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Fourier Analysis of SIJ (ProShares UltraShort Industrial)


SIJ (ProShares UltraShort Industrial) appears to have interesting cyclic behaviour every 47 weeks (36.0105*sine), 43 weeks (30.4089*sine), and 52 weeks (24.2663*cosine).

SIJ (ProShares UltraShort Industrial) has an average price of 270.77 (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 1/17/2017 for SIJ (ProShares UltraShort Industrial), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0270.77   0 
195.29175 300.7397 (1*2π)/521521 weeks
2-78.31024 140.9473 (2*2π)/521261 weeks
3-67.83092 -4.67036 (3*2π)/521174 weeks
427.6565 -25.01616 (4*2π)/521130 weeks
558.994 30.15903 (5*2π)/521104 weeks
621.29727 71.97001 (6*2π)/52187 weeks
7-33.4536 51.20928 (7*2π)/52174 weeks
8-23.42456 -8.73832 (8*2π)/52165 weeks
918.41467 -4.72266 (9*2π)/52158 weeks
1024.26629 11.18367 (10*2π)/52152 weeks
1120.1112 36.01046 (11*2π)/52147 weeks
12-9.61928 30.40891 (12*2π)/52143 weeks
13-7.4699 11.95663 (13*2π)/52140 weeks
14-.41956 7.14952 (14*2π)/52137 weeks
154.8806 11.69234 (15*2π)/52135 weeks
16-2.43689 11.2172 (16*2π)/52133 weeks
174.11914 6.84684 (17*2π)/52131 weeks
183.68134 9.5274 (18*2π)/52129 weeks
197.03264 10.75938 (19*2π)/52127 weeks
203.50839 16.92427 (20*2π)/52126 weeks
21-5.6481 13.13448 (21*2π)/52125 weeks
22-2.28464 .44761 (22*2π)/52124 weeks
239.66155 2.85449 (23*2π)/52123 weeks
2411.63923 19.07769 (24*2π)/52122 weeks
25-9.53759 22.78814 (25*2π)/52121 weeks
26-16.01198 5.74459 (26*2π)/52120 weeks
27-7.40634 -9.37361 (27*2π)/52119 weeks
2814.95997 -7.5435 (28*2π)/52119 weeks
2919.13412 15.83851 (29*2π)/52118 weeks
30-1.19343 26.20171 (30*2π)/52117 weeks
31-19.88227 10.87863 (31*2π)/52117 weeks
32-9.7748 -12.4852 (32*2π)/52116 weeks
3311.91745 -6.60894 (33*2π)/52116 weeks
3412.12688 9.41598 (34*2π)/52115 weeks
35.73466 14.76982 (35*2π)/52115 weeks
36-6.41523 6.37292 (36*2π)/52114 weeks
37-1.59629 .42868 (37*2π)/52114 weeks
382.53901 .7074 (38*2π)/52114 weeks
396.29046 5.56154 (39*2π)/52113 weeks
40-.40283 8.4483 (40*2π)/52113 weeks
41-1.0017 2.57699 (41*2π)/52113 weeks
421.85869 3.44212 (42*2π)/52112 weeks
433.30138 5.49538 (43*2π)/52112 weeks
44-.22756 8.66283 (44*2π)/52112 weeks
45-4.1658 4.37314 (45*2π)/52112 weeks
46-3.28364 .3001 (46*2π)/52111 weeks
471.89393 -.60477 (47*2π)/52111 weeks
484.12889 3.01395 (48*2π)/52111 weeks
49.50823 6.1444 (49*2π)/52111 weeks
50-2.44345 2.8155 (50*2π)/52110 weeks
51-.71444 -1.11393 (51*2π)/52110 weeks
524.57982 -1.99636 (52*2π)/52110 weeks
538.34514 5.14455 (53*2π)/52110 weeks
54-.08218 9.26469 (54*2π)/52110 weeks
