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Fourier Analysis of SMN (ProShares UltraShort Basic Mate)


SMN (ProShares UltraShort Basic Mate) appears to have interesting cyclic behaviour every 43 weeks (40.5543*sine), 47 weeks (29.5946*sine), and 47 weeks (29.1169*cosine).

SMN (ProShares UltraShort Basic Mate) has an average price of 201.49 (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 1/9/2017 for SMN (ProShares UltraShort Basic Mate), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0201.4906   0 
1155.4698 210.3517 (1*2π)/520520 weeks
2-9.01629 156.271 (2*2π)/520260 weeks
3-37.53736 37.41427 (3*2π)/520173 weeks
423.93602 .70586 (4*2π)/520130 weeks
561.48696 38.50893 (5*2π)/520104 weeks
634.25846 84.96935 (6*2π)/52087 weeks
7-26.17973 73.44379 (7*2π)/52074 weeks
8-35.49281 16.46772 (8*2π)/52065 weeks
9-.21257 -6.63339 (9*2π)/52058 weeks
1024.26139 3.1431 (10*2π)/52052 weeks
1129.11686 29.59461 (11*2π)/52047 weeks
125.54378 40.55432 (12*2π)/52043 weeks
13-10.3193 29.45353 (13*2π)/52040 weeks
14-10.27067 10.73657 (14*2π)/52037 weeks
151.35518 5.00624 (15*2π)/52035 weeks
167.1916 5.91993 (16*2π)/52033 weeks
1713.7683 12.46319 (17*2π)/52031 weeks
189.11361 19.29043 (18*2π)/52029 weeks
194.57984 20.31127 (19*2π)/52027 weeks
20.11063 17.69062 (20*2π)/52026 weeks
21-1.56344 12.49021 (21*2π)/52025 weeks
223.16801 6.49754 (22*2π)/52024 weeks
2310.44881 11.17181 (23*2π)/52023 weeks
246.92767 22.21852 (24*2π)/52022 weeks
25-8.43765 22.17261 (25*2π)/52021 weeks
26-13.10557 8.55886 (26*2π)/52020 weeks
27-4.15521 -3.1192 (27*2π)/52019 weeks
2810.66858 1.12631 (28*2π)/52019 weeks
2911.81478 15.19778 (29*2π)/52018 weeks
30-2.13592 21.33257 (30*2π)/52017 weeks
31-13.9664 9.03332 (31*2π)/52017 weeks
32-5.5236 -6.92989 (32*2π)/52016 weeks
339.63489 -3.13826 (33*2π)/52016 weeks
3412.06881 8.33882 (34*2π)/52015 weeks
353.56748 14.43324 (35*2π)/52015 weeks
36-2.40626 9.58884 (36*2π)/52014 weeks
37-1.3468 4.61657 (37*2π)/52014 weeks
382.48112 2.47673 (38*2π)/52014 weeks
396.89162 5.95096 (39*2π)/52013 weeks
404.01217 9.57266 (40*2π)/52013 weeks
411.67705 9.1525 (41*2π)/52013 weeks
42-.05656 8.44964 (42*2π)/52012 weeks
43-.07179 7.86333 (43*2π)/52012 weeks
44-1.85822 6.9772 (44*2π)/52012 weeks
45-1.61035 4.65824 (45*2π)/52012 weeks
46-1.46712 3.01536 (46*2π)/52011 weeks
471.0845 2.88716 (47*2π)/52011 weeks
482.03348 3.81148 (48*2π)/52011 weeks
491.19904 5.59974 (49*2π)/52011 weeks
50-1.54603 4.11837 (50*2π)/52010 weeks
51-.25277 -.19063 (51*2π)/52010 weeks
524.82481 -1.14164 (52*2π)/52010 weeks
539.04623 4.91051 (53*2π)/52010 weeks
