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Fourier Analysis of SDOW (ProShares UltraPro Short Dow30)


SDOW (ProShares UltraPro Short Dow30) appears to have interesting cyclic behaviour every 36 weeks (30.7866*sine), 39 weeks (30.3989*sine), and 43 weeks (26.9068*sine).

SDOW (ProShares UltraPro Short Dow30) has an average price of 262.71 (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 2/11/2010 to 4/23/2018 for SDOW (ProShares UltraPro Short Dow30), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0262.7076   0 
1182.1907 228.4822 (1*2π)/429429 weeks
258.52995 163.414 (2*2π)/429215 weeks
339.40613 118.578 (3*2π)/429143 weeks
427.44194 95.3854 (4*2π)/429107 weeks
517.28381 81.12648 (5*2π)/42986 weeks
610.4614 81.46106 (6*2π)/42972 weeks
7-10.48216 69.30946 (7*2π)/42961 weeks
8-18.70065 42.66659 (8*2π)/42954 weeks
9-4.92319 28.37745 (9*2π)/42948 weeks
103.20525 26.90679 (10*2π)/42943 weeks
115.74071 30.39886 (11*2π)/42939 weeks
12-2.41935 30.78661 (12*2π)/42936 weeks
13-7.62868 17.35707 (13*2π)/42933 weeks
143.86162 12.16416 (14*2π)/42931 weeks
158.1539 16.56098 (15*2π)/42929 weeks
167.13579 15.20526 (16*2π)/42927 weeks
176.63276 15.60989 (17*2π)/42925 weeks
188.59751 17.76973 (18*2π)/42924 weeks
193.68029 13.55314 (19*2π)/42923 weeks
207.58027 10.1641 (20*2π)/42921 weeks
2112.59954 16.0652 (21*2π)/42920 weeks
229.20106 17.45606 (22*2π)/42920 weeks
234.60061 15.17547 (23*2π)/42919 weeks
244.05908 13.30039 (24*2π)/42918 weeks
258.19289 11.63618 (25*2π)/42917 weeks
269.63847 11.56135 (26*2π)/42917 weeks
278.70169 15.09227 (27*2π)/42916 weeks
285.91871 14.87515 (28*2π)/42915 weeks
296.13256 12.05847 (29*2π)/42915 weeks
307.69627 12.54391 (30*2π)/42914 weeks
319.01953 13.31744 (31*2π)/42914 weeks
328.84304 17.37338 (32*2π)/42913 weeks
333.62051 18.81717 (33*2π)/42913 weeks
34-1.26312 14.8163 (34*2π)/42913 weeks
35.87645 9.51029 (35*2π)/42912 weeks
363.47288 9.73856 (36*2π)/42912 weeks
375.04959 12.30379 (37*2π)/42912 weeks
381.85909 11.21884 (38*2π)/42911 weeks
392.30877 10.98471 (39*2π)/42911 weeks
401.19545 9.92529 (40*2π)/42911 weeks
411.08129 6.8399 (41*2π)/42910 weeks
423.25978 6.84546 (42*2π)/42910 weeks
434.55763 7.30808 (43*2π)/42910 weeks
446.05194 8.5688 (44*2π)/42910 weeks
454.55851 9.96184 (45*2π)/42910 weeks
463.43965 11.09047 (46*2π)/4299 weeks
47.7519 10.1029 (47*2π)/4299 weeks
48.09742 7.51018 (48*2π)/4299 weeks
492.54675 5.73416 (49*2π)/4299 weeks
503.17473 7.62698 (50*2π)/4299 weeks
