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Fourier Analysis of SMN (ProShares UltraShort Basic Materials ETF)


SMN (ProShares UltraShort Basic Materials ETF) appears to have interesting cyclic behaviour every 43 weeks (36.8062*sine), 46 weeks (34.0874*sine), and 50 weeks (27.851*cosine).

SMN (ProShares UltraShort Basic Materials ETF) has an average price of 190.4 (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 2/2/2007 to 9/5/2017 for SMN (ProShares UltraShort Basic Materials ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0190.3966   0 
1158.5195 196.1854 (1*2π)/554554 weeks
23.53331 159.0001 (2*2π)/554277 weeks
3-42.61643 54.57167 (3*2π)/554185 weeks
48.40729 3.4328 (4*2π)/554139 weeks
554.64084 21.94163 (5*2π)/554111 weeks
649.50746 66.77454 (6*2π)/55492 weeks
7-1.21488 81.97718 (7*2π)/55479 weeks
8-37.97707 40.83347 (8*2π)/55469 weeks
9-20.65668 -.35627 (9*2π)/55462 weeks
109.82044 -3.50069 (10*2π)/55455 weeks
1127.85098 10.40322 (11*2π)/55450 weeks
1223.2917 34.08741 (12*2π)/55446 weeks
131.55633 36.80618 (13*2π)/55443 weeks
14-10.92844 25.38582 (14*2π)/55440 weeks
15-8.83493 9.10897 (15*2π)/55437 weeks
161.46452 4.71426 (16*2π)/55435 weeks
176.5174 5.6522 (17*2π)/55433 weeks
1812.92684 10.90445 (18*2π)/55431 weeks
199.78281 18.06105 (19*2π)/55429 weeks
205.71002 18.9682 (20*2π)/55428 weeks
211.1109 17.30482 (21*2π)/55426 weeks
22-1.5139 13.30166 (22*2π)/55425 weeks
23-.51839 7.85882 (23*2π)/55424 weeks
247.1259 7.76371 (24*2π)/55423 weeks
2510.41111 16.03571 (25*2π)/55422 weeks
261.77062 23.58249 (26*2π)/55421 weeks
27-10.63113 16.35908 (27*2π)/55421 weeks
28-11.26572 3.83574 (28*2π)/55420 weeks
29-.67351 -4.0579 (29*2π)/55419 weeks
3011.04279 2.92605 (30*2π)/55418 weeks
3110.29329 15.62201 (31*2π)/55418 weeks
32-2.53173 20.0504 (32*2π)/55417 weeks
33-13.04359 8.96272 (33*2π)/55417 weeks
34-6.66962 -5.81633 (34*2π)/55416 weeks
357.65894 -4.36402 (35*2π)/55416 weeks
3611.83738 5.63894 (36*2π)/55415 weeks
376.16495 13.3723 (37*2π)/55415 weeks
38-1.16519 11.03092 (38*2π)/55415 weeks
39-2.01125 5.82784 (39*2π)/55414 weeks
40.39865 2.82656 (40*2π)/55414 weeks
414.69626 2.80067 (41*2π)/55414 weeks
425.58696 7.85571 (42*2π)/55413 weeks
432.68257 9.1606 (43*2π)/55413 weeks
441.30041 8.70106 (44*2π)/55413 weeks
45-.05826 7.59334 (45*2π)/55412 weeks
46-.28022 7.5437 (46*2π)/55412 weeks
47-1.87711 6.34806 (47*2π)/55412 weeks
48-1.44556 4.33732 (48*2π)/55412 weeks
49-1.35616 2.82536 (49*2π)/55411 weeks
501.036 2.63992 (50*2π)/55411 weeks
511.92673 3.42928 (51*2π)/55411 weeks
521.6331 5.04557 (52*2π)/55411 weeks
53-.93913 4.62524 (53*2π)/55410 weeks
54-1.34581 .90329 (54*2π)/55410 weeks
552.3918 -1.19382 (55*2π)/55410 weeks
567.62261 1.20724 (56*2π)/55410 weeks
576.59401 8.27828 (57*2π)/55410 weeks
