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Fourier Analysis of UCO (ProShares Ultra Bloomberg Crude)


UCO (ProShares Ultra Bloomberg Crude) appears to have interesting cyclic behaviour every 24 weeks (21.194*sine), 40 weeks (20.1804*sine), and 33 weeks (17.7115*cosine).

UCO (ProShares Ultra Bloomberg Crude) has an average price of 293.58 (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 11/25/2008 to 3/20/2017 for UCO (ProShares Ultra Bloomberg Crude), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0293.5818   0 
1-60.28458 171.6036 (1*2π)/435435 weeks
2-11.57287 114.3297 (2*2π)/435218 weeks
337.11379 28.33654 (3*2π)/435145 weeks
4-17.61532 27.72352 (4*2π)/435109 weeks
5-8.23379 34.21911 (5*2π)/43587 weeks
62.9465 8.90239 (6*2π)/43573 weeks
719.7221 -13.42503 (7*2π)/43562 weeks
86.22616 35.65348 (8*2π)/43554 weeks
9.74312 21.42888 (9*2π)/43548 weeks
1015.94406 -12.58978 (10*2π)/43544 weeks
1111.73222 20.1804 (11*2π)/43540 weeks
126.16092 8.33844 (12*2π)/43536 weeks
1317.71146 11.21345 (13*2π)/43533 weeks
1413.70516 15.48713 (14*2π)/43531 weeks
15.3533 9.62707 (15*2π)/43529 weeks
167.46237 15.05124 (16*2π)/43527 weeks
1711.64927 4.26047 (17*2π)/43526 weeks
1816.18019 21.19397 (18*2π)/43524 weeks
192.04154 10.10735 (19*2π)/43523 weeks
208.08345 18.02255 (20*2π)/43522 weeks
21-1.56455 14.66024 (21*2π)/43521 weeks
221.74389 8.39742 (22*2π)/43520 weeks
23-3.04221 12.07672 (23*2π)/43519 weeks
245.46714 -2.74001 (24*2π)/43518 weeks
2511.13154 9.52902 (25*2π)/43517 weeks
26-.11357 14.04956 (26*2π)/43517 weeks
271.04736 7.94191 (27*2π)/43516 weeks
286.5504 4.45717 (28*2π)/43516 weeks
291.71694 9.36565 (29*2π)/43515 weeks
302.7438 6.10601 (30*2π)/43515 weeks
316.7369 5.36033 (31*2π)/43514 weeks
325.13648 12.2952 (32*2π)/43514 weeks
33-.91997 8.91917 (33*2π)/43513 weeks
34-.19788 3.66877 (34*2π)/43513 weeks
354.34389 4.63096 (35*2π)/43512 weeks
366.99563 7.51066 (36*2π)/43512 weeks
37-.83221 10.16309 (37*2π)/43512 weeks
38-.23663 8.00182 (38*2π)/43511 weeks
39-.69228 6.42388 (39*2π)/43511 weeks
40-2.58982 4.50514 (40*2π)/43511 weeks
41-2.94843 .41225 (41*2π)/43511 weeks
42-.81843 1.8722 (42*2π)/43510 weeks
432.32653 -2.47667 (43*2π)/43510 weeks
443.38635 -2.26898 (44*2π)/43510 weeks
455.58186 1.14086 (45*2π)/43510 weeks
467.39642 1.20819 (46*2π)/4359 weeks
475.27857 3.86252 (47*2π)/4359 weeks
488.76687 3.6587 (48*2π)/4359 weeks
493.73181 8.09677 (49*2π)/4359 weeks
501.23948 4.2964 (50*2π)/4359 weeks
513.65458 4.26382 (51*2π)/4359 weeks
