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Fourier Analysis of RXD (ProShares UltraShort Health Care ETF)


RXD (ProShares UltraShort Health Care ETF) appears to have interesting cyclic behaviour every 55 weeks (27.819*sine), 46 weeks (26.2587*sine), and 50 weeks (22.3835*sine).

RXD (ProShares UltraShort Health Care ETF) has an average price of 373.7 (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 7/17/2017 for RXD (ProShares UltraShort Health Care ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0373.7015   0 
182.8362 389.3083 (1*2π)/547547 weeks
2-44.03403 153.9292 (2*2π)/547274 weeks
3-55.68248 59.48364 (3*2π)/547182 weeks
4-9.16873 10.42615 (4*2π)/547137 weeks
526.1951 21.36437 (5*2π)/547109 weeks
624.42369 52.34589 (6*2π)/54791 weeks
7-8.93041 48.94566 (7*2π)/54778 weeks
8-12.19936 11.78597 (8*2π)/54768 weeks
915.65848 17.062 (9*2π)/54761 weeks
103.17773 27.81902 (10*2π)/54755 weeks
115.70153 22.38351 (11*2π)/54750 weeks
12-.44625 26.25868 (12*2π)/54746 weeks
13-4.93191 20.06043 (13*2π)/54742 weeks
14-5.80643 13.84463 (14*2π)/54739 weeks
15-1.1676 3.51652 (15*2π)/54736 weeks
166.93541 11.43927 (16*2π)/54734 weeks
172.18668 3.22182 (17*2π)/54732 weeks
1817.81631 9.42012 (18*2π)/54730 weeks
199.23894 22.76735 (19*2π)/54729 weeks
20-1.80139 20.35542 (20*2π)/54727 weeks
21-4.81764 12.31503 (21*2π)/54726 weeks
22-1.66442 6.02687 (22*2π)/54725 weeks
237.92073 4.5426 (23*2π)/54724 weeks
248.79327 13.72478 (24*2π)/54723 weeks
253.76666 19.03551 (25*2π)/54722 weeks
26-6.92136 17.66033 (26*2π)/54721 weeks
27-7.44078 5.32098 (27*2π)/54720 weeks
28-.05403 2.89527 (28*2π)/54720 weeks
295.34632 2.9108 (29*2π)/54719 weeks
309.86864 9.48277 (30*2π)/54718 weeks
312.48144 17.63026 (31*2π)/54718 weeks
32-6.30455 14.71507 (32*2π)/54717 weeks
33-9.29887 6.39323 (33*2π)/54717 weeks
34-2.17503 -1.28899 (34*2π)/54716 weeks
355.06135 3.78594 (35*2π)/54716 weeks
362.2929 7.91648 (36*2π)/54715 weeks
37-1.0235 5.4658 (37*2π)/54715 weeks
382.16845 4.98631 (38*2π)/54714 weeks
392.54775 6.26161 (39*2π)/54714 weeks
40-1.27429 7.17688 (40*2π)/54714 weeks
412.36442 4.60943 (41*2π)/54713 weeks
42-.90837 7.88265 (42*2π)/54713 weeks
43-.57041 2.52988 (43*2π)/54713 weeks
442.19272 4.55476 (44*2π)/54712 weeks
452.56702 5.73348 (45*2π)/54712 weeks
46.38884 8.04557 (46*2π)/54712 weeks
47-2.88994 5.45259 (47*2π)/54712 weeks
48-2.12743 3.88288 (48*2π)/54711 weeks
49-1.22386 1.30437 (49*2π)/54711 weeks
501.67589 1.1503 (50*2π)/54711 weeks
512.94327 4.40862 (51*2π)/54711 weeks
52-.41392 4.50147 (52*2π)/54711 weeks
53-.23845 3.35609 (53*2π)/54710 weeks
54-.57547 1.11921 (54*2π)/54710 weeks
553.28591 1.02492 (55*2π)/54710 weeks
563.65633 4.76758 (56*2π)/54710 weeks
