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Fourier Analysis of SIJ (ProShares UltraShort Industrials)

SIJ (ProShares UltraShort Industrials) appears to have interesting cyclic behaviour every 45 weeks (35.459*sine), 49 weeks (24.3937*sine), and 49 weeks (23.7697*cosine).

SIJ (ProShares UltraShort Industrials) has an average price of 243.65 (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.

Fourier Analysis

Using data from 2/1/2007 to 4/16/2018 for SIJ (ProShares UltraShort Industrials), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0243.6513   0
1121.7679 277.8826 (1*2π)/586586 weeks
2-55.3403 159.2711 (2*2π)/586293 weeks
3-80.98692 37.08152 (3*2π)/586195 weeks
4-8.34651 -27.0891 (4*2π)/586147 weeks
546.40864 -2.61182 (5*2π)/586117 weeks
647.43423 43.79552 (6*2π)/58698 weeks
77.5486 65.36563 (7*2π)/58684 weeks
8-33.12835 40.23082 (8*2π)/58673 weeks
9-20.84083 -7.09095 (9*2π)/58665 weeks
1014.07514 -6.32302 (10*2π)/58659 weeks
1119.86467 8.15169 (11*2π)/58653 weeks
1223.76974 24.39371 (12*2π)/58649 weeks
131.3361 35.45898 (13*2π)/58645 weeks
14-9.91243 18.0542 (14*2π)/58642 weeks
15-4.36862 9.30538 (15*2π)/58639 weeks
161.39356 6.64188 (16*2π)/58637 weeks
174.1133 11.2462 (17*2π)/58634 weeks
18-1.99742 9.98534 (18*2π)/58633 weeks
193.37695 5.87696 (19*2π)/58631 weeks
203.95772 9.12478 (20*2π)/58629 weeks
215.56626 8.29391 (21*2π)/58628 weeks
225.72145 12.82132 (22*2π)/58627 weeks
23-1.10932 14.91891 (23*2π)/58625 weeks
24-6.44824 8.10056 (24*2π)/58624 weeks
251.05418 -.01239 (25*2π)/58623 weeks
269.82935 3.74051 (26*2π)/58623 weeks
2710.25199 17.32753 (27*2π)/58622 weeks
28-6.62039 21.76126 (28*2π)/58621 weeks
29-14.14876 8.35967 (29*2π)/58620 weeks
30-10.38208 -4.54925 (30*2π)/58620 weeks
314.6921 -11.33459 (31*2π)/58619 weeks
3218.24538 1.68571 (32*2π)/58618 weeks
3311.67842 19.93048 (33*2π)/58618 weeks
34-6.07588 22.66561 (34*2π)/58617 weeks
35-18.20079 7.032 (35*2π)/58617 weeks
36-8.51667 -11.22732 (36*2π)/58616 weeks
379.4767 -7.42284 (37*2π)/58616 weeks
3812.12215 5.97126 (38*2π)/58615 weeks
394.4513 13.1222 (39*2π)/58615 weeks
40-4.54303 9.90718 (40*2π)/58615 weeks
41-4.44198 2.18141 (41*2π)/58614 weeks
42.04195 .39343 (42*2π)/58614 weeks
433.20127 .94161 (43*2π)/58614 weeks
445.31912 6.01742 (44*2π)/58613 weeks
45-.40294 7.63501 (45*2π)/58613 weeks
46-1.3844 2.76395 (46*2π)/58613 weeks
471.48759 2.96017 (47*2π)/58612 weeks
482.64912 3.88911 (48*2π)/58612 weeks
491.82759 7.01862 (49*2π)/58612 weeks
50-2.79944 6.90996 (50*2π)/58612 weeks
51-3.42092 2.9305 (51*2π)/58611 weeks
52-1.98867 -.56088 (52*2π)/58611 weeks
532.0992 -.22153 (53*2π)/58611 weeks
543.73399 2.73261 (54*2π)/58611 weeks