522.17188 2.45786 (52*2π)/4358 weeks
535.5258 2.06303 (53*2π)/4358 weeks
547.45615 5.37868 (54*2π)/4358 weeks
55-.48121 7.22712 (55*2π)/4358 weeks
564.77273 3.51677 (56*2π)/4358 weeks
57.48423 2.82487 (57*2π)/4358 weeks
581.25749 1.21427 (58*2π)/4358 weeks
596.91264 -.73061 (59*2π)/4357 weeks
608.08038 6.05927 (60*2π)/4357 weeks
612.21511 6.49583 (61*2π)/4357 weeks
621.12758 4.57758 (62*2π)/4357 weeks
633.99731 3.31204 (63*2π)/4357 weeks
642.10274 4.747 (64*2π)/4357 weeks
65.75738 1.66252 (65*2π)/4357 weeks
666.22692 2.52114 (66*2π)/4357 weeks
673.84157 7.54796 (67*2π)/4356 weeks
68-1.20113 3.48665 (68*2π)/4356 weeks
692.95733 1.75815 (69*2π)/4356 weeks
703.2916 5.1915 (70*2π)/4356 weeks
71.04889 2.58514 (71*2π)/4356 weeks
72.66923 .79596 (72*2π)/4356 weeks
734.49557 .31793 (73*2π)/4356 weeks
743.60093 2.62524 (74*2π)/4356 weeks
755.16553 1.26344 (75*2π)/4356 weeks
764.1321 4.68741 (76*2π)/4356 weeks
774.06898 4.57765 (77*2π)/4356 weeks
78.70573 6.14339 (78*2π)/4356 weeks
79.89352 2.56076 (79*2π)/4356 weeks
80.8086 1.25854 (80*2π)/4355 weeks
814.12149 2.37234 (81*2π)/4355 weeks
821.79278 1.83779 (82*2π)/4355 weeks
831.89582 2.6286 (83*2π)/4355 weeks
842.77658 2.39684 (84*2π)/4355 weeks
853.02163 1.52908 (85*2π)/4355 weeks
862.66026 3.5843 (86*2π)/4355 weeks
872.01571 2.82692 (87*2π)/4355 weeks
881.19207 1.04143 (88*2π)/4355 weeks
892.02121 2.04288 (89*2π)/4355 weeks
904.78303 .87326 (90*2π)/4355 weeks
911.75554 2.85665 (91*2π)/4355 weeks
923.02326 1.79114 (92*2π)/4355 weeks
933.10668 2.45003 (93*2π)/4355 weeks
944.08722 2.40056 (94*2π)/4355 weeks
951.84491 2.68571 (95*2π)/4355 weeks
963.69999 3.82025 (96*2π)/4355 weeks
971.39479 2.27408 (97*2π)/4354 weeks
98.60244 1.63511 (98*2π)/4354 weeks
994.20105 1.45375 (99*2π)/4354 weeks
1003.85203 2.6948 (100*2π)/4354 weeks
1012.16086 3.90518 (101*2π)/4354 weeks
102.83562 1.9786 (102*2π)/4354 weeks
1034.35044 1.49004 (103*2π)/4354 weeks
1041.86467 4.39116 (104*2π)/4354 weeks
1051.76702 4.11843 (105*2π)/4354 weeks
106.49921 2.4712 (106*2π)/4354 weeks
1071.81817 1.87436 (107*2π)/4354 weeks
1081.9176 3.99836 (108*2π)/4354 weeks
109-2.61592 2.23027 (109*2π)/4354 weeks
1101.36799 -1.03358 (110*2π)/4354 weeks
1112.1306 .75569 (111*2π)/4354 weeks
1121.83531 1.36056 (112*2π)/4354 weeks
1133.22659 1.40584 (113*2π)/4354 weeks
1142.31322 2.64745 (114*2π)/4354 weeks
115.15595 1.80598 (115*2π)/4354 weeks
1161.85485 1.86558 (116*2π)/4354 weeks
1171.55485 2.2024 (117*2π)/4354 weeks
