3413.77785 -4.791 (341*2π)/4381 weeks
3423.43958 -4.28572 (342*2π)/4381 weeks
3433.1713 -4.94852 (343*2π)/4381 weeks
3443.29305 -4.40962 (344*2π)/4381 weeks
3452.22377 -4.11764 (345*2π)/4381 weeks
3461.8137 -4.83015 (346*2π)/4381 weeks
3472.11566 -6.12308 (347*2π)/4381 weeks
3483.57074 -5.93631 (348*2π)/4381 weeks
3493.40346 -4.76262 (349*2π)/4381 weeks
3502.51824 -4.40553 (350*2π)/4381 weeks
3512.26027 -4.58642 (351*2π)/4381 weeks
3521.31956 -5.14023 (352*2π)/4381 weeks
3531.35066 -6.45669 (353*2π)/4381 weeks
3542.49478 -6.09403 (354*2π)/4381 weeks
3551.96914 -6.20553 (355*2π)/4381 weeks
3562.474 -6.36023 (356*2π)/4381 weeks
3572.27336 -6.15772 (357*2π)/4381 weeks
3581.59417 -5.92807 (358*2π)/4381 weeks
3591.44854 -6.5815 (359*2π)/4381 weeks
3601.41691 -7.1399 (360*2π)/4381 weeks
3611.31491 -7.32892 (361*2π)/4381 weeks
362.39778 -8.66141 (362*2π)/4381 weeks
3632.29231 -10.46233 (363*2π)/4381 weeks
3644.11147 -9.31138 (364*2π)/4381 weeks
3654.02752 -8.44354 (365*2π)/4381 weeks
3664.17545 -8.11324 (366*2π)/4381 weeks
3673.88783 -7.79917 (367*2π)/4381 weeks
3683.19541 -7.97237 (368*2π)/4381 weeks
3692.73414 -8.08567 (369*2π)/4381 weeks
3702.82642 -9.99602 (370*2π)/4381 weeks
3715.62726 -10.20383 (371*2π)/4381 weeks
3726.08002 -7.30309 (372*2π)/4381 weeks
3734.01566 -7.11735 (373*2π)/4381 weeks
3744.46461 -7.71268 (374*2π)/4381 weeks
3754.1108 -5.47754 (375*2π)/4381 weeks
376-.24981 -5.52263 (376*2π)/4381 weeks
377-2.12654 -11.12083 (377*2π)/4381 weeks
3782.59493 -14.06777 (378*2π)/4381 weeks
3795.42697 -12.23883 (379*2π)/4381 weeks
3804.60069 -10.48564 (380*2π)/4381 weeks
3814.80316 -11.52713 (381*2π)/4381 weeks
3826.38095 -11.50862 (382*2π)/4381 weeks
3837.21401 -8.60918 (383*2π)/4381 weeks
3843.19136 -7.54979 (384*2π)/4381 weeks
3852.86845 -11.9136 (385*2π)/4381 weeks
3865.28243 -11.10201 (386*2π)/4381 weeks
3875.11726 -10.10456 (387*2π)/4381 weeks
3883.18917 -10.64334 (388*2π)/4381 weeks
3894.55575 -12.83854 (389*2π)/4381 weeks
3906.23309 -11.56422 (390*2π)/4381 weeks
3914.69447 -10.38567 (391*2π)/4381 weeks
3923.49362 -11.64522 (392*2π)/4381 weeks
3933.22566 -14.09652 (393*2π)/4381 weeks
3945.97766 -14.82794 (394*2π)/4381 weeks
3957.45497 -13.75283 (395*2π)/4381 weeks
3967.46191 -12.23342 (396*2π)/4381 weeks
3975.93433 -12.79145 (397*2π)/4381 weeks
3986.42145 -13.57279 (398*2π)/4381 weeks
3996.53991 -13.68879 (399*2π)/4381 weeks
4008.60495 -13.353 (400*2π)/4381 weeks
4016.06389 -11.79956 (401*2π)/4381 weeks
4025.14074 -13.96212 (402*2π)/4381 weeks
4038.01728 -14.7475 (403*2π)/4381 weeks
4047.07669 -11.02327 (404*2π)/4381 weeks
4051.92726 -12.2276 (405*2π)/4381 weeks
4061.99154 -18.52478 (406*2π)/4381 weeks
4075.45381 -20.18232 (407*2π)/4381 weeks
4087.87653 -20.47197 (408*2π)/4381 weeks
4098.44643 -19.81386 (409*2π)/4381 weeks
41010.6844 -21.45792 (410*2π)/4381 weeks
41114.20563 -19.0456 (411*2π)/4381 weeks
41212.39581 -15.47491 (412*2π)/4381 weeks
4139.30018 -15.21351 (413*2π)/4381 weeks
41410.09692 -16.9224 (414*2π)/4381 weeks
41510.73871 -16.13012 (415*2π)/4381 weeks
4166.27392 -14.47605 (416*2π)/4381 weeks
4171.32987 -20.86733 (417*2π)/4381 weeks
4186.85266 -25.38237 (418*2π)/4381 weeks
4198.07049 -24.09466 (419*2π)/4381 weeks
4208.35394 -29.40288 (420*2π)/4381 weeks
42112.94538 -29.71859 (421*2π)/4381 weeks
42215.26503 -28.43955 (422*2π)/4381 weeks
42318.26884 -27.50663 (423*2π)/4381 weeks
42415.6356 -21.50383 (424*2π)/4381 weeks
4256.72294 -27.35945 (425*2π)/4381 weeks
42611.10313 -34.17739 (426*2π)/4381 weeks
42712.01808 -33.91137 (427*2π)/4381 weeks
4288.44008 -40.72117 (428*2π)/4381 weeks
42915.31798 -54.43547 (429*2π)/4381 weeks
43034.5064 -54.52171 (430*2π)/4381 weeks
43134.8264 -37.85023 (431*2π)/4381 weeks
43217.09163 -41.16734 (432*2π)/4381 weeks
43316.05916 -63.40806 (433*2π)/4381 weeks
43425.98854 -84.46764 (434*2π)/4381 weeks
43541.83665 -106.3693 (435*2π)/4381 weeks
43664.27103 -139.9822 (436*2π)/4381 weeks



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