513.19188 8.13673 (51*2π)/4298 weeks
52-1.05558 9.19197 (52*2π)/4298 weeks
53-1.18696 3.11541 (53*2π)/4298 weeks
543.53226 2.33073 (54*2π)/4298 weeks
554.23344 4.68757 (55*2π)/4298 weeks
564.03252 5.58944 (56*2π)/4298 weeks
571.93794 6.05949 (57*2π)/4298 weeks
581.77612 3.38692 (58*2π)/4297 weeks
593.0809 .86997 (59*2π)/4297 weeks
608.43548 1.53626 (60*2π)/4297 weeks
619.14988 6.13616 (61*2π)/4297 weeks
626.38446 8.62816 (62*2π)/4297 weeks
633.80389 7.67066 (63*2π)/4297 weeks
644.2319 5.59808 (64*2π)/4297 weeks
656.13114 7.10892 (65*2π)/4297 weeks
664.39189 9.05235 (66*2π)/4297 weeks
672.03875 8.27747 (67*2π)/4296 weeks
682.35215 6.51571 (68*2π)/4296 weeks
691.59098 7.01575 (69*2π)/4296 weeks
701.57643 5.91849 (70*2π)/4296 weeks
712.00319 5.10424 (71*2π)/4296 weeks
721.62537 5.45248 (72*2π)/4296 weeks
73.49356 4.34103 (73*2π)/4296 weeks
741.62206 2.68492 (74*2π)/4296 weeks
753.35642 3.24658 (75*2π)/4296 weeks
763.14355 3.30184 (76*2π)/4296 weeks
773.27796 3.48833 (77*2π)/4296 weeks
782.92098 3.6876 (78*2π)/4296 weeks
794.00959 3.52136 (79*2π)/4295 weeks
803.34314 3.4758 (80*2π)/4295 weeks
813.65669 3.67478 (81*2π)/4295 weeks
823.49307 3.24627 (82*2π)/4295 weeks
835.12677 3.27284 (83*2π)/4295 weeks
844.62572 4.73509 (84*2π)/4295 weeks
853.73255 5.35703 (85*2π)/4295 weeks
863.95277 4.64174 (86*2π)/4295 weeks
873.40286 5.35772 (87*2π)/4295 weeks
882.60437 5.7759 (88*2π)/4295 weeks
891.29592 4.80372 (89*2π)/4295 weeks
901.84257 3.42417 (90*2π)/4295 weeks
911.83249 3.24639 (91*2π)/4295 weeks
922.97856 3.41008 (92*2π)/4295 weeks
932.98927 4.10439 (93*2π)/4295 weeks
941.49272 3.42449 (94*2π)/4295 weeks
952.09299 3.22127 (95*2π)/4295 weeks
961.79537 2.81275 (96*2π)/4294 weeks
972.69918 2.24495 (97*2π)/4294 weeks
982.19991 2.96254 (98*2π)/4294 weeks
991.94659 2.59145 (99*2π)/4294 weeks
1002.14216 1.77289 (100*2π)/4294 weeks
1012.35927 1.6207 (101*2π)/4294 weeks
1022.54839 1.10475 (102*2π)/4294 weeks
1033.09856 1.16073 (103*2π)/4294 weeks
1043.96236 .54794 (104*2π)/4294 weeks
1054.5907 .39428 (105*2π)/4294 weeks
1065.6839 2.11946 (106*2π)/4294 weeks
1075.36088 3.1034 (107*2π)/4294 weeks
1083.8626 3.08722 (108*2π)/4294 weeks
1093.80973 2.26997 (109*2π)/4294 weeks
1105.55647 2.14356 (110*2π)/4294 weeks
1115.92397 3.76979 (111*2π)/4294 weeks
1124.53375 4.80501 (112*2π)/4294 weeks
1133.11296 5.1852 (113*2π)/4294 weeks
1142.84711 4.03272 (114*2π)/4294 weeks
1152.94421 3.54519 (115*2π)/4294 weeks
1163.211 4.47094 (116*2π)/4294 weeks
