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Fourier Analysis of WCPIX (Mobile Telecommunications Ultra)


WCPIX (Mobile Telecommunications Ultra) appears to have interesting cyclic behaviour every 87 weeks (41.3625*sine), 58 weeks (41.0468*sine), and 67 weeks (37.6832*sine).

WCPIX (Mobile Telecommunications Ultra) has an average price of 142.72 (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 6/19/2000 to 3/20/2017 for WCPIX (Mobile Telecommunications Ultra), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0142.715   0 
1102.6415 86.61638 (1*2π)/874874 weeks
292.37126 -.28064 (2*2π)/874437 weeks
3112.1299 69.20833 (3*2π)/874291 weeks
466.59515 66.77288 (4*2π)/874219 weeks
563.769 72.55899 (5*2π)/874175 weeks
633.93829 58.79668 (6*2π)/874146 weeks
737.64758 52.95345 (7*2π)/874125 weeks
823.39683 48.53561 (8*2π)/874109 weeks
929.51378 33.73058 (9*2π)/87497 weeks
1028.80446 41.3625 (10*2π)/87487 weeks
1124.67653 32.3522 (11*2π)/87479 weeks
1231.4155 33.83993 (12*2π)/87473 weeks
1323.03941 37.68324 (13*2π)/87467 weeks
1424.65378 34.30477 (14*2π)/87462 weeks
1519.08661 41.04679 (15*2π)/87458 weeks
1615.13598 33.13918 (16*2π)/87455 weeks
1716.11854 36.34668 (17*2π)/87451 weeks
1812.30248 29.92732 (18*2π)/87449 weeks
1914.42725 32.49645 (19*2π)/87446 weeks
2010.62854 27.42143 (20*2π)/87444 weeks
2113.09789 29.51191 (21*2π)/87442 weeks
229.81069 26.08671 (22*2π)/87440 weeks
2313.89096 28.267 (23*2π)/87438 weeks
246.80089 27.56865 (24*2π)/87436 weeks
258.61793 23.97627 (25*2π)/87435 weeks
269.90834 23.2887 (26*2π)/87434 weeks
279.77423 25.25678 (27*2π)/87432 weeks
285.72064 23.76146 (28*2π)/87431 weeks
298.84625 23.78497 (29*2π)/87430 weeks
304.82688 24.28208 (30*2π)/87429 weeks
316.12294 20.29977 (31*2π)/87428 weeks
326.42079 22.31355 (32*2π)/87427 weeks
335.86814 20.67051 (33*2π)/87426 weeks
346.99486 22.68516 (34*2π)/87426 weeks
354.07403 22.74043 (35*2π)/87425 weeks
364.14736 21.78419 (36*2π)/87424 weeks
372.57249 23.13444 (37*2π)/87424 weeks
38-.65768 22.14857 (38*2π)/87423 weeks
39-1.61974 20.18817 (39*2π)/87422 weeks
40-2.18582 17.91549 (40*2π)/87422 weeks
41-1.86298 16.66352 (41*2π)/87421 weeks
42-2.63773 14.71621 (42*2π)/87421 weeks
43-.80822 13.88592 (43*2π)/87420 weeks
44-1.47423 12.95777 (44*2π)/87420 weeks
45-.27121 11.92402 (45*2π)/87419 weeks
46.62144 12.37805 (46*2π)/87419 weeks
471.2804 13.00175 (47*2π)/87419 weeks
48-.64524 12.31737 (48*2π)/87418 weeks
49.59706 10.60892 (49*2π)/87418 weeks
50.28988 10.58472 (50*2π)/87417 weeks
51.5935 10.05097 (51*2π)/87417 weeks
52.52817 8.33884 (52*2π)/87417 weeks
533.19567 8.53168 (53*2π)/87416 weeks
542.13747 8.42453 (54*2π)/87416 weeks
555.69675 7.72463 (55*2π)/87416 weeks
