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# Fourier Analysis of MZZ (ProShares UltraShort MidCap400)

MZZ (ProShares UltraShort MidCap400) appears to have interesting cyclic behaviour every 62 weeks (50.9016*sine), 56 weeks (42.7193*sine), and 51 weeks (21.3444*cosine).

MZZ (ProShares UltraShort MidCap400) has an average price of 272.99 (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 7/13/2006 to 4/23/2018 for MZZ (ProShares UltraShort MidCap400), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0272.9901   0
1145.2201 312.2647 (1*2π)/616616 weeks
2-58.4421 164.2942 (2*2π)/616308 weeks
3-50.84579 20.61456 (3*2π)/616205 weeks
441.69682 -.01059 (4*2π)/616154 weeks
556.83287 56.32218 (5*2π)/616123 weeks
610.49351 78.21403 (6*2π)/616103 weeks
7-27.31022 40.48551 (7*2π)/61688 weeks
8-4.10943 -1.46993 (8*2π)/61677 weeks
936.97993 16.82971 (9*2π)/61668 weeks
1019.7331 50.90161 (10*2π)/61662 weeks
11-7.52494 42.71929 (11*2π)/61656 weeks
12-21.34441 23.45948 (12*2π)/61651 weeks
13-5.65456 -3.34527 (13*2π)/61647 weeks
1419.21495 7.79815 (14*2π)/61644 weeks
1514.73819 24.68257 (15*2π)/61641 weeks
162.39597 27.82891 (16*2π)/61639 weeks
17-6.23741 19.16081 (17*2π)/61636 weeks
18-4.12146 11.06888 (18*2π)/61634 weeks
19-1.83785 6.1034 (19*2π)/61632 weeks
209.47634 5.72021 (20*2π)/61631 weeks
219.50285 15.6687 (21*2π)/61629 weeks
224.14835 16.628 (22*2π)/61628 weeks
23.77872 15.40312 (23*2π)/61627 weeks
24-1.42193 12.72831 (24*2π)/61626 weeks
25-.25988 8.23024 (25*2π)/61625 weeks
265.51963 10.72762 (26*2π)/61624 weeks
27.92267 15.35491 (27*2π)/61623 weeks
28-7.03283 12.56396 (28*2π)/61622 weeks
29-6.54309 -.21453 (29*2π)/61621 weeks
308.8087 -1.02042 (30*2π)/61621 weeks
3112.95935 10.84364 (31*2π)/61620 weeks
323.79872 20.73171 (32*2π)/61619 weeks
33-11.50743 13.20122 (33*2π)/61619 weeks
34-7.40755 -3.97427 (34*2π)/61618 weeks
3510.55765 -3.47756 (35*2π)/61618 weeks
3615.74135 13.47741 (36*2π)/61617 weeks
37-1.07815 23.57861 (37*2π)/61617 weeks
38-15.36055 8.3861 (38*2π)/61616 weeks
39-4.35805 -6.11916 (39*2π)/61616 weeks
408.25109 -1.27782 (40*2π)/61615 weeks
418.92022 9.55694 (41*2π)/61615 weeks
42-.72156 12.21618 (42*2π)/61615 weeks
43-4.04561 5.37537 (43*2π)/61614 weeks
44-.42813 1.02378 (44*2π)/61614 weeks
454.49827 1.76901 (45*2π)/61614 weeks
465.53477 7.87079 (46*2π)/61613 weeks
47-.36523 7.71922 (47*2π)/61613 weeks
48.30529 3.75639 (48*2π)/61613 weeks
491.75762 4.49499 (49*2π)/61613 weeks
501.46323 5.20354 (50*2π)/61612 weeks
51-.07915 3.88173 (51*2π)/61612 weeks
522.1963 1.44572 (52*2π)/61612 weeks
535.53895 4.11904 (53*2π)/61612 weeks
544.16288 6.38864 (54*2π)/61611 weeks
551.33825 7.42797 (55*2π)/61611 weeks