543.72293 10.05189 (54*2π)/52010 weeks
55-1.91911 7.97471 (55*2π)/5209 weeks
56-2.46533 3.33982 (56*2π)/5209 weeks
57.86249 .83078 (57*2π)/5209 weeks
583.12683 3.76667 (58*2π)/5209 weeks
59.9661 3.9588 (59*2π)/5209 weeks
601.4335 2.81104 (60*2π)/5209 weeks
613.06185 2.18058 (61*2π)/5209 weeks
623.88558 4.59805 (62*2π)/5208 weeks
63.79238 5.60087 (63*2π)/5208 weeks
64.50576 3.88557 (64*2π)/5208 weeks
651.40236 2.46493 (65*2π)/5208 weeks
664.13866 5.15632 (66*2π)/5208 weeks
67-.53422 8.43919 (67*2π)/5208 weeks
68-5.45113 3.86047 (68*2π)/5208 weeks
69-3.38544 -2.58512 (69*2π)/5208 weeks
704.08386 -3.77857 (70*2π)/5207 weeks
716.82068 2.21374 (71*2π)/5207 weeks
724.09552 5.31603 (72*2π)/5207 weeks
73.1966 6.91114 (73*2π)/5207 weeks
74-3.66367 1.55224 (74*2π)/5207 weeks
751.37477 -3.19946 (75*2π)/5207 weeks
766.55922 -.73162 (76*2π)/5207 weeks
777.32938 5.36429 (77*2π)/5207 weeks
781.09129 7.90382 (78*2π)/5207 weeks
79-2.28955 4.31044 (79*2π)/5207 weeks
80-1.72261 -1.01739 (80*2π)/5207 weeks
814.50032 -2.18467 (81*2π)/5206 weeks
826.99205 2.92477 (82*2π)/5206 weeks
833.96701 7.21437 (83*2π)/5206 weeks
84-1.05598 6.20573 (84*2π)/5206 weeks
85-1.61203 1.33567 (85*2π)/5206 weeks
861.93349 -.04644 (86*2π)/5206 weeks
873.90585 2.06837 (87*2π)/5206 weeks
882.5307 4.13059 (88*2π)/5206 weeks
891.34358 3.09004 (89*2π)/5206 weeks
901.90655 3.5974 (90*2π)/5206 weeks
91-.23097 3.74505 (91*2π)/5206 weeks
92-1.48796 1.19725 (92*2π)/5206 weeks
93.65247 -1.4825 (93*2π)/5206 weeks
943.94124 -.47121 (94*2π)/5206 weeks
954.57025 2.87684 (95*2π)/5205 weeks
961.91644 4.82109 (96*2π)/5205 weeks
97-1.18496 2.786 (97*2π)/5205 weeks
98.31364 -1.35898 (98*2π)/5205 weeks
994.45372 -1.4359 (99*2π)/5205 weeks
1007.02114 2.49783 (100*2π)/5205 weeks
1013.8625 6.23269 (101*2π)/5205 weeks
102-.73324 5.55763 (102*2π)/5205 weeks
103-2.03596 .72916 (103*2π)/5205 weeks
1042.2912 -1.78524 (104*2π)/5205 weeks
1056.22564 1.34508 (105*2π)/5205 weeks
1064.44707 6.06353 (106*2π)/5205 weeks
107.20556 6.42423 (107*2π)/5205 weeks
108-3.03604 3.45486 (108*2π)/5205 weeks
109-1.43415 -1.25984 (109*2π)/5205 weeks
1102.36455 -1.65654 (110*2π)/5205 weeks
1114.08737 .69523 (111*2π)/5205 weeks
1123.30754 2.93761 (112*2π)/5205 weeks
1131.23892 2.95094 (113*2π)/5205 weeks
114.76144 1.33376 (114*2π)/5205 weeks
1152.26701 .07614 (115*2π)/5205 weeks
1164.06481 1.58994 (116*2π)/5204 weeks
1172.77606 3.99843 (117*2π)/5204 weeks
118.7641 3.09182 (118*2π)/5204 weeks
119.48381 1.33777 (119*2π)/5204 weeks
1201.8854 .93117 (120*2π)/5204 weeks
1211.87613 1.56951 (121*2π)/5204 weeks
1221.83801 1.19871 (122*2π)/5204 weeks