118.7413 1.69049 (118*2π)/4354 weeks
119.49068 3.14901 (119*2π)/4354 weeks
120-1.40711 .81741 (120*2π)/4354 weeks
121.77136 -1.29746 (121*2π)/4354 weeks
122.9516 .23814 (122*2π)/4354 weeks
1231.1464 -.01171 (123*2π)/4354 weeks
1241.82371 -.67634 (124*2π)/4354 weeks
1252.81874 1.45246 (125*2π)/4353 weeks
126-.10811 1.12259 (126*2π)/4353 weeks
127.25878 -.67932 (127*2π)/4353 weeks
1282.11482 -1.61785 (128*2π)/4353 weeks
1292.97917 .84853 (129*2π)/4353 weeks
1301.0351 1.11547 (130*2π)/4353 weeks
131.67527 -.71705 (131*2π)/4353 weeks
1322.10743 -.58704 (132*2π)/4353 weeks
1331.95327 -.01206 (133*2π)/4353 weeks
1342.39176 -1.49592 (134*2π)/4353 weeks
1352.26788 1.03152 (135*2π)/4353 weeks
1362.83036 .17905 (136*2π)/4353 weeks
1371.6486 .0113 (137*2π)/4353 weeks
1382.14766 .44137 (138*2π)/4353 weeks
1391.02191 -.01043 (139*2π)/4353 weeks
140.72775 -.13029 (140*2π)/4353 weeks
1412.70222 -1.93039 (141*2π)/4353 weeks
1422.35719 1.01509 (142*2π)/4353 weeks
143.64533 -.64326 (143*2π)/4353 weeks
1442.16762 -1.64676 (144*2π)/4353 weeks
1452.27221 -.1828 (145*2π)/4353 weeks
1461.79421 -.28706 (146*2π)/4353 weeks
147.44721 -1.69315 (147*2π)/4353 weeks
1482.90573 -2.70934 (148*2π)/4353 weeks
1494.85998 -.93581 (149*2π)/4353 weeks
1501.34172 .15176 (150*2π)/4353 weeks
1511.52861 -1.35019 (151*2π)/4353 weeks
1523.49036 -1.73517 (152*2π)/4353 weeks
1532.12861 -1.6359 (153*2π)/4353 weeks
1543.00153 -2.92552 (154*2π)/4353 weeks
1555.28193 -1.97012 (155*2π)/4353 weeks
1564.65567 -1.08542 (156*2π)/4353 weeks
1573.61525 -.74912 (157*2π)/4353 weeks
1585.82493 -.33897 (158*2π)/4353 weeks
1593.91887 .15564 (159*2π)/4353 weeks
1603.85693 .67934 (160*2π)/4353 weeks
1612.58007 .9115 (161*2π)/4353 weeks
1622.65847 -1.52132 (162*2π)/4353 weeks
1634.1105 -.39426 (163*2π)/4353 weeks
1643.11097 -.46276 (164*2π)/4353 weeks
1653.49985 -2.00222 (165*2π)/4353 weeks
1665.50787 -.73723 (166*2π)/4353 weeks
1674.995 -.20818 (167*2π)/4353 weeks
1683.60436 .13686 (168*2π)/4353 weeks
1695.80273 -.46469 (169*2π)/4353 weeks
1704.86533 1.6457 (170*2π)/4353 weeks
1714.11699 .27818 (171*2π)/4353 weeks
1724.74501 1.22037 (172*2π)/4353 weeks
1734.32675 2.18184 (173*2π)/4353 weeks
1743.01783 2.17884 (174*2π)/4353 weeks
1751.31873 .7628 (175*2π)/4352 weeks
1763.64889 -.54415 (176*2π)/4352 weeks
1774.56732 1.02608 (177*2π)/4352 weeks
1782.2987 1.18896 (178*2π)/4352 weeks
1793.30453 .11432 (179*2π)/4352 weeks
1803.88763 .73982 (180*2π)/4352 weeks
1813.01224 .66701 (181*2π)/4352 weeks
