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Fourier Analysis of UNG (United States Natural Gas Fund)


UNG (United States Natural Gas Fund) appears to have interesting cyclic behaviour every 52 weeks (71.5198*sine), 48 weeks (68.4118*sine), and 58 weeks (54.8528*sine).

UNG (United States Natural Gas Fund) has an average price of 316.6 (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 4/18/2007 to 4/23/2018 for UNG (United States Natural Gas Fund), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0316.6039   0 
1327.2528 280.1994 (1*2π)/576576 weeks
2133.859 299.2235 (2*2π)/576288 weeks
330.71655 235.0126 (3*2π)/576192 weeks
4-50.0065 159.369 (4*2π)/576144 weeks
5-51.46693 82.38167 (5*2π)/576115 weeks
6-29.11585 35.30777 (6*2π)/57696 weeks
73.07723 5.17179 (7*2π)/57682 weeks
843.3215 17.37092 (8*2π)/57672 weeks
950.66412 31.35725 (9*2π)/57664 weeks
1050.60906 54.8528 (10*2π)/57658 weeks
1133.66712 71.51981 (11*2π)/57652 weeks
1213.93414 68.41178 (12*2π)/57648 weeks
13.43566 61.13399 (13*2π)/57644 weeks
14-9.09743 45.43574 (14*2π)/57641 weeks
15-10.60037 34.25497 (15*2π)/57638 weeks
16-2.36387 20.15472 (16*2π)/57636 weeks
175.27622 17.17984 (17*2π)/57634 weeks
1812.62417 17.42939 (18*2π)/57632 weeks
1919.96938 20.65739 (19*2π)/57630 weeks
2023.50173 29.03677 (20*2π)/57629 weeks
2116.23928 40.28405 (21*2π)/57627 weeks
224.29273 40.37851 (22*2π)/57626 weeks
23-2.70464 30.42535 (23*2π)/57625 weeks
24-.61308 25.97293 (24*2π)/57624 weeks
25-1.35009 21.22496 (25*2π)/57623 weeks
263.36601 16.07997 (26*2π)/57622 weeks
278.82682 17.49634 (27*2π)/57621 weeks
2810.19292 25.3805 (28*2π)/57621 weeks
296.06089 26.37633 (29*2π)/57620 weeks
301.65788 27.59409 (30*2π)/57619 weeks
31-1.90256 26.07479 (31*2π)/57619 weeks
32-5.79064 23.45787 (32*2π)/57618 weeks
33-9.63906 17.26402 (33*2π)/57617 weeks
34-7.08925 9.06331 (34*2π)/57617 weeks
35-.37771 4.44722 (35*2π)/57616 weeks
366.33721 6.57194 (36*2π)/57616 weeks
377.81546 10.79716 (37*2π)/57616 weeks
388.69209 13.05298 (38*2π)/57615 weeks
398.36829 16.52674 (39*2π)/57615 weeks
405.27679 18.53793 (40*2π)/57614 weeks
411.60011 19.03932 (41*2π)/57614 weeks
42-1.27793 15.87886 (42*2π)/57614 weeks
43-1.58908 10.95958 (43*2π)/57613 weeks
441.88195 9.0094 (44*2π)/57613 weeks
454.62774 10.33535 (45*2π)/57613 weeks
464.95672 12.20859 (46*2π)/57613 weeks
473.88439 14.44754 (47*2π)/57612 weeks
483.95173 15.59387 (48*2π)/57612 weeks
49-.20719 15.6659 (49*2π)/57612 weeks
50-2.8255 13.87028 (50*2π)/57612 weeks
51-4.83081 10.22614 (51*2π)/57611 weeks
52-1.87815 5.98269 (52*2π)/57611 weeks
531.02761 6.27514 (53*2π)/57611 weeks
542.2218 7.57435 (54*2π)/57611 weeks
552.52954 8.1016 (55*2π)/57610 weeks
562.02461 8.01696 (56*2π)/57610 weeks
572.38761 9.31139 (57*2π)/57610 weeks
581.58602 9.03397 (58*2π)/57610 weeks
59-.67726 9.50098 (59*2π)/57610 weeks
60-2.63271 6.14386 (60*2π)/57610 weeks