1232.3243 1.35541 (123*2π)/5204 weeks
1242.03681 1.58966 (124*2π)/5204 weeks
1252.29049 1.21853 (125*2π)/5204 weeks
1263.5264 1.74328 (126*2π)/5204 weeks
1272.98293 3.4205 (127*2π)/5204 weeks
1281.54387 3.14472 (128*2π)/5204 weeks
129.6459 2.3246 (129*2π)/5204 weeks
1301.61849 .97319 (130*2π)/5204 weeks
1312.44207 2.5642 (131*2π)/5204 weeks
132.66184 2.63589 (132*2π)/5204 weeks
133.52751 1.36067 (133*2π)/5204 weeks
1341.77967 .55203 (134*2π)/5204 weeks
1352.70578 2.08056 (135*2π)/5204 weeks
1361.30972 2.32041 (136*2π)/5204 weeks
1371.53236 1.34013 (137*2π)/5204 weeks
1381.99147 1.52679 (138*2π)/5204 weeks
1392.2181 2.25101 (139*2π)/5204 weeks
140.81252 3.03558 (140*2π)/5204 weeks
141-.15626 1.49105 (141*2π)/5204 weeks
142.43371 -.21219 (142*2π)/5204 weeks
1432.97416 -.19819 (143*2π)/5204 weeks
1443.00122 1.9351 (144*2π)/5204 weeks
1451.87538 2.2104 (145*2π)/5204 weeks
1461.41979 1.76077 (146*2π)/5204 weeks
1471.28619 1.36848 (147*2π)/5204 weeks
1481.64838 .74283 (148*2π)/5204 weeks
1492.75084 .75701 (149*2π)/5203 weeks
1503.21417 2.61976 (150*2π)/5203 weeks
1511.55504 3.23478 (151*2π)/5203 weeks
152.82267 2.78147 (152*2π)/5203 weeks
153-.03216 2.05022 (153*2π)/5203 weeks
154.30841 .62328 (154*2π)/5203 weeks
1551.69201 .30497 (155*2π)/5203 weeks
1562.2957 1.73849 (156*2π)/5203 weeks
1571.29962 2.6836 (157*2π)/5203 weeks
158-.21177 2.10345 (158*2π)/5203 weeks
159-.47785 .45247 (159*2π)/5203 weeks
160.93983 -.67431 (160*2π)/5203 weeks
1612.37415 .10075 (161*2π)/5203 weeks
1622.31229 1.22231 (162*2π)/5203 weeks
1631.19407 1.71374 (163*2π)/5203 weeks
164.4928 .8887 (164*2π)/5203 weeks
165.96359 -.4806 (165*2π)/5203 weeks
1662.8726 -.84088 (166*2π)/5203 weeks
1674.36483 .89144 (167*2π)/5203 weeks
1683.54418 3.33984 (168*2π)/5203 weeks
169.76348 3.91921 (169*2π)/5203 weeks
170-.74043 1.84925 (170*2π)/5203 weeks
171.27676 -.08114 (171*2π)/5203 weeks
1722.22186 .03072 (172*2π)/5203 weeks
1732.4728 1.71772 (173*2π)/5203 weeks
1741.34139 2.40426 (174*2π)/5203 weeks
175.2801 1.3624 (175*2π)/5203 weeks
176.69288 .70298 (176*2π)/5203 weeks
1771.35086 .2415 (177*2π)/5203 weeks
1782.03004 1.30092 (178*2π)/5203 weeks
179.96964 2.2339 (179*2π)/5203 weeks
180-.34767 1.67385 (180*2π)/5203 weeks
181-.95447 -.25299 (181*2π)/5203 weeks
182.79668 -2.14581 (182*2π)/5203 weeks
1833.13972 -1.88419 (183*2π)/5203 weeks
1845.17772 .39938 (184*2π)/5203 weeks
1853.18623 3.80881 (185*2π)/5203 weeks
186.23951 3.03562 (186*2π)/5203 weeks
187-.50907 .86567 (187*2π)/5203 weeks
1881.09323 -.42858 (188*2π)/5203 weeks
1892.32183 .68211 (189*2π)/5203 weeks
1902.11755 1.45234 (190*2π)/5203 weeks