551.00311 5.49557 (55*2π)/58611 weeks
56-1.98595 3.33411 (56*2π)/58610 weeks
57-1.58416 .02731 (57*2π)/58610 weeks
581.60417 -1.91026 (58*2π)/58610 weeks
596.52653 .23375 (59*2π)/58610 weeks
605.78724 7.57835 (60*2π)/58610 weeks
61-1.36091 7.32204 (61*2π)/58610 weeks
62-3.10747 2.38813 (62*2π)/5869 weeks
63-.04377 -.31271 (63*2π)/5869 weeks
643.43149 .40792 (64*2π)/5869 weeks
654.29566 5.13299 (65*2π)/5869 weeks
66-1.19041 6.67931 (66*2π)/5869 weeks
67-3.38009 2.08869 (67*2π)/5869 weeks
68-1.32438 -1.65376 (68*2π)/5869 weeks
693.92655 -1.43703 (69*2π)/5868 weeks
705.14397 3.52089 (70*2π)/5868 weeks
71.46355 5.2156 (71*2π)/5868 weeks
72-.19821 2.88053 (72*2π)/5868 weeks
73-.33437 .77529 (73*2π)/5868 weeks
744.02912 .66665 (74*2π)/5868 weeks
753.42254 6.38688 (75*2π)/5868 weeks
76-2.56199 6.48244 (76*2π)/5868 weeks
77-4.60451 .99441 (77*2π)/5868 weeks
78-1.65294 -3.01343 (78*2π)/5868 weeks
794.19746 -2.31564 (79*2π)/5867 weeks
804.78936 2.85537 (80*2π)/5867 weeks
811.8185 3.80212 (81*2π)/5867 weeks
821.02503 4.73725 (82*2π)/5867 weeks
83-3.17918 2.94126 (83*2π)/5867 weeks
84-1.19085 -2.58854 (84*2π)/5867 weeks
854.02139 -1.41377 (85*2π)/5867 weeks
865.18031 2.05172 (86*2π)/5867 weeks
873.15419 5.88822 (87*2π)/5867 weeks
88-1.34718 5.23147 (88*2π)/5867 weeks
89-2.76353 2.69093 (89*2π)/5867 weeks
90-2.7612 -1.50252 (90*2π)/5867 weeks
912.72127 -3.40768 (91*2π)/5866 weeks
925.80098 1.25506 (92*2π)/5866 weeks
933.28887 4.99177 (93*2π)/5866 weeks
94-.66292 4.59266 (94*2π)/5866 weeks
95-1.74636 1.32499 (95*2π)/5866 weeks
96.79019 -.5916 (96*2π)/5866 weeks
973.21809 1.05217 (97*2π)/5866 weeks
982.21796 3.80691 (98*2π)/5866 weeks
99-1.1346 3.87446 (99*2π)/5866 weeks
100-2.25597 -.29685 (100*2π)/5866 weeks
1012.15725 -1.46901 (101*2π)/5866 weeks
1023.06503 2.09686 (102*2π)/5866 weeks
103.73768 3.50196 (103*2π)/5866 weeks
104-1.48932 1.68639 (104*2π)/5866 weeks
105-.71611 -1.26438 (105*2π)/5866 weeks
1062.54843 -2.13869 (106*2π)/5866 weeks
1074.73167 .8913 (107*2π)/5865 weeks
1083.46056 4.48593 (108*2π)/5865 weeks
109-.92718 4.72285 (109*2π)/5865 weeks
110-2.9839 .29053 (110*2π)/5865 weeks
111.12352 -3.04433 (111*2π)/5865 weeks
1124.54211 -2.27775 (112*2π)/5865 weeks
1136.17624 2.45103 (113*2π)/5865 weeks
1143.09938 5.66516 (114*2π)/5865 weeks
115-1.55029 5.25808 (115*2π)/5865 weeks
116-3.55857 .68723 (116*2π)/5865 weeks
117-.03167 -2.90453 (117*2π)/5865 weeks
1184.45572 -1.63594 (118*2π)/5865 weeks
1195.01685 2.68224 (119*2π)/5865 weeks
1202.05929 4.80716 (120*2π)/5865 weeks
121-.77002 4.25026 (121*2π)/5865 weeks
122-2.76107 1.31231 (122*2π)/5865 weeks
123-.2376 -1.91318 (123*2π)/5865 weeks
1242.75778 -1.02817 (124*2π)/5865 weeks
1252.96308 1.08209 (125*2π)/5865 weeks