55-3.70878 3.40989 (55*2π)/5219 weeks
56-.10866 -.45453 (56*2π)/5219 weeks
574.26375 .73601 (57*2π)/5219 weeks
583.73009 6.95634 (58*2π)/5219 weeks
59-3.21303 5.83203 (59*2π)/5219 weeks
60-3.1717 .13367 (60*2π)/5219 weeks
612.13038 -2.83445 (61*2π)/5219 weeks
626.09158 2.30443 (62*2π)/5218 weeks
631.20829 6.2463 (63*2π)/5218 weeks
64-.27704 3.22802 (64*2π)/5218 weeks
65-.14162 .41594 (65*2π)/5218 weeks
665.34109 2.02281 (66*2π)/5218 weeks
671.46675 8.18184 (67*2π)/5218 weeks
68-5.04092 4.61026 (68*2π)/5218 weeks
69-3.55115 -1.79842 (69*2π)/5218 weeks
703.12395 -3.73089 (70*2π)/5217 weeks
715.74671 2.47403 (71*2π)/5217 weeks
722.08593 4.226 (72*2π)/5217 weeks
73.74441 5.48651 (73*2π)/5217 weeks
74-3.97855 1.7431 (74*2π)/5217 weeks
751.11414 -3.43008 (75*2π)/5217 weeks
765.38816 .30497 (76*2π)/5217 weeks
775.14875 5.06621 (77*2π)/5217 weeks
78-.41797 6.63652 (78*2π)/5217 weeks
79-2.84257 3.34866 (79*2π)/5217 weeks
80-3.16601 -1.63427 (80*2π)/5217 weeks
813.74105 -3.5777 (81*2π)/5216 weeks
826.25293 2.65159 (82*2π)/5216 weeks
832.09124 5.99113 (83*2π)/5216 weeks
84-1.80661 3.44201 (84*2π)/5216 weeks
85-.4782 -.43918 (85*2π)/5216 weeks
863.11949 .23149 (86*2π)/5216 weeks
872.8486 3.87601 (87*2π)/5216 weeks
88-1.20322 4.35599 (88*2π)/5216 weeks
89-2.19505 -.89044 (89*2π)/5216 weeks
903.27969 -.88207 (90*2π)/5216 weeks
912.64936 3.15588 (91*2π)/5216 weeks
92-.7869 3.30791 (92*2π)/5216 weeks
93-1.70785 -.24746 (93*2π)/5216 weeks
941.59366 -2.53888 (94*2π)/5216 weeks
955.18315 .40362 (95*2π)/5215 weeks
963.91087 4.91591 (96*2π)/5215 weeks
97-1.59584 4.97349 (97*2π)/5215 weeks
98-2.93679 -.91182 (98*2π)/5215 weeks
991.91148 -3.71372 (99*2π)/5215 weeks
1006.77521 -.44196 (100*2π)/5215 weeks
1015.05632 5.31554 (101*2π)/5215 weeks
102-.36472 6.60231 (102*2π)/5215 weeks
103-4.01372 1.66484 (103*2π)/5215 weeks
104-.12561 -3.27584 (104*2π)/5215 weeks
1055.35513 -1.40088 (105*2π)/5215 weeks
1065.07702 3.90219 (106*2π)/5215 weeks
1071.11062 5.35352 (107*2π)/5215 weeks
108-2.23973 3.62349 (108*2π)/5215 weeks
109-1.96708 -1.36414 (109*2π)/5215 weeks
1102.3158 -1.75063 (110*2π)/5215 weeks
1113.35582 1.03875 (111*2π)/5215 weeks
1122.78135 2.76938 (112*2π)/5215 weeks
113.57341 3.21529 (113*2π)/5215 weeks
114-.69686 1.46374 (114*2π)/5215 weeks
115.45547 -1.30064 (115*2π)/5215 weeks
1163.95396 -.55137 (116*2π)/5214 weeks
1174.04862 3.48172 (117*2π)/5214 weeks
118.45344 3.94882 (118*2π)/5214 weeks
119-.80063 1.69828 (119*2π)/5214 weeks
120.55687 .43875 (120*2π)/5214 weeks
1211.13159 1.07945 (121*2π)/5214 weeks
1221.18687 .63752 (122*2π)/5214 weeks