571.46312 4.27977 (57*2π)/54710 weeks
581.16492 4.47783 (58*2π)/5479 weeks
59-1.17617 3.38378 (59*2π)/5479 weeks
602.08409 .61153 (60*2π)/5479 weeks
612.60963 4.62842 (61*2π)/5479 weeks
62.17 3.4428 (62*2π)/5479 weeks
63.50337 3.21207 (63*2π)/5479 weeks
64.90941 1.5178 (64*2π)/5479 weeks
653.10222 2.20739 (65*2π)/5478 weeks
66.70903 4.72877 (66*2π)/5478 weeks
671.43388 1.98823 (67*2π)/5478 weeks
68.6638 2.68321 (68*2π)/5478 weeks
693.54898 1.59679 (69*2π)/5478 weeks
703.2712 5.98072 (70*2π)/5478 weeks
71-1.98198 5.29846 (71*2π)/5478 weeks
72-2.22343 1.03151 (72*2π)/5478 weeks
73-.20763 -1.7241 (73*2π)/5477 weeks
744.66703 -.54771 (74*2π)/5477 weeks
754.68242 3.75366 (75*2π)/5477 weeks
763.57418 5.35661 (76*2π)/5477 weeks
77-1.72145 7.97889 (77*2π)/5477 weeks
78-5.0353 -.42744 (78*2π)/5477 weeks
791.753 -3.26149 (79*2π)/5477 weeks
805.40355 -.19574 (80*2π)/5477 weeks
815.28101 4.29897 (81*2π)/5477 weeks
821.13465 5.99686 (82*2π)/5477 weeks
83-1.18589 2.91014 (83*2π)/5477 weeks
84-.63881 -.33177 (84*2π)/5477 weeks
854.86728 -1.2812 (85*2π)/5476 weeks
866.14044 4.09463 (86*2π)/5476 weeks
872.8311 7.14144 (87*2π)/5476 weeks
88-1.58133 5.48491 (88*2π)/5476 weeks
89-2.88169 2.01969 (89*2π)/5476 weeks
90.3074 -1.26733 (90*2π)/5476 weeks
913.42929 1.27721 (91*2π)/5476 weeks
922.04239 3.62978 (92*2π)/5476 weeks
93.20608 3.11518 (93*2π)/5476 weeks
941.52258 1.45008 (94*2π)/5476 weeks
951.26988 2.99269 (95*2π)/5476 weeks
96.31077 2.70434 (96*2π)/5476 weeks
97-.16749 1.54021 (97*2π)/5476 weeks
98.70018 .56175 (98*2π)/5476 weeks
992.68747 .65715 (99*2π)/5476 weeks
1002.3675 3.27361 (100*2π)/5475 weeks
101-.14459 3.88303 (101*2π)/5475 weeks
102-1.0748 1.39568 (102*2π)/5475 weeks
103-.59366 -.8106 (103*2π)/5475 weeks
1042.39377 -1.71208 (104*2π)/5475 weeks
1054.7504 .49793 (105*2π)/5475 weeks
1064.23216 2.82274 (106*2π)/5475 weeks
1072.60837 5.23225 (107*2π)/5475 weeks
108-1.18398 4.535 (108*2π)/5475 weeks
109-1.70201 1.06856 (109*2π)/5475 weeks
110.49291 -1.74167 (110*2π)/5475 weeks
1114.26685 -.05479 (111*2π)/5475 weeks
1123.56286 3.87902 (112*2π)/5475 weeks
113.30607 4.20591 (113*2π)/5475 weeks
114-1.04501 1.78643 (114*2π)/5475 weeks
115.17197 -.51969 (115*2π)/5475 weeks
1162.84623 .06975 (116*2π)/5475 weeks
1172.9775 1.726 (117*2π)/5475 weeks
1181.98628 3.56008 (118*2π)/5475 weeks
119-.73012 2.35384 (119*2π)/5475 weeks
120.15751 .47548 (120*2π)/5475 weeks
1212.1966 .75801 (121*2π)/5475 weeks
1221.68714 1.66615 (122*2π)/5474 weeks
1231.41702 2.45344 (123*2π)/5474 weeks
124.11764 1.23593 (124*2π)/5474 weeks
1251.1173 .19879 (125*2π)/5474 weeks
1262.34388 1.43992 (126*2π)/5474 weeks
1271.01003 2.6 (127*2π)/5474 weeks
128-.30263 .48885 (128*2π)/5474 weeks
1292.01012 -.99627 (129*2π)/5474 weeks