191.9075 2.65817 (191*2π)/5203 weeks
192-.80802 .87659 (192*2π)/5203 weeks
193-.09615 -.47204 (193*2π)/5203 weeks
1941.32193 -1.66188 (194*2π)/5203 weeks
1953.37639 -.47352 (195*2π)/5203 weeks
1963.12553 1.99367 (196*2π)/5203 weeks
197.51884 2.67316 (197*2π)/5203 weeks
198-.85037 .18209 (198*2π)/5203 weeks
1991.32499 -1.75714 (199*2π)/5203 weeks
2003.35403 -.27309 (200*2π)/5203 weeks
2013.28044 1.87973 (201*2π)/5203 weeks
202.75667 3.03598 (202*2π)/5203 weeks
203-.77497 .48388 (203*2π)/5203 weeks
204.90796 -1.3455 (204*2π)/5203 weeks
2053.20131 -.35886 (205*2π)/5203 weeks
2062.43711 2.01932 (206*2π)/5203 weeks
207.44355 1.61483 (207*2π)/5203 weeks
208.52771 -.12292 (208*2π)/5203 weeks
2092.01413 -.1388 (209*2π)/5202 weeks
2102.48469 .97609 (210*2π)/5202 weeks
2111.63723 2.26972 (211*2π)/5202 weeks
212-.24332 1.76034 (212*2π)/5202 weeks
213-.02794 -.09724 (213*2π)/5202 weeks
2141.14194 -.31587 (214*2π)/5202 weeks
2151.57643 .79548 (215*2π)/5202 weeks
216.22802 1.09419 (216*2π)/5202 weeks
217-.12754 -.03533 (217*2π)/5202 weeks
218.43832 -1.07236 (218*2π)/5202 weeks
2191.80345 -1.25549 (219*2π)/5202 weeks
2202.52028 -.12285 (220*2π)/5202 weeks
2212.00733 1.13115 (221*2π)/5202 weeks
222.26853 1.26704 (222*2π)/5202 weeks
223-.33338 -.71294 (223*2π)/5202 weeks
2241.14445 -1.97497 (224*2π)/5202 weeks
2252.92119 -1.46884 (225*2π)/5202 weeks
2263.68646 .69707 (226*2π)/5202 weeks
2271.76488 1.62165 (227*2π)/5202 weeks
228.69134 1.07022 (228*2π)/5202 weeks
229.20264 -.44432 (229*2π)/5202 weeks
2301.74123 -1.00829 (230*2π)/5202 weeks
2312.41447 -.12617 (231*2π)/5202 weeks
2322.52047 .98039 (232*2π)/5202 weeks
233.9946 1.90923 (233*2π)/5202 weeks
234-.75693 .53083 (234*2π)/5202 weeks
235-.6542 -1.70455 (235*2π)/5202 weeks
2361.90382 -2.86207 (236*2π)/5202 weeks
2374.01768 -1.06034 (237*2π)/5202 weeks
2383.36396 1.10842 (238*2π)/5202 weeks
2391.73009 2.01936 (239*2π)/5202 weeks
240-.38563 1.22667 (240*2π)/5202 weeks
241-.44297 -1.5441 (241*2π)/5202 weeks
2422.12894 -3.00552 (242*2π)/5202 weeks
2434.77738 -.55729 (243*2π)/5202 weeks
2443.16537 2.43072 (244*2π)/5202 weeks
245.49208 2.33931 (245*2π)/5202 weeks
246-1.31195 .01851 (246*2π)/5202 weeks
247.45153 -2.99465 (247*2π)/5202 weeks
2483.88865 -2.33119 (248*2π)/5202 weeks
2494.16966 1.33777 (249*2π)/5202 weeks
2501.48982 2.65188 (250*2π)/5202 weeks
251-1.00768 1.18725 (251*2π)/5202 weeks
252-.99485 -2.06959 (252*2π)/5202 weeks
2532.34276 -3.96172 (253*2π)/5202 weeks
2545.61746 -1.08984 (254*2π)/5202 weeks
2553.76451 2.55031 (255*2π)/5202 weeks
256.64098 2.22553 (256*2π)/5202 weeks
257-.69606 .13437 (257*2π)/5202 weeks