1822.69412 .52906 (182*2π)/4352 weeks
1833.41539 .18584 (183*2π)/4352 weeks
1843.32876 .49428 (184*2π)/4352 weeks
1853.00522 .05772 (185*2π)/4352 weeks
1863.40178 .65677 (186*2π)/4352 weeks
1874.11671 -.01911 (187*2π)/4352 weeks
1883.66342 1.14786 (188*2π)/4352 weeks
1893.32993 1.79351 (189*2π)/4352 weeks
1902.47535 .30135 (190*2π)/4352 weeks
1913.97654 1.62959 (191*2π)/4352 weeks
1921.2066 .73434 (192*2π)/4352 weeks
1932.67529 .2537 (193*2π)/4352 weeks
1943.10984 .4651 (194*2π)/4352 weeks
1952.4586 -.25751 (195*2π)/4352 weeks
1963.76251 .74539 (196*2π)/4352 weeks
1972.69478 .46361 (197*2π)/4352 weeks
1983.46843 1.66987 (198*2π)/4352 weeks
1991.44188 .65825 (199*2π)/4352 weeks
2002.4656 -.08681 (200*2π)/4352 weeks
2012.66753 .74368 (201*2π)/4352 weeks
2021.80193 -.20803 (202*2π)/4352 weeks
2032.30725 -.79413 (203*2π)/4352 weeks
2043.14059 .33002 (204*2π)/4352 weeks
2052.52532 -.837 (205*2π)/4352 weeks
2064.02354 -1.10188 (206*2π)/4352 weeks
2073.6529 1.1289 (207*2π)/4352 weeks
2082.69956 1.42561 (208*2π)/4352 weeks
2091.94241 .44644 (209*2π)/4352 weeks
2101.97064 -1.64459 (210*2π)/4352 weeks
2113.60358 -.66246 (211*2π)/4352 weeks
2124.32573 .90499 (212*2π)/4352 weeks
2132.30981 .39906 (213*2π)/4352 weeks
2141.93532 .27469 (214*2π)/4352 weeks
2152.67408 -.81156 (215*2π)/4352 weeks
2162.92215 -.53361 (216*2π)/4352 weeks
2174.00026 -1.71042 (217*2π)/4352 weeks
2184.00026 1.71042 (218*2π)/4352 weeks
2192.92215 .53361 (219*2π)/4352 weeks
2202.67408 .81156 (220*2π)/4352 weeks
2211.93532 -.27469 (221*2π)/4352 weeks
2222.30981 -.39906 (222*2π)/4352 weeks
2234.32573 -.90499 (223*2π)/4352 weeks
2243.60358 .66246 (224*2π)/4352 weeks
2251.97064 1.64459 (225*2π)/4352 weeks
2261.94241 -.44644 (226*2π)/4352 weeks
2272.69956 -1.42561 (227*2π)/4352 weeks
2283.6529 -1.1289 (228*2π)/4352 weeks
2294.02354 1.10188 (229*2π)/4352 weeks
2302.52532 .837 (230*2π)/4352 weeks
2313.14059 -.33002 (231*2π)/4352 weeks
2322.30725 .79413 (232*2π)/4352 weeks
2331.80193 .20803 (233*2π)/4352 weeks
2342.66753 -.74368 (234*2π)/4352 weeks
2352.4656 .08681 (235*2π)/4352 weeks
2361.44188 -.65825 (236*2π)/4352 weeks
2373.46843 -1.66987 (237*2π)/4352 weeks
2382.69478 -.46361 (238*2π)/4352 weeks
2393.76251 -.74539 (239*2π)/4352 weeks
2402.4586 .25751 (240*2π)/4352 weeks
2413.10984 -.4651 (241*2π)/4352 weeks
2422.67529 -.2537 (242*2π)/4352 weeks
2431.2066 -.73434 (243*2π)/4352 weeks
2443.97654 -1.62959 (244*2π)/4352 weeks
2452.47535 -.30135 (245*2π)/4352 weeks
2463.32993 -1.79351 (246*2π)/4352 weeks