1231.83417 1.22638 (123*2π)/5214 weeks
124.98384 1.91846 (124*2π)/5214 weeks
125.55284 .65061 (125*2π)/5214 weeks
1262.18382 -.08521 (126*2π)/5214 weeks
1272.98361 1.43058 (127*2π)/5214 weeks
1282.32225 2.43639 (128*2π)/5214 weeks
129.76878 3.53595 (129*2π)/5214 weeks
130-.6495 1.801 (130*2π)/5214 weeks
131.26724 1.28385 (131*2π)/5214 weeks
132-.2425 .5942 (132*2π)/5214 weeks
133.99346 -.39599 (133*2π)/5214 weeks
1342.67985 -.26364 (134*2π)/5214 weeks
1353.27919 3.03411 (135*2π)/5214 weeks
136-.89406 3.28035 (136*2π)/5214 weeks
137-1.05669 -.78635 (137*2π)/5214 weeks
1382.17287 -1.14876 (138*2π)/5214 weeks
1393.63343 1.37684 (139*2π)/5214 weeks
1401.37669 3.93935 (140*2π)/5214 weeks
141-1.23418 2.02589 (141*2π)/5214 weeks
142-.95552 -.49332 (142*2π)/5214 weeks
1432.14879 -1.51761 (143*2π)/5214 weeks
1442.91589 1.4243 (144*2π)/5214 weeks
1451.50962 2.03193 (145*2π)/5214 weeks
146.58841 1.66966 (146*2π)/5214 weeks
147.52079 .81808 (147*2π)/5214 weeks
148.75131 .58231 (148*2π)/5214 weeks
1491.41512 -.07675 (149*2π)/5213 weeks
1502.71411 1.49911 (150*2π)/5213 weeks
151.7561 2.13735 (151*2π)/5213 weeks
152.78724 1.40041 (152*2π)/5213 weeks
153.26513 1.50044 (153*2π)/5213 weeks
154.06524 .29332 (154*2π)/5213 weeks
1551.19818 -.49352 (155*2π)/5213 weeks
1562.78339 1.01033 (156*2π)/5213 weeks
1572.04628 2.4925 (157*2π)/5213 weeks
158-.37849 3.00961 (158*2π)/5213 weeks
159-1.5352 .50821 (159*2π)/5213 weeks
160.1127 -1.3105 (160*2π)/5213 weeks
1612.37954 -.50758 (161*2π)/5213 weeks
1622.36087 1.37309 (162*2π)/5213 weeks
163.90882 2.2495 (163*2π)/5213 weeks
164-.28659 1.2353 (164*2π)/5213 weeks
165-.3586 -.20915 (165*2π)/5213 weeks
1661.00787 -1.61125 (166*2π)/5213 weeks
1673.44647 -.67033 (167*2π)/5213 weeks
1683.68816 2.10098 (168*2π)/5213 weeks
169.97669 3.98336 (169*2π)/5213 weeks
170-1.80803 1.79698 (170*2π)/5213 weeks
171-.78986 -1.35962 (171*2π)/5213 weeks
1722.39299 -1.54713 (172*2π)/5213 weeks
1733.34817 1.36951 (173*2π)/5213 weeks
1741.52964 2.7432 (174*2π)/5213 weeks
175-.88636 1.80435 (175*2π)/5213 weeks
176-.09776 -.34294 (176*2π)/5213 weeks
1771.0257 -.51572 (177*2π)/5213 weeks
1782.52197 .72899 (178*2π)/5213 weeks
179.95664 2.2906 (179*2π)/5213 weeks
180-.42332 .96751 (180*2π)/5213 weeks
181-.19999 -.26936 (181*2π)/5213 weeks
1821.08206 -.88609 (182*2π)/5213 weeks
1831.35266 .04182 (183*2π)/5213 weeks
1842.19268 -.77166 (184*2π)/5213 weeks
1852.87369 2.02158 (185*2π)/5213 weeks
186.71472 1.52297 (186*2π)/5213 weeks
187.74029 1.30357 (187*2π)/5213 weeks
188.42196 .64134 (188*2π)/5213 weeks
189.91635 .93771 (189*2π)/5213 weeks
190.01135 .08166 (190*2π)/5213 weeks
