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Fourier Analysis of DUG (ProShares UltraShort Oil & Gas ETF)


DUG (ProShares UltraShort Oil & Gas ETF) appears to have interesting cyclic behaviour every 40 weeks (33.0486*sine), 43 weeks (32.1476*sine), and 46 weeks (26.9325*sine).

DUG (ProShares UltraShort Oil & Gas ETF) has an average price of 219.58 (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 2/1/2007 to 9/5/2017 for DUG (ProShares UltraShort Oil & Gas ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0219.5815   0 
1156.7535 194.2671 (1*2π)/554554 weeks
228.78269 129.8798 (2*2π)/554277 weeks
32.36308 72.6251 (3*2π)/554185 weeks
415.05959 51.34411 (4*2π)/554139 weeks
527.7951 37.06347 (5*2π)/554111 weeks
637.87811 48.05867 (6*2π)/55492 weeks
713.76337 59.72149 (7*2π)/55479 weeks
8-4.87482 37.66846 (8*2π)/55469 weeks
94.73466 22.67382 (9*2π)/55462 weeks
105.5631 24.55868 (10*2π)/55455 weeks
1113.82389 17.01573 (11*2π)/55450 weeks
1222.50963 26.93253 (12*2π)/55446 weeks
1311.56418 32.14763 (13*2π)/55443 weeks
145.36936 33.04859 (14*2π)/55440 weeks
15-3.22058 27.64432 (15*2π)/55437 weeks
16-4.50438 17.83534 (16*2π)/55435 weeks
17-3.06261 9.6475 (17*2π)/55433 weeks
1810.09976 8.64179 (18*2π)/55431 weeks
1913.40875 15.90221 (19*2π)/55429 weeks
2014.41604 21.28044 (20*2π)/55428 weeks
217.08522 25.05855 (21*2π)/55426 weeks
22-1.40255 23.19975 (22*2π)/55425 weeks
23-5.69929 14.26591 (23*2π)/55424 weeks
242.9226 9.76007 (24*2π)/55423 weeks
259.01293 13.93113 (25*2π)/55422 weeks
265.12733 21.53621 (26*2π)/55421 weeks
27-3.81765 17.12816 (27*2π)/55421 weeks
28-6.11595 11.48866 (28*2π)/55420 weeks
29-1.83574 4.99488 (29*2π)/55419 weeks
306.17467 7.90288 (30*2π)/55418 weeks
316.21783 13.56624 (31*2π)/55418 weeks
322.47303 16.44295 (32*2π)/55417 weeks
33-5.13215 13.76698 (33*2π)/55417 weeks
34-4.06219 5.54698 (34*2π)/55416 weeks
35.95108 5.53304 (35*2π)/55416 weeks
362.78621 5.91066 (36*2π)/55415 weeks
374.40692 7.75507 (37*2π)/55415 weeks
383.95873 9.12258 (38*2π)/55415 weeks
392.5039 10.02628 (39*2π)/55414 weeks
40-.19459 8.80784 (40*2π)/55414 weeks
411.3203 5.97579 (41*2π)/55414 weeks
422.98979 7.2537 (42*2π)/55413 weeks
434.27249 6.49386 (43*2π)/55413 weeks
446.0313 10.23374 (44*2π)/55413 weeks
452.04816 14.00009 (45*2π)/55412 weeks
46-3.04462 13.54406 (46*2π)/55412 weeks
47-6.18687 8.27269 (47*2π)/55412 weeks
48-3.60679 2.73378 (48*2π)/55412 weeks
49-.26741 2.04547 (49*2π)/55411 weeks
502.91955 4.03007 (50*2π)/55411 weeks
513.11289 6.5688 (51*2π)/55411 weeks
52.0857 8.06875 (52*2π)/55411 weeks
53-2.80602 5.4127 (53*2π)/55410 weeks
54-2.01897 1.10697 (54*2π)/55410 weeks
553.49705 -.96703 (55*2π)/55410 weeks
568.17784 3.42734 (56*2π)/55410 weeks
576.47325 10.95741 (57*2π)/55410 weeks