58.98116 9.53052 (58*2π)/55410 weeks
59-2.38677 5.85512 (59*2π)/5549 weeks
60-1.62056 2.04674 (60*2π)/5549 weeks
611.89678 .99988 (61*2π)/5549 weeks
622.54476 3.99264 (62*2π)/5549 weeks
63.89126 3.48961 (63*2π)/5549 weeks
641.44308 2.65507 (64*2π)/5549 weeks
652.95238 2.12902 (65*2π)/5549 weeks
663.66771 4.23086 (66*2π)/5548 weeks
671.01923 5.56814 (67*2π)/5548 weeks
68.49973 3.86903 (68*2π)/5548 weeks
69.93338 2.69316 (69*2π)/5548 weeks
703.73748 3.38828 (70*2π)/5548 weeks
711.73222 7.653 (71*2π)/5548 weeks
72-3.83589 6.26528 (72*2π)/5548 weeks
73-4.80299 .29403 (73*2π)/5548 weeks
74-.27164 -4.09074 (74*2π)/5547 weeks
755.86306 -1.48007 (75*2π)/5547 weeks
765.70658 3.69039 (76*2π)/5547 weeks
773.33608 5.52318 (77*2π)/5547 weeks
78-1.05958 6.11561 (78*2π)/5547 weeks
79-3.19958 .42337 (79*2π)/5547 weeks
801.88051 -2.95518 (80*2π)/5547 weeks
816.2893 -.52831 (81*2π)/5547 weeks
827.00702 4.88053 (82*2π)/5547 weeks
831.61721 7.67152 (83*2π)/5547 weeks
84-1.81128 4.70575 (84*2π)/5547 weeks
85-2.24904 .22788 (85*2π)/5547 weeks
862.57784 -2.53971 (86*2π)/5546 weeks
876.54849 1.09545 (87*2π)/5546 weeks
885.57097 5.60526 (88*2π)/5546 weeks
891.12637 6.94845 (89*2π)/5546 weeks
90-2.04489 3.66182 (90*2π)/5546 weeks
91-.21297 .13373 (91*2π)/5546 weeks
922.7334 .44167 (92*2π)/5546 weeks
933.57673 2.76107 (93*2π)/5546 weeks
941.84766 3.93389 (94*2π)/5546 weeks
951.38309 2.88919 (95*2π)/5546 weeks
961.70231 3.6759 (96*2π)/5546 weeks
97-.28045 3.53104 (97*2π)/5546 weeks
98-1.39662 1.20818 (98*2π)/5546 weeks
99.35305 -1.24821 (99*2π)/5546 weeks
1003.42592 -.63627 (100*2π)/5546 weeks
1014.61811 2.20679 (101*2π)/5545 weeks
1022.82273 4.42364 (102*2π)/5545 weeks
103-.27951 3.67601 (103*2π)/5545 weeks
104-.88726 -.12716 (104*2π)/5545 weeks
1052.4754 -1.84878 (105*2π)/5545 weeks
1065.77697 -.05644 (106*2π)/5545 weeks
1075.77443 4.56484 (107*2π)/5545 weeks
1082.15965 6.31473 (108*2π)/5545 weeks
109-1.53647 4.16109 (109*2π)/5545 weeks
110-1.1815 -.41629 (110*2π)/5545 weeks
1113.00091 -1.55934 (111*2π)/5545 weeks
1125.94198 1.87954 (112*2π)/5545 weeks
1133.93131 5.85865 (113*2π)/5545 weeks
114.22773 6.08172 (114*2π)/5545 weeks
115-2.72294 3.58232 (115*2π)/5545 weeks
116-1.82508 -.80587 (116*2π)/5545 weeks
1171.55141 -1.7107 (117*2π)/5545 weeks
1183.65995 .10842 (118*2π)/5545 weeks
1193.62369 2.26265 (119*2π)/5545 weeks
1201.90972 3.11658 (120*2π)/5545 weeks
121.76784 1.98199 (121*2π)/5545 weeks
1221.16307 .54546 (122*2π)/5545 weeks
1233.08198 .47856 (123*2π)/5545 weeks
1243.77105 2.51624 (124*2π)/5544 weeks
1251.66757 3.71989 (125*2π)/5544 weeks
126.50715 2.60348 (126*2π)/5544 weeks
127.75886 1.06989 (127*2π)/5544 weeks
1281.92408 1.10601 (128*2π)/5544 weeks
1291.71414 1.56039 (129*2π)/5544 weeks
1301.68798 1.15824 (130*2π)/5544 weeks