56.50271 5.36692 (56*2π)/61611 weeks
571.28555 4.09606 (57*2π)/61611 weeks
582.53571 5.80096 (58*2π)/61611 weeks
59-.39624 6.89558 (59*2π)/61610 weeks
60-2.5526 4.29278 (60*2π)/61610 weeks
61-1.66698 .26886 (61*2π)/61610 weeks
624.23135 -.91395 (62*2π)/61610 weeks
636.85844 6.01016 (63*2π)/61610 weeks
64.07685 8.08493 (64*2π)/61610 weeks
65-2.5745 3.26012 (65*2π)/6169 weeks
661.00843 .5607 (66*2π)/6169 weeks
673.49081 2.22729 (67*2π)/6169 weeks
682.13184 5.35127 (68*2π)/6169 weeks
69-.8601 2.29526 (69*2π)/6169 weeks
703.52768 .17305 (70*2π)/6169 weeks
715.40644 3.58212 (71*2π)/6169 weeks
723.46696 7.31225 (72*2π)/6169 weeks
73-1.28597 5.79093 (73*2π)/6168 weeks
74-.5764 1.2011 (74*2π)/6168 weeks
752.6877 2.43804 (75*2π)/6168 weeks
762.46192 3.30091 (76*2π)/6168 weeks
771.0585 4.3118 (77*2π)/6168 weeks
78.75554 .96227 (78*2π)/6168 weeks
795.94553 2.06368 (79*2π)/6168 weeks
804.40386 8.29034 (80*2π)/6168 weeks
81-2.23341 8.11139 (81*2π)/6168 weeks
82-4.88505 2.25813 (82*2π)/6168 weeks
83.69893 -2.819 (83*2π)/6167 weeks
845.44929 1.85473 (84*2π)/6167 weeks
852.92826 4.87103 (85*2π)/6167 weeks
86.93762 5.93046 (86*2π)/6167 weeks
87-3.17351 2.5945 (87*2π)/6167 weeks
881.36681 -2.39323 (88*2π)/6167 weeks
896.36516 2.01006 (89*2π)/6167 weeks
904.00062 6.74299 (90*2π)/6167 weeks
91-1.5761 6.97244 (91*2π)/6167 weeks
92-3.24292 1.13829 (92*2π)/6167 weeks
931.26451 -1.16751 (93*2π)/6167 weeks
945.0218 .81773 (94*2π)/6167 weeks
954.60166 6.68625 (95*2π)/6166 weeks
96-2.32846 7.04193 (96*2π)/6166 weeks
97-3.90878 .65414 (97*2π)/6166 weeks
98.74997 -2.63611 (98*2π)/6166 weeks
994.83224 .54908 (99*2π)/6166 weeks
1003.33031 4.47241 (100*2π)/6166 weeks
101.18138 3.87485 (101*2π)/6166 weeks
102-.03024 1.35597 (102*2π)/6166 weeks
1031.90715 .71114 (103*2π)/6166 weeks
1042.4197 2.52111 (104*2π)/6166 weeks
105.78472 2.51049 (105*2π)/6166 weeks
1061.74489 1.6719 (106*2π)/6166 weeks
1071.31459 3.05749 (107*2π)/6166 weeks
108-.2236 1.85761 (108*2π)/6166 weeks
109.62201 -.57626 (109*2π)/6166 weeks
1103.97407 -.61974 (110*2π)/6166 weeks
1115.26667 3.10282 (111*2π)/6166 weeks
1121.9706 5.73394 (112*2π)/6166 weeks
113-1.26683 3.32304 (113*2π)/6165 weeks
114-.00903 -.61783 (114*2π)/6165 weeks
1154.33585 -.16125 (115*2π)/6165 weeks
1164.58698 4.8021 (116*2π)/6165 weeks
117-.01568 6.19549 (117*2π)/6165 weeks
118-3.49047 2.356 (118*2π)/6165 weeks
119-.39095 -2.56219 (119*2π)/6165 weeks
1204.40251 -1.47271 (120*2π)/6165 weeks
1215.5405 3.59054 (121*2π)/6165 weeks
122.57679 6.25751 (122*2π)/6165 weeks
123-2.77208 1.65988 (123*2π)/6165 weeks
124.61184 -2.8152 (124*2π)/6165 weeks
1255.74781 -.52437 (125*2π)/6165 weeks
1265.11421 4.58497 (126*2π)/6165 weeks