61.26999 1.77041 (61*2π)/5769 weeks
624.10344 2.58885 (62*2π)/5769 weeks
637.50557 4.56113 (63*2π)/5769 weeks
646.95109 7.60472 (64*2π)/5769 weeks
655.71524 9.95744 (65*2π)/5769 weeks
663.39904 10.28337 (66*2π)/5769 weeks
672.04634 10.3926 (67*2π)/5769 weeks
68-.78232 9.56137 (68*2π)/5768 weeks
69-2.09115 5.37097 (69*2π)/5768 weeks
70.94146 3.21965 (70*2π)/5768 weeks
713.39016 3.45947 (71*2π)/5768 weeks
723.12025 2.94059 (72*2π)/5768 weeks
735.49631 3.2953 (73*2π)/5768 weeks
746.68274 4.28822 (74*2π)/5768 weeks
756.48152 5.55175 (75*2π)/5768 weeks
767.70898 6.82216 (76*2π)/5768 weeks
777.68239 9.31774 (77*2π)/5767 weeks
785.22787 10.98233 (78*2π)/5767 weeks
792.16037 10.16004 (79*2π)/5767 weeks
802.31386 8.18045 (80*2π)/5767 weeks
812.3738 8.14174 (81*2π)/5767 weeks
821.70086 7.38171 (82*2π)/5767 weeks
832.4821 7.28366 (83*2π)/5767 weeks
842.02493 7.057 (84*2π)/5767 weeks
852.80097 8.09374 (85*2π)/5767 weeks
861.19268 8.31223 (86*2π)/5767 weeks
87-.23251 7.78029 (87*2π)/5767 weeks
88-1.16813 5.89049 (88*2π)/5767 weeks
89-.92333 3.57938 (89*2π)/5766 weeks
902.43147 1.75107 (90*2π)/5766 weeks
914.73041 4.61004 (91*2π)/5766 weeks
923.1353 7.53376 (92*2π)/5766 weeks
93.95462 6.85273 (93*2π)/5766 weeks
94-.45119 5.59167 (94*2π)/5766 weeks
95-.55597 2.96358 (95*2π)/5766 weeks
961.89978 1.80982 (96*2π)/5766 weeks
973.05449 2.74384 (97*2π)/5766 weeks
983.43893 3.82501 (98*2π)/5766 weeks
992.83057 3.98624 (99*2π)/5766 weeks
1003.1967 2.98058 (100*2π)/5766 weeks
1014.65346 3.51809 (101*2π)/5766 weeks
1024.29213 4.57306 (102*2π)/5766 weeks
1033.95171 5.50661 (103*2π)/5766 weeks
1043.52066 5.54604 (104*2π)/5766 weeks
1052.44543 5.56109 (105*2π)/5765 weeks
1061.91058 4.02972 (106*2π)/5765 weeks
1073.58451 4.1235 (107*2π)/5765 weeks
1083.747 4.29383 (108*2π)/5765 weeks
1094.41297 4.6303 (109*2π)/5765 weeks
1104.48384 6.39577 (110*2π)/5765 weeks
1113.11872 7.50658 (111*2π)/5765 weeks
1121.59223 6.95499 (112*2π)/5765 weeks
113.37992 7.24769 (113*2π)/5765 weeks
114-.30545 4.75022 (114*2π)/5765 weeks
115.52659 3.90164 (115*2π)/5765 weeks
116.72279 3.67075 (116*2π)/5765 weeks
1171.76543 3.32737 (117*2π)/5765 weeks
1181.93652 4.60114 (118*2π)/5765 weeks
119.59441 4.61633 (119*2π)/5765 weeks
120-.16095 3.54935 (120*2π)/5765 weeks
121.50829 2.27652 (121*2π)/5765 weeks
1221.93699 2.0296 (122*2π)/5765 weeks
1232.20284 3.52693 (123*2π)/5765 weeks
1241.27205 4.05663 (124*2π)/5765 weeks
125-.66901 2.8221 (125*2π)/5765 weeks
126-.32868 .98078 (126*2π)/5765 weeks
1271.56224 -.44829 (127*2π)/5765 weeks
1283.16086 -.15831 (128*2π)/5765 weeks
1293.97348 1.95633 (129*2π)/5764 weeks
1302.76901 2.22036 (130*2π)/5764 weeks
1312.14481 1.61878 (131*2π)/5764 weeks
1323.09911 .69498 (132*2π)/5764 weeks
1333.22993 1.17487 (133*2π)/5764 weeks
1344.32641 .58924 (134*2π)/5764 weeks
1354.52983 1.11588 (135*2π)/5764 weeks
1365.59552 1.70063 (136*2π)/5764 weeks
