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Fourier Analysis of DUG (ProShares UltraShort Oil & Gas)


DUG (ProShares UltraShort Oil & Gas) appears to have interesting cyclic behaviour every 40 weeks (36.6555*sine), 43 weeks (36.0845*sine), and 47 weeks (24.5373*sine).

DUG (ProShares UltraShort Oil & Gas) has an average price of 235.91 (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 1/9/2017 for DUG (ProShares UltraShort Oil & Gas), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0235.9137   0 
1161.1544 210.7143 (1*2π)/520520 weeks
231.47604 134.8524 (2*2π)/520260 weeks
37.76778 70.73075 (3*2π)/520173 weeks
414.02025 50.78585 (4*2π)/520130 weeks
530.94504 42.12636 (5*2π)/520104 weeks
632.14997 62.94709 (6*2π)/52087 weeks
71.3477 59.0625 (7*2π)/52074 weeks
8-.2193 32.25313 (8*2π)/52065 weeks
910.05594 30.21961 (9*2π)/52058 weeks
1010.25803 20.39573 (10*2π)/52052 weeks
1122.96589 24.53734 (11*2π)/52047 weeks
1214.03322 36.08449 (12*2π)/52043 weeks
137.90004 36.6555 (13*2π)/52040 weeks
14-2.23024 32.08558 (14*2π)/52037 weeks
15-4.70784 21.03101 (15*2π)/52035 weeks
16-3.09173 10.90274 (16*2π)/52033 weeks
1711.24119 10.53856 (17*2π)/52031 weeks
1813.98449 17.98853 (18*2π)/52029 weeks
1914.22325 26.12998 (19*2π)/52027 weeks
205.97882 29.12586 (20*2π)/52026 weeks
21-3.04374 24.25118 (21*2π)/52025 weeks
22-2.10842 11.66512 (22*2π)/52024 weeks
236.08283 11.62828 (23*2π)/52023 weeks
247.98587 20.07658 (24*2π)/52022 weeks
25-2.65589 22.34253 (25*2π)/52021 weeks
26-5.4963 16.16323 (26*2π)/52020 weeks
27-3.20262 8.1274 (27*2π)/52019 weeks
286.07192 8.30816 (28*2π)/52019 weeks
296.76147 14.51116 (29*2π)/52018 weeks
302.75642 17.70773 (30*2π)/52017 weeks
31-5.37054 14.76156 (31*2π)/52017 weeks
32-3.26599 5.98933 (32*2π)/52016 weeks
331.42439 6.75588 (33*2π)/52016 weeks
343.29082 7.21135 (34*2π)/52015 weeks
354.12707 9.39062 (35*2π)/52015 weeks
363.58393 10.6787 (36*2π)/52014 weeks
371.76927 11.32553 (37*2π)/52014 weeks
38.52226 8.14408 (38*2π)/52014 weeks
393.53647 7.64595 (39*2π)/52013 weeks
403.3241 7.91649 (40*2π)/52013 weeks
416.26554 10.02522 (41*2π)/52013 weeks
423.66926 15.09016 (42*2π)/52012 weeks
43-1.86763 15.24426 (43*2π)/52012 weeks
44-6.25365 10.04512 (44*2π)/52012 weeks
45-4.08923 3.68561 (45*2π)/52012 weeks
46-.36533 2.7849 (46*2π)/52011 weeks
472.91221 4.92274 (47*2π)/52011 weeks
482.95687 7.69398 (48*2π)/52011 weeks
49-.55114 8.58278 (49*2π)/52011 weeks
50-2.74199 4.8993 (50*2π)/52010 weeks
51-.31689 .28281 (51*2π)/52010 weeks
526.53638 .87352 (52*2π)/52010 weeks
539.39817 7.86373 (53*2π)/52010 weeks
