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Fourier Analysis of BIS (ProShares UltraShort Nasdaq Biotech)


BIS (ProShares UltraShort Nasdaq Biotech) appears to have interesting cyclic behaviour every 35 weeks (53.2782*sine), 33 weeks (45.2772*sine), and 39 weeks (42.5704*sine).

BIS (ProShares UltraShort Nasdaq Biotech) has an average price of 315.84 (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 4/8/2010 to 5/21/2018 for BIS (ProShares UltraShort Nasdaq Biotech), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0315.8354   0 
1285.9263 328.9298 (1*2π)/425425 weeks
264.50101 233.585 (2*2π)/425213 weeks
328.21802 154.7357 (3*2π)/425142 weeks
424.25697 113.3701 (4*2π)/425106 weeks
527.39962 91.37326 (5*2π)/42585 weeks
622.82255 103.105 (6*2π)/42571 weeks
7-5.73052 92.47851 (7*2π)/42561 weeks
8-15.63535 64.18238 (8*2π)/42553 weeks
9-8.4816 46.48129 (9*2π)/42547 weeks
10.17248 41.70785 (10*2π)/42543 weeks
117.91999 42.57035 (11*2π)/42539 weeks
122.40518 53.27817 (12*2π)/42535 weeks
13-16.8433 45.27722 (13*2π)/42533 weeks
14-14.73214 27.68127 (14*2π)/42530 weeks
15-5.77218 22.18482 (15*2π)/42528 weeks
16-2.96167 22.68449 (16*2π)/42527 weeks
17-3.2432 19.18558 (17*2π)/42525 weeks
183.61594 19.06579 (18*2π)/42524 weeks
19.85927 22.51691 (19*2π)/42522 weeks
20-1.13889 22.82706 (20*2π)/42521 weeks
21-4.81851 20.18946 (21*2π)/42520 weeks
22-3.17059 13.88608 (22*2π)/42519 weeks
23-2.77784 11.91506 (23*2π)/42518 weeks
244.10026 10.2991 (24*2π)/42518 weeks
256.46115 15.90026 (25*2π)/42517 weeks
26.73051 17.16819 (26*2π)/42516 weeks
27-.55685 12.81036 (27*2π)/42516 weeks
284.86178 13.12997 (28*2π)/42515 weeks
292.27805 16.72248 (29*2π)/42515 weeks
301.71421 14.12558 (30*2π)/42514 weeks
31.3648 17.90121 (31*2π)/42514 weeks
32-6.32825 14.44825 (32*2π)/42513 weeks
33-6.08199 5.80369 (33*2π)/42513 weeks
342.40626 3.46142 (34*2π)/42513 weeks
354.8511 8.56144 (35*2π)/42512 weeks
363.29034 9.77197 (36*2π)/42512 weeks
372.76548 9.81712 (37*2π)/42511 weeks
382.50433 11.32387 (38*2π)/42511 weeks
39-1.56077 10.29886 (39*2π)/42511 weeks
40.56182 3.93312 (40*2π)/42511 weeks
417.81366 6.67686 (41*2π)/42510 weeks
425.21272 12.67268 (42*2π)/42510 weeks
431.95612 11.74721 (43*2π)/42510 weeks
44-.08905 12.11646 (44*2π)/42510 weeks
45-2.68303 10.02188 (45*2π)/4259 weeks
46-3.01535 6.24071 (46*2π)/4259 weeks
47.91673 3.18309 (47*2π)/4259 weeks
483.97294 6.58067 (48*2π)/4259 weeks
49.90894 9.61258 (49*2π)/4259 weeks
50-.62436 6.42441 (50*2π)/4259 weeks
51.63457 7.67949 (51*2π)/4258 weeks
52-3.42726 5.25172 (52*2π)/4258 weeks
53-.26553 .45889 (53*2π)/4258 weeks
543.01245 3.04822 (54*2π)/4258 weeks
552.85589 5.35407 (55*2π)/4258 weeks
561.65874 4.21187 (56*2π)/4258 weeks
571.22169 4.30937 (57*2π)/4257 weeks
58-1.66513 3.5597 (58*2π)/4257 weeks
59.26959 -2.60388 (59*2π)/4257 weeks
607.92848 -2.50862 (60*2π)/4257 weeks
619.31609 4.44948 (61*2π)/4257 weeks
624.88893 6.31282 (62*2π)/4257 weeks
634.0491 4.27851 (63*2π)/4257 weeks
643.54293 4.15468 (64*2π)/4257 weeks