1271.03962 6.00948 (127*2π)/6165 weeks
128-2.4856 2.98854 (128*2π)/6165 weeks
129-.26329 -1.55549 (129*2π)/6165 weeks
1303.81037 -.45028 (130*2π)/6165 weeks
1314.02737 3.05977 (131*2π)/6165 weeks
1321.73481 4.43824 (132*2π)/6165 weeks
133-.50968 3.07474 (133*2π)/6165 weeks
134.0106 .38257 (134*2π)/6165 weeks
1352.479 .18812 (135*2π)/6165 weeks
1363.34681 3.14751 (136*2π)/6165 weeks
137.23003 4.48164 (137*2π)/6164 weeks
138-1.94978 1.35059 (138*2π)/6164 weeks
139.99772 -1.2993 (139*2π)/6164 weeks
1403.31869 .40094 (140*2π)/6164 weeks
1412.79453 2.88298 (141*2π)/6164 weeks
142.88462 3.2001 (142*2π)/6164 weeks
143.06402 2.16855 (143*2π)/6164 weeks
144-.22115 .72201 (144*2π)/6164 weeks
1451.25947 -.31871 (145*2π)/6164 weeks
1462.68908 .7581 (146*2π)/6164 weeks
1471.67328 2.09805 (147*2π)/6164 weeks
148.7639 1.00637 (148*2π)/6164 weeks
1492.56209 .11825 (149*2π)/6164 weeks
1503.33286 1.96397 (150*2π)/6164 weeks
1511.8823 3.10016 (151*2π)/6164 weeks
152.22646 3.08665 (152*2π)/6164 weeks
153-.46158 .90163 (153*2π)/6164 weeks
1541.26127 -.10557 (154*2π)/6164 weeks
1551.70928 .42004 (155*2π)/6164 weeks
1562.69435 .56563 (156*2π)/6164 weeks
1572.74106 2.20008 (157*2π)/6164 weeks
1581.77285 2.77795 (158*2π)/6164 weeks
159-.09028 2.02085 (159*2π)/6164 weeks
1601.11196 -.6189 (160*2π)/6164 weeks
1613.62781 1.19816 (161*2π)/6164 weeks
1621.57168 3.64041 (162*2π)/6164 weeks
163-.28271 1.92522 (163*2π)/6164 weeks
164.53028 -.11478 (164*2π)/6164 weeks
1653.04347 .06212 (165*2π)/6164 weeks
1662.9048 2.95751 (166*2π)/6164 weeks
167.47491 3.14568 (167*2π)/6164 weeks
168-.75894 1.14153 (168*2π)/6164 weeks
1691.22723 -.94875 (169*2π)/6164 weeks
1703.17667 1.16406 (170*2π)/6164 weeks
1711.69937 2.39102 (171*2π)/6164 weeks
172.87402 2.05703 (172*2π)/6164 weeks
173.64459 1.23819 (173*2π)/6164 weeks
1741.08272 .78137 (174*2π)/6164 weeks
1751.53209 .7202 (175*2π)/6164 weeks
1761.95491 1.29696 (176*2π)/6164 weeks
177.9532 2.19855 (177*2π)/6163 weeks
178.2559 .44121 (178*2π)/6163 weeks
1791.81925 .31349 (179*2π)/6163 weeks
1801.89567 .79805 (180*2π)/6163 weeks
1812.34573 1.15959 (181*2π)/6163 weeks
1822.05503 2.18227 (182*2π)/6163 weeks
183.59096 2.22516 (183*2π)/6163 weeks
184.14001 .21439 (184*2π)/6163 weeks
1852.22942 -.24698 (185*2π)/6163 weeks
1863.42572 1.40299 (186*2π)/6163 weeks
1872.09616 3.63694 (187*2π)/6163 weeks
188-.6826 2.77143 (188*2π)/6163 weeks
189-.59922 .08417 (189*2π)/6163 weeks
1901.70945 -.68613 (190*2π)/6163 weeks
1912.83299 1.15115 (191*2π)/6163 weeks
1921.63043 2.43902 (192*2π)/6163 weeks
193-.09553 1.64906 (193*2π)/6163 weeks
194.35602 -.15924 (194*2π)/6163 weeks
1952.35205 -.45296 (195*2π)/6163 weeks
1963.49302 1.44335 (196*2π)/6163 weeks