1171.83085 4.61727 (117*2π)/4294 weeks
118.77336 3.62357 (118*2π)/4294 weeks
1191.15479 2.16661 (119*2π)/4294 weeks
1202.1928 2.33139 (120*2π)/4294 weeks
1211.90017 3.01261 (121*2π)/4294 weeks
1221.11379 2.47075 (122*2π)/4294 weeks
123.18421 1.83799 (123*2π)/4293 weeks
124.94458 -.26744 (124*2π)/4293 weeks
1252.94759 -.18618 (125*2π)/4293 weeks
1263.56647 .56483 (126*2π)/4293 weeks
1273.33158 1.10002 (127*2π)/4293 weeks
1283.8184 .37384 (128*2π)/4293 weeks
1294.62555 1.99345 (129*2π)/4293 weeks
1303.03949 2.61122 (130*2π)/4293 weeks
1312.90466 1.71624 (131*2π)/4293 weeks
1323.13122 1.63218 (132*2π)/4293 weeks
1333.20257 1.85562 (133*2π)/4293 weeks
1343.18729 1.46569 (134*2π)/4293 weeks
1353.08425 2.31047 (135*2π)/4293 weeks
1362.56224 1.72609 (136*2π)/4293 weeks
1372.75909 1.18768 (137*2π)/4293 weeks
1382.97866 1.15921 (138*2π)/4293 weeks
1393.40534 1.42145 (139*2π)/4293 weeks
1402.92026 1.67869 (140*2π)/4293 weeks
1412.51902 1.23923 (141*2π)/4293 weeks
1422.98077 .51171 (142*2π)/4293 weeks
1433.88286 1.21823 (143*2π)/4293 weeks
1442.70808 1.72123 (144*2π)/4293 weeks
1452.2524 .68405 (145*2π)/4293 weeks
1463.54069 -.02289 (146*2π)/4293 weeks
1474.06759 .6835 (147*2π)/4293 weeks
1483.706 1.64858 (148*2π)/4293 weeks
1492.93675 1.02176 (149*2π)/4293 weeks
1502.86558 -.02085 (150*2π)/4293 weeks
1514.70984 -.49297 (151*2π)/4293 weeks
1526.12745 1.17469 (152*2π)/4293 weeks
1534.57521 3.5086 (153*2π)/4293 weeks
1542.68226 2.75123 (154*2π)/4293 weeks
1552.55555 1.37557 (155*2π)/4293 weeks
1563.74883 .3756 (156*2π)/4293 weeks
1575.12929 2.19724 (157*2π)/4293 weeks
1583.48965 4.27796 (158*2π)/4293 weeks
1591.2527 3.36338 (159*2π)/4293 weeks
1601.11101 1.39794 (160*2π)/4293 weeks
1611.5137 .81806 (161*2π)/4293 weeks
1622.39444 .77589 (162*2π)/4293 weeks
1632.40302 1.2945 (163*2π)/4293 weeks
1641.71517 1.41548 (164*2π)/4293 weeks
1651.06794 .20246 (165*2π)/4293 weeks
1661.64963 -.8747 (166*2π)/4293 weeks
1673.46912 -.90949 (167*2π)/4293 weeks
1683.33915 .25186 (168*2π)/4293 weeks
1692.73051 .54484 (169*2π)/4293 weeks
1702.62162 .07093 (170*2π)/4293 weeks
1712.52277 -.46402 (171*2π)/4293 weeks
1723.01956 -.78755 (172*2π)/4292 weeks
1733.75665 -1.18918 (173*2π)/4292 weeks
1744.66756 -.4602 (174*2π)/4292 weeks
1754.72695 .7139 (175*2π)/4292 weeks
1763.50946 1.44876 (176*2π)/4292 weeks
1772.77857 -.05533 (177*2π)/4292 weeks
1783.82599 -.90945 (178*2π)/4292 weeks
1794.9781 .3681 (179*2π)/4292 weeks
1804.65815 1.35802 (180*2π)/4292 weeks