1303.33904 1.35301 (130*2π)/5474 weeks
1312.53133 2.13487 (131*2π)/5474 weeks
1321.84969 2.48423 (132*2π)/5474 weeks
133.68586 2.67445 (133*2π)/5474 weeks
134-.42526 1.20466 (134*2π)/5474 weeks
1351.28805 .44679 (135*2π)/5474 weeks
1361.75155 .84145 (136*2π)/5474 weeks
1372.29279 1.48815 (137*2π)/5474 weeks
1381.00037 2.75134 (138*2π)/5474 weeks
139.03014 1.22994 (139*2π)/5474 weeks
140.27944 .41426 (140*2π)/5474 weeks
1412.83216 -.55052 (141*2π)/5474 weeks
1423.46601 3.29414 (142*2π)/5474 weeks
143-.3376 3.33493 (143*2π)/5474 weeks
144-.38173 .20951 (144*2π)/5474 weeks
1451.44506 -.16176 (145*2π)/5474 weeks
1461.97092 1.11865 (146*2π)/5474 weeks
1471.24547 2.0398 (147*2π)/5474 weeks
148.12387 .92179 (148*2π)/5474 weeks
149.91393 -.44255 (149*2π)/5474 weeks
1503.09952 -.40336 (150*2π)/5474 weeks
1513.26379 3.06308 (151*2π)/5474 weeks
152-.23391 2.63626 (152*2π)/5474 weeks
153.02682 .7296 (153*2π)/5474 weeks
1541.09378 -.09142 (154*2π)/5474 weeks
1552.39897 .3412 (155*2π)/5474 weeks
1562.25073 1.53631 (156*2π)/5474 weeks
1571.89265 2.0156 (157*2π)/5473 weeks
158.09029 2.63417 (158*2π)/5473 weeks
159-.1775 -.23912 (159*2π)/5473 weeks
1602.06071 -.47577 (160*2π)/5473 weeks
1612.68411 .9864 (161*2π)/5473 weeks
1622.42446 1.9296 (162*2π)/5473 weeks
1632.08031 2.3579 (163*2π)/5473 weeks
164-.17941 3.09976 (164*2π)/5473 weeks
165-.35607 .74451 (165*2π)/5473 weeks
166-.0509 .7116 (166*2π)/5473 weeks
167.77284 -.73383 (167*2π)/5473 weeks
1682.04254 .19004 (168*2π)/5473 weeks
1692.08226 1.39345 (169*2π)/5473 weeks
170.90793 2.00511 (170*2π)/5473 weeks
171-.2773 .6525 (171*2π)/5473 weeks
1721.21285 -.70408 (172*2π)/5473 weeks
1731.88071 -.02748 (173*2π)/5473 weeks
1742.53203 .59508 (174*2π)/5473 weeks
1751.92268 1.89325 (175*2π)/5473 weeks
176.88101 1.99903 (176*2π)/5473 weeks
177.35658 1.27708 (177*2π)/5473 weeks
178-.15199 .29991 (178*2π)/5473 weeks
1791.01597 -.63558 (179*2π)/5473 weeks
1801.81488 -.65122 (180*2π)/5473 weeks
1813.18356 .52784 (181*2π)/5473 weeks
1822.00623 2.2051 (182*2π)/5473 weeks
1831.08681 1.95435 (183*2π)/5473 weeks
184-.29348 1.31474 (184*2π)/5473 weeks
185.46887 -.68263 (185*2π)/5473 weeks
1862.01128 -.62188 (186*2π)/5473 weeks
1873.32047 .96873 (187*2π)/5473 weeks
1881.43545 3.40053 (188*2π)/5473 weeks
189-1.26449 1.46912 (189*2π)/5473 weeks
190-.96279 -1.04065 (190*2π)/5473 weeks
1911.59617 -2.50016 (191*2π)/5473 weeks
1923.7602 -.33964 (192*2π)/5473 weeks
1933.1956 1.10255 (193*2π)/5473 weeks
1942.56663 2.97123 (194*2π)/5473 weeks
195-.69744 1.65711 (195*2π)/5473 weeks
1961.07295 -.19641 (196*2π)/5473 weeks
1971.44701 .3008 (197*2π)/5473 weeks
1982.4218 .38691 (198*2π)/5473 weeks
1991.79282 2.15954 (199*2π)/5473 weeks
2001.04805 1.43731 (200*2π)/5473 weeks