542.92007 13.64617 (54*2π)/52010 weeks
55-4.76126 10.18342 (55*2π)/5209 weeks
56-5.08765 3.30388 (56*2π)/5209 weeks
57.0127 -1.11137 (57*2π)/5209 weeks
585.00794 2.59616 (58*2π)/5209 weeks
594.1003 5.24849 (59*2π)/5209 weeks
603.38249 6.78711 (60*2π)/5209 weeks
611.82862 6.24507 (61*2π)/5209 weeks
621.08544 5.59029 (62*2π)/5208 weeks
63.33539 5.05449 (63*2π)/5208 weeks
641.75264 5.6051 (64*2π)/5208 weeks
65-.09191 4.69555 (65*2π)/5208 weeks
661.9046 5.10176 (66*2π)/5208 weeks
67-1.4836 6.21551 (67*2π)/5208 weeks
68-3.87332 2.06481 (68*2π)/5208 weeks
69-.54972 -1.85915 (69*2π)/5208 weeks
705.60716 -.79066 (70*2π)/5207 weeks
715.35492 4.54994 (71*2π)/5207 weeks
722.91586 5.07825 (72*2π)/5207 weeks
73.73396 6.94323 (73*2π)/5207 weeks
74-2.1382 2.41473 (74*2π)/5207 weeks
752.55454 -.54152 (75*2π)/5207 weeks
764.65072 1.50129 (76*2π)/5207 weeks
774.86935 4.60044 (77*2π)/5207 weeks
781.27867 5.62863 (78*2π)/5207 weeks
79.59403 3.95746 (79*2π)/5207 weeks
80-.0328 1.07276 (80*2π)/5207 weeks
814.70752 -.60894 (81*2π)/5206 weeks
826.82416 4.21 (82*2π)/5206 weeks
833.73398 8.03629 (83*2π)/5206 weeks
84-.60181 6.97074 (84*2π)/5206 weeks
85-1.79049 2.41714 (85*2π)/5206 weeks
861.46042 .20482 (86*2π)/5206 weeks
873.93185 1.60453 (87*2π)/5206 weeks
883.80683 3.9771 (88*2π)/5206 weeks
892.52065 3.59981 (89*2π)/5206 weeks
903.00773 4.49301 (90*2π)/5206 weeks
91-.20492 4.50649 (91*2π)/5206 weeks
92-1.49113 1.3514 (92*2π)/5206 weeks
931.4922 -1.28434 (93*2π)/5206 weeks
944.95153 .39355 (94*2π)/5206 weeks
955.21578 3.92875 (95*2π)/5205 weeks
962.63554 5.96899 (96*2π)/5205 weeks
97-.78295 4.16312 (97*2π)/5205 weeks
98.42208 -.24496 (98*2π)/5205 weeks
994.25569 -.85268 (99*2π)/5205 weeks
1006.6396 2.13036 (100*2π)/5205 weeks
1014.91076 5.28789 (101*2π)/5205 weeks
1021.48492 6.08488 (102*2π)/5205 weeks
103-.84414 3.06003 (103*2π)/5205 weeks
1041.50872 .42793 (104*2π)/5205 weeks
1054.5789 1.57066 (105*2π)/5205 weeks
1064.77395 4.17058 (106*2π)/5205 weeks
1073.29724 6.21694 (107*2π)/5205 weeks
108-.80915 6.22196 (108*2π)/5205 weeks
109-2.01268 1.95359 (109*2π)/5205 weeks
110-.08346 -.77773 (110*2π)/5205 weeks
1113.39278 -.86255 (111*2π)/5205 weeks
1125.17083 2.39032 (112*2π)/5205 weeks
1132.69632 4.79119 (113*2π)/5205 weeks
114.31202 3.81484 (114*2π)/5205 weeks
115-.23049 .85179 (115*2π)/5205 weeks
1162.50428 -.73657 (116*2π)/5204 weeks
1174.78795 1.18752 (117*2π)/5204 weeks
1184.60662 3.11412 (118*2π)/5204 weeks
1193.03316 3.78126 (119*2π)/5204 weeks
1201.72622 3.80999 (120*2π)/5204 weeks
121.30443 2.60604 (121*2π)/5204 weeks
1221.48115 .1293 (122*2π)/5204 weeks
1234.58063 .84701 (123*2π)/5204 weeks