1813.30355 1.25819 (181*2π)/4292 weeks
1823.23458 .65081 (182*2π)/4292 weeks
1833.51513 .41115 (183*2π)/4292 weeks
1843.77865 .47543 (184*2π)/4292 weeks
1854.04644 .9809 (185*2π)/4292 weeks
1863.25027 1.68706 (186*2π)/4292 weeks
1872.25699 .1006 (187*2π)/4292 weeks
1883.79672 -.55402 (188*2π)/4292 weeks
1894.76603 .85138 (189*2π)/4292 weeks
1903.46076 1.82282 (190*2π)/4292 weeks
1912.36187 1.25849 (191*2π)/4292 weeks
1922.44126 .14516 (192*2π)/4292 weeks
1932.85958 -1.02357 (193*2π)/4292 weeks
1944.50556 -.07683 (194*2π)/4292 weeks
1954.19596 .57948 (195*2π)/4292 weeks
1963.6773 1.09365 (196*2π)/4292 weeks
1973.61849 .76416 (197*2π)/4292 weeks
1983.45167 1.06774 (198*2π)/4292 weeks
1993.89974 .88151 (199*2π)/4292 weeks
2003.47314 2.14142 (200*2π)/4292 weeks
2011.86505 2.24816 (201*2π)/4292 weeks
202.77955 1.08837 (202*2π)/4292 weeks
2031.23259 -.18087 (203*2π)/4292 weeks
2041.56118 -.69306 (204*2π)/4292 weeks
2051.59884 -1.55628 (205*2π)/4292 weeks
2062.67245 -1.29521 (206*2π)/4292 weeks
2072.67605 -1.39982 (207*2π)/4292 weeks
2082.58118 -2.24947 (208*2π)/4292 weeks
2093.99492 -2.36379 (209*2π)/4292 weeks
2105.23296 -1.82382 (210*2π)/4292 weeks
2114.75661 -.9812 (211*2π)/4292 weeks
2124.48013 -.33138 (212*2π)/4292 weeks
2134.68117 -1.01744 (213*2π)/4292 weeks
2145.72215 -.91956 (214*2π)/4292 weeks
2155.72215 .91956 (215*2π)/4292 weeks
2164.68117 1.01744 (216*2π)/4292 weeks
2174.48013 .33138 (217*2π)/4292 weeks
2184.75661 .9812 (218*2π)/4292 weeks
2195.23296 1.82382 (219*2π)/4292 weeks
2203.99492 2.36379 (220*2π)/4292 weeks
2212.58118 2.24947 (221*2π)/4292 weeks
2222.67605 1.39982 (222*2π)/4292 weeks
2232.67245 1.29521 (223*2π)/4292 weeks
2241.59884 1.55628 (224*2π)/4292 weeks
2251.56118 .69306 (225*2π)/4292 weeks
2261.23259 .18087 (226*2π)/4292 weeks
227.77955 -1.08837 (227*2π)/4292 weeks
2281.86505 -2.24816 (228*2π)/4292 weeks
2293.47314 -2.14142 (229*2π)/4292 weeks
2303.89974 -.88151 (230*2π)/4292 weeks
2313.45167 -1.06774 (231*2π)/4292 weeks
2323.61849 -.76416 (232*2π)/4292 weeks
2333.6773 -1.09365 (233*2π)/4292 weeks
2344.19596 -.57948 (234*2π)/4292 weeks
2354.50556 .07683 (235*2π)/4292 weeks
2362.85958 1.02357 (236*2π)/4292 weeks
2372.44126 -.14516 (237*2π)/4292 weeks
2382.36187 -1.25849 (238*2π)/4292 weeks
2393.46076 -1.82282 (239*2π)/4292 weeks
2404.76603 -.85138 (240*2π)/4292 weeks
2413.79672 .55402 (241*2π)/4292 weeks
2422.25699 -.1006 (242*2π)/4292 weeks
2433.25027 -1.68706 (243*2π)/4292 weeks