1375.88528 3.26691 (137*2π)/5764 weeks
1385.0569 4.2257 (138*2π)/5764 weeks
1393.65895 3.92481 (139*2π)/5764 weeks
1403.69558 3.49548 (140*2π)/5764 weeks
1413.7828 4.21681 (141*2π)/5764 weeks
1422.67272 3.66204 (142*2π)/5764 weeks
1432.94762 2.57289 (143*2π)/5764 weeks
1443.72292 2.68931 (144*2π)/5764 weeks
1454.74699 3.03658 (145*2π)/5764 weeks
1464.46346 4.73496 (146*2π)/5764 weeks
1472.99124 5.14116 (147*2π)/5764 weeks
1482.61125 4.26429 (148*2π)/5764 weeks
1492.10689 4.59022 (149*2π)/5764 weeks
1501.86717 4.40735 (150*2π)/5764 weeks
1511.17801 3.66464 (151*2π)/5764 weeks
1521.23912 2.93038 (152*2π)/5764 weeks
1531.60918 2.40871 (153*2π)/5764 weeks
1541.96093 2.22317 (154*2π)/5764 weeks
1552.98686 2.68698 (155*2π)/5764 weeks
1562.78985 3.54651 (156*2π)/5764 weeks
1571.74388 4.0048 (157*2π)/5764 weeks
158.34219 3.40595 (158*2π)/5764 weeks
159-.35731 1.46262 (159*2π)/5764 weeks
1601.06283 .29235 (160*2π)/5764 weeks
1612.672 .0382 (161*2π)/5764 weeks
1623.34207 1.06203 (162*2π)/5764 weeks
1633.1927 1.49313 (163*2π)/5764 weeks
1643.1674 1.25773 (164*2π)/5764 weeks
1654.09308 1.41305 (165*2π)/5763 weeks
1664.15828 2.45224 (166*2π)/5763 weeks
1672.85977 3.36274 (167*2π)/5763 weeks
1682.31714 2.52335 (168*2π)/5763 weeks
1692.26794 2.10218 (169*2π)/5763 weeks
1702.39652 1.5273 (170*2π)/5763 weeks
1713.51428 1.06784 (171*2π)/5763 weeks
1724.09891 2.03301 (172*2π)/5763 weeks
1733.82161 3.47597 (173*2π)/5763 weeks
1742.2709 3.68956 (174*2π)/5763 weeks
1751.36732 2.25043 (175*2π)/5763 weeks
1762.47451 1.28591 (176*2π)/5763 weeks
1773.47673 1.67153 (177*2π)/5763 weeks
1783.57872 3.14548 (178*2π)/5763 weeks
1792.26299 3.78107 (179*2π)/5763 weeks
1801.07932 2.9398 (180*2π)/5763 weeks
181.99582 1.46243 (181*2π)/5763 weeks
1822.11029 .77407 (182*2π)/5763 weeks
1832.6374 1.3373 (183*2π)/5763 weeks
1842.70706 1.16215 (184*2π)/5763 weeks
1852.59127 1.54569 (185*2π)/5763 weeks
1863.18085 .90959 (186*2π)/5763 weeks
1874.08759 1.45309 (187*2π)/5763 weeks
1883.47145 3.07978 (188*2π)/5763 weeks
1892.69641 3.0906 (189*2π)/5763 weeks
1902.00546 2.70125 (190*2π)/5763 weeks
1911.82778 2.28014 (191*2π)/5763 weeks
1921.65027 2.23638 (192*2π)/5763 weeks
1931.0824 1.48592 (193*2π)/5763 weeks
1941.79537 1.04314 (194*2π)/5763 weeks
1951.82494 1.1734 (195*2π)/5763 weeks
1962.02609 .781 (196*2π)/5763 weeks
1972.49516 .33184 (197*2π)/5763 weeks
1982.88973 .77763 (198*2π)/5763 weeks
1993.24464 .8657 (199*2π)/5763 weeks
2003.21161 1.3728 (200*2π)/5763 weeks
2012.8557 1.80237 (201*2π)/5763 weeks
2022.63159 1.83296 (202*2π)/5763 weeks
2032.20998 1.58203 (203*2π)/5763 weeks
2041.76059 1.33584 (204*2π)/5763 weeks
2052.14576 .16782 (205*2π)/5763 weeks
2063.18625 .43968 (206*2π)/5763 weeks
2073.03713 .64007 (207*2π)/5763 weeks
2083.65266 .70821 (208*2π)/5763 weeks
2093.76095 1.8505 (209*2π)/5763 weeks
2102.88177 1.73324 (210*2π)/5763 weeks
2112.80108 .95444 (211*2π)/5763 weeks