2473.66342 -1.14786 (247*2π)/4352 weeks
2484.11671 .01911 (248*2π)/4352 weeks
2493.40178 -.65677 (249*2π)/4352 weeks
2503.00522 -.05772 (250*2π)/4352 weeks
2513.32876 -.49428 (251*2π)/4352 weeks
2523.41539 -.18584 (252*2π)/4352 weeks
2532.69412 -.52906 (253*2π)/4352 weeks
2543.01224 -.66701 (254*2π)/4352 weeks
2553.88763 -.73982 (255*2π)/4352 weeks
2563.30453 -.11432 (256*2π)/4352 weeks
2572.2987 -1.18896 (257*2π)/4352 weeks
2584.56732 -1.02608 (258*2π)/4352 weeks
2593.64889 .54415 (259*2π)/4352 weeks
2601.31873 -.7628 (260*2π)/4352 weeks
2613.01783 -2.17884 (261*2π)/4352 weeks
2624.32675 -2.18184 (262*2π)/4352 weeks
2634.74501 -1.22037 (263*2π)/4352 weeks
2644.11699 -.27818 (264*2π)/4352 weeks
2654.86533 -1.6457 (265*2π)/4352 weeks
2665.80273 .46469 (266*2π)/4352 weeks
2673.60436 -.13686 (267*2π)/4352 weeks
2684.995 .20818 (268*2π)/4352 weeks
2695.50787 .73723 (269*2π)/4352 weeks
2703.49985 2.00222 (270*2π)/4352 weeks
2713.11097 .46276 (271*2π)/4352 weeks
2724.1105 .39426 (272*2π)/4352 weeks
2732.65847 1.52132 (273*2π)/4352 weeks
2742.58007 -.9115 (274*2π)/4352 weeks
2753.85693 -.67934 (275*2π)/4352 weeks
2763.91887 -.15564 (276*2π)/4352 weeks
2775.82493 .33897 (277*2π)/4352 weeks
2783.61525 .74912 (278*2π)/4352 weeks
2794.65567 1.08542 (279*2π)/4352 weeks
2805.28193 1.97012 (280*2π)/4352 weeks
2813.00153 2.92552 (281*2π)/4352 weeks
2822.12861 1.6359 (282*2π)/4352 weeks
2833.49036 1.73517 (283*2π)/4352 weeks
2841.52861 1.35019 (284*2π)/4352 weeks
2851.34172 -.15176 (285*2π)/4352 weeks
2864.85998 .93581 (286*2π)/4352 weeks
2872.90573 2.70934 (287*2π)/4352 weeks
288.44721 1.69315 (288*2π)/4352 weeks
2891.79421 .28706 (289*2π)/4352 weeks
2902.27221 .1828 (290*2π)/4352 weeks
2912.16762 1.64676 (291*2π)/4351 weeks
292.64533 .64326 (292*2π)/4351 weeks
2932.35719 -1.01509 (293*2π)/4351 weeks
2942.70222 1.93039 (294*2π)/4351 weeks
295.72775 .13029 (295*2π)/4351 weeks
2961.02191 .01043 (296*2π)/4351 weeks
2972.14766 -.44137 (297*2π)/4351 weeks
2981.6486 -.0113 (298*2π)/4351 weeks
2992.83036 -.17905 (299*2π)/4351 weeks
3002.26788 -1.03152 (300*2π)/4351 weeks
3012.39176 1.49592 (301*2π)/4351 weeks
3021.95327 .01206 (302*2π)/4351 weeks
3032.10743 .58704 (303*2π)/4351 weeks
304.67527 .71705 (304*2π)/4351 weeks
3051.0351 -1.11547 (305*2π)/4351 weeks
3062.97917 -.84853 (306*2π)/4351 weeks
3072.11482 1.61785 (307*2π)/4351 weeks
308.25878 .67932 (308*2π)/4351 weeks
309-.10811 -1.12259 (309*2π)/4351 weeks
3102.81874 -1.45246 (310*2π)/4351 weeks