565.0458 10.93842 (56*2π)/87416 weeks
574.58376 10.01048 (57*2π)/87415 weeks
584.68775 12.09981 (58*2π)/87415 weeks
593.51844 11.72807 (59*2π)/87415 weeks
603.81583 12.59033 (60*2π)/87415 weeks
612.6441 12.40074 (61*2π)/87414 weeks
622.26999 13.52745 (62*2π)/87414 weeks
63.79546 12.89808 (63*2π)/87414 weeks
64.61513 12.98201 (64*2π)/87414 weeks
65-.65786 12.22573 (65*2π)/87413 weeks
66-1.88664 11.54865 (66*2π)/87413 weeks
67-1.81937 9.95542 (67*2π)/87413 weeks
68-2.05845 9.95846 (68*2π)/87413 weeks
69-2.76048 8.2899 (69*2π)/87413 weeks
70-2.05491 7.28941 (70*2π)/87412 weeks
71-1.43157 6.29803 (71*2π)/87412 weeks
72-.59688 6.16694 (72*2π)/87412 weeks
73-.92104 4.92239 (73*2π)/87412 weeks
74.85916 4.22352 (74*2π)/87412 weeks
75.8715 4.62023 (75*2π)/87412 weeks
762.49204 4.39071 (76*2π)/87412 weeks
773.10532 5.12509 (77*2π)/87411 weeks
784.11474 5.60825 (78*2π)/87411 weeks
793.77923 6.99064 (79*2π)/87411 weeks
803.61178 6.9944 (80*2π)/87411 weeks
813.49641 8.30391 (81*2π)/87411 weeks
822.2972 7.58052 (82*2π)/87411 weeks
833.36859 7.47779 (83*2π)/87411 weeks
842.06635 8.48932 (84*2π)/87410 weeks
852.02169 7.57094 (85*2π)/87410 weeks
861.84714 7.98276 (86*2π)/87410 weeks
871.56116 7.3339 (87*2π)/87410 weeks
881.78069 7.67977 (88*2π)/87410 weeks
89.97806 7.36565 (89*2π)/87410 weeks
901.60491 7.45453 (90*2π)/87410 weeks
911.27033 7.46044 (91*2π)/87410 weeks
921.73138 7.38372 (92*2π)/87410 weeks
931.43484 7.84584 (93*2π)/8749 weeks
941.42947 7.337 (94*2π)/8749 weeks
95.69786 7.26602 (95*2π)/8749 weeks
96.84356 6.72678 (96*2π)/8749 weeks
97.75169 7.28089 (97*2π)/8749 weeks
98.36802 7.03043 (98*2π)/8749 weeks
99.685 6.55201 (99*2π)/8749 weeks
100.44687 6.92924 (100*2π)/8749 weeks
101-.23835 6.40507 (101*2π)/8749 weeks
102-.07231 6.25766 (102*2π)/8749 weeks
103-.03954 5.89024 (103*2π)/8748 weeks
104.11412 5.30263 (104*2π)/8748 weeks
1051.09578 5.06249 (105*2π)/8748 weeks
106.99381 5.63933 (106*2π)/8748 weeks
107.66049 5.22722 (107*2π)/8748 weeks
1081.31097 5.53159 (108*2π)/8748 weeks
109.96605 5.72879 (109*2π)/8748 weeks
110.77638 5.90508 (110*2π)/8748 weeks
111.90158 5.89123 (111*2π)/8748 weeks
1121.09385 5.94569 (112*2π)/8748 weeks
113.58743 5.89402 (113*2π)/8748 weeks
114.70008 5.83439 (114*2π)/8748 weeks
115.38909 5.90165 (115*2π)/8748 weeks
116.74358 6.02501 (116*2π)/8748 weeks
117-.1538 6.47393 (117*2π)/8747 weeks
118.31097 5.28795 (118*2π)/8747 weeks
119.38468 6.37455 (119*2π)/8747 weeks
120-.58122 5.98145 (120*2π)/8747 weeks
121-.08681 5.69882 (121*2π)/8747 weeks
122-.59069 6.29136 (122*2π)/8747 weeks
123-.70529 6.00784 (123*2π)/8747 weeks
124-1.4615 6.02247 (124*2π)/8747 weeks
125-2.08263 5.49733 (125*2π)/8747 weeks