2123.8229 1.11764 (212*2π)/5763 weeks
2133.93063 2.00512 (213*2π)/5763 weeks
2142.9592 2.39864 (214*2π)/5763 weeks
2153.14508 2.45894 (215*2π)/5763 weeks
2161.90304 3.1061 (216*2π)/5763 weeks
217.38508 2.16145 (217*2π)/5763 weeks
218.6678 .00076 (218*2π)/5763 weeks
2192.65033 -1.10896 (219*2π)/5763 weeks
2204.10693 .15577 (220*2π)/5763 weeks
2214.23428 1.73262 (221*2π)/5763 weeks
2223.09564 2.2745 (222*2π)/5763 weeks
2232.29132 1.89626 (223*2π)/5763 weeks
2242.59459 1.63151 (224*2π)/5763 weeks
2252.33002 1.89712 (225*2π)/5763 weeks
2261.71829 1.62751 (226*2π)/5763 weeks
2271.73039 1.48798 (227*2π)/5763 weeks
2281.62442 .67841 (228*2π)/5763 weeks
2292.18598 .30649 (229*2π)/5763 weeks
2302.33418 .34822 (230*2π)/5763 weeks
2312.94947 .37487 (231*2π)/5762 weeks
2322.99641 .93616 (232*2π)/5762 weeks
2332.6728 1.43408 (233*2π)/5762 weeks
2342.36578 1.25667 (234*2π)/5762 weeks
2352.31464 .75492 (235*2π)/5762 weeks
2362.37662 1.24186 (236*2π)/5762 weeks
2372.15918 1.09003 (237*2π)/5762 weeks
2381.82734 .67907 (238*2π)/5762 weeks
2391.77072 .43901 (239*2π)/5762 weeks
2401.96042 -.41452 (240*2π)/5762 weeks
2412.95042 -.58446 (241*2π)/5762 weeks
2423.54039 .04461 (242*2π)/5762 weeks
2433.78688 .616 (243*2π)/5762 weeks
2443.48495 1.20415 (244*2π)/5762 weeks
2453.22001 1.38362 (245*2π)/5762 weeks
2462.60084 1.19764 (246*2π)/5762 weeks
2472.89794 .80586 (247*2π)/5762 weeks
2483.31773 .78634 (248*2π)/5762 weeks
2493.64375 1.67034 (249*2π)/5762 weeks
2503.04953 2.52534 (250*2π)/5762 weeks
2511.88292 2.61143 (251*2π)/5762 weeks
2521.24469 2.08671 (252*2π)/5762 weeks
253.95744 1.79513 (253*2π)/5762 weeks
254.30145 .96152 (254*2π)/5762 weeks
255.65091 .00796 (255*2π)/5762 weeks
2561.04667 -.25449 (256*2π)/5762 weeks
2571.41456 -.63504 (257*2π)/5762 weeks
2582.32981 -.67832 (258*2π)/5762 weeks
2592.5553 .02765 (259*2π)/5762 weeks
2601.95341 .33609 (260*2π)/5762 weeks
2611.88814 -.02888 (261*2π)/5762 weeks
2621.6313 -.33146 (262*2π)/5762 weeks
2632.02177 -.81415 (263*2π)/5762 weeks
2642.20714 -.74622 (264*2π)/5762 weeks
2652.41999 -.83565 (265*2π)/5762 weeks
2662.94982 -.52479 (266*2π)/5762 weeks
2672.46364 .14315 (267*2π)/5762 weeks
2682.10606 -.07408 (268*2π)/5762 weeks
2691.69738 -.60423 (269*2π)/5762 weeks
2701.72133 -1.69104 (270*2π)/5762 weeks
2713.23691 -2.2406 (271*2π)/5762 weeks
2724.53217 -1.49944 (272*2π)/5762 weeks
2734.59891 -.43918 (273*2π)/5762 weeks
2744.35329 .50357 (274*2π)/5762 weeks
2754.00593 1.07918 (275*2π)/5762 weeks
2763.60711 1.90866 (276*2π)/5762 weeks
2771.46688 1.89563 (277*2π)/5762 weeks
278.46843 .48225 (278*2π)/5762 weeks
279.94519 -1.46292 (279*2π)/5762 weeks
2802.12584 -2.40301 (280*2π)/5762 weeks
2813.74201 -2.41401 (281*2π)/5762 weeks
2825.16743 -1.44581 (282*2π)/5762 weeks
2835.29518 .1671 (283*2π)/5762 weeks
2844.59733 1.25958 (284*2π)/5762 weeks
2853.38305 1.85155 (285*2π)/5762 weeks
2862.34886 1.57264 (286*2π)/5762 weeks