1262.50325 2.52437 (126*2π)/5865 weeks
127.75757 2.97314 (127*2π)/5865 weeks
128-.45722 1.6992 (128*2π)/5865 weeks
129-.38167 -.45241 (129*2π)/5865 weeks
1302.31262 -1.22657 (130*2π)/5865 weeks
1314.25736 1.14653 (131*2π)/5864 weeks
1322.46524 3.93075 (132*2π)/5864 weeks
133-.01335 3.18456 (133*2π)/5864 weeks
134-.63246 1.24806 (134*2π)/5864 weeks
135.47812 .42338 (135*2π)/5864 weeks
1361.01285 .95059 (136*2π)/5864 weeks
137.9231 .64359 (137*2π)/5864 weeks
1381.60052 .82522 (138*2π)/5864 weeks
1391.42088 1.59542 (139*2π)/5864 weeks
140.40351 1.21532 (140*2π)/5864 weeks
141.69487 .12698 (141*2π)/5864 weeks
1422.28455 .25461 (142*2π)/5864 weeks
1432.67971 1.51374 (143*2π)/5864 weeks
1442.14868 2.20128 (144*2π)/5864 weeks
145.94323 3.20383 (145*2π)/5864 weeks
146-.51457 2.0766 (146*2π)/5864 weeks
147.21365 1.0194 (147*2π)/5864 weeks
148-.06338 .98276 (148*2π)/5864 weeks
149.13938 -.15256 (149*2π)/5864 weeks
1501.27681 -.31313 (150*2π)/5864 weeks
1512.93349 .30224 (151*2π)/5864 weeks
1522.53618 3.21436 (152*2π)/5864 weeks
153-.888 2.89286 (153*2π)/5864 weeks
154-1.17482 -.4296 (154*2π)/5864 weeks
1551.45255 -1.17966 (155*2π)/5864 weeks
1563.13724 .43702 (156*2π)/5864 weeks
1572.57365 2.93643 (157*2π)/5864 weeks
158-.30285 3.07778 (158*2π)/5864 weeks
159-1.20301 .9802 (159*2π)/5864 weeks
160-.43498 -1.00308 (160*2π)/5864 weeks
1612.35885 -1.07234 (161*2π)/5864 weeks
1622.61663 1.30836 (162*2π)/5864 weeks
1631.47303 1.80931 (163*2π)/5864 weeks
164.67604 1.64381 (164*2π)/5864 weeks
165.40432 .97256 (165*2π)/5864 weeks
166.7213 .62391 (166*2π)/5864 weeks
167.83977 .24781 (167*2π)/5864 weeks
1681.98598 .05218 (168*2π)/5863 weeks
1692.17279 1.89465 (169*2π)/5863 weeks
170.5809 1.74382 (170*2π)/5863 weeks
171.68077 1.29285 (171*2π)/5863 weeks
172.29545 1.41159 (172*2π)/5863 weeks
173-.02604 .49108 (173*2π)/5863 weeks
174.67736 -.24195 (174*2π)/5863 weeks
1752.26492 .01924 (175*2π)/5863 weeks
1762.167 1.63069 (176*2π)/5863 weeks
1771.24034 2.72289 (177*2π)/5863 weeks
178-.9069 2.23662 (178*2π)/5863 weeks
179-1.26463 .09181 (179*2π)/5863 weeks
180.19518 -1.21595 (180*2π)/5863 weeks
1812.04618 -.60013 (181*2π)/5863 weeks
1822.24538 .97736 (182*2π)/5863 weeks
1831.34987 1.91514 (183*2π)/5863 weeks
184.00205 1.48748 (184*2π)/5863 weeks
185-.44994 .49066 (185*2π)/5863 weeks
186-.08145 -.65484 (186*2π)/5863 weeks
1871.54858 -1.45355 (187*2π)/5863 weeks
1883.28667 -.2405 (188*2π)/5863 weeks
1893.24124 2.00143 (189*2π)/5863 weeks
1901.1327 3.58364 (190*2π)/5863 weeks
191-1.36942 2.18548 (191*2π)/5863 weeks
192-1.32142 -.50762 (192*2π)/5863 weeks
193.95172 -1.67875 (193*2π)/5863 weeks
1943.03347 -.19457 (194*2π)/5863 weeks
1952.39654 1.96602 (195*2π)/5863 weeks