654.0465 1.69946 (65*2π)/4257 weeks
667.7344 3.07039 (66*2π)/4256 weeks
677.93293 6.43427 (67*2π)/4256 weeks
685.03996 7.62054 (68*2π)/4256 weeks
692.84641 6.78607 (69*2π)/4256 weeks
703.84171 5.58483 (70*2π)/4256 weeks
714.04737 6.4045 (71*2π)/4256 weeks
723.24766 5.80056 (72*2π)/4256 weeks
733.06178 6.24682 (73*2π)/4256 weeks
741.69616 6.67992 (74*2π)/4256 weeks
75.48947 3.96564 (75*2π)/4256 weeks
763.4049 2.67736 (76*2π)/4256 weeks
774.02964 5.50271 (77*2π)/4256 weeks
78.73187 5.81219 (78*2π)/4255 weeks
791.62166 2.38733 (79*2π)/4255 weeks
803.32233 3.09494 (80*2π)/4255 weeks
813.07983 3.72007 (81*2π)/4255 weeks
822.88024 3.62123 (82*2π)/4255 weeks
833.57994 3.25316 (83*2π)/4255 weeks
842.61572 3.76738 (84*2π)/4255 weeks
852.65955 2.0883 (85*2π)/4255 weeks
865.19741 1.83108 (86*2π)/4255 weeks
875.72462 5.1144 (87*2π)/4255 weeks
883.09132 5.77122 (88*2π)/4255 weeks
892.45672 3.82201 (89*2π)/4255 weeks
903.66292 4.11711 (90*2π)/4255 weeks
912.58452 5.28894 (91*2π)/4255 weeks
921.95143 3.92842 (92*2π)/4255 weeks
933.02844 3.55976 (93*2π)/4255 weeks
941.31785 5.08331 (94*2π)/4255 weeks
95.12756 1.78138 (95*2π)/4254 weeks
963.68473 .94067 (96*2π)/4254 weeks
973.71789 3.68032 (97*2π)/4254 weeks
981.42067 3.58318 (98*2π)/4254 weeks
992.24816 1.05434 (99*2π)/4254 weeks
1003.39547 2.19755 (100*2π)/4254 weeks
1012.86557 1.88002 (101*2π)/4254 weeks
1023.70623 1.69175 (102*2π)/4254 weeks
1034.39773 2.43702 (103*2π)/4254 weeks
1043.71072 2.47404 (104*2π)/4254 weeks
1053.59924 2.36474 (105*2π)/4254 weeks
1064.61501 2.38133 (106*2π)/4254 weeks
1073.32333 4.14635 (107*2π)/4254 weeks
1082.14657 1.63243 (108*2π)/4254 weeks
1095.44389 .57756 (109*2π)/4254 weeks
1106.39962 3.06351 (110*2π)/4254 weeks
1115.04223 4.43597 (111*2π)/4254 weeks
1124.65064 4.93657 (112*2π)/4254 weeks
1133.92063 5.97829 (113*2π)/4254 weeks
1141.09735 5.83339 (114*2π)/4254 weeks
115.87301 2.67755 (115*2π)/4254 weeks
1163.46473 2.76472 (116*2π)/4254 weeks
1172.3001 4.98467 (117*2π)/4254 weeks
118.36176 3.57285 (118*2π)/4254 weeks
1191.53248 2.12679 (119*2π)/4254 weeks
1201.07137 2.40647 (120*2π)/4254 weeks
1211.27169 .487 (121*2π)/4254 weeks
1224.56644 .87084 (122*2π)/4253 weeks
1233.78548 4.61072 (123*2π)/4253 weeks
124.19644 3.54313 (124*2π)/4253 weeks
1251.08455 .88271 (125*2π)/4253 weeks
1262.67046 1.60606 (126*2π)/4253 weeks
1271.11706 1.4137 (127*2π)/4253 weeks
1282.29845 -.63318 (128*2π)/4253 weeks
1294.77199 .75589 (129*2π)/4253 weeks
1303.12375 2.84633 (130*2π)/4253 weeks
1312.02641 .6722 (131*2π)/4253 weeks
1324.09889 .55857 (132*2π)/4253 weeks
1333.61665 2.40629 (133*2π)/4253 weeks
1342.45851 .89046 (134*2π)/4253 weeks
1354.70179 -.34548 (135*2π)/4253 weeks
1365.9689 2.48708 (136*2π)/4253 weeks
1373.99154 3.61716 (137*2π)/4253 weeks
1383.24417 2.51966 (138*2π)/4253 weeks
1393.59563 2.97269 (139*2π)/4253 weeks
1402.32425 2.96338 (140*2π)/4253 weeks
1412.82243 1.24108 (141*2π)/4253 weeks
1424.05663 2.33017 (142*2π)/4253 weeks
1433.19061 3.3079 (143*2π)/4253 weeks