2444.04644 -.9809 (244*2π)/4292 weeks
2453.77865 -.47543 (245*2π)/4292 weeks
2463.51513 -.41115 (246*2π)/4292 weeks
2473.23458 -.65081 (247*2π)/4292 weeks
2483.30355 -1.25819 (248*2π)/4292 weeks
2494.65815 -1.35802 (249*2π)/4292 weeks
2504.9781 -.3681 (250*2π)/4292 weeks
2513.82599 .90945 (251*2π)/4292 weeks
2522.77857 .05533 (252*2π)/4292 weeks
2533.50946 -1.44876 (253*2π)/4292 weeks
2544.72695 -.7139 (254*2π)/4292 weeks
2554.66756 .4602 (255*2π)/4292 weeks
2563.75665 1.18918 (256*2π)/4292 weeks
2573.01956 .78755 (257*2π)/4292 weeks
2582.52277 .46402 (258*2π)/4292 weeks
2592.62162 -.07093 (259*2π)/4292 weeks
2602.73051 -.54484 (260*2π)/4292 weeks
2613.33915 -.25186 (261*2π)/4292 weeks
2623.46912 .90949 (262*2π)/4292 weeks
2631.64963 .8747 (263*2π)/4292 weeks
2641.06794 -.20246 (264*2π)/4292 weeks
2651.71517 -1.41548 (265*2π)/4292 weeks
2662.40302 -1.2945 (266*2π)/4292 weeks
2672.39444 -.77589 (267*2π)/4292 weeks
2681.5137 -.81806 (268*2π)/4292 weeks
2691.11101 -1.39794 (269*2π)/4292 weeks
2701.2527 -3.36338 (270*2π)/4292 weeks
2713.48965 -4.27796 (271*2π)/4292 weeks
2725.12929 -2.19724 (272*2π)/4292 weeks
2733.74883 -.3756 (273*2π)/4292 weeks
2742.55555 -1.37557 (274*2π)/4292 weeks
2752.68226 -2.75123 (275*2π)/4292 weeks
2764.57521 -3.5086 (276*2π)/4292 weeks
2776.12745 -1.17469 (277*2π)/4292 weeks
2784.70984 .49297 (278*2π)/4292 weeks
2792.86558 .02085 (279*2π)/4292 weeks
2802.93675 -1.02176 (280*2π)/4292 weeks
2813.706 -1.64858 (281*2π)/4292 weeks
2824.06759 -.6835 (282*2π)/4292 weeks
2833.54069 .02289 (283*2π)/4292 weeks
2842.2524 -.68405 (284*2π)/4292 weeks
2852.70808 -1.72123 (285*2π)/4292 weeks
2863.88286 -1.21823 (286*2π)/4292 weeks
2872.98077 -.51171 (287*2π)/4291 weeks
2882.51902 -1.23923 (288*2π)/4291 weeks
2892.92026 -1.67869 (289*2π)/4291 weeks
2903.40534 -1.42145 (290*2π)/4291 weeks
2912.97866 -1.15921 (291*2π)/4291 weeks
2922.75909 -1.18768 (292*2π)/4291 weeks
2932.56224 -1.72609 (293*2π)/4291 weeks
2943.08425 -2.31047 (294*2π)/4291 weeks
2953.18729 -1.46569 (295*2π)/4291 weeks
2963.20257 -1.85562 (296*2π)/4291 weeks
2973.13122 -1.63218 (297*2π)/4291 weeks
2982.90466 -1.71624 (298*2π)/4291 weeks
2993.03949 -2.61122 (299*2π)/4291 weeks
3004.62555 -1.99345 (300*2π)/4291 weeks
3013.8184 -.37384 (301*2π)/4291 weeks
3023.33158 -1.10002 (302*2π)/4291 weeks
3033.56647 -.56483 (303*2π)/4291 weeks
3042.94759 .18618 (304*2π)/4291 weeks
305.94458 .26744 (305*2π)/4291 weeks
306.18421 -1.83799 (306*2π)/4291 weeks
