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Fourier Analysis of SIJ (PROSHARES ULTRASHORT INDUSTRIALS PROSHARES ULTRASHORT INDUSTRIALS)


SIJ (PROSHARES ULTRASHORT INDUSTRIALS PROSHARES ULTRASHORT INDUSTRIALS) appears to have interesting cyclic behaviour every 44 weeks (32.0435*sine), 48 weeks (31.0262*sine), and 52 weeks (22.0296*cosine).

SIJ (PROSHARES ULTRASHORT INDUSTRIALS PROSHARES ULTRASHORT INDUSTRIALS) has an average price of 248.81 (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 1/16/2018 for SIJ (PROSHARES ULTRASHORT INDUSTRIALS PROSHARES ULTRASHORT INDUSTRIALS), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0248.8088   0 
1117.5449 282.6403 (1*2π)/573573 weeks
2-59.71443 156.4545 (2*2π)/573287 weeks
3-80.55148 29.37175 (3*2π)/573191 weeks
4-1.74043 -27.91577 (4*2π)/573143 weeks
550.32315 2.76989 (5*2π)/573115 weeks
644.9348 50.24665 (6*2π)/57396 weeks
7.26254 65.83458 (7*2π)/57382 weeks
8-37.1428 31.06751 (8*2π)/57372 weeks
9-13.12725 -11.47541 (9*2π)/57364 weeks
1017.79329 -1.68177 (10*2π)/57357 weeks
1122.02958 10.33857 (11*2π)/57352 weeks
1220.49708 31.0262 (12*2π)/57348 weeks
13-5.60537 32.04345 (13*2π)/57344 weeks
14-8.81928 14.0765 (14*2π)/57341 weeks
15-3.00299 8.20557 (15*2π)/57338 weeks
163.47802 8.00711 (16*2π)/57336 weeks
172.09706 13.20162 (17*2π)/57334 weeks
18-.83789 6.5674 (18*2π)/57332 weeks
194.78923 7.6974 (19*2π)/57330 weeks
203.54695 8.42894 (20*2π)/57329 weeks
216.35043 10.62348 (21*2π)/57327 weeks
223.06402 15.61209 (22*2π)/57326 weeks
23-4.55255 12.733 (23*2π)/57325 weeks
24-4.17873 1.92145 (24*2π)/57324 weeks
256.26915 1.42249 (25*2π)/57323 weeks
2612.77116 11.58594 (26*2π)/57322 weeks
271.11626 23.62514 (27*2π)/57321 weeks
28-13.53747 13.39233 (28*2π)/57320 weeks
29-13.27043 -.52785 (29*2π)/57320 weeks
30-1.7413 -11.12579 (30*2π)/57319 weeks
3116.22864 -3.53549 (31*2π)/57318 weeks
3216.12267 16.55345 (32*2π)/57318 weeks
33-1.27455 23.98492 (33*2π)/57317 weeks
34-17.60028 11.88617 (34*2π)/57317 weeks
35-12.80946 -8.87648 (35*2π)/57316 weeks
367.27358 -9.69019 (36*2π)/57316 weeks
3712.9664 4.22645 (37*2π)/57315 weeks
385.95788 13.00189 (38*2π)/57315 weeks
39-3.94481 11.06645 (39*2π)/57315 weeks
40-4.92215 2.80585 (40*2π)/57314 weeks
41-.18492 .41524 (41*2π)/57314 weeks
423.10324 .9185 (42*2π)/57314 weeks
435.52646 5.99522 (43*2π)/57313 weeks
44-.39677 7.824 (44*2π)/57313 weeks
45-1.32824 2.76144 (45*2π)/57313 weeks
461.55366 3.07954 (46*2π)/57312 weeks
472.80254 4.14284 (47*2π)/57312 weeks
481.55464 7.39669 (48*2π)/57312 weeks
49-3.31228 6.56585 (49*2π)/57312 weeks
50-3.50335 2.67787 (50*2π)/57311 weeks
51-1.31162 -.90106 (51*2π)/57311 weeks
522.58917 .2095 (52*2π)/57311 weeks
533.66729 3.67828 (53*2π)/57311 weeks
54.066 5.5571 (54*2π)/57311 weeks
55-2.17058 2.61568 (55*2π)/57310 weeks
56-.89872 -.71521 (56*2π)/57310 weeks
573.12394 -2.01912 (57*2π)/57310 weeks