1312.13768 1.24735 (131*2π)/5544 weeks
1321.96608 1.52587 (132*2π)/5544 weeks
1332.17272 1.2328 (133*2π)/5544 weeks
1343.21064 1.32537 (134*2π)/5544 weeks
1353.1942 2.83733 (135*2π)/5544 weeks
1361.60262 3.19579 (136*2π)/5544 weeks
137.82197 2.73054 (137*2π)/5544 weeks
138.72928 1.35786 (138*2π)/5544 weeks
1392.39894 1.40439 (139*2π)/5544 weeks
1401.75058 2.91434 (140*2π)/5544 weeks
141.5412 2.05802 (141*2π)/5544 weeks
142.65426 .97467 (142*2π)/5544 weeks
1431.96643 .63935 (143*2π)/5544 weeks
1442.25867 2.18214 (144*2π)/5544 weeks
1451.12702 2.06022 (145*2π)/5544 weeks
1461.52048 1.26612 (146*2π)/5544 weeks
1471.91382 1.48903 (147*2π)/5544 weeks
1482.0922 2.12409 (148*2π)/5544 weeks
1491.0025 2.97379 (149*2π)/5544 weeks
150-.19747 1.71343 (150*2π)/5544 weeks
151.05068 .18726 (151*2π)/5544 weeks
1522.03322 -.71796 (152*2π)/5544 weeks
1533.20753 1.18574 (153*2π)/5544 weeks
1542.16346 2.19651 (154*2π)/5544 weeks
1551.39494 2.01612 (155*2π)/5544 weeks
1561.19913 1.61412 (156*2π)/5544 weeks
1571.17863 1.09478 (157*2π)/5544 weeks
1581.83201 .60428 (158*2π)/5544 weeks
1593.00053 .96009 (159*2π)/5543 weeks
1602.85241 2.80487 (160*2π)/5543 weeks
1611.33319 3.06922 (161*2π)/5543 weeks
162.67445 2.67728 (162*2π)/5543 weeks
163-.11046 1.93902 (163*2π)/5543 weeks
164.1712 .60106 (164*2π)/5543 weeks
1651.39876 .20071 (165*2π)/5543 weeks
1662.27412 1.3979 (166*2π)/5543 weeks
1671.5872 2.45383 (167*2π)/5543 weeks
168.14186 2.41799 (168*2π)/5543 weeks
169-.5808 1.08946 (169*2π)/5543 weeks
170.10829 -.40097 (170*2π)/5543 weeks
1711.70815 -.51311 (171*2π)/5543 weeks
1722.3469 .63507 (172*2π)/5543 weeks
1731.99816 1.57561 (173*2π)/5543 weeks
174.892 1.4744 (174*2π)/5543 weeks
175.39047 .55158 (175*2π)/5543 weeks
1761.09901 -.63461 (176*2π)/5543 weeks
1772.9239 -.68119 (177*2π)/5543 weeks
1784.15728 1.00049 (178*2π)/5543 weeks
1793.36018 3.17207 (179*2π)/5543 weeks
180.88181 3.79335 (180*2π)/5543 weeks
181-.65943 2.07346 (181*2π)/5543 weeks
182-.05034 .15707 (182*2π)/5543 weeks
1831.66076 -.23985 (183*2π)/5543 weeks
1842.48187 1.1171 (184*2π)/5543 weeks
1851.71618 2.05234 (185*2π)/5543 weeks
186.42237 1.89003 (186*2π)/5543 weeks
187.48844 .91712 (187*2π)/5543 weeks
188.77002 .53146 (188*2π)/5543 weeks
1891.72143 .49157 (189*2π)/5543 weeks
1901.72744 1.58259 (190*2π)/5543 weeks
191.51367 1.9706 (191*2π)/5543 weeks
192-.57079 1.29843 (192*2π)/5543 weeks
193-.79309 -.52093 (193*2π)/5543 weeks
194.97462 -1.9622 (194*2π)/5543 weeks
1952.98129 -1.67573 (195*2π)/5543 weeks
1964.78332 .28601 (196*2π)/5543 weeks
1973.28659 3.45094 (197*2π)/5543 weeks
198.51166 3.10894 (198*2π)/5543 weeks
199-.47831 1.34151 (199*2π)/5543 weeks
200.54539 -.24787 (200*2π)/5543 weeks
2012.05269 .17434 (201*2π)/5543 weeks
2021.93135 1.1244 (202*2π)/5543 weeks