201.16471 2.16369 (201*2π)/5473 weeks
202-.87661 -.23538 (202*2π)/5473 weeks
203.87801 -.38354 (203*2π)/5473 weeks
2041.10911 -1.14762 (204*2π)/5473 weeks
2053.04877 -.72507 (205*2π)/5473 weeks
2062.94186 1.70877 (206*2π)/5473 weeks
2071.34507 2.42652 (207*2π)/5473 weeks
208-.66303 1.57998 (208*2π)/5473 weeks
209-.14913 -1.16916 (209*2π)/5473 weeks
2102.08993 -.8322 (210*2π)/5473 weeks
2113.27695 .33133 (211*2π)/5473 weeks
2122.71694 2.72252 (212*2π)/5473 weeks
213-.89239 2.72243 (213*2π)/5473 weeks
214-1.16291 -.15957 (214*2π)/5473 weeks
215.45771 -1.90495 (215*2π)/5473 weeks
2163.38962 -1.5269 (216*2π)/5473 weeks
2173.37715 1.54088 (217*2π)/5473 weeks
2181.78517 1.9745 (218*2π)/5473 weeks
219.71207 2.03561 (219*2π)/5472 weeks
220-.02926 .94021 (220*2π)/5472 weeks
221.59224 -.12213 (221*2π)/5472 weeks
2221.64639 .47472 (222*2π)/5472 weeks
223.5484 1.25022 (223*2π)/5472 weeks
224.35188 -.11416 (224*2π)/5472 weeks
2251.14977 -.43273 (225*2π)/5472 weeks
2262.6071 .50364 (226*2π)/5472 weeks
227.88337 2.17171 (227*2π)/5472 weeks
228-.09998 .66946 (228*2π)/5472 weeks
229.05555 .01509 (229*2π)/5472 weeks
230.92944 -1.18829 (230*2π)/5472 weeks
2312.41718 -.08221 (231*2π)/5472 weeks
2321.86307 1.8137 (232*2π)/5472 weeks
233-.0801 1.52585 (233*2π)/5472 weeks
234-1.06982 .15025 (234*2π)/5472 weeks
235-.15724 -2.04933 (235*2π)/5472 weeks
2362.24605 -1.79239 (236*2π)/5472 weeks
2373.22133 -.15323 (237*2π)/5472 weeks
2382.47815 2.29661 (238*2π)/5472 weeks
239-.06548 1.52704 (239*2π)/5472 weeks
240-.14751 .22477 (240*2π)/5472 weeks
241.00438 -1.36918 (241*2π)/5472 weeks
2421.95926 -1.07009 (242*2π)/5472 weeks
2432.29267 -.115 (243*2π)/5472 weeks
2442.41616 1.06245 (244*2π)/5472 weeks
245.4337 1.78833 (245*2π)/5472 weeks
246-.53959 -.4623 (246*2π)/5472 weeks
247.46548 -1.29014 (247*2π)/5472 weeks
2482.18188 -1.75882 (248*2π)/5472 weeks
2493.39888 .10322 (249*2π)/5472 weeks
2502.2259 1.65155 (250*2π)/5472 weeks
251.68374 1.946 (251*2π)/5472 weeks
252-.44364 .64572 (252*2π)/5472 weeks
253-.4395 -1.03951 (253*2π)/5472 weeks
254.80413 -1.65165 (254*2π)/5472 weeks
2552.98177 -1.74889 (255*2π)/5472 weeks
2563.20917 1.24319 (256*2π)/5472 weeks
2571.02662 1.49301 (257*2π)/5472 weeks
258.13672 .99567 (258*2π)/5472 weeks
259-1.02091 -1.00682 (259*2π)/5472 weeks
2601.79042 -2.40159 (260*2π)/5472 weeks
2613.782 -.38585 (261*2π)/5472 weeks
2621.96385 1.84044 (262*2π)/5472 weeks
263.53424 1.29202 (263*2π)/5472 weeks
264-.71206 .15162 (264*2π)/5472 weeks
265.05028 -1.74273 (265*2π)/5472 weeks
2662.06996 -2.44045 (266*2π)/5472 weeks
2673.99478 -.22143 (267*2π)/5472 weeks
2682.14203 2.06455 (268*2π)/5472 weeks
269.25301 .99797 (269*2π)/5472 weeks
270-.14873 -.32358 (270*2π)/5472 weeks