58-.9189 12.4337 (58*2π)/55410 weeks
59-5.33765 6.74935 (59*2π)/5549 weeks
60-3.97883 1.06246 (60*2π)/5549 weeks
611.79705 -1.31775 (61*2π)/5549 weeks
624.62155 2.83343 (62*2π)/5549 weeks
633.72445 4.79307 (63*2π)/5549 weeks
642.89412 6.34678 (64*2π)/5549 weeks
651.47641 5.69362 (65*2π)/5549 weeks
66.63824 4.94605 (66*2π)/5548 weeks
67.04917 4.53846 (67*2π)/5548 weeks
681.6537 4.29419 (68*2π)/5548 weeks
69-.03113 4.62392 (69*2π)/5548 weeks
701.40923 3.76811 (70*2π)/5548 weeks
71-.19901 6.35374 (71*2π)/5548 weeks
72-3.37623 4.38782 (72*2π)/5548 weeks
73-2.39747 -.41046 (73*2π)/5548 weeks
742.02074 -2.61684 (74*2π)/5547 weeks
756.13326 1.3644 (75*2π)/5547 weeks
764.10934 4.74768 (76*2π)/5547 weeks
772.83106 4.79665 (77*2π)/5547 weeks
78-.68473 5.96273 (78*2π)/5547 weeks
79-2.10321 1.23319 (79*2π)/5547 weeks
802.52201 -.55523 (80*2π)/5547 weeks
814.3213 1.16642 (81*2π)/5547 weeks
824.60606 4.0149 (82*2π)/5547 weeks
831.48308 5.46206 (83*2π)/5547 weeks
84.59554 3.81972 (84*2π)/5547 weeks
85-.49632 1.79142 (85*2π)/5547 weeks
862.56424 -1.0793 (86*2π)/5546 weeks
876.36096 2.05262 (87*2π)/5546 weeks
885.34174 6.06205 (88*2π)/5546 weeks
891.18862 6.97505 (89*2π)/5546 weeks
90-1.94376 4.4398 (90*2π)/5546 weeks
91-.90724 .73518 (91*2π)/5546 weeks
922.03789 .26965 (92*2π)/5546 weeks
933.56039 1.93242 (93*2π)/5546 weeks
942.81072 3.7788 (94*2π)/5546 weeks
952.36084 3.21783 (95*2π)/5546 weeks
962.67784 4.49456 (96*2π)/5546 weeks
97-.33319 4.13112 (97*2π)/5546 weeks
98-1.62002 1.3234 (98*2π)/5546 weeks
99.84815 -1.17548 (99*2π)/5546 weeks
1004.22091 -.0679 (100*2π)/5546 weeks
1015.21109 2.99404 (101*2π)/5545 weeks
1023.50266 5.17662 (102*2π)/5545 weeks
103.17113 4.70089 (103*2π)/5545 weeks
104-1.02349 .78548 (104*2π)/5545 weeks
1051.85248 -1.13391 (105*2π)/5545 weeks
1065.00969 .21391 (106*2π)/5545 weeks
1075.69912 3.7109 (107*2π)/5545 weeks
1083.75075 5.61612 (108*2π)/5545 weeks
109.56779 5.12069 (109*2π)/5545 weeks
110-.53581 1.74759 (110*2π)/5545 weeks
1111.8174 .08502 (111*2π)/5545 weeks
1124.21915 1.56144 (112*2π)/5545 weeks
1134.28903 3.76823 (113*2π)/5545 weeks
1143.07685 5.57129 (114*2π)/5545 weeks
115-.492 5.79514 (115*2π)/5545 weeks
116-2.05876 2.14047 (116*2π)/5545 weeks
117-.72037 -.37884 (117*2π)/5545 weeks
1182.2316 -1.10477 (118*2π)/5545 weeks
1194.67087 1.00739 (119*2π)/5545 weeks
1203.63474 3.96465 (120*2π)/5545 weeks
1211.1107 3.93675 (121*2π)/5545 weeks
122-.48898 2.18689 (122*2π)/5545 weeks
123.57275 -.3361 (123*2π)/5545 weeks
1243.27164 -.4399 (124*2π)/5544 weeks
1254.16162 1.66314 (125*2π)/5544 weeks
1263.72647 3.3078 (126*2π)/5544 weeks
1272.61971 3.49943 (127*2π)/5544 weeks
1281.43588 3.39698 (128*2π)/5544 weeks
129.16735 2.16377 (129*2π)/5544 weeks
1301.30588 .03997 (130*2π)/5544 weeks
1314.03547 .60825 (131*2π)/5544 weeks