2031.691 2.04471 (203*2π)/5543 weeks
204-.3381 2.04587 (204*2π)/5543 weeks
205-.44805 .11361 (205*2π)/5543 weeks
206.15363 -.81696 (206*2π)/5543 weeks
2071.96799 -1.41664 (207*2π)/5543 weeks
2083.36647 .12873 (208*2π)/5543 weeks
2092.61114 2.20243 (209*2π)/5543 weeks
210.20073 2.36321 (210*2π)/5543 weeks
211-.75551 .03369 (211*2π)/5543 weeks
2121.23411 -1.61929 (212*2π)/5543 weeks
2133.10312 -.34449 (213*2π)/5543 weeks
2143.1923 1.5325 (214*2π)/5543 weeks
2151.30202 2.94015 (215*2π)/5543 weeks
216-.7883 1.16244 (216*2π)/5543 weeks
217.12647 -.94466 (217*2π)/5543 weeks
2182.30745 -1.02565 (218*2π)/5543 weeks
2193.03724 1.18152 (219*2π)/5543 weeks
2201.24069 2.08859 (220*2π)/5543 weeks
221.14845 .82451 (221*2π)/5543 weeks
2221.05842 -.36742 (222*2π)/5542 weeks
2232.14207 .16207 (223*2π)/5542 weeks
2242.31426 1.2419 (224*2π)/5542 weeks
2251.21816 2.24483 (225*2π)/5542 weeks
226-.35986 1.45276 (226*2π)/5542 weeks
227.05592 -.10694 (227*2π)/5542 weeks
2281.06663 -.26652 (228*2π)/5542 weeks
2291.49628 .69821 (229*2π)/5542 weeks
230.36524 1.13653 (230*2π)/5542 weeks
231-.10927 .14403 (231*2π)/5542 weeks
232.18824 -.81551 (232*2π)/5542 weeks
2331.22253 -1.27869 (233*2π)/5542 weeks
2342.20381 -.52325 (234*2π)/5542 weeks
2352.19952 .61075 (235*2π)/5542 weeks
2361.11176 1.38095 (236*2π)/5542 weeks
237-.37445 .44223 (237*2π)/5542 weeks
238.0512 -1.27983 (238*2π)/5542 weeks
2391.65596 -1.82132 (239*2π)/5542 weeks
2403.08146 -.99793 (240*2π)/5542 weeks
2413.13122 1.16806 (241*2π)/5542 weeks
2421.46278 1.49348 (242*2π)/5542 weeks
243.57814 .97386 (243*2π)/5542 weeks
244.21585 -.42765 (244*2π)/5542 weeks
2451.57669 -.92473 (245*2π)/5542 weeks
2462.22697 -.15556 (246*2π)/5542 weeks
2472.39798 .71016 (247*2π)/5542 weeks
2481.32499 1.74489 (248*2π)/5542 weeks
249-.49604 1.08514 (249*2π)/5542 weeks
250-.85798 -.74631 (250*2π)/5542 weeks
251.67016 -2.59822 (251*2π)/5542 weeks
2523.07339 -2.07428 (252*2π)/5542 weeks
2533.66844 .18527 (253*2π)/5542 weeks
2542.59926 1.51512 (254*2π)/5542 weeks
255.90823 1.86556 (255*2π)/5542 weeks
256-.77764 .45144 (256*2π)/5542 weeks
257-.07344 -1.8909 (257*2π)/5542 weeks
2582.5611 -2.71371 (258*2π)/5542 weeks
2594.48757 -.12063 (259*2π)/5542 weeks
2602.82322 2.35338 (260*2π)/5542 weeks
261.47531 2.22437 (261*2π)/5542 weeks
262-1.22402 .27645 (262*2π)/5542 weeks
263-.07206 -2.56239 (263*2π)/5542 weeks
2643.01594 -2.55906 (264*2π)/5542 weeks
2654.33461 .51998 (265*2π)/5542 weeks
2662.31666 2.41996 (266*2π)/5542 weeks
267-.17755 1.91824 (267*2π)/5542 weeks
268-1.38894 -.60763 (268*2π)/5542 weeks
269.16439 -3.25097 (269*2π)/5542 weeks
2703.86168 -3.09602 (270*2π)/5542 weeks
2715.13043 .62116 (271*2π)/5542 weeks
2722.49974 2.7109 (272*2π)/5542 weeks
273.16618 1.70888 (273*2π)/5542 weeks