1244.21524 3.86604 (124*2π)/5204 weeks
1252.59032 4.30145 (125*2π)/5204 weeks
1262.2982 4.20553 (126*2π)/5204 weeks
127.79954 3.99031 (127*2π)/5204 weeks
128.78307 1.5188 (128*2π)/5204 weeks
1291.92514 1.49097 (129*2π)/5204 weeks
1302.89842 1.85867 (130*2π)/5204 weeks
1312.66427 4.5283 (131*2π)/5204 weeks
132-.63144 4.39689 (132*2π)/5204 weeks
133-1.58169 1.53887 (133*2π)/5204 weeks
134.63517 -1.08641 (134*2π)/5204 weeks
1353.64625 .57437 (135*2π)/5204 weeks
1363.0269 2.11043 (136*2π)/5204 weeks
1372.79855 2.49393 (137*2π)/5204 weeks
1381.35732 2.98587 (138*2π)/5204 weeks
139.37629 2.17922 (139*2π)/5204 weeks
140.25756 .91312 (140*2π)/5204 weeks
1411.62179 .02724 (141*2π)/5204 weeks
1422.73983 .14977 (142*2π)/5204 weeks
1434.34369 1.71515 (143*2π)/5204 weeks
1442.20607 3.72965 (144*2π)/5204 weeks
145.7934 1.62126 (145*2π)/5204 weeks
1462.12963 .60436 (146*2π)/5204 weeks
1472.93092 1.41965 (147*2π)/5204 weeks
1482.26911 2.01489 (148*2π)/5204 weeks
1492.33362 1.72166 (149*2π)/5203 weeks
1501.92134 2.74541 (150*2π)/5203 weeks
1511.04447 1.47156 (151*2π)/5203 weeks
1522.29132 1.18655 (152*2π)/5203 weeks
1532.29161 1.92025 (153*2π)/5203 weeks
1541.83557 2.0191 (154*2π)/5203 weeks
1551.8309 1.56777 (155*2π)/5203 weeks
1561.45619 1.75922 (156*2π)/5203 weeks
1571.77144 1.37805 (157*2π)/5203 weeks
1581.34045 1.4992 (158*2π)/5203 weeks
1591.62009 1.18951 (159*2π)/5203 weeks
1601.64293 1.25545 (160*2π)/5203 weeks
1611.91957 1.35685 (161*2π)/5203 weeks
1621.30986 1.26398 (162*2π)/5203 weeks
163.98858 .62637 (163*2π)/5203 weeks
1641.77099 .14852 (164*2π)/5203 weeks
1652.65509 .45255 (165*2π)/5203 weeks
1662.91488 1.25548 (166*2π)/5203 weeks
1672.81783 1.65195 (167*2π)/5203 weeks
1682.69455 2.32162 (168*2π)/5203 weeks
1691.09481 2.49317 (169*2π)/5203 weeks
170.99568 1.0351 (170*2π)/5203 weeks
1711.4327 .65317 (171*2π)/5203 weeks
1722.20287 .79051 (172*2π)/5203 weeks
1731.69729 1.35593 (173*2π)/5203 weeks
1741.49255 1.13903 (174*2π)/5203 weeks
1751.57868 .49941 (175*2π)/5203 weeks
1762.17015 .53147 (176*2π)/5203 weeks
1772.53996 .08648 (177*2π)/5203 weeks
1783.47491 1.38656 (178*2π)/5203 weeks
1791.79131 2.36964 (179*2π)/5203 weeks
180.82345 1.57159 (180*2π)/5203 weeks
181.74536 .12799 (181*2π)/5203 weeks
1822.35998 -.906 (182*2π)/5203 weeks
1833.84406 -.27866 (183*2π)/5203 weeks
1844.92697 1.54223 (184*2π)/5203 weeks
1852.82059 4.1799 (185*2π)/5203 weeks
186.3514 2.74708 (186*2π)/5203 weeks
187.21714 .80356 (187*2π)/5203 weeks
1881.68474 -.19784 (188*2π)/5203 weeks
1892.91918 .91345 (189*2π)/5203 weeks
1902.61002 1.57008 (190*2π)/5203 weeks