1971.88598 3.37952 (197*2π)/6163 weeks
198-.50868 2.65441 (198*2π)/6163 weeks
199-.90593 .2087 (199*2π)/6163 weeks
2001.33064 -1.31104 (200*2π)/6163 weeks
2013.46839 .50464 (201*2π)/6163 weeks
2022.29045 2.81105 (202*2π)/6163 weeks
203-.13576 2.45148 (203*2π)/6163 weeks
204-.45391 .03067 (204*2π)/6163 weeks
2051.71595 -.65275 (205*2π)/6163 weeks
2062.81684 .70064 (206*2π)/6163 weeks
2071.71997 2.32211 (207*2π)/6163 weeks
208.44293 1.40825 (208*2π)/6163 weeks
209.79318 .65694 (209*2π)/6163 weeks
2101.80631 .42609 (210*2π)/6163 weeks
2111.9201 1.92313 (211*2π)/6163 weeks
212.07792 2.20747 (212*2π)/6163 weeks
213-.54366 .34081 (213*2π)/6163 weeks
214.57098 -.87958 (214*2π)/6163 weeks
2152.25941 -.69774 (215*2π)/6163 weeks
2162.77697 .73803 (216*2π)/6163 weeks
2172.65538 1.63619 (217*2π)/6163 weeks
2181.0977 3.15869 (218*2π)/6163 weeks
219-1.1197 .97402 (219*2π)/6163 weeks
220.56593 -.59911 (220*2π)/6163 weeks
2211.75432 -.3754 (221*2π)/6163 weeks
2222.29038 .80924 (222*2π)/6163 weeks
2231.36735 1.18084 (223*2π)/6163 weeks
2241.50285 .60408 (224*2π)/6163 weeks
2251.28932 1.04962 (225*2π)/6163 weeks
2261.84519 .23273 (226*2π)/6163 weeks
2272.32006 1.92553 (227*2π)/6163 weeks
2281.05613 2.1222 (228*2π)/6163 weeks
229.12657 2.16998 (229*2π)/6163 weeks
230-.98755 .14699 (230*2π)/6163 weeks
2311.28044 -1.34032 (231*2π)/6163 weeks
2323.20775 .79121 (232*2π)/6163 weeks
2331.49695 2.93355 (233*2π)/6163 weeks
234-1.21332 1.64201 (234*2π)/6163 weeks
235-.11976 -1.40565 (235*2π)/6163 weeks
2362.90149 -.52434 (236*2π)/6163 weeks
2372.37964 2.12051 (237*2π)/6163 weeks
238.05002 2.47298 (238*2π)/6163 weeks
239-1.53002 .24651 (239*2π)/6163 weeks
240.92013 -2.28401 (240*2π)/6163 weeks
2413.54775 -.23898 (241*2π)/6163 weeks
2422.40729 2.5981 (242*2π)/6163 weeks
243-.54448 2.06459 (243*2π)/6163 weeks
244-.28191 -.81801 (244*2π)/6163 weeks
2452.3197 -.56191 (245*2π)/6163 weeks
2461.90711 1.53126 (246*2π)/6163 weeks
247.32271 1.09635 (247*2π)/6162 weeks
248.67779 -.11619 (248*2π)/6162 weeks
2491.6112 -.38581 (249*2π)/6162 weeks
2502.87052 .88925 (250*2π)/6162 weeks
2511.27168 2.86507 (251*2π)/6162 weeks
252-.88308 1.41226 (252*2π)/6162 weeks
253-.1892 -.38664 (253*2π)/6162 weeks
2541.57876 -.58329 (254*2π)/6162 weeks
2551.69275 1.58665 (255*2π)/6162 weeks
256-.59427 1.26463 (256*2π)/6162 weeks
257-.56098 -.51974 (257*2π)/6162 weeks
258.81692 -1.5519 (258*2π)/6162 weeks
2592.66201 -.74218 (259*2π)/6162 weeks
2601.99746 1.40544 (260*2π)/6162 weeks
261.06934 1.22406 (261*2π)/6162 weeks
262-.33904 -.66222 (262*2π)/6162 weeks
2631.74764 -1.85675 (263*2π)/6162 weeks
2643.57301 .31415 (264*2π)/6162 weeks
2651.84009 2.4938 (265*2π)/6162 weeks