1324.02121 3.33805 (132*2π)/5544 weeks
1332.63465 3.86522 (133*2π)/5544 weeks
1342.2504 3.4562 (134*2π)/5544 weeks
1351.05363 3.65808 (135*2π)/5544 weeks
136-.18137 2.02159 (136*2π)/5544 weeks
1371.24543 1.45569 (137*2π)/5544 weeks
1382.09519 1.59708 (138*2π)/5544 weeks
1393.31805 2.69993 (139*2π)/5544 weeks
1401.40324 4.56872 (140*2π)/5544 weeks
141-1.10475 3.03294 (141*2π)/5544 weeks
142-1.29934 .40938 (142*2π)/5544 weeks
1431.27654 -1.20414 (143*2π)/5544 weeks
1443.21892 .91367 (144*2π)/5544 weeks
1452.61684 1.95655 (145*2π)/5544 weeks
1462.53902 2.27275 (146*2π)/5544 weeks
1471.24436 2.69835 (147*2π)/5544 weeks
148.35343 2.09417 (148*2π)/5544 weeks
149.18394 1.06541 (149*2π)/5544 weeks
1501.22168 -.02266 (150*2π)/5544 weeks
1512.24954 -.00665 (151*2π)/5544 weeks
1523.69557 .50762 (152*2π)/5544 weeks
1533.1079 2.98402 (153*2π)/5544 weeks
154.57168 2.39575 (154*2π)/5544 weeks
155.96646 .7089 (155*2π)/5544 weeks
1562.25091 .78174 (156*2π)/5544 weeks
1572.51822 1.68658 (157*2π)/5544 weeks
1581.95321 1.69309 (158*2π)/5544 weeks
1592.29876 1.63493 (159*2π)/5543 weeks
1601.38286 2.43372 (160*2π)/5543 weeks
161.93401 1.13218 (161*2π)/5543 weeks
1622.02637 1.06998 (162*2π)/5543 weeks
1632.00302 1.67262 (163*2π)/5543 weeks
1641.63241 1.74811 (164*2π)/5543 weeks
1651.52648 1.3392 (165*2π)/5543 weeks
1661.35314 1.68864 (166*2π)/5543 weeks
1671.3706 1.23577 (167*2π)/5543 weeks
1681.26388 1.59541 (168*2π)/5543 weeks
1691.27689 1.09672 (169*2π)/5543 weeks
1701.49227 1.11803 (170*2π)/5543 weeks
1711.58015 1.00714 (171*2π)/5543 weeks
1721.48611 1.48977 (172*2π)/5543 weeks
1731.18804 1.16711 (173*2π)/5543 weeks
1741.17279 .2788 (174*2π)/5543 weeks
1751.80068 -.00012 (175*2π)/5543 weeks
1762.43294 .39596 (176*2π)/5543 weeks
1772.53466 1.10776 (177*2π)/5543 weeks
1782.52743 1.4826 (178*2π)/5543 weeks
1792.44895 2.12924 (179*2π)/5543 weeks
1801.01642 2.34321 (180*2π)/5543 weeks
181.74325 .98742 (181*2π)/5543 weeks
1821.15242 .60815 (182*2π)/5543 weeks
1831.83885 .49295 (183*2π)/5543 weeks
1841.80953 1.24417 (184*2π)/5543 weeks
1851.52266 1.02209 (185*2π)/5543 weeks
1861.25401 .62778 (186*2π)/5543 weeks
1871.65827 .26041 (187*2π)/5543 weeks
1881.70138 .36395 (188*2π)/5543 weeks
1892.76173 .2518 (189*2π)/5543 weeks
1902.87843 1.84913 (190*2π)/5543 weeks
1911.32642 1.88739 (191*2π)/5543 weeks
192.57011 1.14261 (192*2π)/5543 weeks
193.65794 -.1132 (193*2π)/5543 weeks
1942.18483 -.80226 (194*2π)/5543 weeks
1953.43674 -.27684 (195*2π)/5543 weeks
1964.41711 1.24812 (196*2π)/5543 weeks
1972.82966 3.72828 (197*2π)/5543 weeks
198.39538 2.76787 (198*2π)/5543 weeks
199.00613 1.0834 (199*2π)/5543 weeks
2001.00753 -.12711 (200*2π)/5543 weeks
2012.44502 .26681 (201*2π)/5543 weeks
2022.23353 1.27961 (202*2π)/5543 weeks