2871.71364 .60941 (287*2π)/5762 weeks
2882.02351   (288*2π)/5762 weeks
2891.71364 -.60941 (289*2π)/5762 weeks
2902.34886 -1.57264 (290*2π)/5762 weeks
2913.38305 -1.85155 (291*2π)/5762 weeks
2924.59733 -1.25958 (292*2π)/5762 weeks
2935.29518 -.1671 (293*2π)/5762 weeks
2945.16743 1.44581 (294*2π)/5762 weeks
2953.74201 2.41401 (295*2π)/5762 weeks
2962.12584 2.40301 (296*2π)/5762 weeks
297.94519 1.46292 (297*2π)/5762 weeks
298.46843 -.48225 (298*2π)/5762 weeks
2991.46688 -1.89563 (299*2π)/5762 weeks
3003.60711 -1.90866 (300*2π)/5762 weeks
3014.00593 -1.07918 (301*2π)/5762 weeks
3024.35329 -.50357 (302*2π)/5762 weeks
3034.59891 .43918 (303*2π)/5762 weeks
3044.53217 1.49944 (304*2π)/5762 weeks
3053.23691 2.2406 (305*2π)/5762 weeks
3061.72133 1.69104 (306*2π)/5762 weeks
3071.69738 .60423 (307*2π)/5762 weeks
3082.10606 .07408 (308*2π)/5762 weeks
3092.46364 -.14315 (309*2π)/5762 weeks
3102.94982 .52479 (310*2π)/5762 weeks
3112.41999 .83565 (311*2π)/5762 weeks
3122.20714 .74622 (312*2π)/5762 weeks
3132.02177 .81415 (313*2π)/5762 weeks
3141.6313 .33146 (314*2π)/5762 weeks
3151.88814 .02888 (315*2π)/5762 weeks
3161.95341 -.33609 (316*2π)/5762 weeks
3172.5553 -.02765 (317*2π)/5762 weeks
3182.32981 .67832 (318*2π)/5762 weeks
3191.41456 .63504 (319*2π)/5762 weeks
3201.04667 .25449 (320*2π)/5762 weeks
321.65091 -.00796 (321*2π)/5762 weeks
322.30145 -.96152 (322*2π)/5762 weeks
323.95744 -1.79513 (323*2π)/5762 weeks
3241.24469 -2.08671 (324*2π)/5762 weeks
3251.88292 -2.61143 (325*2π)/5762 weeks
3263.04953 -2.52534 (326*2π)/5762 weeks
3273.64375 -1.67034 (327*2π)/5762 weeks
3283.31773 -.78634 (328*2π)/5762 weeks
3292.89794 -.80586 (329*2π)/5762 weeks
3302.60084 -1.19764 (330*2π)/5762 weeks
3313.22001 -1.38362 (331*2π)/5762 weeks
3323.48495 -1.20415 (332*2π)/5762 weeks
3333.78688 -.616 (333*2π)/5762 weeks
3343.54039 -.04461 (334*2π)/5762 weeks
3352.95042 .58446 (335*2π)/5762 weeks
3361.96042 .41452 (336*2π)/5762 weeks
3371.77072 -.43901 (337*2π)/5762 weeks
3381.82734 -.67907 (338*2π)/5762 weeks
3392.15918 -1.09003 (339*2π)/5762 weeks
3402.37662 -1.24186 (340*2π)/5762 weeks
3412.31464 -.75492 (341*2π)/5762 weeks
3422.36578 -1.25667 (342*2π)/5762 weeks
3432.6728 -1.43408 (343*2π)/5762 weeks
3442.99641 -.93616 (344*2π)/5762 weeks
3452.94947 -.37487 (345*2π)/5762 weeks
3462.33418 -.34822 (346*2π)/5762 weeks
3472.18598 -.30649 (347*2π)/5762 weeks
3481.62442 -.67841 (348*2π)/5762 weeks
3491.73039 -1.48798 (349*2π)/5762 weeks
3501.71829 -1.62751 (350*2π)/5762 weeks
3512.33002 -1.89712 (351*2π)/5762 weeks
3522.59459 -1.63151 (352*2π)/5762 weeks
3532.29132 -1.89626 (353*2π)/5762 weeks
3543.09564 -2.2745 (354*2π)/5762 weeks
3554.23428 -1.73262 (355*2π)/5762 weeks
3564.10693 -.15577 (356*2π)/5762 weeks
3572.65033 1.10896 (357*2π)/5762 weeks
358.6678 -.00076 (358*2π)/5762 weeks
359.38508 -2.16145 (359*2π)/5762 weeks
3601.90304 -3.1061 (360*2π)/5762 weeks