266-.30075 1.61591 (266*2π)/6162 weeks
267-.83249 -.09911 (267*2π)/6162 weeks
2681.07472 -1.93046 (268*2π)/6162 weeks
2692.47571 .08005 (269*2π)/6162 weeks
2701.69358 .85578 (270*2π)/6162 weeks
271.57732 1.23952 (271*2π)/6162 weeks
272.1785 -.24464 (272*2π)/6162 weeks
2731.07694 -.30881 (273*2π)/6162 weeks
2741.39411 -.37566 (274*2π)/6162 weeks
2752.11137 .48411 (275*2π)/6162 weeks
276.78654 1.50737 (276*2π)/6162 weeks
277-.52347 .17183 (277*2π)/6162 weeks
278-.01272 -1.28427 (278*2π)/6162 weeks
2792.21601 -1.77551 (279*2π)/6162 weeks
2803.21845 .54237 (280*2π)/6162 weeks
2811.19581 2.20372 (281*2π)/6162 weeks
282-.70668 .9899 (282*2π)/6162 weeks
283-.85777 -1.20779 (283*2π)/6162 weeks
2841.34397 -2.64487 (284*2π)/6162 weeks
2854.00633 -.6854 (285*2π)/6162 weeks
2862.84648 2.41591 (286*2π)/6162 weeks
287-.93033 2.80545 (287*2π)/6162 weeks
288-2.38562 -1.50145 (288*2π)/6162 weeks
2891.47582 -3.44757 (289*2π)/6162 weeks
2903.78901 -.93725 (290*2π)/6162 weeks
2912.81978 2.04095 (291*2π)/6162 weeks
292-.82323 1.9438 (292*2π)/6162 weeks
293-1.6205 -1.8785 (293*2π)/6162 weeks
2942.08099 -3.71358 (294*2π)/6162 weeks
2954.27389 -.25903 (295*2π)/6162 weeks
2962.07156 1.87532 (296*2π)/6162 weeks
297-.3158 .78311 (297*2π)/6162 weeks
298-.07885 -2.00921 (298*2π)/6162 weeks
2992.60752 -2.7608 (299*2π)/6162 weeks
3004.79974 -.25385 (300*2π)/6162 weeks
3012.76368 2.90256 (301*2π)/6162 weeks
302-.61186 1.21897 (302*2π)/6162 weeks
303.49754 -1.5296 (303*2π)/6162 weeks
3042.38185 -1.09697 (304*2π)/6162 weeks
3052.99005 .29882 (305*2π)/6162 weeks
3062.25636 1.35545 (306*2π)/6162 weeks
307.75806 1.85502 (307*2π)/6162 weeks
308-.85662   (308*2π)/6162 weeks
309.75806 -1.85502 (309*2π)/6162 weeks
3102.25636 -1.35545 (310*2π)/6162 weeks
3112.99005 -.29882 (311*2π)/6162 weeks
3122.38185 1.09697 (312*2π)/6162 weeks
313.49754 1.5296 (313*2π)/6162 weeks
314-.61186 -1.21897 (314*2π)/6162 weeks
3152.76368 -2.90256 (315*2π)/6162 weeks
3164.79974 .25385 (316*2π)/6162 weeks
3172.60752 2.7608 (317*2π)/6162 weeks
318-.07885 2.00921 (318*2π)/6162 weeks
319-.3158 -.78311 (319*2π)/6162 weeks
3202.07156 -1.87532 (320*2π)/6162 weeks
3214.27389 .25903 (321*2π)/6162 weeks
3222.08099 3.71358 (322*2π)/6162 weeks
323-1.6205 1.8785 (323*2π)/6162 weeks
324-.82323 -1.9438 (324*2π)/6162 weeks
3252.81978 -2.04095 (325*2π)/6162 weeks
3263.78901 .93725 (326*2π)/6162 weeks
3271.47582 3.44757 (327*2π)/6162 weeks
328-2.38562 1.50145 (328*2π)/6162 weeks
329-.93033 -2.80545 (329*2π)/6162 weeks
3302.84648 -2.41591 (330*2π)/6162 weeks
3314.00633 .6854 (331*2π)/6162 weeks
3321.34397 2.64487 (332*2π)/6162 weeks
333-.85777 1.20779 (333*2π)/6162 weeks
334-.70668 -.9899 (334*2π)/6162 weeks