2032.12144 2.19341 (203*2π)/5543 weeks
204.07745 2.19044 (204*2π)/5543 weeks
205.14657 .09961 (205*2π)/5543 weeks
206.86364 -.63533 (206*2π)/5543 weeks
2072.58021 -1.13141 (207*2π)/5543 weeks
2084.00137 .45432 (208*2π)/5543 weeks
2093.01093 2.90074 (209*2π)/5543 weeks
210.36226 3.10281 (210*2π)/5543 weeks
211-.91024 .55274 (211*2π)/5543 weeks
2121.02854 -1.7673 (212*2π)/5543 weeks
2133.37215 -.66061 (213*2π)/5543 weeks
2143.69049 1.35088 (214*2π)/5543 weeks
2152.40263 3.26478 (215*2π)/5543 weeks
216-.14326 2.2347 (216*2π)/5543 weeks
217-.18987 .20168 (217*2π)/5543 weeks
2181.31439 -.85554 (218*2π)/5543 weeks
2192.78556 .39813 (219*2π)/5543 weeks
2202.04287 1.44319 (220*2π)/5543 weeks
2211.43843 1.16214 (221*2π)/5543 weeks
2221.50357 1.22913 (222*2π)/5542 weeks
223.82878 1.56986 (223*2π)/5542 weeks
224.57961 .53634 (224*2π)/5542 weeks
2251.16529 .54693 (225*2π)/5542 weeks
226.96193 .42018 (226*2π)/5542 weeks
2271.43817 .33395 (227*2π)/5542 weeks
228.83788 .66312 (228*2π)/5542 weeks
229.3467 .72062 (229*2π)/5542 weeks
230-.18919 -.07156 (230*2π)/5542 weeks
2311.02122 -1.24581 (231*2π)/5542 weeks
2322.14951 -.95614 (232*2π)/5542 weeks
2332.28473 -.25983 (233*2π)/5542 weeks
2342.01639 .87642 (234*2π)/5542 weeks
2351.0211 1.10846 (235*2π)/5542 weeks
236.08113 .45469 (236*2π)/5542 weeks
237-.10738 -.95578 (237*2π)/5542 weeks
2381.15436 -1.96061 (238*2π)/5542 weeks
2392.58826 -1.62686 (239*2π)/5542 weeks
2403.20002 -.59602 (240*2π)/5542 weeks
2412.69778 1.11565 (241*2π)/5542 weeks
2421.32198 .44303 (242*2π)/5542 weeks
2431.27925 .04702 (243*2π)/5542 weeks
2441.347 -1.0688 (244*2π)/5542 weeks
2452.69444 -.45148 (245*2π)/5542 weeks
2462.70453 .45739 (246*2π)/5542 weeks
2472.19353 1.15436 (247*2π)/5542 weeks
248.51472 1.11143 (248*2π)/5542 weeks
249-.21955 -.39315 (249*2π)/5542 weeks
250.72944 -1.67289 (250*2π)/5542 weeks
2512.3857 -2.32997 (251*2π)/5542 weeks
2523.80968 -.98796 (252*2π)/5542 weeks
2533.29156 .85743 (253*2π)/5542 weeks
2542.01294 1.28269 (254*2π)/5542 weeks
255.83667 .68398 (255*2π)/5542 weeks
256.37068 -.59866 (256*2π)/5542 weeks
2571.53282 -1.69521 (257*2π)/5542 weeks
2583.42544 -1.88475 (258*2π)/5542 weeks
2594.3 .61881 (259*2π)/5542 weeks
2602.11065 2.09398 (260*2π)/5542 weeks
261.64769 1.30251 (261*2π)/5542 weeks
262-.06405 -.5295 (262*2π)/5542 weeks
2631.13984 -2.44987 (263*2π)/5542 weeks
2643.45884 -1.76171 (264*2π)/5542 weeks
2653.79792 .78838 (265*2π)/5542 weeks
2662.13309 1.46823 (266*2π)/5542 weeks
267.41515 .5746 (267*2π)/5542 weeks
268.10904 -1.40605 (268*2π)/5542 weeks
2691.54095 -3.02381 (269*2π)/5542 weeks
2704.6035 -2.62677 (270*2π)/5542 weeks
2715.15689 .53027 (271*2π)/5542 weeks
2723.12688 1.89907 (272*2π)/5542 weeks
2731.51892 1.12104 (273*2π)/5542 weeks
274.78038 -.22499 (274*2π)/5542 weeks