196.82642 2.61761 (196*2π)/5863 weeks
197-.86686 1.25532 (197*2π)/5863 weeks
198-.00161 -.31193 (198*2π)/5863 weeks
199.83774 -.40972 (199*2π)/5863 weeks
2002.18246 .26365 (200*2π)/5863 weeks
2011.48327 1.89386 (201*2π)/5863 weeks
202-.1965 1.47429 (202*2π)/5863 weeks
203-.34771 .36199 (203*2π)/5863 weeks
204.17996 -.52625 (204*2π)/5863 weeks
2051.37094 -.56711 (205*2π)/5863 weeks
2061.14572 -.01607 (206*2π)/5863 weeks
2072.07517 -.6399 (207*2π)/5863 weeks
2082.77831 1.65311 (208*2π)/5863 weeks
209.75123 1.62924 (209*2π)/5863 weeks
210.80469 1.16377 (210*2π)/5863 weeks
211.37539 .97031 (211*2π)/5863 weeks
212.77501 .49345 (212*2π)/5863 weeks
213.43939 .98704 (213*2π)/5863 weeks
214.41147 -.29986 (214*2π)/5863 weeks
2151.62012 .60613 (215*2π)/5863 weeks
216.45628 .75314 (216*2π)/5863 weeks
217.89088 .52614 (217*2π)/5863 weeks
218-.17684 .81196 (218*2π)/5863 weeks
219.23927 -1.14067 (219*2π)/5863 weeks
2202.29012 -.8954 (220*2π)/5863 weeks
2212.52809 1.17561 (221*2π)/5863 weeks
222.94871 2.14134 (222*2π)/5863 weeks
223-.84709 .95903 (223*2π)/5863 weeks
224-.07822 -1.26158 (224*2π)/5863 weeks
2252.04132 -.79748 (225*2π)/5863 weeks
2262.46353 .48945 (226*2π)/5863 weeks
2272.04151 2.09366 (227*2π)/5863 weeks
228-.66363 2.36107 (228*2π)/5863 weeks
229-1.305 -.44544 (229*2π)/5863 weeks
230.79788 -1.80175 (230*2π)/5863 weeks
2312.72715 -.59067 (231*2π)/5863 weeks
2322.23033 1.63476 (232*2π)/5863 weeks
233.1226 1.53415 (233*2π)/5863 weeks
234.11462 -.23844 (234*2π)/5863 weeks
2351.55677 -.32613 (235*2π)/5862 weeks
2361.86867 .73576 (236*2π)/5862 weeks
2371.64654 1.52451 (237*2π)/5862 weeks
238.17548 2.37286 (238*2π)/5862 weeks
239-1.64207 .69296 (239*2π)/5862 weeks
240-.38 -1.51816 (240*2π)/5862 weeks
2411.52088 -1.42703 (241*2π)/5862 weeks
2422.92395 .2943 (242*2π)/5862 weeks
2431.21034 2.47619 (243*2π)/5862 weeks
244-.65745 1.19144 (244*2π)/5862 weeks
245-.93592 -.0748 (245*2π)/5862 weeks
246-.14831 -1.54689 (246*2π)/5862 weeks
2471.98032 -1.4217 (247*2π)/5862 weeks
2482.66228 .47874 (248*2π)/5862 weeks
2491.5026 1.83829 (249*2π)/5862 weeks
250-.53611 1.82573 (250*2π)/5862 weeks
251-1.48744 -.4679 (251*2π)/5862 weeks
252.17443 -2.06232 (252*2π)/5862 weeks
2532.00919 -1.53279 (253*2π)/5862 weeks
2542.85895 -.30727 (254*2π)/5862 weeks
2552.10729 1.86062 (255*2π)/5862 weeks
256.14911 1.13274 (256*2π)/5862 weeks
257.23994 .39257 (257*2π)/5862 weeks
258.27396 -.44586 (258*2π)/5862 weeks
2591.20683 -.15455 (259*2π)/5862 weeks
260.79379 .00918 (260*2π)/5862 weeks
2611.24948 -.27718 (261*2π)/5862 weeks
2621.35069 .58534 (262*2π)/5862 weeks
263.33643 .65914 (263*2π)/5862 weeks
264.36454 .02433 (264*2π)/5862 weeks
265.06093 -.76182 (265*2π)/5862 weeks
