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Fourier Analysis of DUG (ProShares UltraShort Oil & Gas)

DUG (ProShares UltraShort Oil & Gas) appears to have interesting cyclic behaviour every 40 weeks (30.9704*sine), 43 weeks (30.1036*sine), and 46 weeks (27.2986*sine).

DUG (ProShares UltraShort Oil & Gas) has an average price of 207.07 (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.

Fourier Analysis

Using data from 2/1/2007 to 6/18/2018 for DUG (ProShares UltraShort Oil & Gas), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0207.0739   0
1158.8645 180.2935 (1*2π)/595595 weeks
231.98493 131.9559 (2*2π)/595298 weeks
33.51271 81.13842 (3*2π)/595198 weeks
416.01112 49.84689 (4*2π)/595149 weeks
519.5776 33.35262 (5*2π)/595119 weeks
630.36123 36.00411 (6*2π)/59599 weeks
723.69557 55.80214 (7*2π)/59585 weeks
8-.21356 51.37973 (8*2π)/59574 weeks
9-2.5275 29.18895 (9*2π)/59566 weeks
108.09786 22.88917 (10*2π)/59560 weeks
115.10943 20.41096 (11*2π)/59554 weeks
1214.65597 16.72199 (12*2π)/59550 weeks
1320.49105 27.29855 (13*2π)/59546 weeks
1410.68972 30.10357 (14*2π)/59543 weeks
155.19767 30.97042 (15*2π)/59540 weeks
16-2.63892 26.82002 (16*2π)/59537 weeks
17-4.941 18.34939 (17*2π)/59535 weeks
18-3.75422 12.50751 (18*2π)/59533 weeks
196.83831 6.34325 (19*2π)/59531 weeks
2012.57226 12.01922 (20*2π)/59530 weeks
2112.27751 16.07105 (21*2π)/59528 weeks
229.12404 23.40857 (22*2π)/59527 weeks
233.24556 24.75239 (23*2π)/59526 weeks
24-2.92306 20.25082 (24*2π)/59525 weeks
25-3.45136 10.35574 (25*2π)/59524 weeks
263.64139 9.50603 (26*2π)/59523 weeks
278.30336 14.61059 (27*2π)/59522 weeks
284.05258 20.82648 (28*2π)/59521 weeks
29-3.57033 16.28224 (29*2π)/59521 weeks
30-5.76082 11.67727 (30*2π)/59520 weeks
31-2.57629 5.86175 (31*2π)/59519 weeks
325.34235 6.46097 (32*2π)/59519 weeks
336.6031 11.38567 (33*2π)/59518 weeks
343.65519 14.49496 (34*2π)/59518 weeks
35-2.16518 15.66488 (35*2π)/59517 weeks
36-5.42448 8.95993 (36*2π)/59517 weeks
37-.57878 4.49889 (37*2π)/59516 weeks
381.6141 5.37798 (38*2π)/59516 weeks
393.31616 5.85441 (39*2π)/59515 weeks
404.03941 7.84228 (40*2π)/59515 weeks
413.692 8.93304 (41*2π)/59515 weeks
422.34381 9.48589 (42*2π)/59514 weeks
43-.0798 8.05745 (43*2π)/59514 weeks
441.18946 5.57349 (44*2π)/59514 weeks
452.87014 6.64096 (45*2π)/59513 weeks
463.34608 5.98417 (46*2π)/59513 weeks
475.52912 8.53701 (47*2π)/59513 weeks
483.47816 12.73599 (48*2π)/59512 weeks
49-.77965 13.16545 (49*2π)/59512 weeks
50-5.19835 10.1317 (50*2π)/59512 weeks
51-5.63495 4.93784 (51*2π)/59512 weeks
52-1.74925 2.53114 (52*2π)/59511 weeks
531.16818 2.12209 (53*2π)/59511 weeks
542.79792 4.56529 (54*2π)/59511 weeks
552.58963 6.94309 (55*2π)/59511 weeks