3351.19581 -2.20372 (335*2π)/6162 weeks
3363.21845 -.54237 (336*2π)/6162 weeks
3372.21601 1.77551 (337*2π)/6162 weeks
338-.01272 1.28427 (338*2π)/6162 weeks
339-.52347 -.17183 (339*2π)/6162 weeks
340.78654 -1.50737 (340*2π)/6162 weeks
3412.11137 -.48411 (341*2π)/6162 weeks
3421.39411 .37566 (342*2π)/6162 weeks
3431.07694 .30881 (343*2π)/6162 weeks
344.1785 .24464 (344*2π)/6162 weeks
345.57732 -1.23952 (345*2π)/6162 weeks
3461.69358 -.85578 (346*2π)/6162 weeks
3472.47571 -.08005 (347*2π)/6162 weeks
3481.07472 1.93046 (348*2π)/6162 weeks
349-.83249 .09911 (349*2π)/6162 weeks
350-.30075 -1.61591 (350*2π)/6162 weeks
3511.84009 -2.4938 (351*2π)/6162 weeks
3523.57301 -.31415 (352*2π)/6162 weeks
3531.74764 1.85675 (353*2π)/6162 weeks
354-.33904 .66222 (354*2π)/6162 weeks
355.06934 -1.22406 (355*2π)/6162 weeks
3561.99746 -1.40544 (356*2π)/6162 weeks
3572.66201 .74218 (357*2π)/6162 weeks
358.81692 1.5519 (358*2π)/6162 weeks
359-.56098 .51974 (359*2π)/6162 weeks
360-.59427 -1.26463 (360*2π)/6162 weeks
3611.69275 -1.58665 (361*2π)/6162 weeks
3621.57876 .58329 (362*2π)/6162 weeks
363-.1892 .38664 (363*2π)/6162 weeks
364-.88308 -1.41226 (364*2π)/6162 weeks
3651.27168 -2.86507 (365*2π)/6162 weeks
3662.87052 -.88925 (366*2π)/6162 weeks
3671.6112 .38581 (367*2π)/6162 weeks
368.67779 .11619 (368*2π)/6162 weeks
369.32271 -1.09635 (369*2π)/6162 weeks
3701.90711 -1.53126 (370*2π)/6162 weeks
3712.3197 .56191 (371*2π)/6162 weeks
372-.28191 .81801 (372*2π)/6162 weeks
373-.54448 -2.06459 (373*2π)/6162 weeks
3742.40729 -2.5981 (374*2π)/6162 weeks
3753.54775 .23898 (375*2π)/6162 weeks
376.92013 2.28401 (376*2π)/6162 weeks
377-1.53002 -.24651 (377*2π)/6162 weeks
378.05002 -2.47298 (378*2π)/6162 weeks
3792.37964 -2.12051 (379*2π)/6162 weeks
3802.90149 .52434 (380*2π)/6162 weeks
381-.11976 1.40565 (381*2π)/6162 weeks
382-1.21332 -1.64201 (382*2π)/6162 weeks
3831.49695 -2.93355 (383*2π)/6162 weeks
3843.20775 -.79121 (384*2π)/6162 weeks
3851.28044 1.34032 (385*2π)/6162 weeks
386-.98755 -.14699 (386*2π)/6162 weeks
387.12657 -2.16998 (387*2π)/6162 weeks
3881.05613 -2.1222 (388*2π)/6162 weeks
3892.32006 -1.92553 (389*2π)/6162 weeks
3901.84519 -.23273 (390*2π)/6162 weeks
3911.28932 -1.04962 (391*2π)/6162 weeks
3921.50285 -.60408 (392*2π)/6162 weeks
3931.36735 -1.18084 (393*2π)/6162 weeks
3942.29038 -.80924 (394*2π)/6162 weeks
3951.75432 .3754 (395*2π)/6162 weeks
396.56593 .59911 (396*2π)/6162 weeks
397-1.1197 -.97402 (397*2π)/6162 weeks
3981.0977 -3.15869 (398*2π)/6162 weeks
3992.65538 -1.63619 (399*2π)/6162 weeks
4002.77697 -.73803 (400*2π)/6162 weeks
4012.25941 .69774 (401*2π)/6162 weeks
402.57098 .87958 (402*2π)/6162 weeks
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