274-.67424 -.37595 (274*2π)/5542 weeks
275.49982 -2.27619 (275*2π)/5542 weeks
2763.08579 -2.70171 (276*2π)/5542 weeks
2775.12073   (277*2π)/5542 weeks
2783.08579 2.70171 (278*2π)/5542 weeks
279.49982 2.27619 (279*2π)/5542 weeks
280-.67424 .37595 (280*2π)/5542 weeks
281.16618 -1.70888 (281*2π)/5542 weeks
2822.49974 -2.7109 (282*2π)/5542 weeks
2835.13043 -.62116 (283*2π)/5542 weeks
2843.86168 3.09602 (284*2π)/5542 weeks
285.16439 3.25097 (285*2π)/5542 weeks
286-1.38894 .60763 (286*2π)/5542 weeks
287-.17755 -1.91824 (287*2π)/5542 weeks
2882.31666 -2.41996 (288*2π)/5542 weeks
2894.33461 -.51998 (289*2π)/5542 weeks
2903.01594 2.55906 (290*2π)/5542 weeks
291-.07206 2.56239 (291*2π)/5542 weeks
292-1.22402 -.27645 (292*2π)/5542 weeks
293.47531 -2.22437 (293*2π)/5542 weeks
2942.82322 -2.35338 (294*2π)/5542 weeks
2954.48757 .12063 (295*2π)/5542 weeks
2962.5611 2.71371 (296*2π)/5542 weeks
297-.07344 1.8909 (297*2π)/5542 weeks
298-.77764 -.45144 (298*2π)/5542 weeks
299.90823 -1.86556 (299*2π)/5542 weeks
3002.59926 -1.51512 (300*2π)/5542 weeks
3013.66844 -.18527 (301*2π)/5542 weeks
3023.07339 2.07428 (302*2π)/5542 weeks
303.67016 2.59822 (303*2π)/5542 weeks
304-.85798 .74631 (304*2π)/5542 weeks
305-.49604 -1.08514 (305*2π)/5542 weeks
3061.32499 -1.74489 (306*2π)/5542 weeks
3072.39798 -.71016 (307*2π)/5542 weeks
3082.22697 .15556 (308*2π)/5542 weeks
3091.57669 .92473 (309*2π)/5542 weeks
310.21585 .42765 (310*2π)/5542 weeks
311.57814 -.97386 (311*2π)/5542 weeks
3121.46278 -1.49348 (312*2π)/5542 weeks
3133.13122 -1.16806 (313*2π)/5542 weeks
3143.08146 .99793 (314*2π)/5542 weeks
3151.65596 1.82132 (315*2π)/5542 weeks
316.0512 1.27983 (316*2π)/5542 weeks
317-.37445 -.44223 (317*2π)/5542 weeks
3181.11176 -1.38095 (318*2π)/5542 weeks
3192.19952 -.61075 (319*2π)/5542 weeks
3202.20381 .52325 (320*2π)/5542 weeks
3211.22253 1.27869 (321*2π)/5542 weeks
322.18824 .81551 (322*2π)/5542 weeks
323-.10927 -.14403 (323*2π)/5542 weeks
324.36524 -1.13653 (324*2π)/5542 weeks
3251.49628 -.69821 (325*2π)/5542 weeks
3261.06663 .26652 (326*2π)/5542 weeks
327.05592 .10694 (327*2π)/5542 weeks
328-.35986 -1.45276 (328*2π)/5542 weeks
3291.21816 -2.24483 (329*2π)/5542 weeks
3302.31426 -1.2419 (330*2π)/5542 weeks
3312.14207 -.16207 (331*2π)/5542 weeks
3321.05842 .36742 (332*2π)/5542 weeks
333.14845 -.82451 (333*2π)/5542 weeks
3341.24069 -2.08859 (334*2π)/5542 weeks
3353.03724 -1.18152 (335*2π)/5542 weeks
3362.30745 1.02565 (336*2π)/5542 weeks
337.12647 .94466 (337*2π)/5542 weeks
338-.7883 -1.16244 (338*2π)/5542 weeks
3391.30202 -2.94015 (339*2π)/5542 weeks
3403.1923 -1.5325 (340*2π)/5542 weeks
3413.10312 .34449 (341*2π)/5542 weeks
3421.23411 1.61929 (342*2π)/5542 weeks
343-.75551 -.03369 (343*2π)/5542 weeks
344.20073 -2.36321 (344*2π)/5542 weeks