3613.14508 -2.45894 (361*2π)/5762 weeks
3622.9592 -2.39864 (362*2π)/5762 weeks
3633.93063 -2.00512 (363*2π)/5762 weeks
3643.8229 -1.11764 (364*2π)/5762 weeks
3652.80108 -.95444 (365*2π)/5762 weeks
3662.88177 -1.73324 (366*2π)/5762 weeks
3673.76095 -1.8505 (367*2π)/5762 weeks
3683.65266 -.70821 (368*2π)/5762 weeks
3693.03713 -.64007 (369*2π)/5762 weeks
3703.18625 -.43968 (370*2π)/5762 weeks
3712.14576 -.16782 (371*2π)/5762 weeks
3721.76059 -1.33584 (372*2π)/5762 weeks
3732.20998 -1.58203 (373*2π)/5762 weeks
3742.63159 -1.83296 (374*2π)/5762 weeks
3752.8557 -1.80237 (375*2π)/5762 weeks
3763.21161 -1.3728 (376*2π)/5762 weeks
3773.24464 -.8657 (377*2π)/5762 weeks
3782.88973 -.77763 (378*2π)/5762 weeks
3792.49516 -.33184 (379*2π)/5762 weeks
3802.02609 -.781 (380*2π)/5762 weeks
3811.82494 -1.1734 (381*2π)/5762 weeks
3821.79537 -1.04314 (382*2π)/5762 weeks
3831.0824 -1.48592 (383*2π)/5762 weeks
3841.65027 -2.23638 (384*2π)/5762 weeks
3851.82778 -2.28014 (385*2π)/5761 weeks
3862.00546 -2.70125 (386*2π)/5761 weeks
3872.69641 -3.0906 (387*2π)/5761 weeks
3883.47145 -3.07978 (388*2π)/5761 weeks
3894.08759 -1.45309 (389*2π)/5761 weeks
3903.18085 -.90959 (390*2π)/5761 weeks
3912.59127 -1.54569 (391*2π)/5761 weeks
3922.70706 -1.16215 (392*2π)/5761 weeks
3932.6374 -1.3373 (393*2π)/5761 weeks
3942.11029 -.77407 (394*2π)/5761 weeks
395.99582 -1.46243 (395*2π)/5761 weeks
3961.07932 -2.9398 (396*2π)/5761 weeks
3972.26299 -3.78107 (397*2π)/5761 weeks
3983.57872 -3.14548 (398*2π)/5761 weeks
3993.47673 -1.67153 (399*2π)/5761 weeks
4002.47451 -1.28591 (400*2π)/5761 weeks
4011.36732 -2.25043 (401*2π)/5761 weeks
4022.2709 -3.68956 (402*2π)/5761 weeks
4033.82161 -3.47597 (403*2π)/5761 weeks
4044.09891 -2.03301 (404*2π)/5761 weeks
4053.51428 -1.06784 (405*2π)/5761 weeks
4062.39652 -1.5273 (406*2π)/5761 weeks
4072.26794 -2.10218 (407*2π)/5761 weeks
4082.31714 -2.52335 (408*2π)/5761 weeks
4092.85977 -3.36274 (409*2π)/5761 weeks
4104.15828 -2.45224 (410*2π)/5761 weeks
4114.09308 -1.41305 (411*2π)/5761 weeks
4123.1674 -1.25773 (412*2π)/5761 weeks
4133.1927 -1.49313 (413*2π)/5761 weeks
4143.34207 -1.06203 (414*2π)/5761 weeks
4152.672 -.0382 (415*2π)/5761 weeks
4161.06283 -.29235 (416*2π)/5761 weeks
417-.35731 -1.46262 (417*2π)/5761 weeks
418.34219 -3.40595 (418*2π)/5761 weeks
4191.74388 -4.0048 (419*2π)/5761 weeks
4202.78985 -3.54651 (420*2π)/5761 weeks
4212.98686 -2.68698 (421*2π)/5761 weeks
4221.96093 -2.22317 (422*2π)/5761 weeks
4231.60918 -2.40871 (423*2π)/5761 weeks
4241.23912 -2.93038 (424*2π)/5761 weeks
4251.17801 -3.66464 (425*2π)/5761 weeks
4261.86717 -4.40735 (426*2π)/5761 weeks
4272.10689 -4.59022 (427*2π)/5761 weeks
4282.61125 -4.26429 (428*2π)/5761 weeks
4292.99124 -5.14116 (429*2π)/5761 weeks
4304.46346 -4.73496 (430*2π)/5761 weeks
4314.74699 -3.03658 (431*2π)/5761 weeks
4323.72292 -2.68931 (432*2π)/5761 weeks
4332.94762 -2.57289 (433*2π)/5761 weeks