587.60136 2.30549 (58*2π)/57310 weeks
593.11361 9.03837 (59*2π)/57310 weeks
60-2.66653 5.89996 (60*2π)/57310 weeks
61-2.16776 .81258 (61*2π)/5739 weeks
621.40133 -.41633 (62*2π)/5739 weeks
634.70988 2.05724 (63*2π)/5739 weeks
642.21913 7.04192 (64*2π)/5739 weeks
65-3.17835 4.76158 (65*2π)/5739 weeks
66-2.81936 .15588 (66*2π)/5739 weeks
671.40366 -2.54102 (67*2π)/5739 weeks
685.44289 1.14741 (68*2π)/5738 weeks
692.82558 5.84181 (69*2π)/5738 weeks
70-.29903 3.46661 (70*2π)/5738 weeks
71-.60269 2.03316 (71*2π)/5738 weeks
722.28201 -.3197 (72*2π)/5738 weeks
734.84541 4.65597 (73*2π)/5738 weeks
74-.75715 7.44822 (74*2π)/5738 weeks
75-4.92188 2.83822 (75*2π)/5738 weeks
76-2.83785 -2.06916 (76*2π)/5738 weeks
772.96902 -3.32573 (77*2π)/5737 weeks
785.41663 1.87915 (78*2π)/5737 weeks
792.26546 4.11746 (79*2π)/5737 weeks
801.54307 4.44002 (80*2π)/5737 weeks
81-2.72228 3.85267 (81*2π)/5737 weeks
82-1.99267 -2.12431 (82*2π)/5737 weeks
833.75637 -1.87566 (83*2π)/5737 weeks
845.27344 1.75379 (84*2π)/5737 weeks
853.56094 5.83519 (85*2π)/5737 weeks
86-1.21324 5.50663 (86*2π)/5737 weeks
87-2.76552 2.8186 (87*2π)/5737 weeks
88-2.81601 -1.52426 (88*2π)/5737 weeks
892.91691 -3.44615 (89*2π)/5736 weeks
905.92533 1.50468 (90*2π)/5736 weeks
913.11992 5.21313 (91*2π)/5736 weeks
92-.91606 4.44003 (92*2π)/5736 weeks
93-1.65583 .95035 (93*2π)/5736 weeks
941.20303 -.58625 (94*2π)/5736 weeks
953.37042 1.59133 (95*2π)/5736 weeks
961.76419 4.21594 (96*2π)/5736 weeks
97-1.80091 3.43547 (97*2π)/5736 weeks
98-1.51504 -1.2359 (98*2π)/5736 weeks
993.06478 -.71594 (99*2π)/5736 weeks
1002.62574 2.73563 (100*2π)/5736 weeks
101-.17036 3.36243 (101*2π)/5736 weeks
102-1.6915 .7611 (102*2π)/5736 weeks
103.18592 -1.88846 (103*2π)/5736 weeks
1043.95694 -1.3689 (104*2π)/5736 weeks
1054.83515 2.24035 (105*2π)/5735 weeks
1061.74271 5.28988 (106*2π)/5735 weeks
107-2.61769 3.34021 (107*2π)/5735 weeks
108-2.03261 -1.6591 (108*2π)/5735 weeks
1092.32324 -3.25775 (109*2π)/5735 weeks
1106.23573 -.23496 (110*2π)/5735 weeks
1114.92622 4.66507 (111*2π)/5735 weeks
112.64945 6.28582 (112*2π)/5735 weeks
113-3.29418 3.10118 (113*2π)/5735 weeks
114-1.91174 -2.12615 (114*2π)/5735 weeks
1152.9153 -2.8463 (115*2π)/5735 weeks
1165.49801 1.17963 (116*2π)/5735 weeks
1173.29262 4.62231 (117*2π)/5735 weeks
118.12649 4.7121 (118*2π)/5735 weeks
119-2.48457 2.58905 (119*2π)/5735 weeks
120-1.3321 -1.55656 (120*2π)/5735 weeks
1212.1788 -1.55345 (121*2π)/5735 weeks
1223.1583 .84556 (122*2π)/5735 weeks
1232.84975 2.26003 (123*2π)/5735 weeks
1241.16936 3.08144 (124*2π)/5735 weeks
125-.34988 1.96593 (125*2π)/5735 weeks
126-.58941 -.10805 (126*2π)/5735 weeks
1272.01879 -1.34523 (127*2π)/5735 weeks
1284.30691 .83088 (128*2π)/5734 weeks
1292.77415 3.92703 (129*2π)/5734 weeks
130.06783 3.32607 (130*2π)/5734 weeks
131-.66345 1.32984 (131*2π)/5734 weeks
132.49047 .4314 (132*2π)/5734 weeks