2751.54899 -1.45485 (275*2π)/5542 weeks
2763.21726 -1.78215 (276*2π)/5542 weeks
2774.96798   (277*2π)/5542 weeks
2783.21726 1.78215 (278*2π)/5542 weeks
2791.54899 1.45485 (279*2π)/5542 weeks
280.78038 .22499 (280*2π)/5542 weeks
2811.51892 -1.12104 (281*2π)/5542 weeks
2823.12688 -1.89907 (282*2π)/5542 weeks
2835.15689 -.53027 (283*2π)/5542 weeks
2844.6035 2.62677 (284*2π)/5542 weeks
2851.54095 3.02381 (285*2π)/5542 weeks
286.10904 1.40605 (286*2π)/5542 weeks
287.41515 -.5746 (287*2π)/5542 weeks
2882.13309 -1.46823 (288*2π)/5542 weeks
2893.79792 -.78838 (289*2π)/5542 weeks
2903.45884 1.76171 (290*2π)/5542 weeks
2911.13984 2.44987 (291*2π)/5542 weeks
292-.06405 .5295 (292*2π)/5542 weeks
293.64769 -1.30251 (293*2π)/5542 weeks
2942.11065 -2.09398 (294*2π)/5542 weeks
2954.3 -.61881 (295*2π)/5542 weeks
2963.42544 1.88475 (296*2π)/5542 weeks
2971.53282 1.69521 (297*2π)/5542 weeks
298.37068 .59866 (298*2π)/5542 weeks
299.83667 -.68398 (299*2π)/5542 weeks
3002.01294 -1.28269 (300*2π)/5542 weeks
3013.29156 -.85743 (301*2π)/5542 weeks
3023.80968 .98796 (302*2π)/5542 weeks
3032.3857 2.32997 (303*2π)/5542 weeks
304.72944 1.67289 (304*2π)/5542 weeks
305-.21955 .39315 (305*2π)/5542 weeks
306.51472 -1.11143 (306*2π)/5542 weeks
3072.19353 -1.15436 (307*2π)/5542 weeks
3082.70453 -.45739 (308*2π)/5542 weeks
3092.69444 .45148 (309*2π)/5542 weeks
3101.347 1.0688 (310*2π)/5542 weeks
3111.27925 -.04702 (311*2π)/5542 weeks
3121.32198 -.44303 (312*2π)/5542 weeks
3132.69778 -1.11565 (313*2π)/5542 weeks
3143.20002 .59602 (314*2π)/5542 weeks
3152.58826 1.62686 (315*2π)/5542 weeks
3161.15436 1.96061 (316*2π)/5542 weeks
317-.10738 .95578 (317*2π)/5542 weeks
318.08113 -.45469 (318*2π)/5542 weeks
3191.0211 -1.10846 (319*2π)/5542 weeks
3202.01639 -.87642 (320*2π)/5542 weeks
3212.28473 .25983 (321*2π)/5542 weeks
3222.14951 .95614 (322*2π)/5542 weeks
3231.02122 1.24581 (323*2π)/5542 weeks
324-.18919 .07156 (324*2π)/5542 weeks
325.3467 -.72062 (325*2π)/5542 weeks
326.83788 -.66312 (326*2π)/5542 weeks
3271.43817 -.33395 (327*2π)/5542 weeks
328.96193 -.42018 (328*2π)/5542 weeks
3291.16529 -.54693 (329*2π)/5542 weeks
330.57961 -.53634 (330*2π)/5542 weeks
331.82878 -1.56986 (331*2π)/5542 weeks
3321.50357 -1.22913 (332*2π)/5542 weeks
3331.43843 -1.16214 (333*2π)/5542 weeks
3342.04287 -1.44319 (334*2π)/5542 weeks
3352.78556 -.39813 (335*2π)/5542 weeks
3361.31439 .85554 (336*2π)/5542 weeks
337-.18987 -.20168 (337*2π)/5542 weeks
338-.14326 -2.2347 (338*2π)/5542 weeks
3392.40263 -3.26478 (339*2π)/5542 weeks
3403.69049 -1.35088 (340*2π)/5542 weeks
3413.37215 .66061 (341*2π)/5542 weeks
3421.02854 1.7673 (342*2π)/5542 weeks
343-.91024 -.55274 (343*2π)/5542 weeks
344.36226 -3.10281 (344*2π)/5542 weeks
3453.01093 -2.90074 (345*2π)/5542 weeks