258.31489 -2.18499 (258*2π)/5202 weeks
2593.09608 -2.91203 (259*2π)/5202 weeks
2605.46066   (260*2π)/5202 weeks
2613.09608 2.91203 (261*2π)/5202 weeks
262.31489 2.18499 (262*2π)/5202 weeks
263-.69606 -.13437 (263*2π)/5202 weeks
264.64098 -2.22553 (264*2π)/5202 weeks
2653.76451 -2.55031 (265*2π)/5202 weeks
2665.61746 1.08984 (266*2π)/5202 weeks
2672.34276 3.96172 (267*2π)/5202 weeks
268-.99485 2.06959 (268*2π)/5202 weeks
269-1.00768 -1.18725 (269*2π)/5202 weeks
2701.48982 -2.65188 (270*2π)/5202 weeks
2714.16966 -1.33777 (271*2π)/5202 weeks
2723.88865 2.33119 (272*2π)/5202 weeks
273.45153 2.99465 (273*2π)/5202 weeks
274-1.31195 -.01851 (274*2π)/5202 weeks
275.49208 -2.33931 (275*2π)/5202 weeks
2763.16537 -2.43072 (276*2π)/5202 weeks
2774.77738 .55729 (277*2π)/5202 weeks
2782.12894 3.00552 (278*2π)/5202 weeks
279-.44297 1.5441 (279*2π)/5202 weeks
280-.38563 -1.22667 (280*2π)/5202 weeks
2811.73009 -2.01936 (281*2π)/5202 weeks
2823.36396 -1.10842 (282*2π)/5202 weeks
2834.01768 1.06034 (283*2π)/5202 weeks
2841.90382 2.86207 (284*2π)/5202 weeks
285-.6542 1.70455 (285*2π)/5202 weeks
286-.75693 -.53083 (286*2π)/5202 weeks
287.9946 -1.90923 (287*2π)/5202 weeks
2882.52047 -.98039 (288*2π)/5202 weeks
2892.41447 .12617 (289*2π)/5202 weeks
2901.74123 1.00829 (290*2π)/5202 weeks
291.20264 .44432 (291*2π)/5202 weeks
292.69134 -1.07022 (292*2π)/5202 weeks
2931.76488 -1.62165 (293*2π)/5202 weeks
2943.68646 -.69707 (294*2π)/5202 weeks
2952.92119 1.46884 (295*2π)/5202 weeks
2961.14445 1.97497 (296*2π)/5202 weeks
297-.33338 .71294 (297*2π)/5202 weeks
298.26853 -1.26704 (298*2π)/5202 weeks
2992.00733 -1.13115 (299*2π)/5202 weeks
3002.52028 .12285 (300*2π)/5202 weeks
3011.80345 1.25549 (301*2π)/5202 weeks
302.43832 1.07236 (302*2π)/5202 weeks
303-.12754 .03533 (303*2π)/5202 weeks
304.22802 -1.09419 (304*2π)/5202 weeks
3051.57643 -.79548 (305*2π)/5202 weeks
3061.14194 .31587 (306*2π)/5202 weeks
307-.02794 .09724 (307*2π)/5202 weeks
308-.24332 -1.76034 (308*2π)/5202 weeks
3091.63723 -2.26972 (309*2π)/5202 weeks
3102.48469 -.97609 (310*2π)/5202 weeks
3112.01413 .1388 (311*2π)/5202 weeks
312.52771 .12292 (312*2π)/5202 weeks
313.44355 -1.61483 (313*2π)/5202 weeks
3142.43711 -2.01932 (314*2π)/5202 weeks
3153.20131 .35886 (315*2π)/5202 weeks
316.90796 1.3455 (316*2π)/5202 weeks
317-.77497 -.48388 (317*2π)/5202 weeks
318.75667 -3.03598 (318*2π)/5202 weeks
3193.28044 -1.87973 (319*2π)/5202 weeks
3203.35403 .27309 (320*2π)/5202 weeks
3211.32499 1.75714 (321*2π)/5202 weeks
322-.85037 -.18209 (322*2π)/5202 weeks
323.51884 -2.67316 (323*2π)/5202 weeks