56-.30697 7.58583 (56*2π)/59511 weeks
57-2.57704 4.87886 (57*2π)/59510 weeks
58-1.81331 1.11646 (58*2π)/59510 weeks
592.87549 -.86378 (59*2π)/59510 weeks
607.28186 2.58188 (60*2π)/59510 weeks
617.23663 9.14823 (61*2π)/59510 weeks
621.23547 11.95214 (62*2π)/59510 weeks
63-4.37524 8.43502 (63*2π)/5959 weeks
64-4.68313 3.12716 (64*2π)/5959 weeks
65-1.3163 -.82235 (65*2π)/5959 weeks
663.95325 .49769 (66*2π)/5959 weeks
674.14418 3.66852 (67*2π)/5959 weeks
683.4374 4.75613 (68*2π)/5959 weeks
692.06804 6.05328 (69*2π)/5959 weeks
701.34095 5.42638 (70*2π)/5959 weeks
71.73494 4.5584 (71*2π)/5958 weeks
72.04181 4.1368 (72*2π)/5958 weeks
731.48602 3.9571 (73*2π)/5958 weeks
74.00624 4.58613 (74*2π)/5958 weeks
75.91011 3.45283 (75*2π)/5958 weeks
76.77693 5.91925 (76*2π)/5958 weeks
77-2.16626 5.09475 (77*2π)/5958 weeks
78-3.20256 .99399 (78*2π)/5958 weeks
79-.44067 -1.80582 (79*2π)/5958 weeks
804.49492 -1.19028 (80*2π)/5957 weeks
815.25786 3.293 (81*2π)/5957 weeks
823.04364 4.72324 (82*2π)/5957 weeks
832.6075 5.27166 (83*2π)/5957 weeks
84-1.29363 4.84791 (84*2π)/5957 weeks
85-1.53926 .48557 (85*2π)/5957 weeks
862.63169 -.2851 (86*2π)/5957 weeks
874.1021 1.15748 (87*2π)/5957 weeks
884.41295 3.64026 (88*2π)/5957 weeks
891.93586 5.35032 (89*2π)/5957 weeks
90.75661 3.6984 (90*2π)/5957 weeks
91-.26164 2.5355 (91*2π)/5957 weeks
92.94644 -.48569 (92*2π)/5956 weeks
935.1887 .13349 (93*2π)/5956 weeks
945.78356 3.93637 (94*2π)/5956 weeks
953.21937 6.80078 (95*2π)/5956 weeks
96-.02122 6.16137 (96*2π)/5956 weeks
97-1.73522 2.88294 (97*2π)/5956 weeks
98.01963 .18737 (98*2π)/5956 weeks
992.35828 .33459 (99*2π)/5956 weeks
1003.377 1.93539 (100*2π)/5956 weeks
1012.5398 3.50987 (101*2π)/5956 weeks
1022.20715 2.98838 (102*2π)/5956 weeks
1032.61706 3.89892 (103*2π)/5956 weeks
104-.10035 4.19364 (104*2π)/5956 weeks
105-1.51241 2.26465 (105*2π)/5956 weeks
106.02286 -.4994 (106*2π)/5956 weeks
1073.25401 -.85039 (107*2π)/5956 weeks
1084.95786 1.17352 (108*2π)/5956 weeks
1094.12393 3.70832 (109*2π)/5955 weeks
1101.71515 5.11811 (110*2π)/5955 weeks
111-.8299 3.63141 (111*2π)/5955 weeks
112-.17584 .00123 (112*2π)/5955 weeks
1132.52979 -1.09599 (113*2π)/5955 weeks
1144.9497 .54048 (114*2π)/5955 weeks
1155.16596 3.71129 (115*2π)/5955 weeks
1163.51556 5.28678 (116*2π)/5955 weeks
117.7154 4.87666 (117*2π)/5955 weeks
118-.67518 2.08894 (118*2π)/5955 weeks
1191.17647 .28726 (119*2π)/5955 weeks
1203.6633 .90059 (120*2π)/5955 weeks
1214.19917 2.8112 (121*2π)/5955 weeks
1223.4218 4.42413 (122*2π)/5955 weeks
1231.22203 5.86015 (123*2π)/5955 weeks
124-1.78131 4.15765 (124*2π)/5955 weeks
125-1.4523 1.13466 (125*2π)/5955 weeks
126.23235 -.83711 (126*2π)/5955 weeks