1331.0359 .9741 (133*2π)/5734 weeks
134.97267 .63605 (134*2π)/5734 weeks
1351.6639 .8875 (135*2π)/5734 weeks
1361.38176 1.68038 (136*2π)/5734 weeks
137.40068 1.09887 (137*2π)/5734 weeks
138.87505 -.03613 (138*2π)/5734 weeks
1392.44498 .43938 (139*2π)/5734 weeks
1402.6294 1.79759 (140*2π)/5734 weeks
1412.18288 2.46835 (141*2π)/5734 weeks
142.51345 3.17477 (142*2π)/5734 weeks
143-.55552 1.63071 (143*2π)/5734 weeks
144.27684 1.17455 (144*2π)/5734 weeks
145-.15182 .76245 (145*2π)/5734 weeks
146.61505 -.35814 (146*2π)/5734 weeks
1471.73885 -.41121 (147*2π)/5734 weeks
1483.34823 1.23637 (148*2π)/5734 weeks
1491.16632 3.84528 (149*2π)/5734 weeks
150-1.63717 1.72446 (150*2π)/5734 weeks
151-.00702 -1.18574 (151*2π)/5734 weeks
1522.50056 -.69486 (152*2π)/5734 weeks
1533.32509 1.61501 (153*2π)/5734 weeks
1541.17331 3.61518 (154*2π)/5734 weeks
155-1.09309 2.0323 (155*2π)/5734 weeks
156-1.04031 -.07494 (156*2π)/5734 weeks
1571.1087 -1.62697 (157*2π)/5734 weeks
1583.03422 .45532 (158*2π)/5734 weeks
1591.87423 1.80978 (159*2π)/5734 weeks
160.98627 1.83162 (160*2π)/5734 weeks
161.42899 1.23912 (161*2π)/5734 weeks
162.64007 .65253 (162*2π)/5734 weeks
163.74738 .42965 (163*2π)/5734 weeks
1641.55068 -.07097 (164*2π)/5733 weeks
1652.508 1.46326 (165*2π)/5733 weeks
166.78512 2.09292 (166*2π)/5733 weeks
167.68499 1.35469 (167*2π)/5733 weeks
168.48278 1.49622 (168*2π)/5733 weeks
169-.04882 .69408 (169*2π)/5733 weeks
170.5795 -.15653 (170*2π)/5733 weeks
1712.14647 -.17536 (171*2π)/5733 weeks
1722.291 1.57145 (172*2π)/5733 weeks
1731.41262 2.71064 (173*2π)/5733 weeks
174-.82913 2.38945 (174*2π)/5733 weeks
175-1.30308 .16114 (175*2π)/5733 weeks
176.20084 -1.23521 (176*2π)/5733 weeks
1772.12565 -.58641 (177*2π)/5733 weeks
1782.2874 1.05196 (178*2π)/5733 weeks
1791.30556 1.99815 (179*2π)/5733 weeks
180-.02796 1.44266 (180*2π)/5733 weeks
181-.43613 .35657 (181*2π)/5733 weeks
182.03896 -.84615 (182*2π)/5733 weeks
1831.9236 -1.42379 (183*2π)/5733 weeks
1843.53576 .1461 (184*2π)/5733 weeks
1853.11115 2.46613 (185*2π)/5733 weeks
186.4832 3.61164 (186*2π)/5733 weeks
187-1.63641 1.56123 (187*2π)/5733 weeks
188-.84218 -1.11003 (188*2π)/5733 weeks
1891.74986 -1.59828 (189*2π)/5733 weeks
1903.20771 .6058 (190*2π)/5733 weeks
1911.93981 2.28699 (191*2π)/5733 weeks
192.02456 2.52372 (192*2π)/5733 weeks
193-.78755 .45243 (193*2π)/5733 weeks
194.48806 -.34781 (194*2π)/5733 weeks
1951.45242 -.50644 (195*2π)/5733 weeks
1962.20072 1.12579 (196*2π)/5733 weeks
197.59876 2.06543 (197*2π)/5733 weeks
198-.3519 .84398 (198*2π)/5733 weeks
199-.17977 -.19417 (199*2π)/5733 weeks
200.76976 -.83109 (200*2π)/5733 weeks
2011.43252 -.00414 (201*2π)/5733 weeks
2021.37602 -.5432 (202*2π)/5733 weeks
2033.15259 .49576 (203*2π)/5733 weeks
2041.25269 2.12445 (204*2π)/5733 weeks
205.80325 1.16247 (205*2π)/5733 weeks
206.53447 1.15174 (206*2π)/5733 weeks
207.55122 .4736 (207*2π)/5733 weeks