3452.61114 -2.20243 (345*2π)/5542 weeks
3463.36647 -.12873 (346*2π)/5542 weeks
3471.96799 1.41664 (347*2π)/5542 weeks
348.15363 .81696 (348*2π)/5542 weeks
349-.44805 -.11361 (349*2π)/5542 weeks
350-.3381 -2.04587 (350*2π)/5542 weeks
3511.691 -2.04471 (351*2π)/5542 weeks
3521.93135 -1.1244 (352*2π)/5542 weeks
3532.05269 -.17434 (353*2π)/5542 weeks
354.54539 .24787 (354*2π)/5542 weeks
355-.47831 -1.34151 (355*2π)/5542 weeks
356.51166 -3.10894 (356*2π)/5542 weeks
3573.28659 -3.45094 (357*2π)/5542 weeks
3584.78332 -.28601 (358*2π)/5542 weeks
3592.98129 1.67573 (359*2π)/5542 weeks
360.97462 1.9622 (360*2π)/5542 weeks
361-.79309 .52093 (361*2π)/5542 weeks
362-.57079 -1.29843 (362*2π)/5542 weeks
363.51367 -1.9706 (363*2π)/5542 weeks
3641.72744 -1.58259 (364*2π)/5542 weeks
3651.72143 -.49157 (365*2π)/5542 weeks
366.77002 -.53146 (366*2π)/5542 weeks
367.48844 -.91712 (367*2π)/5542 weeks
368.42237 -1.89003 (368*2π)/5542 weeks
3691.71618 -2.05234 (369*2π)/5542 weeks
3702.48187 -1.1171 (370*2π)/5541 weeks
3711.66076 .23985 (371*2π)/5541 weeks
372-.05034 -.15707 (372*2π)/5541 weeks
373-.65943 -2.07346 (373*2π)/5541 weeks
374.88181 -3.79335 (374*2π)/5541 weeks
3753.36018 -3.17207 (375*2π)/5541 weeks
3764.15728 -1.00049 (376*2π)/5541 weeks
3772.9239 .68119 (377*2π)/5541 weeks
3781.09901 .63461 (378*2π)/5541 weeks
379.39047 -.55158 (379*2π)/5541 weeks
380.892 -1.4744 (380*2π)/5541 weeks
3811.99816 -1.57561 (381*2π)/5541 weeks
3822.3469 -.63507 (382*2π)/5541 weeks
3831.70815 .51311 (383*2π)/5541 weeks
384.10829 .40097 (384*2π)/5541 weeks
385-.5808 -1.08946 (385*2π)/5541 weeks
386.14186 -2.41799 (386*2π)/5541 weeks
3871.5872 -2.45383 (387*2π)/5541 weeks
3882.27412 -1.3979 (388*2π)/5541 weeks
3891.39876 -.20071 (389*2π)/5541 weeks
390.1712 -.60106 (390*2π)/5541 weeks
391-.11046 -1.93902 (391*2π)/5541 weeks
392.67445 -2.67728 (392*2π)/5541 weeks
3931.33319 -3.06922 (393*2π)/5541 weeks
3942.85241 -2.80487 (394*2π)/5541 weeks
3953.00053 -.96009 (395*2π)/5541 weeks
3961.83201 -.60428 (396*2π)/5541 weeks
3971.17863 -1.09478 (397*2π)/5541 weeks
3981.19913 -1.61412 (398*2π)/5541 weeks
3991.39494 -2.01612 (399*2π)/5541 weeks
4002.16346 -2.19651 (400*2π)/5541 weeks
4013.20753 -1.18574 (401*2π)/5541 weeks
4022.03322 .71796 (402*2π)/5541 weeks
403.05068 -.18726 (403*2π)/5541 weeks
404-.19747 -1.71343 (404*2π)/5541 weeks
4051.0025 -2.97379 (405*2π)/5541 weeks
4062.0922 -2.12409 (406*2π)/5541 weeks
4071.91382 -1.48903 (407*2π)/5541 weeks
4081.52048 -1.26612 (408*2π)/5541 weeks
4091.12702 -2.06022 (409*2π)/5541 weeks
4102.25867 -2.18214 (410*2π)/5541 weeks
4111.96643 -.63935 (411*2π)/5541 weeks
412.65426 -.97467 (412*2π)/5541 weeks
413.5412 -2.05802 (413*2π)/5541 weeks
4141.75058 -2.91434 (414*2π)/5541 weeks
4152.39894 -1.40439 (415*2π)/5541 weeks