1911.77029 .30751 (191*2π)/5213 weeks
192.46824 .90094 (192*2π)/5213 weeks
193.98332 .65559 (193*2π)/5213 weeks
194-.50295 .47682 (194*2π)/5213 weeks
195.98654 -1.52079 (195*2π)/5213 weeks
1963.05592 .05116 (196*2π)/5213 weeks
1971.88357 2.16723 (197*2π)/5213 weeks
198-.57492 1.79327 (198*2π)/5213 weeks
199-.49294 -1.08668 (199*2π)/5213 weeks
2002.2371 -.97742 (200*2π)/5213 weeks
2012.74606 .66718 (201*2π)/5213 weeks
2021.82227 2.75121 (202*2π)/5213 weeks
203-1.54329 1.71837 (203*2π)/5213 weeks
204-.62409 -1.5563 (204*2π)/5213 weeks
2052.32764 -1.5247 (205*2π)/5213 weeks
2062.99765 1.22869 (206*2π)/5213 weeks
207.41539 2.01357 (207*2π)/5213 weeks
208.00943 -.19268 (208*2π)/5213 weeks
2091.81408 -.30612 (209*2π)/5212 weeks
2102.03304 .96277 (210*2π)/5212 weeks
2111.55507 2.1343 (211*2π)/5212 weeks
212-1.0039 2.24095 (212*2π)/5212 weeks
213-1.44271 -.96108 (213*2π)/5212 weeks
2141.13383 -1.76477 (214*2π)/5212 weeks
2153.19193 -.216 (215*2π)/5212 weeks
2161.55688 2.74352 (216*2π)/5212 weeks
217-.76673 1.23425 (217*2π)/5212 weeks
218-1.01225 -.41007 (218*2π)/5212 weeks
219.56857 -2.05726 (219*2π)/5212 weeks
2202.85716 -.75307 (220*2π)/5212 weeks
2212.34555 1.57801 (221*2π)/5212 weeks
222.11871 2.33974 (222*2π)/5212 weeks
223-1.79712 .02608 (223*2π)/5212 weeks
224.02247 -2.27167 (224*2π)/5212 weeks
2252.31516 -1.63056 (225*2π)/5212 weeks
2263.32147 .05926 (226*2π)/5212 weeks
2271.34404 2.22504 (227*2π)/5212 weeks
228.1303 .64276 (228*2π)/5212 weeks
229.03729 .00698 (229*2π)/5212 weeks
2301.20626 -.51687 (230*2π)/5212 weeks
231.94693 .07818 (231*2π)/5212 weeks
2321.34847 -.34554 (232*2π)/5212 weeks
2331.4508 .70374 (233*2π)/5212 weeks
234.22593 .51115 (234*2π)/5212 weeks
235.26612 .01644 (235*2π)/5212 weeks
236.63963 -1.40188 (236*2π)/5212 weeks
2372.52368 -1.10829 (237*2π)/5212 weeks
2382.59727 .98115 (238*2π)/5212 weeks
2391.41058 1.88462 (239*2π)/5212 weeks
240-.4447 1.84221 (240*2π)/5212 weeks
241-1.85189 -.37817 (241*2π)/5212 weeks
242-.39087 -3.01411 (242*2π)/5212 weeks
2433.77709 -2.86235 (243*2π)/5212 weeks
2444.30136 1.64288 (244*2π)/5212 weeks
2451.00183 2.91225 (245*2π)/5212 weeks
246-1.51624 1.68429 (246*2π)/5212 weeks
247-1.41497 -2.21462 (247*2π)/5212 weeks
2482.56306 -2.98266 (248*2π)/5212 weeks
2494.25644 .9243 (249*2π)/5212 weeks
250.92169 2.55098 (250*2π)/5212 weeks
251-1.04724 .69704 (251*2π)/5212 weeks
252-.52755 -1.72993 (252*2π)/5212 weeks
2531.64614 -2.55371 (253*2π)/5212 weeks
2544.13307 -.54927 (254*2π)/5212 weeks
2552.26125 3.01798 (255*2π)/5212 weeks
256-1.05549 1.29928 (256*2π)/5212 weeks
257-.07956 -1.32913 (257*2π)/5212 weeks