1911.40693 2.80709 (191*2π)/5203 weeks
192-.3174 .86906 (192*2π)/5203 weeks
193.6988 -.35834 (193*2π)/5203 weeks
1942.09617 -1.30861 (194*2π)/5203 weeks
1954.13088 -.03255 (195*2π)/5203 weeks
1963.78512 2.86614 (196*2π)/5203 weeks
197.85204 3.55266 (197*2π)/5203 weeks
198-.91291 .81096 (198*2π)/5203 weeks
1991.21222 -1.87332 (199*2π)/5203 weeks
2003.81816 -.54879 (200*2π)/5203 weeks
2014.0187 1.72708 (201*2π)/5203 weeks
2021.98514 3.70559 (202*2π)/5203 weeks
203-.27747 1.85336 (203*2π)/5203 weeks
204.2662 -.26119 (204*2π)/5203 weeks
2052.3763 -.69654 (205*2π)/5203 weeks
2062.78631 1.15449 (206*2π)/5203 weeks
2071.78434 1.49831 (207*2π)/5203 weeks
2081.7413 1.27176 (208*2π)/5203 weeks
2091.4217 1.7451 (209*2π)/5202 weeks
210.53072 .88259 (210*2π)/5202 weeks
2111.22751 .4838 (211*2π)/5202 weeks
2121.0334 .49727 (212*2π)/5202 weeks
2131.52735 .30805 (213*2π)/5202 weeks
214.95938 .75166 (214*2π)/5202 weeks
215.37755 .75057 (215*2π)/5202 weeks
216-.22109 -.32539 (216*2π)/5202 weeks
2171.30306 -1.27636 (217*2π)/5202 weeks
2182.49966 -.63351 (218*2π)/5202 weeks
2192.7793 .10089 (219*2π)/5202 weeks
2201.91418 1.11746 (220*2π)/5202 weeks
221.67476 1.00094 (221*2π)/5202 weeks
222-.13042 -.20713 (222*2π)/5202 weeks
223.60406 -1.89037 (223*2π)/5202 weeks
2242.34586 -2.10188 (224*2π)/5202 weeks
2253.39624 -1.00103 (225*2π)/5202 weeks
2263.49059 .81305 (226*2π)/5202 weeks
2271.5868 .66467 (227*2π)/5202 weeks
2281.51029 .10413 (228*2π)/5202 weeks
2291.48607 -1.08742 (229*2π)/5202 weeks
2302.97682 -.44427 (230*2π)/5202 weeks
2312.93297 .58444 (231*2π)/5202 weeks
2322.25281 1.4441 (232*2π)/5202 weeks
233.40885 .89032 (233*2π)/5202 weeks
234.04805 -1.08018 (234*2π)/5202 weeks
2351.23406 -2.22556 (235*2π)/5202 weeks
2363.48988 -2.05396 (236*2π)/5202 weeks
2374.27568 .03571 (237*2π)/5202 weeks
2382.90767 1.25876 (238*2π)/5202 weeks
2391.41732 1.13301 (239*2π)/5202 weeks
240.60122 -.06046 (240*2π)/5202 weeks
2411.4432 -1.73593 (241*2π)/5202 weeks
2423.26694 -2.25269 (242*2π)/5202 weeks
2434.78749 .27022 (243*2π)/5202 weeks
2442.52967 2.20637 (244*2π)/5202 weeks
245.80622 1.35319 (245*2π)/5202 weeks
246.08146 -.72298 (246*2π)/5202 weeks
2471.78346 -2.74514 (247*2π)/5202 weeks
2484.14897 -1.55983 (248*2π)/5202 weeks
2493.48837 1.13276 (249*2π)/5202 weeks
2501.59235 1.47738 (250*2π)/5202 weeks
251.20641 -.14886 (251*2π)/5202 weeks
252.84098 -2.39625 (252*2π)/5202 weeks
2533.50728 -3.58877 (253*2π)/5202 weeks
2545.92743 -.80442 (254*2π)/5202 weeks
2554.22647 1.7574 (255*2π)/5202 weeks
2562.00052 1.45973 (256*2π)/5202 weeks
2571.01151 .20223 (257*2π)/5202 weeks