126-2.15855 5.26408 (126*2π)/8747 weeks
127-2.97994 4.62133 (127*2π)/8747 weeks
128-2.70463 3.67889 (128*2π)/8747 weeks
129-2.75461 3.35502 (129*2π)/8747 weeks
130-2.6333 2.4145 (130*2π)/8747 weeks
131-2.16374 1.93421 (131*2π)/8747 weeks
132-1.64924 1.68697 (132*2π)/8747 weeks
133-1.24921 1.54868 (133*2π)/8747 weeks
134-1.17018 1.57763 (134*2π)/8747 weeks
135-1.04744 .90689 (135*2π)/8746 weeks
136-.14843 .91496 (136*2π)/8746 weeks
137-.26251 .97334 (137*2π)/8746 weeks
138.60818 .7377 (138*2π)/8746 weeks
139.52261 1.25424 (139*2π)/8746 weeks
1401.17668 .74176 (140*2π)/8746 weeks
1411.26583 1.34615 (141*2π)/8746 weeks
1421.56394 .91307 (142*2π)/8746 weeks
1431.97694 1.72239 (143*2π)/8746 weeks
1441.90404 1.49568 (144*2π)/8746 weeks
1452.67691 1.85177 (145*2π)/8746 weeks
1462.34945 2.44845 (146*2π)/8746 weeks
1472.55836 2.86117 (147*2π)/8746 weeks
1481.98757 3.6857 (148*2π)/8746 weeks
1491.43379 3.59585 (149*2π)/8746 weeks
1501.10255 3.78683 (150*2π)/8746 weeks
151.65576 3.39268 (151*2π)/8746 weeks
152.61336 3.27024 (152*2π)/8746 weeks
153.11452 3.02834 (153*2π)/8746 weeks
154.28976 2.33977 (154*2π)/8746 weeks
155.56981 2.60181 (155*2π)/8746 weeks
156.48714 2.0178 (156*2π)/8746 weeks
1571.25954 2.37243 (157*2π)/8746 weeks
158.84575 2.6614 (158*2π)/8746 weeks
159.64048 2.57927 (159*2π)/8745 weeks
160.46762 2.54599 (160*2π)/8745 weeks
161-.01304 2.5859 (161*2π)/8745 weeks
162-.12205 1.8079 (162*2π)/8745 weeks
163.10144 1.60217 (163*2π)/8745 weeks
164.40241 .95404 (164*2π)/8745 weeks
165.95598 1.23218 (165*2π)/8745 weeks
1661.12852 1.14962 (166*2π)/8745 weeks
1671.32087 1.57443 (167*2π)/8745 weeks
1681.12531 1.39089 (168*2π)/8745 weeks
1691.40048 2.10004 (169*2π)/8745 weeks
170.8668 1.83734 (170*2π)/8745 weeks
1711.37593 1.99401 (171*2π)/8745 weeks
172.87549 1.9048 (172*2π)/8745 weeks
1731.2119 1.57559 (173*2π)/8745 weeks
1741.1378 1.98461 (174*2π)/8745 weeks
175.79155 1.71078 (175*2π)/8745 weeks
176.95235 1.53227 (176*2π)/8745 weeks
177.90868 1.45181 (177*2π)/8745 weeks
1781.25674 1.22047 (178*2π)/8745 weeks
1791.18683 1.53474 (179*2π)/8745 weeks
1801.25105 1.25662 (180*2π)/8745 weeks
1811.43241 1.75722 (181*2π)/8745 weeks
1821.07804 1.50418 (182*2π)/8745 weeks
1831.37822 1.80272 (183*2π)/8745 weeks
1841.12141 1.44014 (184*2π)/8745 weeks
1851.64719 1.97618 (185*2π)/8745 weeks
186.69567 1.81375 (186*2π)/8745 weeks
1871.1347 1.52009 (187*2π)/8745 weeks
188.5441 1.80251 (188*2π)/8745 weeks
189.68784 1.16341 (189*2π)/8745 weeks
190.60494 1.3646 (190*2π)/8745 weeks
191.25289 1.12326 (191*2π)/8745 weeks
192.09345 .81551 (192*2π)/8745 weeks
193.22511 .43269 (193*2π)/8745 weeks
194.57524 .17598 (194*2π)/8745 weeks
195.56479 -.00629 (195*2π)/8744 weeks