2711.05442 -1.38646 (271*2π)/5472 weeks
2721.5348 -1.75873 (272*2π)/5472 weeks
2733.68148 -1.43685 (273*2π)/5472 weeks
2743.68148 1.43685 (274*2π)/5472 weeks
2751.5348 1.75873 (275*2π)/5472 weeks
2761.05442 1.38646 (276*2π)/5472 weeks
277-.14873 .32358 (277*2π)/5472 weeks
278.25301 -.99797 (278*2π)/5472 weeks
2792.14203 -2.06455 (279*2π)/5472 weeks
2803.99478 .22143 (280*2π)/5472 weeks
2812.06996 2.44045 (281*2π)/5472 weeks
282.05028 1.74273 (282*2π)/5472 weeks
283-.71206 -.15162 (283*2π)/5472 weeks
284.53424 -1.29202 (284*2π)/5472 weeks
2851.96385 -1.84044 (285*2π)/5472 weeks
2863.782 .38585 (286*2π)/5472 weeks
2871.79042 2.40159 (287*2π)/5472 weeks
288-1.02091 1.00682 (288*2π)/5472 weeks
289.13672 -.99567 (289*2π)/5472 weeks
2901.02662 -1.49301 (290*2π)/5472 weeks
2913.20917 -1.24319 (291*2π)/5472 weeks
2922.98177 1.74889 (292*2π)/5472 weeks
293.80413 1.65165 (293*2π)/5472 weeks
294-.4395 1.03951 (294*2π)/5472 weeks
295-.44364 -.64572 (295*2π)/5472 weeks
296.68374 -1.946 (296*2π)/5472 weeks
2972.2259 -1.65155 (297*2π)/5472 weeks
2983.39888 -.10322 (298*2π)/5472 weeks
2992.18188 1.75882 (299*2π)/5472 weeks
300.46548 1.29014 (300*2π)/5472 weeks
301-.53959 .4623 (301*2π)/5472 weeks
302.4337 -1.78833 (302*2π)/5472 weeks
3032.41616 -1.06245 (303*2π)/5472 weeks
3042.29267 .115 (304*2π)/5472 weeks
3051.95926 1.07009 (305*2π)/5472 weeks
306.00438 1.36918 (306*2π)/5472 weeks
307-.14751 -.22477 (307*2π)/5472 weeks
308-.06548 -1.52704 (308*2π)/5472 weeks
3092.47815 -2.29661 (309*2π)/5472 weeks
3103.22133 .15323 (310*2π)/5472 weeks
3112.24605 1.79239 (311*2π)/5472 weeks
312-.15724 2.04933 (312*2π)/5472 weeks
313-1.06982 -.15025 (313*2π)/5472 weeks
314-.0801 -1.52585 (314*2π)/5472 weeks
3151.86307 -1.8137 (315*2π)/5472 weeks
3162.41718 .08221 (316*2π)/5472 weeks
317.92944 1.18829 (317*2π)/5472 weeks
318.05555 -.01509 (318*2π)/5472 weeks
319-.09998 -.66946 (319*2π)/5472 weeks
320.88337 -2.17171 (320*2π)/5472 weeks
3212.6071 -.50364 (321*2π)/5472 weeks
3221.14977 .43273 (322*2π)/5472 weeks
323.35188 .11416 (323*2π)/5472 weeks
324.5484 -1.25022 (324*2π)/5472 weeks
3251.64639 -.47472 (325*2π)/5472 weeks
326.59224 .12213 (326*2π)/5472 weeks
327-.02926 -.94021 (327*2π)/5472 weeks
328.71207 -2.03561 (328*2π)/5472 weeks
3291.78517 -1.9745 (329*2π)/5472 weeks
3303.37715 -1.54088 (330*2π)/5472 weeks
3313.38962 1.5269 (331*2π)/5472 weeks
332.45771 1.90495 (332*2π)/5472 weeks
333-1.16291 .15957 (333*2π)/5472 weeks
334-.89239 -2.72243 (334*2π)/5472 weeks
3352.71694 -2.72252 (335*2π)/5472 weeks
3363.27695 -.33133 (336*2π)/5472 weeks
3372.08993 .8322 (337*2π)/5472 weeks
338-.14913 1.16916 (338*2π)/5472 weeks
339-.66303 -1.57998 (339*2π)/5472 weeks
3401.34507 -2.42652 (340*2π)/5472 weeks