3243.12553 -1.99367 (324*2π)/5202 weeks
3253.37639 .47352 (325*2π)/5202 weeks
3261.32193 1.66188 (326*2π)/5202 weeks
327-.09615 .47204 (327*2π)/5202 weeks
328-.80802 -.87659 (328*2π)/5202 weeks
329.9075 -2.65817 (329*2π)/5202 weeks
3302.11755 -1.45234 (330*2π)/5202 weeks
3312.32183 -.68211 (331*2π)/5202 weeks
3321.09323 .42858 (332*2π)/5202 weeks
333-.50907 -.86567 (333*2π)/5202 weeks
334.23951 -3.03562 (334*2π)/5202 weeks
3353.18623 -3.80881 (335*2π)/5202 weeks
3365.17772 -.39938 (336*2π)/5202 weeks
3373.13972 1.88419 (337*2π)/5202 weeks
338.79668 2.14581 (338*2π)/5202 weeks
339-.95447 .25299 (339*2π)/5202 weeks
340-.34767 -1.67385 (340*2π)/5202 weeks
341.96964 -2.2339 (341*2π)/5202 weeks
3422.03004 -1.30092 (342*2π)/5202 weeks
3431.35086 -.2415 (343*2π)/5202 weeks
344.69288 -.70298 (344*2π)/5202 weeks
345.2801 -1.3624 (345*2π)/5202 weeks
3461.34139 -2.40426 (346*2π)/5202 weeks
3472.4728 -1.71772 (347*2π)/5201 weeks
3482.22186 -.03072 (348*2π)/5201 weeks
349.27676 .08114 (349*2π)/5201 weeks
350-.74043 -1.84925 (350*2π)/5201 weeks
351.76348 -3.91921 (351*2π)/5201 weeks
3523.54418 -3.33984 (352*2π)/5201 weeks
3534.36483 -.89144 (353*2π)/5201 weeks
3542.8726 .84088 (354*2π)/5201 weeks
355.96359 .4806 (355*2π)/5201 weeks
356.4928 -.8887 (356*2π)/5201 weeks
3571.19407 -1.71374 (357*2π)/5201 weeks
3582.31229 -1.22231 (358*2π)/5201 weeks
3592.37415 -.10075 (359*2π)/5201 weeks
360.93983 .67431 (360*2π)/5201 weeks
361-.47785 -.45247 (361*2π)/5201 weeks
362-.21177 -2.10345 (362*2π)/5201 weeks
3631.29962 -2.6836 (363*2π)/5201 weeks
3642.2957 -1.73849 (364*2π)/5201 weeks
3651.69201 -.30497 (365*2π)/5201 weeks
366.30841 -.62328 (366*2π)/5201 weeks
367-.03216 -2.05022 (367*2π)/5201 weeks
368.82267 -2.78147 (368*2π)/5201 weeks
3691.55504 -3.23478 (369*2π)/5201 weeks
3703.21417 -2.61976 (370*2π)/5201 weeks
3712.75084 -.75701 (371*2π)/5201 weeks
3721.64838 -.74283 (372*2π)/5201 weeks
3731.28619 -1.36848 (373*2π)/5201 weeks
3741.41979 -1.76077 (374*2π)/5201 weeks
3751.87538 -2.2104 (375*2π)/5201 weeks
3763.00122 -1.9351 (376*2π)/5201 weeks
3772.97416 .19819 (377*2π)/5201 weeks
378.43371 .21219 (378*2π)/5201 weeks
379-.15626 -1.49105 (379*2π)/5201 weeks
380.81252 -3.03558 (380*2π)/5201 weeks
3812.2181 -2.25101 (381*2π)/5201 weeks
3821.99147 -1.52679 (382*2π)/5201 weeks
3831.53236 -1.34013 (383*2π)/5201 weeks
3841.30972 -2.32041 (384*2π)/5201 weeks
3852.70578 -2.08056 (385*2π)/5201 weeks
3861.77967 -.55203 (386*2π)/5201 weeks
387.52751 -1.36067 (387*2π)/5201 weeks
388.66184 -2.63589 (388*2π)/5201 weeks
3892.44207 -2.5642 (389*2π)/5201 weeks
3901.61849 -.97319 (390*2π)/5201 weeks