1961.22423 -.50572 (196*2π)/8744 weeks
1971.41912 .12037 (197*2π)/8744 weeks
1981.65617 -.10865 (198*2π)/8744 weeks
1991.9358 .2648 (199*2π)/8744 weeks
2002.13341 -.02702 (200*2π)/8744 weeks
2012.50996 .66291 (201*2π)/8744 weeks
2021.73452 .66584 (202*2π)/8744 weeks
2032.04597 .60004 (203*2π)/8744 weeks
2041.34112 .85822 (204*2π)/8744 weeks
2051.32208 .20447 (205*2π)/8744 weeks
2061.37075 .07813 (206*2π)/8744 weeks
2071.77319 -.36749 (207*2π)/8744 weeks
2082.02303 -.3191 (208*2π)/8744 weeks
2092.36733 -.4871 (209*2π)/8744 weeks
2102.80728 -.30275 (210*2π)/8744 weeks
2113.02367 .09796 (211*2π)/8744 weeks
2123.19123 .58755 (212*2π)/8744 weeks
2133.01126 .83377 (213*2π)/8744 weeks
2143.10105 1.09849 (214*2π)/8744 weeks
2152.76622 1.36004 (215*2π)/8744 weeks
2162.54832 1.3435 (216*2π)/8744 weeks
2172.10514 1.27747 (217*2π)/8744 weeks
2182.16911 1.1323 (218*2π)/8744 weeks
2191.93679 1.14461 (219*2π)/8744 weeks
2202.05384 1.09266 (220*2π)/8744 weeks
2211.91065 1.12141 (221*2π)/8744 weeks
2221.66973 .80456 (222*2π)/8744 weeks
2231.86915 .72229 (223*2π)/8744 weeks
2241.66046 .81431 (224*2π)/8744 weeks
2251.68877 .32219 (225*2π)/8744 weeks
2262.01098 .32343 (226*2π)/8744 weeks
2271.92772 .40274 (227*2π)/8744 weeks
2281.83088 -.0151 (228*2π)/8744 weeks
2292.41398 -.02427 (229*2π)/8744 weeks
2302.32002 .0409 (230*2π)/8744 weeks
2312.40226 -.27437 (231*2π)/8744 weeks
2322.57394 -.03339 (232*2π)/8744 weeks
2332.3726 -.37355 (233*2π)/8744 weeks
2342.98432 -.72707 (234*2π)/8744 weeks
2353.25513 -.3665 (235*2π)/8744 weeks
2363.46423 -.52103 (236*2π)/8744 weeks
2373.83065 -.19406 (237*2π)/8744 weeks
2383.82576 -.05351 (238*2π)/8744 weeks
2393.98732 .14156 (239*2π)/8744 weeks
2404.28654 .18562 (240*2π)/8744 weeks
2414.28059 .85159 (241*2π)/8744 weeks
2424.23669 .60478 (242*2π)/8744 weeks
2434.71457 .9658 (243*2π)/8744 weeks
2444.57952 1.27268 (244*2π)/8744 weeks
2454.66488 1.75537 (245*2π)/8744 weeks
2464.30282 2.12678 (246*2π)/8744 weeks
2474.23059 2.39925 (247*2π)/8744 weeks
2483.68633 2.72166 (248*2π)/8744 weeks
2493.45497 2.50637 (249*2π)/8744 weeks
2503.3009 2.70888 (250*2π)/8743 weeks
2513.01223 2.62239 (251*2π)/8743 weeks
2522.81418 2.63788 (252*2π)/8743 weeks
2532.49897 2.32029 (253*2π)/8743 weeks
2542.6639 2.34613 (254*2π)/8743 weeks
2552.42191 2.39865 (255*2π)/8743 weeks
2562.33501 2.23055 (256*2π)/8743 weeks
2572.45128 2.28546 (257*2π)/8743 weeks
2582.20772 2.30429 (258*2π)/8743 weeks
2592.19033 2.02745 (259*2π)/8743 weeks
2601.97704 2.29237 (260*2π)/8743 weeks
2611.6322 1.81078 (261*2π)/8743 weeks
2621.96023 1.71168 (262*2π)/8743 weeks
2631.65618 1.44328 (263*2π)/8743 weeks
2642.28619 1.0914 (264*2π)/8743 weeks
2652.27112 1.62349 (265*2π)/8743 weeks