3464.00137 -.45432 (346*2π)/5542 weeks
3472.58021 1.13141 (347*2π)/5542 weeks
348.86364 .63533 (348*2π)/5542 weeks
349.14657 -.09961 (349*2π)/5542 weeks
350.07745 -2.19044 (350*2π)/5542 weeks
3512.12144 -2.19341 (351*2π)/5542 weeks
3522.23353 -1.27961 (352*2π)/5542 weeks
3532.44502 -.26681 (353*2π)/5542 weeks
3541.00753 .12711 (354*2π)/5542 weeks
355.00613 -1.0834 (355*2π)/5542 weeks
356.39538 -2.76787 (356*2π)/5542 weeks
3572.82966 -3.72828 (357*2π)/5542 weeks
3584.41711 -1.24812 (358*2π)/5542 weeks
3593.43674 .27684 (359*2π)/5542 weeks
3602.18483 .80226 (360*2π)/5542 weeks
361.65794 .1132 (361*2π)/5542 weeks
362.57011 -1.14261 (362*2π)/5542 weeks
3631.32642 -1.88739 (363*2π)/5542 weeks
3642.87843 -1.84913 (364*2π)/5542 weeks
3652.76173 -.2518 (365*2π)/5542 weeks
3661.70138 -.36395 (366*2π)/5542 weeks
3671.65827 -.26041 (367*2π)/5542 weeks
3681.25401 -.62778 (368*2π)/5542 weeks
3691.52266 -1.02209 (369*2π)/5542 weeks
3701.80953 -1.24417 (370*2π)/5541 weeks
3711.83885 -.49295 (371*2π)/5541 weeks
3721.15242 -.60815 (372*2π)/5541 weeks
373.74325 -.98742 (373*2π)/5541 weeks
3741.01642 -2.34321 (374*2π)/5541 weeks
3752.44895 -2.12924 (375*2π)/5541 weeks
3762.52743 -1.4826 (376*2π)/5541 weeks
3772.53466 -1.10776 (377*2π)/5541 weeks
3782.43294 -.39596 (378*2π)/5541 weeks
3791.80068 .00012 (379*2π)/5541 weeks
3801.17279 -.2788 (380*2π)/5541 weeks
3811.18804 -1.16711 (381*2π)/5541 weeks
3821.48611 -1.48977 (382*2π)/5541 weeks
3831.58015 -1.00714 (383*2π)/5541 weeks
3841.49227 -1.11803 (384*2π)/5541 weeks
3851.27689 -1.09672 (385*2π)/5541 weeks
3861.26388 -1.59541 (386*2π)/5541 weeks
3871.3706 -1.23577 (387*2π)/5541 weeks
3881.35314 -1.68864 (388*2π)/5541 weeks
3891.52648 -1.3392 (389*2π)/5541 weeks
3901.63241 -1.74811 (390*2π)/5541 weeks
3912.00302 -1.67262 (391*2π)/5541 weeks
3922.02637 -1.06998 (392*2π)/5541 weeks
393.93401 -1.13218 (393*2π)/5541 weeks
3941.38286 -2.43372 (394*2π)/5541 weeks
3952.29876 -1.63493 (395*2π)/5541 weeks
3961.95321 -1.69309 (396*2π)/5541 weeks
3972.51822 -1.68658 (397*2π)/5541 weeks
3982.25091 -.78174 (398*2π)/5541 weeks
399.96646 -.7089 (399*2π)/5541 weeks
400.57168 -2.39575 (400*2π)/5541 weeks
4013.1079 -2.98402 (401*2π)/5541 weeks
4023.69557 -.50762 (402*2π)/5541 weeks
4032.24954 .00665 (403*2π)/5541 weeks
4041.22168 .02266 (404*2π)/5541 weeks
405.18394 -1.06541 (405*2π)/5541 weeks
406.35343 -2.09417 (406*2π)/5541 weeks
4071.24436 -2.69835 (407*2π)/5541 weeks
4082.53902 -2.27275 (408*2π)/5541 weeks
4092.61684 -1.95655 (409*2π)/5541 weeks
4103.21892 -.91367 (410*2π)/5541 weeks
4111.27654 1.20414 (411*2π)/5541 weeks
412-1.29934 -.40938 (412*2π)/5541 weeks
413-1.10475 -3.03294 (413*2π)/5541 weeks
4141.40324 -4.56872 (414*2π)/5541 weeks
4153.31805 -2.69993 (415*2π)/5541 weeks
4162.09519 -1.59708 (416*2π)/5541 weeks