208.73618 .95472 (208*2π)/5733 weeks
209.05773 .02716 (209*2π)/5733 weeks
2101.61701 .1641 (210*2π)/5733 weeks
211.57607 1.00211 (211*2π)/5733 weeks
212.81536 .42917 (212*2π)/5733 weeks
213.10229 1.01542 (213*2π)/5733 weeks
214-.04401 -.97769 (214*2π)/5733 weeks
2152.0956 -1.0946 (215*2π)/5733 weeks
2162.66602 1.02654 (216*2π)/5733 weeks
2171.1125 2.18027 (217*2π)/5733 weeks
218-.83104 1.11804 (218*2π)/5733 weeks
219-.16312 -1.23215 (219*2π)/5733 weeks
2202.07089 -.81849 (220*2π)/5733 weeks
2212.5138 .5286 (221*2π)/5733 weeks
2222.02227 2.21876 (222*2π)/5733 weeks
223-.84249 2.29493 (223*2π)/5733 weeks
224-1.23338 -.65012 (224*2π)/5733 weeks
2251.07578 -1.80741 (225*2π)/5733 weeks
2262.90385 -.29307 (226*2π)/5733 weeks
2271.9726 1.87685 (227*2π)/5733 weeks
228-.08908 1.26719 (228*2π)/5733 weeks
229.3964 -.44398 (229*2π)/5733 weeks
2301.79472 -.10849 (230*2π)/5732 weeks
2311.83654 .93403 (231*2π)/5732 weeks
2321.48555 1.8943 (232*2π)/5732 weeks
233-.51177 2.27383 (233*2π)/5732 weeks
234-1.62143 -.18562 (234*2π)/5732 weeks
235.35245 -1.67625 (235*2π)/5732 weeks
2362.20154 -1.12025 (236*2π)/5732 weeks
2372.78479 1.40474 (237*2π)/5732 weeks
238.05908 2.29691 (238*2π)/5732 weeks
239-.78991 .72814 (239*2π)/5732 weeks
240-.758 -.76261 (240*2π)/5732 weeks
241.89436 -1.91854 (241*2π)/5732 weeks
2422.64391 -.6099 (242*2π)/5732 weeks
2432.21897 1.35789 (243*2π)/5732 weeks
244.50208 2.15731 (244*2π)/5732 weeks
245-1.47377 .74065 (245*2π)/5732 weeks
246-.68881 -1.68981 (246*2π)/5732 weeks
2471.4727 -1.99255 (247*2π)/5732 weeks
2482.62148 -.84663 (248*2π)/5732 weeks
2492.88914 1.19322 (249*2π)/5732 weeks
250.48624 1.68096 (250*2π)/5732 weeks
251.23936 .46829 (251*2π)/5732 weeks
252.08481 -.14777 (252*2π)/5732 weeks
2531.13783 -.41456 (253*2π)/5732 weeks
254.87515 .10593 (254*2π)/5732 weeks
2551.08674 -.31424 (255*2π)/5732 weeks
2561.48755 .44188 (256*2π)/5732 weeks
257.52215 .80719 (257*2π)/5732 weeks
258.36147 .01883 (258*2π)/5732 weeks
259.00906 -.58698 (259*2π)/5732 weeks
2601.26978 -1.41132 (260*2π)/5732 weeks
2612.6993 -.43247 (261*2π)/5732 weeks
2622.17705 1.10526 (262*2π)/5732 weeks
2631.14845 1.76822 (263*2π)/5732 weeks
264-.44509 1.61961 (264*2π)/5732 weeks
265-1.66494 -.21957 (265*2π)/5732 weeks
266-.64244 -2.45648 (266*2π)/5732 weeks
2672.61521 -3.17376 (267*2π)/5732 weeks
2684.52306 .21896 (268*2π)/5732 weeks
2692.20871 2.67905 (269*2π)/5732 weeks
270-.12755 2.2878 (270*2π)/5732 weeks
271-1.98868 .16252 (271*2π)/5732 weeks
272-.31039 -2.77275 (272*2π)/5732 weeks
2733.04893 -2.21333 (273*2π)/5732 weeks
2743.59709 1.38446 (274*2π)/5732 weeks
275.74142 2.30933 (275*2π)/5732 weeks
276-.92734 .74382 (276*2π)/5732 weeks
277-.7444 -1.32386 (277*2π)/5732 weeks
278.94487 -2.25593 (278*2π)/5732 weeks
2793.30549 -1.49635 (279*2π)/5732 weeks
2803.50636 1.62147 (280*2π)/5732 weeks
281.10816 2.39871 (281*2π)/5732 weeks