391.6459 -2.3246 (391*2π)/5201 weeks
3921.54387 -3.14472 (392*2π)/5201 weeks
3932.98293 -3.4205 (393*2π)/5201 weeks
3943.5264 -1.74328 (394*2π)/5201 weeks
3952.29049 -1.21853 (395*2π)/5201 weeks
3962.03681 -1.58966 (396*2π)/5201 weeks
3972.3243 -1.35541 (397*2π)/5201 weeks
3981.83801 -1.19871 (398*2π)/5201 weeks
3991.87613 -1.56951 (399*2π)/5201 weeks
4001.8854 -.93117 (400*2π)/5201 weeks
401.48381 -1.33777 (401*2π)/5201 weeks
402.7641 -3.09182 (402*2π)/5201 weeks
4032.77606 -3.99843 (403*2π)/5201 weeks
4044.06481 -1.58994 (404*2π)/5201 weeks
4052.26701 -.07614 (405*2π)/5201 weeks
406.76144 -1.33376 (406*2π)/5201 weeks
4071.23892 -2.95094 (407*2π)/5201 weeks
4083.30754 -2.93761 (408*2π)/5201 weeks
4094.08737 -.69523 (409*2π)/5201 weeks
4102.36455 1.65654 (410*2π)/5201 weeks
411-1.43415 1.25984 (411*2π)/5201 weeks
412-3.03604 -3.45486 (412*2π)/5201 weeks
413.20556 -6.42423 (413*2π)/5201 weeks
4144.44707 -6.06353 (414*2π)/5201 weeks
4156.22564 -1.34508 (415*2π)/5201 weeks
4162.2912 1.78524 (416*2π)/5201 weeks
417-2.03596 -.72916 (417*2π)/5201 weeks
418-.73324 -5.55763 (418*2π)/5201 weeks
4193.8625 -6.23269 (419*2π)/5201 weeks
4207.02114 -2.49783 (420*2π)/5201 weeks
4214.45372 1.4359 (421*2π)/5201 weeks
422.31364 1.35898 (422*2π)/5201 weeks
423-1.18496 -2.786 (423*2π)/5201 weeks
4241.91644 -4.82109 (424*2π)/5201 weeks
4254.57025 -2.87684 (425*2π)/5201 weeks
4263.94124 .47121 (426*2π)/5201 weeks
427.65247 1.4825 (427*2π)/5201 weeks
428-1.48796 -1.19725 (428*2π)/5201 weeks
429-.23097 -3.74505 (429*2π)/5201 weeks
4301.90655 -3.5974 (430*2π)/5201 weeks
4311.34358 -3.09004 (431*2π)/5201 weeks
4322.5307 -4.13059 (432*2π)/5201 weeks
4333.90585 -2.06837 (433*2π)/5201 weeks
4341.93349 .04644 (434*2π)/5201 weeks
435-1.61203 -1.33567 (435*2π)/5201 weeks
436-1.05598 -6.20573 (436*2π)/5201 weeks
4373.96701 -7.21437 (437*2π)/5201 weeks
4386.99205 -2.92477 (438*2π)/5201 weeks
4394.50032 2.18467 (439*2π)/5201 weeks
440-1.72261 1.01739 (440*2π)/5201 weeks
441-2.28955 -4.31044 (441*2π)/5201 weeks
4421.09129 -7.90382 (442*2π)/5201 weeks
4437.32938 -5.36429 (443*2π)/5201 weeks
4446.55922 .73162 (444*2π)/5201 weeks
4451.37477 3.19946 (445*2π)/5201 weeks
446-3.66367 -1.55224 (446*2π)/5201 weeks
447.1966 -6.91114 (447*2π)/5201 weeks
4484.09552 -5.31603 (448*2π)/5201 weeks
4496.82068 -2.21374 (449*2π)/5201 weeks
4504.08386 3.77857 (450*2π)/5201 weeks
451-3.38544 2.58512 (451*2π)/5201 weeks
452-5.45113 -3.86047 (452*2π)/5201 weeks
453-.53422 -8.43919 (453*2π)/5201 weeks
4544.13866 -5.15632 (454*2π)/5201 weeks
4551.40236 -2.46493 (455*2π)/5201 weeks