3111.82371 .67634 (311*2π)/4351 weeks
3121.1464 .01171 (312*2π)/4351 weeks
313.9516 -.23814 (313*2π)/4351 weeks
314.77136 1.29746 (314*2π)/4351 weeks
315-1.40711 -.81741 (315*2π)/4351 weeks
316.49068 -3.14901 (316*2π)/4351 weeks
317.7413 -1.69049 (317*2π)/4351 weeks
3181.55485 -2.2024 (318*2π)/4351 weeks
3191.85485 -1.86558 (319*2π)/4351 weeks
320.15595 -1.80598 (320*2π)/4351 weeks
3212.31322 -2.64745 (321*2π)/4351 weeks
3223.22659 -1.40584 (322*2π)/4351 weeks
3231.83531 -1.36056 (323*2π)/4351 weeks
3242.1306 -.75569 (324*2π)/4351 weeks
3251.36799 1.03358 (325*2π)/4351 weeks
326-2.61592 -2.23027 (326*2π)/4351 weeks
3271.9176 -3.99836 (327*2π)/4351 weeks
3281.81817 -1.87436 (328*2π)/4351 weeks
329.49921 -2.4712 (329*2π)/4351 weeks
3301.76702 -4.11843 (330*2π)/4351 weeks
3311.86467 -4.39116 (331*2π)/4351 weeks
3324.35044 -1.49004 (332*2π)/4351 weeks
333.83562 -1.9786 (333*2π)/4351 weeks
3342.16086 -3.90518 (334*2π)/4351 weeks
3353.85203 -2.6948 (335*2π)/4351 weeks
3364.20105 -1.45375 (336*2π)/4351 weeks
337.60244 -1.63511 (337*2π)/4351 weeks
3381.39479 -2.27408 (338*2π)/4351 weeks
3393.69999 -3.82025 (339*2π)/4351 weeks
3401.84491 -2.68571 (340*2π)/4351 weeks
3414.08722 -2.40056 (341*2π)/4351 weeks
3423.10668 -2.45003 (342*2π)/4351 weeks
3433.02326 -1.79114 (343*2π)/4351 weeks
3441.75554 -2.85665 (344*2π)/4351 weeks
3454.78303 -.87326 (345*2π)/4351 weeks
3462.02121 -2.04288 (346*2π)/4351 weeks
3471.19207 -1.04143 (347*2π)/4351 weeks
3482.01571 -2.82692 (348*2π)/4351 weeks
3492.66026 -3.5843 (349*2π)/4351 weeks
3503.02163 -1.52908 (350*2π)/4351 weeks
3512.77658 -2.39684 (351*2π)/4351 weeks
3521.89582 -2.6286 (352*2π)/4351 weeks
3531.79278 -1.83779 (353*2π)/4351 weeks
3544.12149 -2.37234 (354*2π)/4351 weeks
355.8086 -1.25854 (355*2π)/4351 weeks
356.89352 -2.56076 (356*2π)/4351 weeks
357.70573 -6.14339 (357*2π)/4351 weeks
3584.06898 -4.57765 (358*2π)/4351 weeks
3594.1321 -4.68741 (359*2π)/4351 weeks
3605.16553 -1.26344 (360*2π)/4351 weeks
3613.60093 -2.62524 (361*2π)/4351 weeks
3624.49557 -.31793 (362*2π)/4351 weeks
363.66923 -.79596 (363*2π)/4351 weeks
364.04889 -2.58514 (364*2π)/4351 weeks
3653.2916 -5.1915 (365*2π)/4351 weeks
3662.95733 -1.75815 (366*2π)/4351 weeks
367-1.20113 -3.48665 (367*2π)/4351 weeks
3683.84157 -7.54796 (368*2π)/4351 weeks
3696.22692 -2.52114 (369*2π)/4351 weeks
370.75738 -1.66252 (370*2π)/4351 weeks
3712.10274 -4.747 (371*2π)/4351 weeks
3723.99731 -3.31204 (372*2π)/4351 weeks
3731.12758 -4.57758 (373*2π)/4351 weeks