3071.11379 -2.47075 (307*2π)/4291 weeks
3081.90017 -3.01261 (308*2π)/4291 weeks
3092.1928 -2.33139 (309*2π)/4291 weeks
3101.15479 -2.16661 (310*2π)/4291 weeks
311.77336 -3.62357 (311*2π)/4291 weeks
3121.83085 -4.61727 (312*2π)/4291 weeks
3133.211 -4.47094 (313*2π)/4291 weeks
3142.94421 -3.54519 (314*2π)/4291 weeks
3152.84711 -4.03272 (315*2π)/4291 weeks
3163.11296 -5.1852 (316*2π)/4291 weeks
3174.53375 -4.80501 (317*2π)/4291 weeks
3185.92397 -3.76979 (318*2π)/4291 weeks
3195.55647 -2.14356 (319*2π)/4291 weeks
3203.80973 -2.26997 (320*2π)/4291 weeks
3213.8626 -3.08722 (321*2π)/4291 weeks
3225.36088 -3.1034 (322*2π)/4291 weeks
3235.6839 -2.11946 (323*2π)/4291 weeks
3244.5907 -.39428 (324*2π)/4291 weeks
3253.96236 -.54794 (325*2π)/4291 weeks
3263.09856 -1.16073 (326*2π)/4291 weeks
3272.54839 -1.10475 (327*2π)/4291 weeks
3282.35927 -1.6207 (328*2π)/4291 weeks
3292.14216 -1.77289 (329*2π)/4291 weeks
3301.94659 -2.59145 (330*2π)/4291 weeks
3312.19991 -2.96254 (331*2π)/4291 weeks
3322.69918 -2.24495 (332*2π)/4291 weeks
3331.79537 -2.81275 (333*2π)/4291 weeks
3342.09299 -3.22127 (334*2π)/4291 weeks
3351.49272 -3.42449 (335*2π)/4291 weeks
3362.98927 -4.10439 (336*2π)/4291 weeks
3372.97856 -3.41008 (337*2π)/4291 weeks
3381.83249 -3.24639 (338*2π)/4291 weeks
3391.84257 -3.42417 (339*2π)/4291 weeks
3401.29592 -4.80372 (340*2π)/4291 weeks
3412.60437 -5.7759 (341*2π)/4291 weeks
3423.40286 -5.35772 (342*2π)/4291 weeks
3433.95277 -4.64174 (343*2π)/4291 weeks
3443.73255 -5.35703 (344*2π)/4291 weeks
3454.62572 -4.73509 (345*2π)/4291 weeks
3465.12677 -3.27284 (346*2π)/4291 weeks
3473.49307 -3.24627 (347*2π)/4291 weeks
3483.65669 -3.67478 (348*2π)/4291 weeks
3493.34314 -3.4758 (349*2π)/4291 weeks
3504.00959 -3.52136 (350*2π)/4291 weeks
3512.92098 -3.6876 (351*2π)/4291 weeks
3523.27796 -3.48833 (352*2π)/4291 weeks
3533.14355 -3.30184 (353*2π)/4291 weeks
3543.35642 -3.24658 (354*2π)/4291 weeks
3551.62206 -2.68492 (355*2π)/4291 weeks
356.49356 -4.34103 (356*2π)/4291 weeks
3571.62537 -5.45248 (357*2π)/4291 weeks
3582.00319 -5.10424 (358*2π)/4291 weeks
3591.57643 -5.91849 (359*2π)/4291 weeks
3601.59098 -7.01575 (360*2π)/4291 weeks
3612.35215 -6.51571 (361*2π)/4291 weeks
3622.03875 -8.27747 (362*2π)/4291 weeks
3634.39189 -9.05235 (363*2π)/4291 weeks
3646.13114 -7.10892 (364*2π)/4291 weeks
3654.2319 -5.59808 (365*2π)/4291 weeks
3663.80389 -7.67066 (366*2π)/4291 weeks
3676.38446 -8.62816 (367*2π)/4291 weeks
3689.14988 -6.13616 (368*2π)/4291 weeks