2581.53504 -1.39803 (258*2π)/5212 weeks
2591.69104 -.404 (259*2π)/5212 weeks
2602.00606 -.54065 (260*2π)/5212 weeks
2612.00606 .54065 (261*2π)/5212 weeks
2621.69104 .404 (262*2π)/5212 weeks
2631.53504 1.39803 (263*2π)/5212 weeks
264-.07956 1.32913 (264*2π)/5212 weeks
265-1.05549 -1.29928 (265*2π)/5212 weeks
2662.26125 -3.01798 (266*2π)/5212 weeks
2674.13307 .54927 (267*2π)/5212 weeks
2681.64614 2.55371 (268*2π)/5212 weeks
269-.52755 1.72993 (269*2π)/5212 weeks
270-1.04724 -.69704 (270*2π)/5212 weeks
271.92169 -2.55098 (271*2π)/5212 weeks
2724.25644 -.9243 (272*2π)/5212 weeks
2732.56306 2.98266 (273*2π)/5212 weeks
274-1.41497 2.21462 (274*2π)/5212 weeks
275-1.51624 -1.68429 (275*2π)/5212 weeks
2761.00183 -2.91225 (276*2π)/5212 weeks
2774.30136 -1.64288 (277*2π)/5212 weeks
2783.77709 2.86235 (278*2π)/5212 weeks
279-.39087 3.01411 (279*2π)/5212 weeks
280-1.85189 .37817 (280*2π)/5212 weeks
281-.4447 -1.84221 (281*2π)/5212 weeks
2821.41058 -1.88462 (282*2π)/5212 weeks
2832.59727 -.98115 (283*2π)/5212 weeks
2842.52368 1.10829 (284*2π)/5212 weeks
285.63963 1.40188 (285*2π)/5212 weeks
286.26612 -.01644 (286*2π)/5212 weeks
287.22593 -.51115 (287*2π)/5212 weeks
2881.4508 -.70374 (288*2π)/5212 weeks
2891.34847 .34554 (289*2π)/5212 weeks
290.94693 -.07818 (290*2π)/5212 weeks
2911.20626 .51687 (291*2π)/5212 weeks
292.03729 -.00698 (292*2π)/5212 weeks
293.1303 -.64276 (293*2π)/5212 weeks
2941.34404 -2.22504 (294*2π)/5212 weeks
2953.32147 -.05926 (295*2π)/5212 weeks
2962.31516 1.63056 (296*2π)/5212 weeks
297.02247 2.27167 (297*2π)/5212 weeks
298-1.79712 -.02608 (298*2π)/5212 weeks
299.11871 -2.33974 (299*2π)/5212 weeks
3002.34555 -1.57801 (300*2π)/5212 weeks
3012.85716 .75307 (301*2π)/5212 weeks
302.56857 2.05726 (302*2π)/5212 weeks
303-1.01225 .41007 (303*2π)/5212 weeks
304-.76673 -1.23425 (304*2π)/5212 weeks
3051.55688 -2.74352 (305*2π)/5212 weeks
3063.19193 .216 (306*2π)/5212 weeks
3071.13383 1.76477 (307*2π)/5212 weeks
308-1.44271 .96108 (308*2π)/5212 weeks
309-1.0039 -2.24095 (309*2π)/5212 weeks
3101.55507 -2.1343 (310*2π)/5212 weeks
3112.03304 -.96277 (311*2π)/5212 weeks
3121.81408 .30612 (312*2π)/5212 weeks
313.00943 .19268 (313*2π)/5212 weeks
314.41539 -2.01357 (314*2π)/5212 weeks
3152.99765 -1.22869 (315*2π)/5212 weeks
3162.32764 1.5247 (316*2π)/5212 weeks
317-.62409 1.5563 (317*2π)/5212 weeks
318-1.54329 -1.71837 (318*2π)/5212 weeks
3191.82227 -2.75121 (319*2π)/5212 weeks
3202.74606 -.66718 (320*2π)/5212 weeks
3212.2371 .97742 (321*2π)/5212 weeks
322-.49294 1.08668 (322*2π)/5212 weeks
323-.57492 -1.79327 (323*2π)/5212 weeks