3742.21511 -6.49583 (374*2π)/4351 weeks
3758.08038 -6.05927 (375*2π)/4351 weeks
3766.91264 .73061 (376*2π)/4351 weeks
3771.25749 -1.21427 (377*2π)/4351 weeks
378.48423 -2.82487 (378*2π)/4351 weeks
3794.77273 -3.51677 (379*2π)/4351 weeks
380-.48121 -7.22712 (380*2π)/4351 weeks
3817.45615 -5.37868 (381*2π)/4351 weeks
3825.5258 -2.06303 (382*2π)/4351 weeks
3832.17188 -2.45786 (383*2π)/4351 weeks
3843.65458 -4.26382 (384*2π)/4351 weeks
3851.23948 -4.2964 (385*2π)/4351 weeks
3863.73181 -8.09677 (386*2π)/4351 weeks
3878.76687 -3.6587 (387*2π)/4351 weeks
3885.27857 -3.86252 (388*2π)/4351 weeks
3897.39642 -1.20819 (389*2π)/4351 weeks
3905.58186 -1.14086 (390*2π)/4351 weeks
3913.38635 2.26898 (391*2π)/4351 weeks
3922.32653 2.47667 (392*2π)/4351 weeks
393-.81843 -1.8722 (393*2π)/4351 weeks
394-2.94843 -.41225 (394*2π)/4351 weeks
395-2.58982 -4.50514 (395*2π)/4351 weeks
396-.69228 -6.42388 (396*2π)/4351 weeks
397-.23663 -8.00182 (397*2π)/4351 weeks
398-.83221 -10.16309 (398*2π)/4351 weeks
3996.99563 -7.51066 (399*2π)/4351 weeks
4004.34389 -4.63096 (400*2π)/4351 weeks
401-.19788 -3.66877 (401*2π)/4351 weeks
402-.91997 -8.91917 (402*2π)/4351 weeks
4035.13648 -12.2952 (403*2π)/4351 weeks
4046.7369 -5.36033 (404*2π)/4351 weeks
4052.7438 -6.10601 (405*2π)/4351 weeks
4061.71694 -9.36565 (406*2π)/4351 weeks
4076.5504 -4.45717 (407*2π)/4351 weeks
4081.04736 -7.94191 (408*2π)/4351 weeks
409-.11357 -14.04956 (409*2π)/4351 weeks
41011.13154 -9.52902 (410*2π)/4351 weeks
4115.46714 2.74001 (411*2π)/4351 weeks
412-3.04221 -12.07672 (412*2π)/4351 weeks
4131.74389 -8.39742 (413*2π)/4351 weeks
414-1.56455 -14.66024 (414*2π)/4351 weeks
4158.08345 -18.02255 (415*2π)/4351 weeks
4162.04154 -10.10735 (416*2π)/4351 weeks
41716.18019 -21.19397 (417*2π)/4351 weeks
41811.64927 -4.26047 (418*2π)/4351 weeks
4197.46237 -15.05124 (419*2π)/4351 weeks
420.3533 -9.62707 (420*2π)/4351 weeks
42113.70516 -15.48713 (421*2π)/4351 weeks
42217.71146 -11.21345 (422*2π)/4351 weeks
4236.16092 -8.33844 (423*2π)/4351 weeks
42411.73222 -20.1804 (424*2π)/4351 weeks
42515.94406 12.58978 (425*2π)/4351 weeks
426.74312 -21.42888 (426*2π)/4351 weeks
4276.22616 -35.65348 (427*2π)/4351 weeks
42819.7221 13.42503 (428*2π)/4351 weeks
4292.9465 -8.90239 (429*2π)/4351 weeks
430-8.23379 -34.21911 (430*2π)/4351 weeks
431-17.61532 -27.72352 (431*2π)/4351 weeks
43237.11379 -28.33654 (432*2π)/4351 weeks
433-11.57287 -114.3297 (433*2π)/4351 weeks

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