282-1.08996 -.0973 (282*2π)/5732 weeks
283.41315 -1.31313 (283*2π)/5732 weeks
2841.67402 -1.0368 (284*2π)/5732 weeks
2851.54534 -.39879 (285*2π)/5732 weeks
2861.94897 -.48209 (286*2π)/5732 weeks
2871.94897 .48209 (287*2π)/5732 weeks
2881.54534 .39879 (288*2π)/5732 weeks
2891.67402 1.0368 (289*2π)/5732 weeks
290.41315 1.31313 (290*2π)/5732 weeks
291-1.08996 .0973 (291*2π)/5732 weeks
292.10816 -2.39871 (292*2π)/5732 weeks
2933.50636 -1.62147 (293*2π)/5732 weeks
2943.30549 1.49635 (294*2π)/5732 weeks
295.94487 2.25593 (295*2π)/5732 weeks
296-.7444 1.32386 (296*2π)/5732 weeks
297-.92734 -.74382 (297*2π)/5732 weeks
298.74142 -2.30933 (298*2π)/5732 weeks
2993.59709 -1.38446 (299*2π)/5732 weeks
3003.04893 2.21333 (300*2π)/5732 weeks
301-.31039 2.77275 (301*2π)/5732 weeks
302-1.98868 -.16252 (302*2π)/5732 weeks
303-.12755 -2.2878 (303*2π)/5732 weeks
3042.20871 -2.67905 (304*2π)/5732 weeks
3054.52306 -.21896 (305*2π)/5732 weeks
3062.61521 3.17376 (306*2π)/5732 weeks
307-.64244 2.45648 (307*2π)/5732 weeks
308-1.66494 .21957 (308*2π)/5732 weeks
309-.44509 -1.61961 (309*2π)/5732 weeks
3101.14845 -1.76822 (310*2π)/5732 weeks
3112.17705 -1.10526 (311*2π)/5732 weeks
3122.6993 .43247 (312*2π)/5732 weeks
3131.26978 1.41132 (313*2π)/5732 weeks
314.00906 .58698 (314*2π)/5732 weeks
315.36147 -.01883 (315*2π)/5732 weeks
316.52215 -.80719 (316*2π)/5732 weeks
3171.48755 -.44188 (317*2π)/5732 weeks
3181.08674 .31424 (318*2π)/5732 weeks
319.87515 -.10593 (319*2π)/5732 weeks
3201.13783 .41456 (320*2π)/5732 weeks
321.08481 .14777 (321*2π)/5732 weeks
322.23936 -.46829 (322*2π)/5732 weeks
323.48624 -1.68096 (323*2π)/5732 weeks
3242.88914 -1.19322 (324*2π)/5732 weeks
3252.62148 .84663 (325*2π)/5732 weeks
3261.4727 1.99255 (326*2π)/5732 weeks
327-.68881 1.68981 (327*2π)/5732 weeks
328-1.47377 -.74065 (328*2π)/5732 weeks
329.50208 -2.15731 (329*2π)/5732 weeks
3302.21897 -1.35789 (330*2π)/5732 weeks
3312.64391 .6099 (331*2π)/5732 weeks
332.89436 1.91854 (332*2π)/5732 weeks
333-.758 .76261 (333*2π)/5732 weeks
334-.78991 -.72814 (334*2π)/5732 weeks
335.05908 -2.29691 (335*2π)/5732 weeks
3362.78479 -1.40474 (336*2π)/5732 weeks
3372.20154 1.12025 (337*2π)/5732 weeks
338.35245 1.67625 (338*2π)/5732 weeks
339-1.62143 .18562 (339*2π)/5732 weeks
340-.51177 -2.27383 (340*2π)/5732 weeks
3411.48555 -1.8943 (341*2π)/5732 weeks
3421.83654 -.93403 (342*2π)/5732 weeks
3431.79472 .10849 (343*2π)/5732 weeks
344.3964 .44398 (344*2π)/5732 weeks
345-.08908 -1.26719 (345*2π)/5732 weeks
3461.9726 -1.87685 (346*2π)/5732 weeks
3472.90385 .29307 (347*2π)/5732 weeks
3481.07578 1.80741 (348*2π)/5732 weeks
349-1.23338 .65012 (349*2π)/5732 weeks
350-.84249 -2.29493 (350*2π)/5732 weeks
3512.02227 -2.21876 (351*2π)/5732 weeks
3522.5138 -.5286 (352*2π)/5732 weeks
3532.07089 .81849 (353*2π)/5732 weeks
354-.16312 1.23215 (354*2π)/5732 weeks
355-.83104 -1.11804 (355*2π)/5732 weeks