1272.82831 -.81828 (127*2π)/5955 weeks
1284.45363 1.53423 (128*2π)/5955 weeks
1293.1187 3.89431 (129*2π)/5955 weeks
130.99968 3.66807 (130*2π)/5955 weeks
131-.41134 2.14007 (131*2π)/5955 weeks
132.35084 -.11122 (132*2π)/5955 weeks
1332.68401 -.52791 (133*2π)/5954 weeks
1344.01028 1.22915 (134*2π)/5954 weeks
1353.90945 2.56025 (135*2π)/5954 weeks
1362.63952 3.15183 (136*2π)/5954 weeks
1371.76085 3.3838 (137*2π)/5954 weeks
138.74668 2.9849 (138*2π)/5954 weeks
139.35169 1.09879 (139*2π)/5954 weeks
1402.20364 -.19019 (140*2π)/5954 weeks
1414.19566 1.25738 (141*2π)/5954 weeks
1423.35284 3.33794 (142*2π)/5954 weeks
1432.24298 3.64534 (143*2π)/5954 weeks
1442.13253 3.36639 (144*2π)/5954 weeks
1451.02989 3.44607 (145*2π)/5954 weeks
146-.16388 2.10424 (146*2π)/5954 weeks
1471.19222 1.41222 (147*2π)/5954 weeks
1481.97098 1.41442 (148*2π)/5954 weeks
1492.93164 1.79447 (149*2π)/5954 weeks
1502.14511 3.91863 (150*2π)/5954 weeks
151-.41967 3.80168 (151*2π)/5954 weeks
152-1.28775 1.72775 (152*2π)/5954 weeks
153-.23318 -.63609 (153*2π)/5954 weeks
1542.48073 -.78127 (154*2π)/5954 weeks
1552.78901 1.23224 (155*2π)/5954 weeks
1562.23583 1.8499 (156*2π)/5954 weeks
1572.27852 2.378 (157*2π)/5954 weeks
1581.09271 2.44313 (158*2π)/5954 weeks
159.30393 1.87695 (159*2π)/5954 weeks
160.16504 1.01315 (160*2π)/5954 weeks
1611.01225 -.02826 (161*2π)/5954 weeks
1621.91325 -.06453 (162*2π)/5954 weeks
1632.94851 .13136 (163*2π)/5954 weeks
1643.3422 2.28791 (164*2π)/5954 weeks
1651.16411 3.07751 (165*2π)/5954 weeks
166.60389 1.30511 (166*2π)/5954 weeks
1671.6645 .48989 (167*2π)/5954 weeks
1682.36238 1.01886 (168*2π)/5954 weeks
1692.07796 1.76699 (169*2π)/5954 weeks
1701.8342 1.55482 (170*2π)/5954 weeks
1712.25423 1.80021 (171*2π)/5953 weeks
1721.13114 2.16942 (172*2π)/5953 weeks
173.96709 .97279 (173*2π)/5953 weeks
1741.91027 1.01226 (174*2π)/5953 weeks
1751.89507 1.54387 (175*2π)/5953 weeks
1761.55312 1.64204 (176*2π)/5953 weeks
1771.29988 1.36086 (177*2π)/5953 weeks
1781.45948 1.66799 (178*2π)/5953 weeks
1791.20964 1.3267 (179*2π)/5953 weeks
1801.5302 1.42774 (180*2π)/5953 weeks
1811.11472 1.15585 (181*2π)/5953 weeks
1821.35093 .9624 (182*2π)/5953 weeks
1831.38181 1.01913 (183*2π)/5953 weeks
1841.61449 1.00547 (184*2π)/5953 weeks
1851.18515 1.31583 (185*2π)/5953 weeks
186.99969 1.08424 (186*2π)/5953 weeks
1871.21996 .25509 (187*2π)/5953 weeks
1881.75252 .00312 (188*2π)/5953 weeks
1892.26946 .36655 (189*2π)/5953 weeks
1902.41085 1.01901 (190*2π)/5953 weeks
1912.41306 1.30796 (191*2π)/5953 weeks
1922.37695 1.71719 (192*2π)/5953 weeks
1931.36917 2.32864 (193*2π)/5953 weeks
194.47498 1.33011 (194*2π)/5953 weeks
195.92797 .7486 (195*2π)/5953 weeks
1961.31242 .43953 (196*2π)/5953 weeks