416.72928 -1.35786 (416*2π)/5541 weeks
417.82197 -2.73054 (417*2π)/5541 weeks
4181.60262 -3.19579 (418*2π)/5541 weeks
4193.1942 -2.83733 (419*2π)/5541 weeks
4203.21064 -1.32537 (420*2π)/5541 weeks
4212.17272 -1.2328 (421*2π)/5541 weeks
4221.96608 -1.52587 (422*2π)/5541 weeks
4232.13768 -1.24735 (423*2π)/5541 weeks
4241.68798 -1.15824 (424*2π)/5541 weeks
4251.71414 -1.56039 (425*2π)/5541 weeks
4261.92408 -1.10601 (426*2π)/5541 weeks
427.75886 -1.06989 (427*2π)/5541 weeks
428.50715 -2.60348 (428*2π)/5541 weeks
4291.66757 -3.71989 (429*2π)/5541 weeks
4303.77105 -2.51624 (430*2π)/5541 weeks
4313.08198 -.47856 (431*2π)/5541 weeks
4321.16307 -.54546 (432*2π)/5541 weeks
433.76784 -1.98199 (433*2π)/5541 weeks
4341.90972 -3.11658 (434*2π)/5541 weeks
4353.62369 -2.26265 (435*2π)/5541 weeks
4363.65995 -.10842 (436*2π)/5541 weeks
4371.55141 1.7107 (437*2π)/5541 weeks
438-1.82508 .80587 (438*2π)/5541 weeks
439-2.72294 -3.58232 (439*2π)/5541 weeks
440.22773 -6.08172 (440*2π)/5541 weeks
4413.93131 -5.85865 (441*2π)/5541 weeks
4425.94198 -1.87954 (442*2π)/5541 weeks
4433.00091 1.55934 (443*2π)/5541 weeks
444-1.1815 .41629 (444*2π)/5541 weeks
445-1.53647 -4.16109 (445*2π)/5541 weeks
4462.15965 -6.31473 (446*2π)/5541 weeks
4475.77443 -4.56484 (447*2π)/5541 weeks
4485.77697 .05644 (448*2π)/5541 weeks
4492.4754 1.84878 (449*2π)/5541 weeks
450-.88726 .12716 (450*2π)/5541 weeks
451-.27951 -3.67601 (451*2π)/5541 weeks
4522.82273 -4.42364 (452*2π)/5541 weeks
4534.61811 -2.20679 (453*2π)/5541 weeks
4543.42592 .63627 (454*2π)/5541 weeks
455.35305 1.24821 (455*2π)/5541 weeks
456-1.39662 -1.20818 (456*2π)/5541 weeks
457-.28045 -3.53104 (457*2π)/5541 weeks
4581.70231 -3.6759 (458*2π)/5541 weeks
4591.38309 -2.88919 (459*2π)/5541 weeks
4601.84766 -3.93389 (460*2π)/5541 weeks
4613.57673 -2.76107 (461*2π)/5541 weeks
4622.7334 -.44167 (462*2π)/5541 weeks
463-.21297 -.13373 (463*2π)/5541 weeks
464-2.04489 -3.66182 (464*2π)/5541 weeks
4651.12637 -6.94845 (465*2π)/5541 weeks
4665.57097 -5.60526 (466*2π)/5541 weeks
4676.54849 -1.09545 (467*2π)/5541 weeks
4682.57784 2.53971 (468*2π)/5541 weeks
469-2.24904 -.22788 (469*2π)/5541 weeks
470-1.81128 -4.70575 (470*2π)/5541 weeks
4711.61721 -7.67152 (471*2π)/5541 weeks
4727.00702 -4.88053 (472*2π)/5541 weeks
4736.2893 .52831 (473*2π)/5541 weeks
4741.88051 2.95518 (474*2π)/5541 weeks
475-3.19958 -.42337 (475*2π)/5541 weeks
476-1.05958 -6.11561 (476*2π)/5541 weeks
4773.33608 -5.52318 (477*2π)/5541 weeks
4785.70658 -3.69039 (478*2π)/5541 weeks
4795.86306 1.48007 (479*2π)/5541 weeks
480-.27164 4.09074 (480*2π)/5541 weeks
481-4.80299 -.29403 (481*2π)/5541 weeks
482-3.83589 -6.26528 (482*2π)/5541 weeks
4831.73222 -7.653 (483*2π)/5541 weeks
4843.73748 -3.38828 (484*2π)/5541 weeks
485.93338 -2.69316 (485*2π)/5541 weeks