3561.1125 -2.18027 (356*2π)/5732 weeks
3572.66602 -1.02654 (357*2π)/5732 weeks
3582.0956 1.0946 (358*2π)/5732 weeks
359-.04401 .97769 (359*2π)/5732 weeks
360.10229 -1.01542 (360*2π)/5732 weeks
361.81536 -.42917 (361*2π)/5732 weeks
362.57607 -1.00211 (362*2π)/5732 weeks
3631.61701 -.1641 (363*2π)/5732 weeks
364.05773 -.02716 (364*2π)/5732 weeks
365.73618 -.95472 (365*2π)/5732 weeks
366.55122 -.4736 (366*2π)/5732 weeks
367.53447 -1.15174 (367*2π)/5732 weeks
368.80325 -1.16247 (368*2π)/5732 weeks
3691.25269 -2.12445 (369*2π)/5732 weeks
3703.15259 -.49576 (370*2π)/5732 weeks
3711.37602 .5432 (371*2π)/5732 weeks
3721.43252 .00414 (372*2π)/5732 weeks
373.76976 .83109 (373*2π)/5732 weeks
374-.17977 .19417 (374*2π)/5732 weeks
375-.3519 -.84398 (375*2π)/5732 weeks
376.59876 -2.06543 (376*2π)/5732 weeks
3772.20072 -1.12579 (377*2π)/5732 weeks
3781.45242 .50644 (378*2π)/5732 weeks
379.48806 .34781 (379*2π)/5732 weeks
380-.78755 -.45243 (380*2π)/5732 weeks
381.02456 -2.52372 (381*2π)/5732 weeks
3821.93981 -2.28699 (382*2π)/5732 weeks
3833.20771 -.6058 (383*2π)/5731 weeks
3841.74986 1.59828 (384*2π)/5731 weeks
385-.84218 1.11003 (385*2π)/5731 weeks
386-1.63641 -1.56123 (386*2π)/5731 weeks
387.4832 -3.61164 (387*2π)/5731 weeks
3883.11115 -2.46613 (388*2π)/5731 weeks
3893.53576 -.1461 (389*2π)/5731 weeks
3901.9236 1.42379 (390*2π)/5731 weeks
391.03896 .84615 (391*2π)/5731 weeks
392-.43613 -.35657 (392*2π)/5731 weeks
393-.02796 -1.44266 (393*2π)/5731 weeks
3941.30556 -1.99815 (394*2π)/5731 weeks
3952.2874 -1.05196 (395*2π)/5731 weeks
3962.12565 .58641 (396*2π)/5731 weeks
397.20084 1.23521 (397*2π)/5731 weeks
398-1.30308 -.16114 (398*2π)/5731 weeks
399-.82913 -2.38945 (399*2π)/5731 weeks
4001.41262 -2.71064 (400*2π)/5731 weeks
4012.291 -1.57145 (401*2π)/5731 weeks
4022.14647 .17536 (402*2π)/5731 weeks
403.5795 .15653 (403*2π)/5731 weeks
404-.04882 -.69408 (404*2π)/5731 weeks
405.48278 -1.49622 (405*2π)/5731 weeks
406.68499 -1.35469 (406*2π)/5731 weeks
407.78512 -2.09292 (407*2π)/5731 weeks
4082.508 -1.46326 (408*2π)/5731 weeks
4091.55068 .07097 (409*2π)/5731 weeks
410.74738 -.42965 (410*2π)/5731 weeks
411.64007 -.65253 (411*2π)/5731 weeks
412.42899 -1.23912 (412*2π)/5731 weeks
413.98627 -1.83162 (413*2π)/5731 weeks
4141.87423 -1.80978 (414*2π)/5731 weeks
4153.03422 -.45532 (415*2π)/5731 weeks
4161.1087 1.62697 (416*2π)/5731 weeks
417-1.04031 .07494 (417*2π)/5731 weeks
418-1.09309 -2.0323 (418*2π)/5731 weeks
4191.17331 -3.61518 (419*2π)/5731 weeks
4203.32509 -1.61501 (420*2π)/5731 weeks
4212.50056 .69486 (421*2π)/5731 weeks
422-.00702 1.18574 (422*2π)/5731 weeks
423-1.63717 -1.72446 (423*2π)/5731 weeks
4241.16632 -3.84528 (424*2π)/5731 weeks
4253.34823 -1.23637 (425*2π)/5731 weeks
4261.73885 .41121 (426*2π)/5731 weeks
427.61505 .35814 (427*2π)/5731 weeks
428-.15182 -.76245 (428*2π)/5731 weeks
429.27684 -1.17455 (429*2π)/5731 weeks