3412.94186 -1.70877 (341*2π)/5472 weeks
3423.04877 .72507 (342*2π)/5472 weeks
3431.10911 1.14762 (343*2π)/5472 weeks
344.87801 .38354 (344*2π)/5472 weeks
345-.87661 .23538 (345*2π)/5472 weeks
346.16471 -2.16369 (346*2π)/5472 weeks
3471.04805 -1.43731 (347*2π)/5472 weeks
3481.79282 -2.15954 (348*2π)/5472 weeks
3492.4218 -.38691 (349*2π)/5472 weeks
3501.44701 -.3008 (350*2π)/5472 weeks
3511.07295 .19641 (351*2π)/5472 weeks
352-.69744 -1.65711 (352*2π)/5472 weeks
3532.56663 -2.97123 (353*2π)/5472 weeks
3543.1956 -1.10255 (354*2π)/5472 weeks
3553.7602 .33964 (355*2π)/5472 weeks
3561.59617 2.50016 (356*2π)/5472 weeks
357-.96279 1.04065 (357*2π)/5472 weeks
358-1.26449 -1.46912 (358*2π)/5472 weeks
3591.43545 -3.40053 (359*2π)/5472 weeks
3603.32047 -.96873 (360*2π)/5472 weeks
3612.01128 .62188 (361*2π)/5472 weeks
362.46887 .68263 (362*2π)/5472 weeks
363-.29348 -1.31474 (363*2π)/5472 weeks
3641.08681 -1.95435 (364*2π)/5472 weeks
3652.00623 -2.2051 (365*2π)/5471 weeks
3663.18356 -.52784 (366*2π)/5471 weeks
3671.81488 .65122 (367*2π)/5471 weeks
3681.01597 .63558 (368*2π)/5471 weeks
369-.15199 -.29991 (369*2π)/5471 weeks
370.35658 -1.27708 (370*2π)/5471 weeks
371.88101 -1.99903 (371*2π)/5471 weeks
3721.92268 -1.89325 (372*2π)/5471 weeks
3732.53203 -.59508 (373*2π)/5471 weeks
3741.88071 .02748 (374*2π)/5471 weeks
3751.21285 .70408 (375*2π)/5471 weeks
376-.2773 -.6525 (376*2π)/5471 weeks
377.90793 -2.00511 (377*2π)/5471 weeks
3782.08226 -1.39345 (378*2π)/5471 weeks
3792.04254 -.19004 (379*2π)/5471 weeks
380.77284 .73383 (380*2π)/5471 weeks
381-.0509 -.7116 (381*2π)/5471 weeks
382-.35607 -.74451 (382*2π)/5471 weeks
383-.17941 -3.09976 (383*2π)/5471 weeks
3842.08031 -2.3579 (384*2π)/5471 weeks
3852.42446 -1.9296 (385*2π)/5471 weeks
3862.68411 -.9864 (386*2π)/5471 weeks
3872.06071 .47577 (387*2π)/5471 weeks
388-.1775 .23912 (388*2π)/5471 weeks
389.09029 -2.63417 (389*2π)/5471 weeks
3901.89265 -2.0156 (390*2π)/5471 weeks
3912.25073 -1.53631 (391*2π)/5471 weeks
3922.39897 -.3412 (392*2π)/5471 weeks
3931.09378 .09142 (393*2π)/5471 weeks
394.02682 -.7296 (394*2π)/5471 weeks
395-.23391 -2.63626 (395*2π)/5471 weeks
3963.26379 -3.06308 (396*2π)/5471 weeks
3973.09952 .40336 (397*2π)/5471 weeks
398.91393 .44255 (398*2π)/5471 weeks
399.12387 -.92179 (399*2π)/5471 weeks
4001.24547 -2.0398 (400*2π)/5471 weeks
4011.97092 -1.11865 (401*2π)/5471 weeks
4021.44506 .16176 (402*2π)/5471 weeks
403-.38173 -.20951 (403*2π)/5471 weeks
404-.3376 -3.33493 (404*2π)/5471 weeks
4053.46601 -3.29414 (405*2π)/5471 weeks
4062.83216 .55052 (406*2π)/5471 weeks
407.27944 -.41426 (407*2π)/5471 weeks
408.03014 -1.22994 (408*2π)/5471 weeks
4091.00037 -2.75134 (409*2π)/5471 weeks
4102.29279 -1.48815 (410*2π)/5471 weeks