1442.33739 2.39745 (144*2π)/4253 weeks
1453.35173 1.68785 (145*2π)/4253 weeks
1463.83376 3.04918 (146*2π)/4253 weeks
1472.11937 3.04033 (147*2π)/4253 weeks
1483.17105 1.78914 (148*2π)/4253 weeks
1494.39753 3.66182 (149*2π)/4253 weeks
1502.22297 5.12461 (150*2π)/4253 weeks
151.30334 3.67288 (151*2π)/4253 weeks
152.84862 2.05818 (152*2π)/4253 weeks
1531.02381 2.10638 (153*2π)/4253 weeks
1541.65758 .89683 (154*2π)/4253 weeks
1553.94918 2.51322 (155*2π)/4253 weeks
1561.01356 5.10688 (156*2π)/4253 weeks
157-1.82156 2.0739 (157*2π)/4253 weeks
158.6305 -.27477 (158*2π)/4253 weeks
1591.48069 1.73527 (159*2π)/4253 weeks
160.36144 .93452 (160*2π)/4253 weeks
1611.58114 .25098 (161*2π)/4253 weeks
1621.32119 1.81125 (162*2π)/4253 weeks
163-1.42823 1.07788 (163*2π)/4253 weeks
164-.35305 -2.54571 (164*2π)/4253 weeks
1653.17686 -2.45308 (165*2π)/4253 weeks
1663.40501 .46015 (166*2π)/4253 weeks
1672.10469 -.11676 (167*2π)/4253 weeks
1683.21595 -.08838 (168*2π)/4253 weeks
1692.45046 1.54641 (169*2π)/4253 weeks
170.96852 .31387 (170*2π)/4253 weeks
1712.09129 -1.00984 (171*2π)/4252 weeks
1722.6477 .20398 (172*2π)/4252 weeks
1731.72427 -.1604 (173*2π)/4252 weeks
1742.83382 -.72964 (174*2π)/4252 weeks
1753.16843 1.03402 (175*2π)/4252 weeks
176.87124 .94142 (176*2π)/4252 weeks
1771.21258 -1.64984 (177*2π)/4252 weeks
1783.20915 -1.13854 (178*2π)/4252 weeks
1792.28091 .37932 (179*2π)/4252 weeks
1801.33189 -1.55708 (180*2π)/4252 weeks
1813.82556 -2.07028 (181*2π)/4252 weeks
1823.86064 .06674 (182*2π)/4252 weeks
1832.02303 -.50243 (183*2π)/4252 weeks
1843.42791 -2.03056 (184*2π)/4252 weeks
1855.47498 -.01988 (185*2π)/4252 weeks
1863.04147 1.57758 (186*2π)/4252 weeks
1871.96393 -.01667 (187*2π)/4252 weeks
1882.81378 -.51804 (188*2π)/4252 weeks
1892.21348 -.6351 (189*2π)/4252 weeks
1903.22798 -1.86482 (190*2π)/4252 weeks
1915.24425 -.48055 (191*2π)/4252 weeks
1923.4046 1.31953 (192*2π)/4252 weeks
1932.05039 -.29587 (193*2π)/4252 weeks
1943.49636 -1.0351 (194*2π)/4252 weeks
1953.81207 .06976 (195*2π)/4252 weeks
1962.78658 -.52162 (196*2π)/4252 weeks
1974.56947 -.69226 (197*2π)/4252 weeks
1983.89077 1.82997 (198*2π)/4252 weeks
199.73107 .9651 (199*2π)/4252 weeks
2001.5758 -2.54555 (200*2π)/4252 weeks
2014.76475 -1.5836 (201*2π)/4252 weeks
2023.04959 .49266 (202*2π)/4252 weeks
2032.59618 -2.25412 (203*2π)/4252 weeks
2045.33648 -1.59635 (204*2π)/4252 weeks
2054.20928 1.03691 (205*2π)/4252 weeks
2062.32152 -.799 (206*2π)/4252 weeks
2074.37629 -2.17649 (207*2π)/4252 weeks
2085.10035 -.24233 (208*2π)/4252 weeks
2093.60883 -.1384 (209*2π)/4252 weeks
2104.08606 -1.34731 (210*2π)/4252 weeks
2115.57892 -.317 (211*2π)/4252 weeks
2124.43915 .52082 (212*2π)/4252 weeks
2134.43915 -.52082 (213*2π)/4252 weeks
2145.57892 .317 (214*2π)/4252 weeks
2154.08606 1.34731 (215*2π)/4252 weeks
2163.60883 .1384 (216*2π)/4252 weeks
2175.10035 .24233 (217*2π)/4252 weeks
2184.37629 2.17649 (218*2π)/4252 weeks
2192.32152 .799 (219*2π)/4252 weeks
2204.20928 -1.03691 (220*2π)/4252 weeks
2215.33648 1.59635 (221*2π)/4252 weeks