2581.67756 -1.34357 (258*2π)/5202 weeks
2593.44115 -1.88597 (259*2π)/5202 weeks
2605.40382   (260*2π)/5202 weeks
2613.44115 1.88597 (261*2π)/5202 weeks
2621.67756 1.34357 (262*2π)/5202 weeks
2631.01151 -.20223 (263*2π)/5202 weeks
2642.00052 -1.45973 (264*2π)/5202 weeks
2654.22647 -1.7574 (265*2π)/5202 weeks
2665.92743 .80442 (266*2π)/5202 weeks
2673.50728 3.58877 (267*2π)/5202 weeks
268.84098 2.39625 (268*2π)/5202 weeks
269.20641 .14886 (269*2π)/5202 weeks
2701.59235 -1.47738 (270*2π)/5202 weeks
2713.48837 -1.13276 (271*2π)/5202 weeks
2724.14897 1.55983 (272*2π)/5202 weeks
2731.78346 2.74514 (273*2π)/5202 weeks
274.08146 .72298 (274*2π)/5202 weeks
275.80622 -1.35319 (275*2π)/5202 weeks
2762.52967 -2.20637 (276*2π)/5202 weeks
2774.78749 -.27022 (277*2π)/5202 weeks
2783.26694 2.25269 (278*2π)/5202 weeks
2791.4432 1.73593 (279*2π)/5202 weeks
280.60122 .06046 (280*2π)/5202 weeks
2811.41732 -1.13301 (281*2π)/5202 weeks
2822.90767 -1.25876 (282*2π)/5202 weeks
2834.27568 -.03571 (283*2π)/5202 weeks
2843.48988 2.05396 (284*2π)/5202 weeks
2851.23406 2.22556 (285*2π)/5202 weeks
286.04805 1.08018 (286*2π)/5202 weeks
287.40885 -.89032 (287*2π)/5202 weeks
2882.25281 -1.4441 (288*2π)/5202 weeks
2892.93297 -.58444 (289*2π)/5202 weeks
2902.97682 .44427 (290*2π)/5202 weeks
2911.48607 1.08742 (291*2π)/5202 weeks
2921.51029 -.10413 (292*2π)/5202 weeks
2931.5868 -.66467 (293*2π)/5202 weeks
2943.49059 -.81305 (294*2π)/5202 weeks
2953.39624 1.00103 (295*2π)/5202 weeks
2962.34586 2.10188 (296*2π)/5202 weeks
297.60406 1.89037 (297*2π)/5202 weeks
298-.13042 .20713 (298*2π)/5202 weeks
299.67476 -1.00094 (299*2π)/5202 weeks
3001.91418 -1.11746 (300*2π)/5202 weeks
3012.7793 -.10089 (301*2π)/5202 weeks
3022.49966 .63351 (302*2π)/5202 weeks
3031.30306 1.27636 (303*2π)/5202 weeks
304-.22109 .32539 (304*2π)/5202 weeks
305.37755 -.75057 (305*2π)/5202 weeks
306.95938 -.75166 (306*2π)/5202 weeks
3071.52735 -.30805 (307*2π)/5202 weeks
3081.0334 -.49727 (308*2π)/5202 weeks
3091.22751 -.4838 (309*2π)/5202 weeks
310.53072 -.88259 (310*2π)/5202 weeks
3111.4217 -1.7451 (311*2π)/5202 weeks
3121.7413 -1.27176 (312*2π)/5202 weeks
3131.78434 -1.49831 (313*2π)/5202 weeks
3142.78631 -1.15449 (314*2π)/5202 weeks
3152.3763 .69654 (315*2π)/5202 weeks
316.2662 .26119 (316*2π)/5202 weeks
317-.27747 -1.85336 (317*2π)/5202 weeks
3181.98514 -3.70559 (318*2π)/5202 weeks
3194.0187 -1.72708 (319*2π)/5202 weeks
3203.81816 .54879 (320*2π)/5202 weeks
3211.21222 1.87332 (321*2π)/5202 weeks
322-.91291 -.81096 (322*2π)/5202 weeks
323.85204 -3.55266 (323*2π)/5202 weeks
3243.78512 -2.86614 (324*2π)/5202 weeks