486.49973 -3.86903 (486*2π)/5541 weeks
4871.01923 -5.56814 (487*2π)/5541 weeks
4883.66771 -4.23086 (488*2π)/5541 weeks
4892.95238 -2.12902 (489*2π)/5541 weeks
4901.44308 -2.65507 (490*2π)/5541 weeks
491.89126 -3.48961 (491*2π)/5541 weeks
4922.54476 -3.99264 (492*2π)/5541 weeks
4931.89678 -.99988 (493*2π)/5541 weeks
494-1.62056 -2.04674 (494*2π)/5541 weeks
495-2.38677 -5.85512 (495*2π)/5541 weeks
496.98116 -9.53052 (496*2π)/5541 weeks
4976.59401 -8.27828 (497*2π)/5541 weeks
4987.62261 -1.20724 (498*2π)/5541 weeks
4992.3918 1.19382 (499*2π)/5541 weeks
500-1.34581 -.90329 (500*2π)/5541 weeks
501-.93913 -4.62524 (501*2π)/5541 weeks
5021.6331 -5.04557 (502*2π)/5541 weeks
5031.92673 -3.42928 (503*2π)/5541 weeks
5041.036 -2.63992 (504*2π)/5541 weeks
505-1.35616 -2.82536 (505*2π)/5541 weeks
506-1.44556 -4.33732 (506*2π)/5541 weeks
507-1.87711 -6.34806 (507*2π)/5541 weeks
508-.28022 -7.5437 (508*2π)/5541 weeks
509-.05826 -7.59334 (509*2π)/5541 weeks
5101.30041 -8.70106 (510*2π)/5541 weeks
5112.68257 -9.1606 (511*2π)/5541 weeks
5125.58696 -7.85571 (512*2π)/5541 weeks
5134.69626 -2.80067 (513*2π)/5541 weeks
514.39865 -2.82656 (514*2π)/5541 weeks
515-2.01125 -5.82784 (515*2π)/5541 weeks
516-1.16519 -11.03092 (516*2π)/5541 weeks
5176.16495 -13.3723 (517*2π)/5541 weeks
51811.83738 -5.63894 (518*2π)/5541 weeks
5197.65894 4.36402 (519*2π)/5541 weeks
520-6.66962 5.81633 (520*2π)/5541 weeks
521-13.04359 -8.96272 (521*2π)/5541 weeks
522-2.53173 -20.0504 (522*2π)/5541 weeks
52310.29329 -15.62201 (523*2π)/5541 weeks
52411.04279 -2.92605 (524*2π)/5541 weeks
525-.67351 4.0579 (525*2π)/5541 weeks
526-11.26572 -3.83574 (526*2π)/5541 weeks
527-10.63113 -16.35908 (527*2π)/5541 weeks
5281.77062 -23.58249 (528*2π)/5541 weeks
52910.41111 -16.03571 (529*2π)/5541 weeks
5307.1259 -7.76371 (530*2π)/5541 weeks
531-.51839 -7.85882 (531*2π)/5541 weeks
532-1.5139 -13.30166 (532*2π)/5541 weeks
5331.1109 -17.30482 (533*2π)/5541 weeks
5345.71002 -18.9682 (534*2π)/5541 weeks
5359.78281 -18.06105 (535*2π)/5541 weeks
53612.92684 -10.90445 (536*2π)/5541 weeks
5376.5174 -5.6522 (537*2π)/5541 weeks
5381.46452 -4.71426 (538*2π)/5541 weeks
539-8.83493 -9.10897 (539*2π)/5541 weeks
540-10.92844 -25.38582 (540*2π)/5541 weeks
5411.55633 -36.80618 (541*2π)/5541 weeks
54223.2917 -34.08741 (542*2π)/5541 weeks
54327.85098 -10.40322 (543*2π)/5541 weeks
5449.82044 3.50069 (544*2π)/5541 weeks
545-20.65668 .35627 (545*2π)/5541 weeks
546-37.97707 -40.83347 (546*2π)/5541 weeks
547-1.21488 -81.97718 (547*2π)/5541 weeks
54849.50746 -66.77454 (548*2π)/5541 weeks
54954.64084 -21.94163 (549*2π)/5541 weeks
5508.40729 -3.4328 (550*2π)/5541 weeks
551-42.61643 -54.57167 (551*2π)/5541 weeks
5523.53331 -159.0001 (552*2π)/5541 weeks



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