456.50576 -3.88557 (456*2π)/5201 weeks
457.79238 -5.60087 (457*2π)/5201 weeks
4583.88558 -4.59805 (458*2π)/5201 weeks
4593.06185 -2.18058 (459*2π)/5201 weeks
4601.4335 -2.81104 (460*2π)/5201 weeks
461.9661 -3.9588 (461*2π)/5201 weeks
4623.12683 -3.76667 (462*2π)/5201 weeks
463.86249 -.83078 (463*2π)/5201 weeks
464-2.46533 -3.33982 (464*2π)/5201 weeks
465-1.91911 -7.97471 (465*2π)/5201 weeks
4663.72293 -10.05189 (466*2π)/5201 weeks
4679.04623 -4.91051 (467*2π)/5201 weeks
4684.82481 1.14164 (468*2π)/5201 weeks
469-.25277 .19063 (469*2π)/5201 weeks
470-1.54603 -4.11837 (470*2π)/5201 weeks
4711.19904 -5.59974 (471*2π)/5201 weeks
4722.03348 -3.81148 (472*2π)/5201 weeks
4731.0845 -2.88716 (473*2π)/5201 weeks
474-1.46712 -3.01536 (474*2π)/5201 weeks
475-1.61035 -4.65824 (475*2π)/5201 weeks
476-1.85822 -6.9772 (476*2π)/5201 weeks
477-.07179 -7.86333 (477*2π)/5201 weeks
478-.05656 -8.44964 (478*2π)/5201 weeks
4791.67705 -9.1525 (479*2π)/5201 weeks
4804.01217 -9.57266 (480*2π)/5201 weeks
4816.89162 -5.95096 (481*2π)/5201 weeks
4822.48112 -2.47673 (482*2π)/5201 weeks
483-1.3468 -4.61657 (483*2π)/5201 weeks
484-2.40626 -9.58884 (484*2π)/5201 weeks
4853.56748 -14.43324 (485*2π)/5201 weeks
48612.06881 -8.33882 (486*2π)/5201 weeks
4879.63489 3.13826 (487*2π)/5201 weeks
488-5.5236 6.92989 (488*2π)/5201 weeks
489-13.9664 -9.03332 (489*2π)/5201 weeks
490-2.13592 -21.33257 (490*2π)/5201 weeks
49111.81478 -15.19778 (491*2π)/5201 weeks
49210.66858 -1.12631 (492*2π)/5201 weeks
493-4.15521 3.1192 (493*2π)/5201 weeks
494-13.10557 -8.55886 (494*2π)/5201 weeks
495-8.43765 -22.17261 (495*2π)/5201 weeks
4966.92767 -22.21852 (496*2π)/5201 weeks
49710.44881 -11.17181 (497*2π)/5201 weeks
4983.16801 -6.49754 (498*2π)/5201 weeks
499-1.56344 -12.49021 (499*2π)/5201 weeks
500.11063 -17.69062 (500*2π)/5201 weeks
5014.57984 -20.31127 (501*2π)/5201 weeks
5029.11361 -19.29043 (502*2π)/5201 weeks
50313.7683 -12.46319 (503*2π)/5201 weeks
5047.1916 -5.91993 (504*2π)/5201 weeks
5051.35518 -5.00624 (505*2π)/5201 weeks
506-10.27067 -10.73657 (506*2π)/5201 weeks
507-10.3193 -29.45353 (507*2π)/5201 weeks
5085.54378 -40.55432 (508*2π)/5201 weeks
50929.11686 -29.59461 (509*2π)/5201 weeks
51024.26139 -3.1431 (510*2π)/5201 weeks
511-.21257 6.63339 (511*2π)/5201 weeks
512-35.49281 -16.46772 (512*2π)/5201 weeks
513-26.17973 -73.44379 (513*2π)/5201 weeks
51434.25846 -84.96935 (514*2π)/5201 weeks
51561.48696 -38.50893 (515*2π)/5201 weeks
51623.93602 -.70586 (516*2π)/5201 weeks
517-37.53736 -37.41427 (517*2π)/5201 weeks
518-9.01629 -156.271 (518*2π)/5201 weeks

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