1971.89018 .79487 (197*2π)/5953 weeks
1981.40808 1.16347 (198*2π)/5953 weeks
1991.31244 1.06382 (199*2π)/5953 weeks
2001.25211 .57947 (200*2π)/5953 weeks
2011.68196 .33711 (201*2π)/5953 weeks
2021.63149 .33843 (202*2π)/5953 weeks
2032.62496 .31051 (203*2π)/5953 weeks
2042.79527 1.69237 (204*2π)/5953 weeks
2051.37874 1.90416 (205*2π)/5953 weeks
206.70463 1.35304 (206*2π)/5953 weeks
207.61585 .29204 (207*2π)/5953 weeks
2081.60325 -.77404 (208*2π)/5953 weeks
2092.78375 -.52189 (209*2π)/5953 weeks
2103.775 .3495 (210*2π)/5953 weeks
2114.025 2.44839 (211*2π)/5953 weeks
2121.56926 3.44171 (212*2π)/5953 weeks
213.19531 2.03113 (213*2π)/5953 weeks
214.17215 .58953 (214*2π)/5953 weeks
2151.22693 -.21438 (215*2π)/5953 weeks
2162.37306 .38359 (216*2π)/5953 weeks
2172.07593 1.18402 (217*2π)/5953 weeks
2182.00667 2.01975 (218*2π)/5953 weeks
219.26731 2.18975 (219*2π)/5953 weeks
220-.02388 .25687 (220*2π)/5953 weeks
221.65406 -.40029 (221*2π)/5953 weeks
2221.77132 -1.12055 (222*2π)/5953 weeks
2233.35558 -.21715 (223*2π)/5953 weeks
2243.63334 1.9305 (224*2π)/5953 weeks
2251.715 3.11921 (225*2π)/5953 weeks
226-.52417 2.03732 (226*2π)/5953 weeks
227-.58828 -.42548 (227*2π)/5953 weeks
2281.84385 -1.55003 (228*2π)/5953 weeks
2293.40847 -.18462 (229*2π)/5953 weeks
2303.40621 1.52652 (230*2π)/5953 weeks
2312.03001 3.15179 (231*2π)/5953 weeks
232-.10832 2.0874 (232*2π)/5953 weeks
233-.17687 .31083 (233*2π)/5953 weeks
2341.04018 -.72569 (234*2π)/5953 weeks
2352.59734 .03477 (235*2π)/5953 weeks
2362.1925 1.23292 (236*2π)/5953 weeks
2371.43496 1.23553 (237*2π)/5953 weeks
2381.45513 1.05843 (238*2π)/5953 weeks
2391.30353 1.37849 (239*2π)/5952 weeks
240.42136 1.00162 (240*2π)/5952 weeks
241.79577 .32787 (241*2π)/5952 weeks
242.97608 .62781 (242*2π)/5952 weeks
243.94691 .37466 (243*2π)/5952 weeks
2441.44036 .55309 (244*2π)/5952 weeks
245.85798 .5823 (245*2π)/5952 weeks
246.32774 .63254 (246*2π)/5952 weeks
247-.12705 -.02676 (247*2π)/5952 weeks
248.88221 -1.186 (248*2π)/5952 weeks
2491.84146 -1.05464 (249*2π)/5952 weeks
2502.02959 -.26934 (250*2π)/5952 weeks
2512.20239 .63473 (251*2π)/5952 weeks
2521.39606 1.04854 (252*2π)/5952 weeks
253.47413 .78309 (253*2π)/5952 weeks
254-.09497 -.16287 (254*2π)/5952 weeks
255.3394 -1.47521 (255*2π)/5952 weeks
2561.62125 -1.86071 (256*2π)/5952 weeks
2572.69461 -1.23075 (257*2π)/5952 weeks
2583.12994 -.29521 (258*2π)/5952 weeks
2592.21699 1.11721 (259*2π)/5952 weeks
2601.26016 .3382 (260*2π)/5952 weeks
2611.21169 .03302 (261*2π)/5952 weeks
2621.19819 -.93234 (262*2π)/5952 weeks
2632.51252 -.54754 (263*2π)/5952 weeks
2642.60777 .2412 (264*2π)/5952 weeks
2652.19498 .84772 (265*2π)/5952 weeks
266.9938 1.37853 (266*2π)/5952 weeks