4342.67272 -3.66204 (434*2π)/5761 weeks
4353.7828 -4.21681 (435*2π)/5761 weeks
4363.69558 -3.49548 (436*2π)/5761 weeks
4373.65895 -3.92481 (437*2π)/5761 weeks
4385.0569 -4.2257 (438*2π)/5761 weeks
4395.88528 -3.26691 (439*2π)/5761 weeks
4405.59552 -1.70063 (440*2π)/5761 weeks
4414.52983 -1.11588 (441*2π)/5761 weeks
4424.32641 -.58924 (442*2π)/5761 weeks
4433.22993 -1.17487 (443*2π)/5761 weeks
4443.09911 -.69498 (444*2π)/5761 weeks
4452.14481 -1.61878 (445*2π)/5761 weeks
4462.76901 -2.22036 (446*2π)/5761 weeks
4473.97348 -1.95633 (447*2π)/5761 weeks
4483.16086 .15831 (448*2π)/5761 weeks
4491.56224 .44829 (449*2π)/5761 weeks
450-.32868 -.98078 (450*2π)/5761 weeks
451-.66901 -2.8221 (451*2π)/5761 weeks
4521.27205 -4.05663 (452*2π)/5761 weeks
4532.20284 -3.52693 (453*2π)/5761 weeks
4541.93699 -2.0296 (454*2π)/5761 weeks
455.50829 -2.27652 (455*2π)/5761 weeks
456-.16095 -3.54935 (456*2π)/5761 weeks
457.59441 -4.61633 (457*2π)/5761 weeks
4581.93652 -4.60114 (458*2π)/5761 weeks
4591.76543 -3.32737 (459*2π)/5761 weeks
460.72279 -3.67075 (460*2π)/5761 weeks
461.52659 -3.90164 (461*2π)/5761 weeks
462-.30545 -4.75022 (462*2π)/5761 weeks
463.37992 -7.24769 (463*2π)/5761 weeks
4641.59223 -6.95499 (464*2π)/5761 weeks
4653.11872 -7.50658 (465*2π)/5761 weeks
4664.48384 -6.39577 (466*2π)/5761 weeks
4674.41297 -4.6303 (467*2π)/5761 weeks
4683.747 -4.29383 (468*2π)/5761 weeks
4693.58451 -4.1235 (469*2π)/5761 weeks
4701.91058 -4.02972 (470*2π)/5761 weeks
4712.44543 -5.56109 (471*2π)/5761 weeks
4723.52066 -5.54604 (472*2π)/5761 weeks
4733.95171 -5.50661 (473*2π)/5761 weeks
4744.29213 -4.57306 (474*2π)/5761 weeks
4754.65346 -3.51809 (475*2π)/5761 weeks
4763.1967 -2.98058 (476*2π)/5761 weeks
4772.83057 -3.98624 (477*2π)/5761 weeks
4783.43893 -3.82501 (478*2π)/5761 weeks
4793.05449 -2.74384 (479*2π)/5761 weeks
4801.89978 -1.80982 (480*2π)/5761 weeks
481-.55597 -2.96358 (481*2π)/5761 weeks
482-.45119 -5.59167 (482*2π)/5761 weeks
483.95462 -6.85273 (483*2π)/5761 weeks
4843.1353 -7.53376 (484*2π)/5761 weeks
4854.73041 -4.61004 (485*2π)/5761 weeks
4862.43147 -1.75107 (486*2π)/5761 weeks
487-.92333 -3.57938 (487*2π)/5761 weeks
488-1.16813 -5.89049 (488*2π)/5761 weeks
489-.23251 -7.78029 (489*2π)/5761 weeks
4901.19268 -8.31223 (490*2π)/5761 weeks
4912.80097 -8.09374 (491*2π)/5761 weeks
4922.02493 -7.057 (492*2π)/5761 weeks
4932.4821 -7.28366 (493*2π)/5761 weeks
4941.70086 -7.38171 (494*2π)/5761 weeks
4952.3738 -8.14174 (495*2π)/5761 weeks
4962.31386 -8.18045 (496*2π)/5761 weeks
4972.16037 -10.16004 (497*2π)/5761 weeks
4985.22787 -10.98233 (498*2π)/5761 weeks
4997.68239 -9.31774 (499*2π)/5761 weeks
5007.70898 -6.82216 (500*2π)/5761 weeks
5016.48152 -5.55175 (501*2π)/5761 weeks
5026.68274 -4.28822 (502*2π)/5761 weeks
5035.49631 -3.2953 (503*2π)/5761 weeks
5043.12025 -2.94059 (504*2π)/5761 weeks
5053.39016 -3.45947 (505*2π)/5761 weeks