430-.55552 -1.63071 (430*2π)/5731 weeks
431.51345 -3.17477 (431*2π)/5731 weeks
4322.18288 -2.46835 (432*2π)/5731 weeks
4332.6294 -1.79759 (433*2π)/5731 weeks
4342.44498 -.43938 (434*2π)/5731 weeks
435.87505 .03613 (435*2π)/5731 weeks
436.40068 -1.09887 (436*2π)/5731 weeks
4371.38176 -1.68038 (437*2π)/5731 weeks
4381.6639 -.8875 (438*2π)/5731 weeks
439.97267 -.63605 (439*2π)/5731 weeks
4401.0359 -.9741 (440*2π)/5731 weeks
441.49047 -.4314 (441*2π)/5731 weeks
442-.66345 -1.32984 (442*2π)/5731 weeks
443.06783 -3.32607 (443*2π)/5731 weeks
4442.77415 -3.92703 (444*2π)/5731 weeks
4454.30691 -.83088 (445*2π)/5731 weeks
4462.01879 1.34523 (446*2π)/5731 weeks
447-.58941 .10805 (447*2π)/5731 weeks
448-.34988 -1.96593 (448*2π)/5731 weeks
4491.16936 -3.08144 (449*2π)/5731 weeks
4502.84975 -2.26003 (450*2π)/5731 weeks
4513.1583 -.84556 (451*2π)/5731 weeks
4522.1788 1.55345 (452*2π)/5731 weeks
453-1.3321 1.55656 (453*2π)/5731 weeks
454-2.48457 -2.58905 (454*2π)/5731 weeks
455.12649 -4.7121 (455*2π)/5731 weeks
4563.29262 -4.62231 (456*2π)/5731 weeks
4575.49801 -1.17963 (457*2π)/5731 weeks
4582.9153 2.8463 (458*2π)/5731 weeks
459-1.91174 2.12615 (459*2π)/5731 weeks
460-3.29418 -3.10118 (460*2π)/5731 weeks
461.64945 -6.28582 (461*2π)/5731 weeks
4624.92622 -4.66507 (462*2π)/5731 weeks
4636.23573 .23496 (463*2π)/5731 weeks
4642.32324 3.25775 (464*2π)/5731 weeks
465-2.03261 1.6591 (465*2π)/5731 weeks
466-2.61769 -3.34021 (466*2π)/5731 weeks
4671.74271 -5.28988 (467*2π)/5731 weeks
4684.83515 -2.24035 (468*2π)/5731 weeks
4693.95694 1.3689 (469*2π)/5731 weeks
470.18592 1.88846 (470*2π)/5731 weeks
471-1.6915 -.7611 (471*2π)/5731 weeks
472-.17036 -3.36243 (472*2π)/5731 weeks
4732.62574 -2.73563 (473*2π)/5731 weeks
4743.06478 .71594 (474*2π)/5731 weeks
475-1.51504 1.2359 (475*2π)/5731 weeks
476-1.80091 -3.43547 (476*2π)/5731 weeks
4771.76419 -4.21594 (477*2π)/5731 weeks
4783.37042 -1.59133 (478*2π)/5731 weeks
4791.20303 .58625 (479*2π)/5731 weeks
480-1.65583 -.95035 (480*2π)/5731 weeks
481-.91606 -4.44003 (481*2π)/5731 weeks
4823.11992 -5.21313 (482*2π)/5731 weeks
4835.92533 -1.50468 (483*2π)/5731 weeks
4842.91691 3.44615 (484*2π)/5731 weeks
485-2.81601 1.52426 (485*2π)/5731 weeks
486-2.76552 -2.8186 (486*2π)/5731 weeks
487-1.21324 -5.50663 (487*2π)/5731 weeks
4883.56094 -5.83519 (488*2π)/5731 weeks
4895.27344 -1.75379 (489*2π)/5731 weeks
4903.75637 1.87566 (490*2π)/5731 weeks
491-1.99267 2.12431 (491*2π)/5731 weeks
492-2.72228 -3.85267 (492*2π)/5731 weeks
4931.54307 -4.44002 (493*2π)/5731 weeks
4942.26546 -4.11746 (494*2π)/5731 weeks
4955.41663 -1.87915 (495*2π)/5731 weeks
4962.96902 3.32573 (496*2π)/5731 weeks
497-2.83785 2.06916 (497*2π)/5731 weeks
498-4.92188 -2.83822 (498*2π)/5731 weeks
499-.75715 -7.44822 (499*2π)/5731 weeks
5004.84541 -4.65597 (500*2π)/5731 weeks
5012.28201 .3197 (501*2π)/5731 weeks
502-.60269 -2.03316 (502*2π)/5731 weeks