3241.88357 -2.16723 (324*2π)/5212 weeks
3253.05592 -.05116 (325*2π)/5212 weeks
326.98654 1.52079 (326*2π)/5212 weeks
327-.50295 -.47682 (327*2π)/5212 weeks
328.98332 -.65559 (328*2π)/5212 weeks
329.46824 -.90094 (329*2π)/5212 weeks
3301.77029 -.30751 (330*2π)/5212 weeks
331.01135 -.08166 (331*2π)/5212 weeks
332.91635 -.93771 (332*2π)/5212 weeks
333.42196 -.64134 (333*2π)/5212 weeks
334.74029 -1.30357 (334*2π)/5212 weeks
335.71472 -1.52297 (335*2π)/5212 weeks
3362.87369 -2.02158 (336*2π)/5212 weeks
3372.19268 .77166 (337*2π)/5212 weeks
3381.35266 -.04182 (338*2π)/5212 weeks
3391.08206 .88609 (339*2π)/5212 weeks
340-.19999 .26936 (340*2π)/5212 weeks
341-.42332 -.96751 (341*2π)/5212 weeks
342.95664 -2.2906 (342*2π)/5212 weeks
3432.52197 -.72899 (343*2π)/5212 weeks
3441.0257 .51572 (344*2π)/5212 weeks
345-.09776 .34294 (345*2π)/5212 weeks
346-.88636 -1.80435 (346*2π)/5212 weeks
3471.52964 -2.7432 (347*2π)/5212 weeks
3483.34817 -1.36951 (348*2π)/5211 weeks
3492.39299 1.54713 (349*2π)/5211 weeks
350-.78986 1.35962 (350*2π)/5211 weeks
351-1.80803 -1.79698 (351*2π)/5211 weeks
352.97669 -3.98336 (352*2π)/5211 weeks
3533.68816 -2.10098 (353*2π)/5211 weeks
3543.44647 .67033 (354*2π)/5211 weeks
3551.00787 1.61125 (355*2π)/5211 weeks
356-.3586 .20915 (356*2π)/5211 weeks
357-.28659 -1.2353 (357*2π)/5211 weeks
358.90882 -2.2495 (358*2π)/5211 weeks
3592.36087 -1.37309 (359*2π)/5211 weeks
3602.37954 .50758 (360*2π)/5211 weeks
361.1127 1.3105 (361*2π)/5211 weeks
362-1.5352 -.50821 (362*2π)/5211 weeks
363-.37849 -3.00961 (363*2π)/5211 weeks
3642.04628 -2.4925 (364*2π)/5211 weeks
3652.78339 -1.01033 (365*2π)/5211 weeks
3661.19818 .49352 (366*2π)/5211 weeks
367.06524 -.29332 (367*2π)/5211 weeks
368.26513 -1.50044 (368*2π)/5211 weeks
369.78724 -1.40041 (369*2π)/5211 weeks
370.7561 -2.13735 (370*2π)/5211 weeks
3712.71411 -1.49911 (371*2π)/5211 weeks
3721.41512 .07675 (372*2π)/5211 weeks
373.75131 -.58231 (373*2π)/5211 weeks
374.52079 -.81808 (374*2π)/5211 weeks
375.58841 -1.66966 (375*2π)/5211 weeks
3761.50962 -2.03193 (376*2π)/5211 weeks
3772.91589 -1.4243 (377*2π)/5211 weeks
3782.14879 1.51761 (378*2π)/5211 weeks
379-.95552 .49332 (379*2π)/5211 weeks
380-1.23418 -2.02589 (380*2π)/5211 weeks
3811.37669 -3.93935 (381*2π)/5211 weeks
3823.63343 -1.37684 (382*2π)/5211 weeks
3832.17287 1.14876 (383*2π)/5211 weeks
384-1.05669 .78635 (384*2π)/5211 weeks
385-.89406 -3.28035 (385*2π)/5211 weeks
3863.27919 -3.03411 (386*2π)/5211 weeks
3872.67985 .26364 (387*2π)/5211 weeks
388.99346 .39599 (388*2π)/5211 weeks
389-.2425 -.5942 (389*2π)/5211 weeks
390.26724 -1.28385 (390*2π)/5211 weeks