506.94146 -3.21965 (506*2π)/5761 weeks
507-2.09115 -5.37097 (507*2π)/5761 weeks
508-.78232 -9.56137 (508*2π)/5761 weeks
5092.04634 -10.3926 (509*2π)/5761 weeks
5103.39904 -10.28337 (510*2π)/5761 weeks
5115.71524 -9.95744 (511*2π)/5761 weeks
5126.95109 -7.60472 (512*2π)/5761 weeks
5137.50557 -4.56113 (513*2π)/5761 weeks
5144.10344 -2.58885 (514*2π)/5761 weeks
515.26999 -1.77041 (515*2π)/5761 weeks
516-2.63271 -6.14386 (516*2π)/5761 weeks
517-.67726 -9.50098 (517*2π)/5761 weeks
5181.58602 -9.03397 (518*2π)/5761 weeks
5192.38761 -9.31139 (519*2π)/5761 weeks
5202.02461 -8.01696 (520*2π)/5761 weeks
5212.52954 -8.1016 (521*2π)/5761 weeks
5222.2218 -7.57435 (522*2π)/5761 weeks
5231.02761 -6.27514 (523*2π)/5761 weeks
524-1.87815 -5.98269 (524*2π)/5761 weeks
525-4.83081 -10.22614 (525*2π)/5761 weeks
526-2.8255 -13.87028 (526*2π)/5761 weeks
527-.20719 -15.6659 (527*2π)/5761 weeks
5283.95173 -15.59387 (528*2π)/5761 weeks
5293.88439 -14.44754 (529*2π)/5761 weeks
5304.95672 -12.20859 (530*2π)/5761 weeks
5314.62774 -10.33535 (531*2π)/5761 weeks
5321.88195 -9.0094 (532*2π)/5761 weeks
533-1.58908 -10.95958 (533*2π)/5761 weeks
534-1.27793 -15.87886 (534*2π)/5761 weeks
5351.60011 -19.03932 (535*2π)/5761 weeks
5365.27679 -18.53793 (536*2π)/5761 weeks
5378.36829 -16.52674 (537*2π)/5761 weeks
5388.69209 -13.05298 (538*2π)/5761 weeks
5397.81546 -10.79716 (539*2π)/5761 weeks
5406.33721 -6.57194 (540*2π)/5761 weeks
541-.37771 -4.44722 (541*2π)/5761 weeks
542-7.08925 -9.06331 (542*2π)/5761 weeks
543-9.63906 -17.26402 (543*2π)/5761 weeks
544-5.79064 -23.45787 (544*2π)/5761 weeks
545-1.90256 -26.07479 (545*2π)/5761 weeks
5461.65788 -27.59409 (546*2π)/5761 weeks
5476.06089 -26.37633 (547*2π)/5761 weeks
54810.19292 -25.3805 (548*2π)/5761 weeks
5498.82682 -17.49634 (549*2π)/5761 weeks
5503.36601 -16.07997 (550*2π)/5761 weeks
551-1.35009 -21.22496 (551*2π)/5761 weeks
552-.61308 -25.97293 (552*2π)/5761 weeks
553-2.70464 -30.42535 (553*2π)/5761 weeks
5544.29273 -40.37851 (554*2π)/5761 weeks
55516.23928 -40.28405 (555*2π)/5761 weeks
55623.50173 -29.03677 (556*2π)/5761 weeks
55719.96938 -20.65739 (557*2π)/5761 weeks
55812.62417 -17.42939 (558*2π)/5761 weeks
5595.27622 -17.17984 (559*2π)/5761 weeks
560-2.36387 -20.15472 (560*2π)/5761 weeks
561-10.60037 -34.25497 (561*2π)/5761 weeks
562-9.09743 -45.43574 (562*2π)/5761 weeks
563.43566 -61.13399 (563*2π)/5761 weeks
56413.93414 -68.41178 (564*2π)/5761 weeks
56533.66712 -71.51981 (565*2π)/5761 weeks
56650.60906 -54.8528 (566*2π)/5761 weeks
56750.66412 -31.35725 (567*2π)/5761 weeks
56843.3215 -17.37092 (568*2π)/5761 weeks
5693.07723 -5.17179 (569*2π)/5761 weeks
570-29.11585 -35.30777 (570*2π)/5761 weeks
571-51.46693 -82.38167 (571*2π)/5761 weeks
572-50.0065 -159.369 (572*2π)/5761 weeks
57330.71655 -235.0126 (573*2π)/5761 weeks
574133.859 -299.2235 (574*2π)/5761 weeks



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