4171.24543 -1.45569 (417*2π)/5541 weeks
418-.18137 -2.02159 (418*2π)/5541 weeks
4191.05363 -3.65808 (419*2π)/5541 weeks
4202.2504 -3.4562 (420*2π)/5541 weeks
4212.63465 -3.86522 (421*2π)/5541 weeks
4224.02121 -3.33805 (422*2π)/5541 weeks
4234.03547 -.60825 (423*2π)/5541 weeks
4241.30588 -.03997 (424*2π)/5541 weeks
425.16735 -2.16377 (425*2π)/5541 weeks
4261.43588 -3.39698 (426*2π)/5541 weeks
4272.61971 -3.49943 (427*2π)/5541 weeks
4283.72647 -3.3078 (428*2π)/5541 weeks
4294.16162 -1.66314 (429*2π)/5541 weeks
4303.27164 .4399 (430*2π)/5541 weeks
431.57275 .3361 (431*2π)/5541 weeks
432-.48898 -2.18689 (432*2π)/5541 weeks
4331.1107 -3.93675 (433*2π)/5541 weeks
4343.63474 -3.96465 (434*2π)/5541 weeks
4354.67087 -1.00739 (435*2π)/5541 weeks
4362.2316 1.10477 (436*2π)/5541 weeks
437-.72037 .37884 (437*2π)/5541 weeks
438-2.05876 -2.14047 (438*2π)/5541 weeks
439-.492 -5.79514 (439*2π)/5541 weeks
4403.07685 -5.57129 (440*2π)/5541 weeks
4414.28903 -3.76823 (441*2π)/5541 weeks
4424.21915 -1.56144 (442*2π)/5541 weeks
4431.8174 -.08502 (443*2π)/5541 weeks
444-.53581 -1.74759 (444*2π)/5541 weeks
445.56779 -5.12069 (445*2π)/5541 weeks
4463.75075 -5.61612 (446*2π)/5541 weeks
4475.69912 -3.7109 (447*2π)/5541 weeks
4485.00969 -.21391 (448*2π)/5541 weeks
4491.85248 1.13391 (449*2π)/5541 weeks
450-1.02349 -.78548 (450*2π)/5541 weeks
451.17113 -4.70089 (451*2π)/5541 weeks
4523.50266 -5.17662 (452*2π)/5541 weeks
4535.21109 -2.99404 (453*2π)/5541 weeks
4544.22091 .0679 (454*2π)/5541 weeks
455.84815 1.17548 (455*2π)/5541 weeks
456-1.62002 -1.3234 (456*2π)/5541 weeks
457-.33319 -4.13112 (457*2π)/5541 weeks
4582.67784 -4.49456 (458*2π)/5541 weeks
4592.36084 -3.21783 (459*2π)/5541 weeks
4602.81072 -3.7788 (460*2π)/5541 weeks
4613.56039 -1.93242 (461*2π)/5541 weeks
4622.03789 -.26965 (462*2π)/5541 weeks
463-.90724 -.73518 (463*2π)/5541 weeks
464-1.94376 -4.4398 (464*2π)/5541 weeks
4651.18862 -6.97505 (465*2π)/5541 weeks
4665.34174 -6.06205 (466*2π)/5541 weeks
4676.36096 -2.05262 (467*2π)/5541 weeks
4682.56424 1.0793 (468*2π)/5541 weeks
469-.49632 -1.79142 (469*2π)/5541 weeks
470.59554 -3.81972 (470*2π)/5541 weeks
4711.48308 -5.46206 (471*2π)/5541 weeks
4724.60606 -4.0149 (472*2π)/5541 weeks
4734.3213 -1.16642 (473*2π)/5541 weeks
4742.52201 .55523 (474*2π)/5541 weeks
475-2.10321 -1.23319 (475*2π)/5541 weeks
476-.68473 -5.96273 (476*2π)/5541 weeks
4772.83106 -4.79665 (477*2π)/5541 weeks
4784.10934 -4.74768 (478*2π)/5541 weeks
4796.13326 -1.3644 (479*2π)/5541 weeks
4802.02074 2.61684 (480*2π)/5541 weeks
481-2.39747 .41046 (481*2π)/5541 weeks
482-3.37623 -4.38782 (482*2π)/5541 weeks
483-.19901 -6.35374 (483*2π)/5541 weeks
4841.40923 -3.76811 (484*2π)/5541 weeks
485-.03113 -4.62392 (485*2π)/5541 weeks