267.02019 .34567 (267*2π)/5952 weeks
268.28449 -1.23621 (268*2π)/5952 weeks
2691.18447 -2.01692 (269*2π)/5952 weeks
2702.93995 -1.79386 (270*2π)/5952 weeks
2713.70058 -.28238 (271*2π)/5952 weeks
2722.77954 .96855 (272*2π)/5952 weeks
2731.66713 1.16984 (273*2π)/5952 weeks
274.73249 .51441 (274*2π)/5952 weeks
275.37888 -.64791 (275*2π)/5952 weeks
2761.43758 -1.56153 (276*2π)/5952 weeks
2773.01807 -1.84352 (277*2π)/5952 weeks
2784.12913 .18349 (278*2π)/5952 weeks
2792.59349 1.95867 (279*2π)/5952 weeks
2801.01943 1.36491 (280*2π)/5952 weeks
281-.05982 .159 (281*2π)/5952 weeks
282.25901 -1.53913 (282*2π)/5952 weeks
2832.41181 -2.25202 (283*2π)/5952 weeks
2843.86674 -.86834 (284*2π)/5952 weeks
2852.82816 1.07145 (285*2π)/5952 weeks
2861.39506 1.381 (286*2π)/5952 weeks
287.20311 .2284 (287*2π)/5952 weeks
288.26026 -1.57775 (288*2π)/5952 weeks
2891.6471 -2.91129 (289*2π)/5952 weeks
2904.34686 -2.39816 (290*2π)/5952 weeks
2914.8921 .36139 (291*2π)/5952 weeks
2923.18282 1.72032 (292*2π)/5952 weeks
2931.55788 1.22369 (293*2π)/5952 weeks
294.77763 .29496 (294*2π)/5952 weeks
2951.22511 -.99642 (295*2π)/5952 weeks
2962.41556 -1.73187 (296*2π)/5952 weeks
2974.05717 -1.2623 (297*2π)/5952 weeks
2984.05717 1.2623 (298*2π)/5952 weeks
2992.41556 1.73187 (299*2π)/5952 weeks
3001.22511 .99642 (300*2π)/5952 weeks
301.77763 -.29496 (301*2π)/5952 weeks
3021.55788 -1.22369 (302*2π)/5952 weeks
3033.18282 -1.72032 (303*2π)/5952 weeks
3044.8921 -.36139 (304*2π)/5952 weeks
3054.34686 2.39816 (305*2π)/5952 weeks
3061.6471 2.91129 (306*2π)/5952 weeks
307.26026 1.57775 (307*2π)/5952 weeks
308.20311 -.2284 (308*2π)/5952 weeks
3091.39506 -1.381 (309*2π)/5952 weeks
3102.82816 -1.07145 (310*2π)/5952 weeks
3113.86674 .86834 (311*2π)/5952 weeks
3122.41181 2.25202 (312*2π)/5952 weeks
313.25901 1.53913 (313*2π)/5952 weeks
314-.05982 -.159 (314*2π)/5952 weeks
3151.01943 -1.36491 (315*2π)/5952 weeks
3162.59349 -1.95867 (316*2π)/5952 weeks
3174.12913 -.18349 (317*2π)/5952 weeks
3183.01807 1.84352 (318*2π)/5952 weeks
3191.43758 1.56153 (319*2π)/5952 weeks
320.37888 .64791 (320*2π)/5952 weeks
321.73249 -.51441 (321*2π)/5952 weeks
3221.66713 -1.16984 (322*2π)/5952 weeks
3232.77954 -.96855 (323*2π)/5952 weeks
3243.70058 .28238 (324*2π)/5952 weeks
3252.93995 1.79386 (325*2π)/5952 weeks
3261.18447 2.01692 (326*2π)/5952 weeks
327.28449 1.23621 (327*2π)/5952 weeks
328.02019 -.34567 (328*2π)/5952 weeks
329.9938 -1.37853 (329*2π)/5952 weeks
3302.19498 -.84772 (330*2π)/5952 weeks
3312.60777 -.2412 (331*2π)/5952 weeks
3322.51252 .54754 (332*2π)/5952 weeks
3331.19819 .93234 (333*2π)/5952 weeks
3341.21169 -.03302 (334*2π)/5952 weeks
3351.26016 -.3382 (335*2π)/5952 weeks