4111.75155 -.84145 (411*2π)/5471 weeks
4121.28805 -.44679 (412*2π)/5471 weeks
413-.42526 -1.20466 (413*2π)/5471 weeks
414.68586 -2.67445 (414*2π)/5471 weeks
4151.84969 -2.48423 (415*2π)/5471 weeks
4162.53133 -2.13487 (416*2π)/5471 weeks
4173.33904 -1.35301 (417*2π)/5471 weeks
4182.01012 .99627 (418*2π)/5471 weeks
419-.30263 -.48885 (419*2π)/5471 weeks
4201.01003 -2.6 (420*2π)/5471 weeks
4212.34388 -1.43992 (421*2π)/5471 weeks
4221.1173 -.19879 (422*2π)/5471 weeks
423.11764 -1.23593 (423*2π)/5471 weeks
4241.41702 -2.45344 (424*2π)/5471 weeks
4251.68714 -1.66615 (425*2π)/5471 weeks
4262.1966 -.75801 (426*2π)/5471 weeks
427.15751 -.47548 (427*2π)/5471 weeks
428-.73012 -2.35384 (428*2π)/5471 weeks
4291.98628 -3.56008 (429*2π)/5471 weeks
4302.9775 -1.726 (430*2π)/5471 weeks
4312.84623 -.06975 (431*2π)/5471 weeks
432.17197 .51969 (432*2π)/5471 weeks
433-1.04501 -1.78643 (433*2π)/5471 weeks
434.30607 -4.20591 (434*2π)/5471 weeks
4353.56286 -3.87902 (435*2π)/5471 weeks
4364.26685 .05479 (436*2π)/5471 weeks
437.49291 1.74167 (437*2π)/5471 weeks
438-1.70201 -1.06856 (438*2π)/5471 weeks
439-1.18398 -4.535 (439*2π)/5471 weeks
4402.60837 -5.23225 (440*2π)/5471 weeks
4414.23216 -2.82274 (441*2π)/5471 weeks
4424.7504 -.49793 (442*2π)/5471 weeks
4432.39377 1.71208 (443*2π)/5471 weeks
444-.59366 .8106 (444*2π)/5471 weeks
445-1.0748 -1.39568 (445*2π)/5471 weeks
446-.14459 -3.88303 (446*2π)/5471 weeks
4472.3675 -3.27361 (447*2π)/5471 weeks
4482.68747 -.65715 (448*2π)/5471 weeks
449.70018 -.56175 (449*2π)/5471 weeks
450-.16749 -1.54021 (450*2π)/5471 weeks
451.31077 -2.70434 (451*2π)/5471 weeks
4521.26988 -2.99269 (452*2π)/5471 weeks
4531.52258 -1.45008 (453*2π)/5471 weeks
454.20608 -3.11518 (454*2π)/5471 weeks
4552.04239 -3.62978 (455*2π)/5471 weeks
4563.42929 -1.27721 (456*2π)/5471 weeks
457.3074 1.26733 (457*2π)/5471 weeks
458-2.88169 -2.01969 (458*2π)/5471 weeks
459-1.58133 -5.48491 (459*2π)/5471 weeks
4602.8311 -7.14144 (460*2π)/5471 weeks
4616.14044 -4.09463 (461*2π)/5471 weeks
4624.86728 1.2812 (462*2π)/5471 weeks
463-.63881 .33177 (463*2π)/5471 weeks
464-1.18589 -2.91014 (464*2π)/5471 weeks
4651.13465 -5.99686 (465*2π)/5471 weeks
4665.28101 -4.29897 (466*2π)/5471 weeks
4675.40355 .19574 (467*2π)/5471 weeks
4681.753 3.26149 (468*2π)/5471 weeks
469-5.0353 .42744 (469*2π)/5471 weeks
470-1.72145 -7.97889 (470*2π)/5471 weeks
4713.57418 -5.35661 (471*2π)/5471 weeks
4724.68242 -3.75366 (472*2π)/5471 weeks
4734.66703 .54771 (473*2π)/5471 weeks
474-.20763 1.7241 (474*2π)/5471 weeks
475-2.22343 -1.03151 (475*2π)/5471 weeks
476-1.98198 -5.29846 (476*2π)/5471 weeks
4773.2712 -5.98072 (477*2π)/5471 weeks
4783.54898 -1.59679 (478*2π)/5471 weeks
479.6638 -2.68321 (479*2π)/5471 weeks