503-.29903 -3.46661 (503*2π)/5731 weeks
5042.82558 -5.84181 (504*2π)/5731 weeks
5055.44289 -1.14741 (505*2π)/5731 weeks
5061.40366 2.54102 (506*2π)/5731 weeks
507-2.81936 -.15588 (507*2π)/5731 weeks
508-3.17835 -4.76158 (508*2π)/5731 weeks
5092.21913 -7.04192 (509*2π)/5731 weeks
5104.70988 -2.05724 (510*2π)/5731 weeks
5111.40133 .41633 (511*2π)/5731 weeks
512-2.16776 -.81258 (512*2π)/5731 weeks
513-2.66653 -5.89996 (513*2π)/5731 weeks
5143.11361 -9.03837 (514*2π)/5731 weeks
5157.60136 -2.30549 (515*2π)/5731 weeks
5163.12394 2.01912 (516*2π)/5731 weeks
517-.89872 .71521 (517*2π)/5731 weeks
518-2.17058 -2.61568 (518*2π)/5731 weeks
519.066 -5.5571 (519*2π)/5731 weeks
5203.66729 -3.67828 (520*2π)/5731 weeks
5212.58917 -.2095 (521*2π)/5731 weeks
522-1.31162 .90106 (522*2π)/5731 weeks
523-3.50335 -2.67787 (523*2π)/5731 weeks
524-3.31228 -6.56585 (524*2π)/5731 weeks
5251.55464 -7.39669 (525*2π)/5731 weeks
5262.80254 -4.14284 (526*2π)/5731 weeks
5271.55366 -3.07954 (527*2π)/5731 weeks
528-1.32824 -2.76144 (528*2π)/5731 weeks
529-.39677 -7.824 (529*2π)/5731 weeks
5305.52646 -5.99522 (530*2π)/5731 weeks
5313.10324 -.9185 (531*2π)/5731 weeks
532-.18492 -.41524 (532*2π)/5731 weeks
533-4.92215 -2.80585 (533*2π)/5731 weeks
534-3.94481 -11.06645 (534*2π)/5731 weeks
5355.95788 -13.00189 (535*2π)/5731 weeks
53612.9664 -4.22645 (536*2π)/5731 weeks
5377.27358 9.69019 (537*2π)/5731 weeks
538-12.80946 8.87648 (538*2π)/5731 weeks
539-17.60028 -11.88617 (539*2π)/5731 weeks
540-1.27455 -23.98492 (540*2π)/5731 weeks
54116.12267 -16.55345 (541*2π)/5731 weeks
54216.22864 3.53549 (542*2π)/5731 weeks
543-1.7413 11.12579 (543*2π)/5731 weeks
544-13.27043 .52785 (544*2π)/5731 weeks
545-13.53747 -13.39233 (545*2π)/5731 weeks
5461.11626 -23.62514 (546*2π)/5731 weeks
54712.77116 -11.58594 (547*2π)/5731 weeks
5486.26915 -1.42249 (548*2π)/5731 weeks
549-4.17873 -1.92145 (549*2π)/5731 weeks
550-4.55255 -12.733 (550*2π)/5731 weeks
5513.06402 -15.61209 (551*2π)/5731 weeks
5526.35043 -10.62348 (552*2π)/5731 weeks
5533.54695 -8.42894 (553*2π)/5731 weeks
5544.78923 -7.6974 (554*2π)/5731 weeks
555-.83789 -6.5674 (555*2π)/5731 weeks
5562.09706 -13.20162 (556*2π)/5731 weeks
5573.47802 -8.00711 (557*2π)/5731 weeks
558-3.00299 -8.20557 (558*2π)/5731 weeks
559-8.81928 -14.0765 (559*2π)/5731 weeks
560-5.60537 -32.04345 (560*2π)/5731 weeks
56120.49708 -31.0262 (561*2π)/5731 weeks
56222.02958 -10.33857 (562*2π)/5731 weeks
56317.79329 1.68177 (563*2π)/5731 weeks
564-13.12725 11.47541 (564*2π)/5731 weeks
565-37.1428 -31.06751 (565*2π)/5731 weeks
566.26254 -65.83458 (566*2π)/5731 weeks
56744.9348 -50.24665 (567*2π)/5731 weeks
56850.32315 -2.76989 (568*2π)/5731 weeks
569-1.74043 27.91577 (569*2π)/5731 weeks
570-80.55148 -29.37175 (570*2π)/5731 weeks
571-59.71443 -156.4545 (571*2π)/5731 weeks



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