2661.39115 -1.36809 (266*2π)/5862 weeks
2672.67953 -.26834 (267*2π)/5862 weeks
2682.08404 1.12292 (268*2π)/5862 weeks
2691.08348 1.73969 (269*2π)/5862 weeks
270-.44994 1.57091 (270*2π)/5862 weeks
271-1.62587 -.18763 (271*2π)/5862 weeks
272-.687 -2.33926 (272*2π)/5862 weeks
2732.34771 -3.18855 (273*2π)/5862 weeks
2744.45586 -.10897 (274*2π)/5862 weeks
2752.44847 2.53157 (275*2π)/5862 weeks
276.09936 2.31738 (276*2π)/5862 weeks
277-1.84327 .65572 (277*2π)/5862 weeks
278-.81273 -2.39495 (278*2π)/5862 weeks
2792.45496 -2.54954 (279*2π)/5862 weeks
2803.8904 .57707 (280*2π)/5862 weeks
2811.30989 2.32999 (281*2π)/5862 weeks
282-.71119 1.21764 (282*2π)/5862 weeks
283-1.01159 -.71763 (283*2π)/5862 weeks
284.41619 -2.03459 (284*2π)/5862 weeks
2852.51717 -2.06589 (285*2π)/5862 weeks
2863.78299 .4303 (286*2π)/5862 weeks
2871.33832 2.74817 (287*2π)/5862 weeks
288-.96948 .98781 (288*2π)/5862 weeks
289-.16562 -1.16564 (289*2π)/5862 weeks
2901.11209 -1.37183 (290*2π)/5862 weeks
2911.65252 -.48508 (291*2π)/5862 weeks
2921.55356 -.50969 (292*2π)/5862 weeks
2932.14957   (293*2π)/5862 weeks
2941.55356 .50969 (294*2π)/5862 weeks
2951.65252 .48508 (295*2π)/5862 weeks
2961.11209 1.37183 (296*2π)/5862 weeks
297-.16562 1.16564 (297*2π)/5862 weeks
298-.96948 -.98781 (298*2π)/5862 weeks
2991.33832 -2.74817 (299*2π)/5862 weeks
3003.78299 -.4303 (300*2π)/5862 weeks
3012.51717 2.06589 (301*2π)/5862 weeks
302.41619 2.03459 (302*2π)/5862 weeks
303-1.01159 .71763 (303*2π)/5862 weeks
304-.71119 -1.21764 (304*2π)/5862 weeks
3051.30989 -2.32999 (305*2π)/5862 weeks
3063.8904 -.57707 (306*2π)/5862 weeks
3072.45496 2.54954 (307*2π)/5862 weeks
308-.81273 2.39495 (308*2π)/5862 weeks
309-1.84327 -.65572 (309*2π)/5862 weeks
310.09936 -2.31738 (310*2π)/5862 weeks
3112.44847 -2.53157 (311*2π)/5862 weeks
3124.45586 .10897 (312*2π)/5862 weeks
3132.34771 3.18855 (313*2π)/5862 weeks
314-.687 2.33926 (314*2π)/5862 weeks
315-1.62587 .18763 (315*2π)/5862 weeks
316-.44994 -1.57091 (316*2π)/5862 weeks
3171.08348 -1.73969 (317*2π)/5862 weeks
3182.08404 -1.12292 (318*2π)/5862 weeks
3192.67953 .26834 (319*2π)/5862 weeks
3201.39115 1.36809 (320*2π)/5862 weeks
321.06093 .76182 (321*2π)/5862 weeks
322.36454 -.02433 (322*2π)/5862 weeks
323.33643 -.65914 (323*2π)/5862 weeks
3241.35069 -.58534 (324*2π)/5862 weeks
3251.24948 .27718 (325*2π)/5862 weeks
326.79379 -.00918 (326*2π)/5862 weeks
3271.20683 .15455 (327*2π)/5862 weeks
328.27396 .44586 (328*2π)/5862 weeks
329.23994 -.39257 (329*2π)/5862 weeks
330.14911 -1.13274 (330*2π)/5862 weeks
3312.10729 -1.86062 (331*2π)/5862 weeks
3322.85895 .30727 (332*2π)/5862 weeks
3332.00919 1.53279 (333*2π)/5862 weeks
334.17443 2.06232 (334*2π)/5862 weeks