3254.13088 .03255 (325*2π)/5202 weeks
3262.09617 1.30861 (326*2π)/5202 weeks
327.6988 .35834 (327*2π)/5202 weeks
328-.3174 -.86906 (328*2π)/5202 weeks
3291.40693 -2.80709 (329*2π)/5202 weeks
3302.61002 -1.57008 (330*2π)/5202 weeks
3312.91918 -.91345 (331*2π)/5202 weeks
3321.68474 .19784 (332*2π)/5202 weeks
333.21714 -.80356 (333*2π)/5202 weeks
334.3514 -2.74708 (334*2π)/5202 weeks
3352.82059 -4.1799 (335*2π)/5202 weeks
3364.92697 -1.54223 (336*2π)/5202 weeks
3373.84406 .27866 (337*2π)/5202 weeks
3382.35998 .906 (338*2π)/5202 weeks
339.74536 -.12799 (339*2π)/5202 weeks
340.82345 -1.57159 (340*2π)/5202 weeks
3411.79131 -2.36964 (341*2π)/5202 weeks
3423.47491 -1.38656 (342*2π)/5202 weeks
3432.53996 -.08648 (343*2π)/5202 weeks
3442.17015 -.53147 (344*2π)/5202 weeks
3451.57868 -.49941 (345*2π)/5202 weeks
3461.49255 -1.13903 (346*2π)/5202 weeks
3471.69729 -1.35593 (347*2π)/5201 weeks
3482.20287 -.79051 (348*2π)/5201 weeks
3491.4327 -.65317 (349*2π)/5201 weeks
350.99568 -1.0351 (350*2π)/5201 weeks
3511.09481 -2.49317 (351*2π)/5201 weeks
3522.69455 -2.32162 (352*2π)/5201 weeks
3532.81783 -1.65195 (353*2π)/5201 weeks
3542.91488 -1.25548 (354*2π)/5201 weeks
3552.65509 -.45255 (355*2π)/5201 weeks
3561.77099 -.14852 (356*2π)/5201 weeks
357.98858 -.62637 (357*2π)/5201 weeks
3581.30986 -1.26398 (358*2π)/5201 weeks
3591.91957 -1.35685 (359*2π)/5201 weeks
3601.64293 -1.25545 (360*2π)/5201 weeks
3611.62009 -1.18951 (361*2π)/5201 weeks
3621.34045 -1.4992 (362*2π)/5201 weeks
3631.77144 -1.37805 (363*2π)/5201 weeks
3641.45619 -1.75922 (364*2π)/5201 weeks
3651.8309 -1.56777 (365*2π)/5201 weeks
3661.83557 -2.0191 (366*2π)/5201 weeks
3672.29161 -1.92025 (367*2π)/5201 weeks
3682.29132 -1.18655 (368*2π)/5201 weeks
3691.04447 -1.47156 (369*2π)/5201 weeks
3701.92134 -2.74541 (370*2π)/5201 weeks
3712.33362 -1.72166 (371*2π)/5201 weeks
3722.26911 -2.01489 (372*2π)/5201 weeks
3732.93092 -1.41965 (373*2π)/5201 weeks
3742.12963 -.60436 (374*2π)/5201 weeks
375.7934 -1.62126 (375*2π)/5201 weeks
3762.20607 -3.72965 (376*2π)/5201 weeks
3774.34369 -1.71515 (377*2π)/5201 weeks
3782.73983 -.14977 (378*2π)/5201 weeks
3791.62179 -.02724 (379*2π)/5201 weeks
380.25756 -.91312 (380*2π)/5201 weeks
381.37629 -2.17922 (381*2π)/5201 weeks
3821.35732 -2.98587 (382*2π)/5201 weeks
3832.79855 -2.49393 (383*2π)/5201 weeks
3843.0269 -2.11043 (384*2π)/5201 weeks
3853.64625 -.57437 (385*2π)/5201 weeks
386.63517 1.08641 (386*2π)/5201 weeks
387-1.58169 -1.53887 (387*2π)/5201 weeks
388-.63144 -4.39689 (388*2π)/5201 weeks
3892.66427 -4.5283 (389*2π)/5201 weeks
3902.89842 -1.85867 (390*2π)/5201 weeks