2662.21576 1.30284 (266*2π)/8743 weeks
2672.61602 1.54535 (267*2π)/8743 weeks
2682.22394 1.82122 (268*2π)/8743 weeks
2692.07791 1.39593 (269*2π)/8743 weeks
2702.38995 1.60457 (270*2π)/8743 weeks
2712.04737 1.81374 (271*2π)/8743 weeks
2721.94728 1.38068 (272*2π)/8743 weeks
2732.07489 1.42666 (273*2π)/8743 weeks
2741.9391 1.32845 (274*2π)/8743 weeks
2751.84113 1.13077 (275*2π)/8743 weeks
2762.37657 1.04147 (276*2π)/8743 weeks
2772.1903 1.34478 (277*2π)/8743 weeks
2782.33117 1.03475 (278*2π)/8743 weeks
2792.22247 1.48218 (279*2π)/8743 weeks
2802.07388 1.16318 (280*2π)/8743 weeks
2812.24815 1.48233 (281*2π)/8743 weeks
2821.87579 1.18707 (282*2π)/8743 weeks
2832.20327 1.03653 (283*2π)/8743 weeks
2842.09996 .78186 (284*2π)/8743 weeks
2852.52075 .8634 (285*2π)/8743 weeks
2862.52934 .8445 (286*2π)/8743 weeks
2872.84657 .98088 (287*2π)/8743 weeks
2882.89168 1.21623 (288*2π)/8743 weeks
2892.96339 1.54063 (289*2π)/8743 weeks
2902.66597 1.46916 (290*2π)/8743 weeks
2912.76097 1.78623 (291*2π)/8743 weeks
2922.14945 1.97502 (292*2π)/8743 weeks
2932.22098 1.52273 (293*2π)/8743 weeks
2942.2071 1.7292 (294*2π)/8743 weeks
2952.04604 1.4881 (295*2π)/8743 weeks
2962.21078 1.57603 (296*2π)/8743 weeks
2971.93041 1.39075 (297*2π)/8743 weeks
2982.22776 1.25281 (298*2π)/8743 weeks
2991.97134 1.37733 (299*2π)/8743 weeks
3002.32746 1.16656 (300*2π)/8743 weeks
3012.2262 1.49167 (301*2π)/8743 weeks
3022.37881 1.05212 (302*2π)/8743 weeks
3032.50472 1.51184 (303*2π)/8743 weeks
3042.38245 1.50643 (304*2π)/8743 weeks
3052.17211 1.67254 (305*2π)/8743 weeks
3062.14358 1.46755 (306*2π)/8743 weeks
3072.05714 1.86617 (307*2π)/8743 weeks
3081.64163 1.35111 (308*2π)/8743 weeks
3091.99094 1.24008 (309*2π)/8743 weeks
3101.79037 1.22633 (310*2π)/8743 weeks
3112.05863 1.21143 (311*2π)/8743 weeks
3122.17445 1.13566 (312*2π)/8743 weeks
3132.31921 1.29225 (313*2π)/8743 weeks
3142.14551 1.46756 (314*2π)/8743 weeks
3152.27332 1.30957 (315*2π)/8743 weeks
3162.34995 1.64712 (316*2π)/8743 weeks
3172.05429 1.58485 (317*2π)/8743 weeks
3182.15703 1.74561 (318*2π)/8743 weeks
3191.7249 1.5968 (319*2π)/8743 weeks
3202.00357 1.5246 (320*2π)/8743 weeks
3211.68389 1.74916 (321*2π)/8743 weeks
3221.73298 1.15299 (322*2π)/8743 weeks
3231.88409 1.34456 (323*2π)/8743 weeks
3241.86395 1.10558 (324*2π)/8743 weeks
3252.1123 1.26246 (325*2π)/8743 weeks
3262.12062 1.24076 (326*2π)/8743 weeks
3272.42438 1.56327 (327*2π)/8743 weeks
3282.13054 1.73699 (328*2π)/8743 weeks
3292.39365 1.82788 (329*2π)/8743 weeks
3301.96535 2.13951 (330*2π)/8743 weeks
3311.8634 1.91333 (331*2π)/8743 weeks
3321.52652 2.23466 (332*2π)/8743 weeks
3331.27493 1.92904 (333*2π)/8743 weeks
3341.29114 2.16777 (334*2π)/8743 weeks