335-1.48744 .4679 (335*2π)/5862 weeks
336-.53611 -1.82573 (336*2π)/5862 weeks
3371.5026 -1.83829 (337*2π)/5862 weeks
3382.66228 -.47874 (338*2π)/5862 weeks
3391.98032 1.4217 (339*2π)/5862 weeks
340-.14831 1.54689 (340*2π)/5862 weeks
341-.93592 .0748 (341*2π)/5862 weeks
342-.65745 -1.19144 (342*2π)/5862 weeks
3431.21034 -2.47619 (343*2π)/5862 weeks
3442.92395 -.2943 (344*2π)/5862 weeks
3451.52088 1.42703 (345*2π)/5862 weeks
346-.38 1.51816 (346*2π)/5862 weeks
347-1.64207 -.69296 (347*2π)/5862 weeks
348.17548 -2.37286 (348*2π)/5862 weeks
3491.64654 -1.52451 (349*2π)/5862 weeks
3501.86867 -.73576 (350*2π)/5862 weeks
3511.55677 .32613 (351*2π)/5862 weeks
352.11462 .23844 (352*2π)/5862 weeks
353.1226 -1.53415 (353*2π)/5862 weeks
3542.23033 -1.63476 (354*2π)/5862 weeks
3552.72715 .59067 (355*2π)/5862 weeks
356.79788 1.80175 (356*2π)/5862 weeks
357-1.305 .44544 (357*2π)/5862 weeks
358-.66363 -2.36107 (358*2π)/5862 weeks
3592.04151 -2.09366 (359*2π)/5862 weeks
3602.46353 -.48945 (360*2π)/5862 weeks
3612.04132 .79748 (361*2π)/5862 weeks
362-.07822 1.26158 (362*2π)/5862 weeks
363-.84709 -.95903 (363*2π)/5862 weeks
364.94871 -2.14134 (364*2π)/5862 weeks
3652.52809 -1.17561 (365*2π)/5862 weeks
3662.29012 .8954 (366*2π)/5862 weeks
367.23927 1.14067 (367*2π)/5862 weeks
368-.17684 -.81196 (368*2π)/5862 weeks
369.89088 -.52614 (369*2π)/5862 weeks
370.45628 -.75314 (370*2π)/5862 weeks
3711.62012 -.60613 (371*2π)/5862 weeks
372.41147 .29986 (372*2π)/5862 weeks
373.43939 -.98704 (373*2π)/5862 weeks
374.77501 -.49345 (374*2π)/5862 weeks
375.37539 -.97031 (375*2π)/5862 weeks
376.80469 -1.16377 (376*2π)/5862 weeks
377.75123 -1.62924 (377*2π)/5862 weeks
3782.77831 -1.65311 (378*2π)/5862 weeks
3792.07517 .6399 (379*2π)/5862 weeks
3801.14572 .01607 (380*2π)/5862 weeks
3811.37094 .56711 (381*2π)/5862 weeks
382.17996 .52625 (382*2π)/5862 weeks
383-.34771 -.36199 (383*2π)/5862 weeks
384-.1965 -1.47429 (384*2π)/5862 weeks
3851.48327 -1.89386 (385*2π)/5862 weeks
3862.18246 -.26365 (386*2π)/5862 weeks
387.83774 .40972 (387*2π)/5862 weeks
388-.00161 .31193 (388*2π)/5862 weeks
389-.86686 -1.25532 (389*2π)/5862 weeks
390.82642 -2.61761 (390*2π)/5862 weeks
3912.39654 -1.96602 (391*2π)/5861 weeks
3923.03347 .19457 (392*2π)/5861 weeks
393.95172 1.67875 (393*2π)/5861 weeks
394-1.32142 .50762 (394*2π)/5861 weeks
395-1.36942 -2.18548 (395*2π)/5861 weeks
3961.1327 -3.58364 (396*2π)/5861 weeks
3973.24124 -2.00143 (397*2π)/5861 weeks
3983.28667 .2405 (398*2π)/5861 weeks
3991.54858 1.45355 (399*2π)/5861 weeks
400-.08145 .65484 (400*2π)/5861 weeks
401-.44994 -.49066 (401*2π)/5861 weeks
402.00205 -1.48748 (402*2π)/5861 weeks
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