391-.6495 -1.801 (391*2π)/5211 weeks
392.76878 -3.53595 (392*2π)/5211 weeks
3932.32225 -2.43639 (393*2π)/5211 weeks
3942.98361 -1.43058 (394*2π)/5211 weeks
3952.18382 .08521 (395*2π)/5211 weeks
396.55284 -.65061 (396*2π)/5211 weeks
397.98384 -1.91846 (397*2π)/5211 weeks
3981.83417 -1.22638 (398*2π)/5211 weeks
3991.18687 -.63752 (399*2π)/5211 weeks
4001.13159 -1.07945 (400*2π)/5211 weeks
401.55687 -.43875 (401*2π)/5211 weeks
402-.80063 -1.69828 (402*2π)/5211 weeks
403.45344 -3.94882 (403*2π)/5211 weeks
4044.04862 -3.48172 (404*2π)/5211 weeks
4053.95396 .55137 (405*2π)/5211 weeks
406.45547 1.30064 (406*2π)/5211 weeks
407-.69686 -1.46374 (407*2π)/5211 weeks
408.57341 -3.21529 (408*2π)/5211 weeks
4092.78135 -2.76938 (409*2π)/5211 weeks
4103.35582 -1.03875 (410*2π)/5211 weeks
4112.3158 1.75063 (411*2π)/5211 weeks
412-1.96708 1.36414 (412*2π)/5211 weeks
413-2.23973 -3.62349 (413*2π)/5211 weeks
4141.11062 -5.35352 (414*2π)/5211 weeks
4155.07702 -3.90219 (415*2π)/5211 weeks
4165.35513 1.40088 (416*2π)/5211 weeks
417-.12561 3.27584 (417*2π)/5211 weeks
418-4.01372 -1.66484 (418*2π)/5211 weeks
419-.36472 -6.60231 (419*2π)/5211 weeks
4205.05632 -5.31554 (420*2π)/5211 weeks
4216.77521 .44196 (421*2π)/5211 weeks
4221.91148 3.71372 (422*2π)/5211 weeks
423-2.93679 .91182 (423*2π)/5211 weeks
424-1.59584 -4.97349 (424*2π)/5211 weeks
4253.91087 -4.91591 (425*2π)/5211 weeks
4265.18315 -.40362 (426*2π)/5211 weeks
4271.59366 2.53888 (427*2π)/5211 weeks
428-1.70785 .24746 (428*2π)/5211 weeks
429-.7869 -3.30791 (429*2π)/5211 weeks
4302.64936 -3.15588 (430*2π)/5211 weeks
4313.27969 .88207 (431*2π)/5211 weeks
432-2.19505 .89044 (432*2π)/5211 weeks
433-1.20322 -4.35599 (433*2π)/5211 weeks
4342.8486 -3.87601 (434*2π)/5211 weeks
4353.11949 -.23149 (435*2π)/5211 weeks
436-.4782 .43918 (436*2π)/5211 weeks
437-1.80661 -3.44201 (437*2π)/5211 weeks
4382.09124 -5.99113 (438*2π)/5211 weeks
4396.25293 -2.65159 (439*2π)/5211 weeks
4403.74105 3.5777 (440*2π)/5211 weeks
441-3.16601 1.63427 (441*2π)/5211 weeks
442-2.84257 -3.34866 (442*2π)/5211 weeks
443-.41797 -6.63652 (443*2π)/5211 weeks
4445.14875 -5.06621 (444*2π)/5211 weeks
4455.38816 -.30497 (445*2π)/5211 weeks
4461.11414 3.43008 (446*2π)/5211 weeks
447-3.97855 -1.7431 (447*2π)/5211 weeks
448.74441 -5.48651 (448*2π)/5211 weeks
4492.08593 -4.226 (449*2π)/5211 weeks
4505.74671 -2.47403 (450*2π)/5211 weeks
4513.12395 3.73089 (451*2π)/5211 weeks
452-3.55115 1.79842 (452*2π)/5211 weeks
453-5.04092 -4.61026 (453*2π)/5211 weeks
4541.46675 -8.18184 (454*2π)/5211 weeks
4555.34109 -2.02281 (455*2π)/5211 weeks
456-.14162 -.41594 (456*2π)/5211 weeks