3911.92514 -1.49097 (391*2π)/5201 weeks
392.78307 -1.5188 (392*2π)/5201 weeks
393.79954 -3.99031 (393*2π)/5201 weeks
3942.2982 -4.20553 (394*2π)/5201 weeks
3952.59032 -4.30145 (395*2π)/5201 weeks
3964.21524 -3.86604 (396*2π)/5201 weeks
3974.58063 -.84701 (397*2π)/5201 weeks
3981.48115 -.1293 (398*2π)/5201 weeks
399.30443 -2.60604 (399*2π)/5201 weeks
4001.72622 -3.80999 (400*2π)/5201 weeks
4013.03316 -3.78126 (401*2π)/5201 weeks
4024.60662 -3.11412 (402*2π)/5201 weeks
4034.78795 -1.18752 (403*2π)/5201 weeks
4042.50428 .73657 (404*2π)/5201 weeks
405-.23049 -.85179 (405*2π)/5201 weeks
406.31202 -3.81484 (406*2π)/5201 weeks
4072.69632 -4.79119 (407*2π)/5201 weeks
4085.17083 -2.39032 (408*2π)/5201 weeks
4093.39278 .86255 (409*2π)/5201 weeks
410-.08346 .77773 (410*2π)/5201 weeks
411-2.01268 -1.95359 (411*2π)/5201 weeks
412-.80915 -6.22196 (412*2π)/5201 weeks
4133.29724 -6.21694 (413*2π)/5201 weeks
4144.77395 -4.17058 (414*2π)/5201 weeks
4154.5789 -1.57066 (415*2π)/5201 weeks
4161.50872 -.42793 (416*2π)/5201 weeks
417-.84414 -3.06003 (417*2π)/5201 weeks
4181.48492 -6.08488 (418*2π)/5201 weeks
4194.91076 -5.28789 (419*2π)/5201 weeks
4206.6396 -2.13036 (420*2π)/5201 weeks
4214.25569 .85268 (421*2π)/5201 weeks
422.42208 .24496 (422*2π)/5201 weeks
423-.78295 -4.16312 (423*2π)/5201 weeks
4242.63554 -5.96899 (424*2π)/5201 weeks
4255.21578 -3.92875 (425*2π)/5201 weeks
4264.95153 -.39355 (426*2π)/5201 weeks
4271.4922 1.28434 (427*2π)/5201 weeks
428-1.49113 -1.3514 (428*2π)/5201 weeks
429-.20492 -4.50649 (429*2π)/5201 weeks
4303.00773 -4.49301 (430*2π)/5201 weeks
4312.52065 -3.59981 (431*2π)/5201 weeks
4323.80683 -3.9771 (432*2π)/5201 weeks
4333.93185 -1.60453 (433*2π)/5201 weeks
4341.46042 -.20482 (434*2π)/5201 weeks
435-1.79049 -2.41714 (435*2π)/5201 weeks
436-.60181 -6.97074 (436*2π)/5201 weeks
4373.73398 -8.03629 (437*2π)/5201 weeks
4386.82416 -4.21 (438*2π)/5201 weeks
4394.70752 .60894 (439*2π)/5201 weeks
440-.0328 -1.07276 (440*2π)/5201 weeks
441.59403 -3.95746 (441*2π)/5201 weeks
4421.27867 -5.62863 (442*2π)/5201 weeks
4434.86935 -4.60044 (443*2π)/5201 weeks
4444.65072 -1.50129 (444*2π)/5201 weeks
4452.55454 .54152 (445*2π)/5201 weeks
446-2.1382 -2.41473 (446*2π)/5201 weeks
447.73396 -6.94323 (447*2π)/5201 weeks
4482.91586 -5.07825 (448*2π)/5201 weeks
4495.35492 -4.54994 (449*2π)/5201 weeks
4505.60716 .79066 (450*2π)/5201 weeks
451-.54972 1.85915 (451*2π)/5201 weeks
452-3.87332 -2.06481 (452*2π)/5201 weeks
453-1.4836 -6.21551 (453*2π)/5201 weeks
4541.9046 -5.10176 (454*2π)/5201 weeks
455-.09191 -4.69555 (455*2π)/5201 weeks
4561.75264 -5.6051 (456*2π)/5201 weeks