335.75795 1.9767 (335*2π)/8743 weeks
336.96297 1.70428 (336*2π)/8743 weeks
337.65453 1.87597 (337*2π)/8743 weeks
338.64257 1.50596 (338*2π)/8743 weeks
339.56702 1.46235 (339*2π)/8743 weeks
340.36918 1.15496 (340*2π)/8743 weeks
341.20799 .80833 (341*2π)/8743 weeks
342.53317 .42829 (342*2π)/8743 weeks
343.41305 .73942 (343*2π)/8743 weeks
344.62312 .05048 (344*2π)/8743 weeks
345.91819 .44934 (345*2π)/8743 weeks
346.54897 -.06799 (346*2π)/8743 weeks
3471.10451 -.14792 (347*2π)/8743 weeks
348.99555 -.13028 (348*2π)/8743 weeks
3491.32005 -.40847 (349*2π)/8743 weeks
3501.55051 -.2935 (350*2π)/8742 weeks
3511.89656 -.35483 (351*2π)/8742 weeks
3522.08459 -.14687 (352*2π)/8742 weeks
3532.45038 -.13253 (353*2π)/8742 weeks
3542.46274 .41959 (354*2π)/8742 weeks
3552.33221 .34145 (355*2π)/8742 weeks
3562.56262 .84099 (356*2π)/8742 weeks
3571.95085 .9453 (357*2π)/8742 weeks
3582.17913 .87878 (358*2π)/8742 weeks
3591.75876 1.06827 (359*2π)/8742 weeks
3601.69325 .79849 (360*2π)/8742 weeks
3611.58285 .79465 (361*2π)/8742 weeks
3621.42787 .48458 (362*2π)/8742 weeks
3631.87733 .21661 (363*2π)/8742 weeks
3641.88831 .46888 (364*2π)/8742 weeks
3652.05811 .41183 (365*2π)/8742 weeks
3662.16084 .73069 (366*2π)/8742 weeks
3672.0209 .86586 (367*2π)/8742 weeks
3681.97182 .86752 (368*2π)/8742 weeks
3692.08106 .96652 (369*2π)/8742 weeks
3701.84419 1.10414 (370*2π)/8742 weeks
3711.68486 .92827 (371*2π)/8742 weeks
3721.67621 .89647 (372*2π)/8742 weeks
3731.64287 .97893 (373*2π)/8742 weeks
3741.38079 .95804 (374*2π)/8742 weeks
3751.42928 .67506 (375*2π)/8742 weeks
3761.43635 .68304 (376*2π)/8742 weeks
3771.50291 .53945 (377*2π)/8742 weeks
3781.58082 .60649 (378*2π)/8742 weeks
3791.57591 .61287 (379*2π)/8742 weeks
3801.67854 .6514 (380*2π)/8742 weeks
3811.71242 .59383 (381*2π)/8742 weeks
3821.83796 .80894 (382*2π)/8742 weeks
3831.76394 .99124 (383*2π)/8742 weeks
3841.50103 1.06824 (384*2π)/8742 weeks
3851.42318 .8365 (385*2π)/8742 weeks
3861.39906 1.01059 (386*2π)/8742 weeks
3871.25314 1.02422 (387*2π)/8742 weeks
388.9621 .86059 (388*2π)/8742 weeks
389.95704 .62571 (389*2π)/8742 weeks
3901.07017 .6253 (390*2π)/8742 weeks
3911.06219 .51915 (391*2π)/8742 weeks
3921.03828 .55813 (392*2π)/8742 weeks
393.87178 .35888 (393*2π)/8742 weeks
3941.09426 .3634 (394*2π)/8742 weeks
395.84865 .50252 (395*2π)/8742 weeks
3961.01647 .29518 (396*2π)/8742 weeks
397.84797 .46201 (397*2π)/8742 weeks
398.57082 .0563 (398*2π)/8742 weeks
399.78129 -.00051 (399*2π)/8742 weeks
400.60519 -.12294 (400*2π)/8742 weeks
401.81836 -.32881 (401*2π)/8742 weeks
402.87499 -.40229 (402*2π)/8742 weeks
403.82787 -.63214 (403*2π)/8742 weeks
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