457-.27704 -3.22802 (457*2π)/5211 weeks
4581.20829 -6.2463 (458*2π)/5211 weeks
4596.09158 -2.30443 (459*2π)/5211 weeks
4602.13038 2.83445 (460*2π)/5211 weeks
461-3.1717 -.13367 (461*2π)/5211 weeks
462-3.21303 -5.83203 (462*2π)/5211 weeks
4633.73009 -6.95634 (463*2π)/5211 weeks
4644.26375 -.73601 (464*2π)/5211 weeks
465-.10866 .45453 (465*2π)/5211 weeks
466-3.70878 -3.40989 (466*2π)/5211 weeks
467-.08218 -9.26469 (467*2π)/5211 weeks
4688.34514 -5.14455 (468*2π)/5211 weeks
4694.57982 1.99636 (469*2π)/5211 weeks
470-.71444 1.11393 (470*2π)/5211 weeks
471-2.44345 -2.8155 (471*2π)/5211 weeks
472.50823 -6.1444 (472*2π)/5211 weeks
4734.12889 -3.01395 (473*2π)/5211 weeks
4741.89393 .60477 (474*2π)/5211 weeks
475-3.28364 -.3001 (475*2π)/5211 weeks
476-4.1658 -4.37314 (476*2π)/5211 weeks
477-.22756 -8.66283 (477*2π)/5211 weeks
4783.30138 -5.49538 (478*2π)/5211 weeks
4791.85869 -3.44212 (479*2π)/5211 weeks
480-1.0017 -2.57699 (480*2π)/5211 weeks
481-.40283 -8.4483 (481*2π)/5211 weeks
4826.29046 -5.56154 (482*2π)/5211 weeks
4832.53901 -.7074 (483*2π)/5211 weeks
484-1.59629 -.42868 (484*2π)/5211 weeks
485-6.41523 -6.37292 (485*2π)/5211 weeks
486.73466 -14.76982 (486*2π)/5211 weeks
48712.12688 -9.41598 (487*2π)/5211 weeks
48811.91745 6.60894 (488*2π)/5211 weeks
489-9.7748 12.4852 (489*2π)/5211 weeks
490-19.88227 -10.87863 (490*2π)/5211 weeks
491-1.19343 -26.20171 (491*2π)/5211 weeks
49219.13412 -15.83851 (492*2π)/5211 weeks
49314.95997 7.5435 (493*2π)/5211 weeks
494-7.40634 9.37361 (494*2π)/5211 weeks
495-16.01198 -5.74459 (495*2π)/5211 weeks
496-9.53759 -22.78814 (496*2π)/5211 weeks
49711.63923 -19.07769 (497*2π)/5211 weeks
4989.66155 -2.85449 (498*2π)/5211 weeks
499-2.28464 -.44761 (499*2π)/5211 weeks
500-5.6481 -13.13448 (500*2π)/5211 weeks
5013.50839 -16.92427 (501*2π)/5211 weeks
5027.03264 -10.75938 (502*2π)/5211 weeks
5033.68134 -9.5274 (503*2π)/5211 weeks
5044.11914 -6.84684 (504*2π)/5211 weeks
505-2.43689 -11.2172 (505*2π)/5211 weeks
5064.8806 -11.69234 (506*2π)/5211 weeks
507-.41956 -7.14952 (507*2π)/5211 weeks
508-7.4699 -11.95663 (508*2π)/5211 weeks
509-9.61928 -30.40891 (509*2π)/5211 weeks
51020.1112 -36.01046 (510*2π)/5211 weeks
51124.26629 -11.18367 (511*2π)/5211 weeks
51218.41467 4.72266 (512*2π)/5211 weeks
513-23.42456 8.73832 (513*2π)/5211 weeks
514-33.4536 -51.20928 (514*2π)/5211 weeks
51521.29727 -71.97001 (515*2π)/5211 weeks
51658.994 -30.15903 (516*2π)/5211 weeks
51727.6565 25.01616 (517*2π)/5211 weeks
518-67.83092 4.67036 (518*2π)/5211 weeks
519-78.31024 -140.9473 (519*2π)/5211 weeks

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