4801.43388 -1.98823 (480*2π)/5471 weeks
481.70903 -4.72877 (481*2π)/5471 weeks
4823.10222 -2.20739 (482*2π)/5471 weeks
483.90941 -1.5178 (483*2π)/5471 weeks
484.50337 -3.21207 (484*2π)/5471 weeks
485.17 -3.4428 (485*2π)/5471 weeks
4862.60963 -4.62842 (486*2π)/5471 weeks
4872.08409 -.61153 (487*2π)/5471 weeks
488-1.17617 -3.38378 (488*2π)/5471 weeks
4891.16492 -4.47783 (489*2π)/5471 weeks
4901.46312 -4.27977 (490*2π)/5471 weeks
4913.65633 -4.76758 (491*2π)/5471 weeks
4923.28591 -1.02492 (492*2π)/5471 weeks
493-.57547 -1.11921 (493*2π)/5471 weeks
494-.23845 -3.35609 (494*2π)/5471 weeks
495-.41392 -4.50147 (495*2π)/5471 weeks
4962.94327 -4.40862 (496*2π)/5471 weeks
4971.67589 -1.1503 (497*2π)/5471 weeks
498-1.22386 -1.30437 (498*2π)/5471 weeks
499-2.12743 -3.88288 (499*2π)/5471 weeks
500-2.88994 -5.45259 (500*2π)/5471 weeks
501.38884 -8.04557 (501*2π)/5471 weeks
5022.56702 -5.73348 (502*2π)/5471 weeks
5032.19272 -4.55476 (503*2π)/5471 weeks
504-.57041 -2.52988 (504*2π)/5471 weeks
505-.90837 -7.88265 (505*2π)/5471 weeks
5062.36442 -4.60943 (506*2π)/5471 weeks
507-1.27429 -7.17688 (507*2π)/5471 weeks
5082.54775 -6.26161 (508*2π)/5471 weeks
5092.16845 -4.98631 (509*2π)/5471 weeks
510-1.0235 -5.4658 (510*2π)/5471 weeks
5112.2929 -7.91648 (511*2π)/5471 weeks
5125.06135 -3.78594 (512*2π)/5471 weeks
513-2.17503 1.28899 (513*2π)/5471 weeks
514-9.29887 -6.39323 (514*2π)/5471 weeks
515-6.30455 -14.71507 (515*2π)/5471 weeks
5162.48144 -17.63026 (516*2π)/5471 weeks
5179.86864 -9.48277 (517*2π)/5471 weeks
5185.34632 -2.9108 (518*2π)/5471 weeks
519-.05403 -2.89527 (519*2π)/5471 weeks
520-7.44078 -5.32098 (520*2π)/5471 weeks
521-6.92136 -17.66033 (521*2π)/5471 weeks
5223.76666 -19.03551 (522*2π)/5471 weeks
5238.79327 -13.72478 (523*2π)/5471 weeks
5247.92073 -4.5426 (524*2π)/5471 weeks
525-1.66442 -6.02687 (525*2π)/5471 weeks
526-4.81764 -12.31503 (526*2π)/5471 weeks
527-1.80139 -20.35542 (527*2π)/5471 weeks
5289.23894 -22.76735 (528*2π)/5471 weeks
52917.81631 -9.42012 (529*2π)/5471 weeks
5302.18668 -3.22182 (530*2π)/5471 weeks
5316.93541 -11.43927 (531*2π)/5471 weeks
532-1.1676 -3.51652 (532*2π)/5471 weeks
533-5.80643 -13.84463 (533*2π)/5471 weeks
534-4.93191 -20.06043 (534*2π)/5471 weeks
535-.44625 -26.25868 (535*2π)/5471 weeks
5365.70153 -22.38351 (536*2π)/5471 weeks
5373.17773 -27.81902 (537*2π)/5471 weeks
53815.65848 -17.062 (538*2π)/5471 weeks
539-12.19936 -11.78597 (539*2π)/5471 weeks
540-8.93041 -48.94566 (540*2π)/5471 weeks
54124.42369 -52.34589 (541*2π)/5471 weeks
54226.1951 -21.36437 (542*2π)/5471 weeks
543-9.16873 -10.42615 (543*2π)/5471 weeks
544-55.68248 -59.48364 (544*2π)/5471 weeks
545-44.03403 -153.9292 (545*2π)/5471 weeks



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