457.33539 -5.05449 (457*2π)/5201 weeks
4581.08544 -5.59029 (458*2π)/5201 weeks
4591.82862 -6.24507 (459*2π)/5201 weeks
4603.38249 -6.78711 (460*2π)/5201 weeks
4614.1003 -5.24849 (461*2π)/5201 weeks
4625.00794 -2.59616 (462*2π)/5201 weeks
463.0127 1.11137 (463*2π)/5201 weeks
464-5.08765 -3.30388 (464*2π)/5201 weeks
465-4.76126 -10.18342 (465*2π)/5201 weeks
4662.92007 -13.64617 (466*2π)/5201 weeks
4679.39817 -7.86373 (467*2π)/5201 weeks
4686.53638 -.87352 (468*2π)/5201 weeks
469-.31689 -.28281 (469*2π)/5201 weeks
470-2.74199 -4.8993 (470*2π)/5201 weeks
471-.55114 -8.58278 (471*2π)/5201 weeks
4722.95687 -7.69398 (472*2π)/5201 weeks
4732.91221 -4.92274 (473*2π)/5201 weeks
474-.36533 -2.7849 (474*2π)/5201 weeks
475-4.08923 -3.68561 (475*2π)/5201 weeks
476-6.25365 -10.04512 (476*2π)/5201 weeks
477-1.86763 -15.24426 (477*2π)/5201 weeks
4783.66926 -15.09016 (478*2π)/5201 weeks
4796.26554 -10.02522 (479*2π)/5201 weeks
4803.3241 -7.91649 (480*2π)/5201 weeks
4813.53647 -7.64595 (481*2π)/5201 weeks
482.52226 -8.14408 (482*2π)/5201 weeks
4831.76927 -11.32553 (483*2π)/5201 weeks
4843.58393 -10.6787 (484*2π)/5201 weeks
4854.12707 -9.39062 (485*2π)/5201 weeks
4863.29082 -7.21135 (486*2π)/5201 weeks
4871.42439 -6.75588 (487*2π)/5201 weeks
488-3.26599 -5.98933 (488*2π)/5201 weeks
489-5.37054 -14.76156 (489*2π)/5201 weeks
4902.75642 -17.70773 (490*2π)/5201 weeks
4916.76147 -14.51116 (491*2π)/5201 weeks
4926.07192 -8.30816 (492*2π)/5201 weeks
493-3.20262 -8.1274 (493*2π)/5201 weeks
494-5.4963 -16.16323 (494*2π)/5201 weeks
495-2.65589 -22.34253 (495*2π)/5201 weeks
4967.98587 -20.07658 (496*2π)/5201 weeks
4976.08283 -11.62828 (497*2π)/5201 weeks
498-2.10842 -11.66512 (498*2π)/5201 weeks
499-3.04374 -24.25118 (499*2π)/5201 weeks
5005.97882 -29.12586 (500*2π)/5201 weeks
50114.22325 -26.12998 (501*2π)/5201 weeks
50213.98449 -17.98853 (502*2π)/5201 weeks
50311.24119 -10.53856 (503*2π)/5201 weeks
504-3.09173 -10.90274 (504*2π)/5201 weeks
505-4.70784 -21.03101 (505*2π)/5201 weeks
506-2.23024 -32.08558 (506*2π)/5201 weeks
5077.90004 -36.6555 (507*2π)/5201 weeks
50814.03322 -36.08449 (508*2π)/5201 weeks
50922.96589 -24.53734 (509*2π)/5201 weeks
51010.25803 -20.39573 (510*2π)/5201 weeks
51110.05594 -30.21961 (511*2π)/5201 weeks
512-.2193 -32.25313 (512*2π)/5201 weeks
5131.3477 -59.0625 (513*2π)/5201 weeks
51432.14997 -62.94709 (514*2π)/5201 weeks
51530.94504 -42.12636 (515*2π)/5201 weeks
51614.02025 -50.78585 (516*2π)/5201 weeks
5177.76778 -70.73075 (517*2π)/5201 weeks
51831.47604 -134.8524 (518*2π)/5201 weeks

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