4861.6537 -4.29419 (486*2π)/5541 weeks
487.04917 -4.53846 (487*2π)/5541 weeks
488.63824 -4.94605 (488*2π)/5541 weeks
4891.47641 -5.69362 (489*2π)/5541 weeks
4902.89412 -6.34678 (490*2π)/5541 weeks
4913.72445 -4.79307 (491*2π)/5541 weeks
4924.62155 -2.83343 (492*2π)/5541 weeks
4931.79705 1.31775 (493*2π)/5541 weeks
494-3.97883 -1.06246 (494*2π)/5541 weeks
495-5.33765 -6.74935 (495*2π)/5541 weeks
496-.9189 -12.4337 (496*2π)/5541 weeks
4976.47325 -10.95741 (497*2π)/5541 weeks
4988.17784 -3.42734 (498*2π)/5541 weeks
4993.49705 .96703 (499*2π)/5541 weeks
500-2.01897 -1.10697 (500*2π)/5541 weeks
501-2.80602 -5.4127 (501*2π)/5541 weeks
502.0857 -8.06875 (502*2π)/5541 weeks
5033.11289 -6.5688 (503*2π)/5541 weeks
5042.91955 -4.03007 (504*2π)/5541 weeks
505-.26741 -2.04547 (505*2π)/5541 weeks
506-3.60679 -2.73378 (506*2π)/5541 weeks
507-6.18687 -8.27269 (507*2π)/5541 weeks
508-3.04462 -13.54406 (508*2π)/5541 weeks
5092.04816 -14.00009 (509*2π)/5541 weeks
5106.0313 -10.23374 (510*2π)/5541 weeks
5114.27249 -6.49386 (511*2π)/5541 weeks
5122.98979 -7.2537 (512*2π)/5541 weeks
5131.3203 -5.97579 (513*2π)/5541 weeks
514-.19459 -8.80784 (514*2π)/5541 weeks
5152.5039 -10.02628 (515*2π)/5541 weeks
5163.95873 -9.12258 (516*2π)/5541 weeks
5174.40692 -7.75507 (517*2π)/5541 weeks
5182.78621 -5.91066 (518*2π)/5541 weeks
519.95108 -5.53304 (519*2π)/5541 weeks
520-4.06219 -5.54698 (520*2π)/5541 weeks
521-5.13215 -13.76698 (521*2π)/5541 weeks
5222.47303 -16.44295 (522*2π)/5541 weeks
5236.21783 -13.56624 (523*2π)/5541 weeks
5246.17467 -7.90288 (524*2π)/5541 weeks
525-1.83574 -4.99488 (525*2π)/5541 weeks
526-6.11595 -11.48866 (526*2π)/5541 weeks
527-3.81765 -17.12816 (527*2π)/5541 weeks
5285.12733 -21.53621 (528*2π)/5541 weeks
5299.01293 -13.93113 (529*2π)/5541 weeks
5302.9226 -9.76007 (530*2π)/5541 weeks
531-5.69929 -14.26591 (531*2π)/5541 weeks
532-1.40255 -23.19975 (532*2π)/5541 weeks
5337.08522 -25.05855 (533*2π)/5541 weeks
53414.41604 -21.28044 (534*2π)/5541 weeks
53513.40875 -15.90221 (535*2π)/5541 weeks
53610.09976 -8.64179 (536*2π)/5541 weeks
537-3.06261 -9.6475 (537*2π)/5541 weeks
538-4.50438 -17.83534 (538*2π)/5541 weeks
539-3.22058 -27.64432 (539*2π)/5541 weeks
5405.36936 -33.04859 (540*2π)/5541 weeks
54111.56418 -32.14763 (541*2π)/5541 weeks
54222.50963 -26.93253 (542*2π)/5541 weeks
54313.82389 -17.01573 (543*2π)/5541 weeks
5445.5631 -24.55868 (544*2π)/5541 weeks
5454.73466 -22.67382 (545*2π)/5541 weeks
546-4.87482 -37.66846 (546*2π)/5541 weeks
54713.76337 -59.72149 (547*2π)/5541 weeks
54837.87811 -48.05867 (548*2π)/5541 weeks
54927.7951 -37.06347 (549*2π)/5541 weeks
55015.05959 -51.34411 (550*2π)/5541 weeks
5512.36308 -72.6251 (551*2π)/5541 weeks
55228.78269 -129.8798 (552*2π)/5541 weeks



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