3362.21699 -1.11721 (336*2π)/5952 weeks
3373.12994 .29521 (337*2π)/5952 weeks
3382.69461 1.23075 (338*2π)/5952 weeks
3391.62125 1.86071 (339*2π)/5952 weeks
340.3394 1.47521 (340*2π)/5952 weeks
341-.09497 .16287 (341*2π)/5952 weeks
342.47413 -.78309 (342*2π)/5952 weeks
3431.39606 -1.04854 (343*2π)/5952 weeks
3442.20239 -.63473 (344*2π)/5952 weeks
3452.02959 .26934 (345*2π)/5952 weeks
3461.84146 1.05464 (346*2π)/5952 weeks
347.88221 1.186 (347*2π)/5952 weeks
348-.12705 .02676 (348*2π)/5952 weeks
349.32774 -.63254 (349*2π)/5952 weeks
350.85798 -.5823 (350*2π)/5952 weeks
3511.44036 -.55309 (351*2π)/5952 weeks
352.94691 -.37466 (352*2π)/5952 weeks
353.97608 -.62781 (353*2π)/5952 weeks
354.79577 -.32787 (354*2π)/5952 weeks
355.42136 -1.00162 (355*2π)/5952 weeks
3561.30353 -1.37849 (356*2π)/5952 weeks
3571.45513 -1.05843 (357*2π)/5952 weeks
3581.43496 -1.23553 (358*2π)/5952 weeks
3592.1925 -1.23292 (359*2π)/5952 weeks
3602.59734 -.03477 (360*2π)/5952 weeks
3611.04018 .72569 (361*2π)/5952 weeks
362-.17687 -.31083 (362*2π)/5952 weeks
363-.10832 -2.0874 (363*2π)/5952 weeks
3642.03001 -3.15179 (364*2π)/5952 weeks
3653.40621 -1.52652 (365*2π)/5952 weeks
3663.40847 .18462 (366*2π)/5952 weeks
3671.84385 1.55003 (367*2π)/5952 weeks
368-.58828 .42548 (368*2π)/5952 weeks
369-.52417 -2.03732 (369*2π)/5952 weeks
3701.715 -3.11921 (370*2π)/5952 weeks
3713.63334 -1.9305 (371*2π)/5952 weeks
3723.35558 .21715 (372*2π)/5952 weeks
3731.77132 1.12055 (373*2π)/5952 weeks
374.65406 .40029 (374*2π)/5952 weeks
375-.02388 -.25687 (375*2π)/5952 weeks
376.26731 -2.18975 (376*2π)/5952 weeks
3772.00667 -2.01975 (377*2π)/5952 weeks
3782.07593 -1.18402 (378*2π)/5952 weeks
3792.37306 -.38359 (379*2π)/5952 weeks
3801.22693 .21438 (380*2π)/5952 weeks
381.17215 -.58953 (381*2π)/5952 weeks
382.19531 -2.03113 (382*2π)/5952 weeks
3831.56926 -3.44171 (383*2π)/5952 weeks
3844.025 -2.44839 (384*2π)/5952 weeks
3853.775 -.3495 (385*2π)/5952 weeks
3862.78375 .52189 (386*2π)/5952 weeks
3871.60325 .77404 (387*2π)/5952 weeks
388.61585 -.29204 (388*2π)/5952 weeks
389.70463 -1.35304 (389*2π)/5952 weeks
3901.37874 -1.90416 (390*2π)/5952 weeks
3912.79527 -1.69237 (391*2π)/5952 weeks
3922.62496 -.31051 (392*2π)/5952 weeks
3931.63149 -.33843 (393*2π)/5952 weeks
3941.68196 -.33711 (394*2π)/5952 weeks
3951.25211 -.57947 (395*2π)/5952 weeks
3961.31244 -1.06382 (396*2π)/5952 weeks
3971.40808 -1.16347 (397*2π)/5951 weeks
3981.89018 -.79487 (398*2π)/5951 weeks
3991.31242 -.43953 (399*2π)/5951 weeks
400.92797 -.7486 (400*2π)/5951 weeks
401.47498 -1.33011 (401*2π)/5951 weeks
4021.36917 -2.32864 (402*2π)/5951 weeks
4032.37695 -1.71719 (403*2π)/5951 weeks
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