3698.43548 -1.53626 (369*2π)/4291 weeks
3703.0809 -.86997 (370*2π)/4291 weeks
3711.77612 -3.38692 (371*2π)/4291 weeks
3721.93794 -6.05949 (372*2π)/4291 weeks
3734.03252 -5.58944 (373*2π)/4291 weeks
3744.23344 -4.68757 (374*2π)/4291 weeks
3753.53226 -2.33073 (375*2π)/4291 weeks
376-1.18696 -3.11541 (376*2π)/4291 weeks
377-1.05558 -9.19197 (377*2π)/4291 weeks
3783.19188 -8.13673 (378*2π)/4291 weeks
3793.17473 -7.62698 (379*2π)/4291 weeks
3802.54675 -5.73416 (380*2π)/4291 weeks
381.09742 -7.51018 (381*2π)/4291 weeks
382.7519 -10.1029 (382*2π)/4291 weeks
3833.43965 -11.09047 (383*2π)/4291 weeks
3844.55851 -9.96184 (384*2π)/4291 weeks
3856.05194 -8.5688 (385*2π)/4291 weeks
3864.55763 -7.30808 (386*2π)/4291 weeks
3873.25978 -6.84546 (387*2π)/4291 weeks
3881.08129 -6.8399 (388*2π)/4291 weeks
3891.19545 -9.92529 (389*2π)/4291 weeks
3902.30877 -10.98471 (390*2π)/4291 weeks
3911.85909 -11.21884 (391*2π)/4291 weeks
3925.04959 -12.30379 (392*2π)/4291 weeks
3933.47288 -9.73856 (393*2π)/4291 weeks
394.87645 -9.51029 (394*2π)/4291 weeks
395-1.26312 -14.8163 (395*2π)/4291 weeks
3963.62051 -18.81717 (396*2π)/4291 weeks
3978.84304 -17.37338 (397*2π)/4291 weeks
3989.01953 -13.31744 (398*2π)/4291 weeks
3997.69627 -12.54391 (399*2π)/4291 weeks
4006.13256 -12.05847 (400*2π)/4291 weeks
4015.91871 -14.87515 (401*2π)/4291 weeks
4028.70169 -15.09227 (402*2π)/4291 weeks
4039.63847 -11.56135 (403*2π)/4291 weeks
4048.19289 -11.63618 (404*2π)/4291 weeks
4054.05908 -13.30039 (405*2π)/4291 weeks
4064.60061 -15.17547 (406*2π)/4291 weeks
4079.20106 -17.45606 (407*2π)/4291 weeks
40812.59954 -16.0652 (408*2π)/4291 weeks
4097.58027 -10.1641 (409*2π)/4291 weeks
4103.68029 -13.55314 (410*2π)/4291 weeks
4118.59751 -17.76973 (411*2π)/4291 weeks
4126.63276 -15.60989 (412*2π)/4291 weeks
4137.13579 -15.20526 (413*2π)/4291 weeks
4148.1539 -16.56098 (414*2π)/4291 weeks
4153.86162 -12.16416 (415*2π)/4291 weeks
416-7.62868 -17.35707 (416*2π)/4291 weeks
417-2.41935 -30.78661 (417*2π)/4291 weeks
4185.74071 -30.39886 (418*2π)/4291 weeks
4193.20525 -26.90679 (419*2π)/4291 weeks
420-4.92319 -28.37745 (420*2π)/4291 weeks
421-18.70065 -42.66659 (421*2π)/4291 weeks
422-10.48216 -69.30946 (422*2π)/4291 weeks
42310.4614 -81.46106 (423*2π)/4291 weeks
42417.28381 -81.12648 (424*2π)/4291 weeks
42527.44194 -95.3854 (425*2π)/4291 weeks
42639.40613 -118.578 (426*2π)/4291 weeks
42758.52995 -163.414 (427*2π)/4291 weeks



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