2222.59618 2.25412 (222*2π)/4252 weeks
2233.04959 -.49266 (223*2π)/4252 weeks
2244.76475 1.5836 (224*2π)/4252 weeks
2251.5758 2.54555 (225*2π)/4252 weeks
226.73107 -.9651 (226*2π)/4252 weeks
2273.89077 -1.82997 (227*2π)/4252 weeks
2284.56947 .69226 (228*2π)/4252 weeks
2292.78658 .52162 (229*2π)/4252 weeks
2303.81207 -.06976 (230*2π)/4252 weeks
2313.49636 1.0351 (231*2π)/4252 weeks
2322.05039 .29587 (232*2π)/4252 weeks
2333.4046 -1.31953 (233*2π)/4252 weeks
2345.24425 .48055 (234*2π)/4252 weeks
2353.22798 1.86482 (235*2π)/4252 weeks
2362.21348 .6351 (236*2π)/4252 weeks
2372.81378 .51804 (237*2π)/4252 weeks
2381.96393 .01667 (238*2π)/4252 weeks
2393.04147 -1.57758 (239*2π)/4252 weeks
2405.47498 .01988 (240*2π)/4252 weeks
2413.42791 2.03056 (241*2π)/4252 weeks
2422.02303 .50243 (242*2π)/4252 weeks
2433.86064 -.06674 (243*2π)/4252 weeks
2443.82556 2.07028 (244*2π)/4252 weeks
2451.33189 1.55708 (245*2π)/4252 weeks
2462.28091 -.37932 (246*2π)/4252 weeks
2473.20915 1.13854 (247*2π)/4252 weeks
2481.21258 1.64984 (248*2π)/4252 weeks
249.87124 -.94142 (249*2π)/4252 weeks
2503.16843 -1.03402 (250*2π)/4252 weeks
2512.83382 .72964 (251*2π)/4252 weeks
2521.72427 .1604 (252*2π)/4252 weeks
2532.6477 -.20398 (253*2π)/4252 weeks
2542.09129 1.00984 (254*2π)/4252 weeks
255.96852 -.31387 (255*2π)/4252 weeks
2562.45046 -1.54641 (256*2π)/4252 weeks
2573.21595 .08838 (257*2π)/4252 weeks
2582.10469 .11676 (258*2π)/4252 weeks
2593.40501 -.46015 (259*2π)/4252 weeks
2603.17686 2.45308 (260*2π)/4252 weeks
261-.35305 2.54571 (261*2π)/4252 weeks
262-1.42823 -1.07788 (262*2π)/4252 weeks
2631.32119 -1.81125 (263*2π)/4252 weeks
2641.58114 -.25098 (264*2π)/4252 weeks
265.36144 -.93452 (265*2π)/4252 weeks
2661.48069 -1.73527 (266*2π)/4252 weeks
267.6305 .27477 (267*2π)/4252 weeks
268-1.82156 -2.0739 (268*2π)/4252 weeks
2691.01356 -5.10688 (269*2π)/4252 weeks
2703.94918 -2.51322 (270*2π)/4252 weeks
2711.65758 -.89683 (271*2π)/4252 weeks
2721.02381 -2.10638 (272*2π)/4252 weeks
273.84862 -2.05818 (273*2π)/4252 weeks
274.30334 -3.67288 (274*2π)/4252 weeks
2752.22297 -5.12461 (275*2π)/4252 weeks
2764.39753 -3.66182 (276*2π)/4252 weeks
2773.17105 -1.78914 (277*2π)/4252 weeks
2782.11937 -3.04033 (278*2π)/4252 weeks
2793.83376 -3.04918 (279*2π)/4252 weeks
2803.35173 -1.68785 (280*2π)/4252 weeks
2812.33739 -2.39745 (281*2π)/4252 weeks
2823.19061 -3.3079 (282*2π)/4252 weeks
2834.05663 -2.33017 (283*2π)/4252 weeks
2842.82243 -1.24108 (284*2π)/4251 weeks
2852.32425 -2.96338 (285*2π)/4251 weeks
2863.59563 -2.97269 (286*2π)/4251 weeks
2873.24417 -2.51966 (287*2π)/4251 weeks
2883.99154 -3.61716 (288*2π)/4251 weeks
2895.9689 -2.48708 (289*2π)/4251 weeks
2904.70179 .34548 (290*2π)/4251 weeks
2912.45851 -.89046 (291*2π)/4251 weeks
2923.61665 -2.40629 (292*2π)/4251 weeks
2934.09889 -.55857 (293*2π)/4251 weeks
2942.02641 -.6722 (294*2π)/4251 weeks
2953.12375 -2.84633 (295*2π)/4251 weeks
2964.77199 -.75589 (296*2π)/4251 weeks
2972.29845 .63318 (297*2π)/4251 weeks
2981.11706 -1.4137 (298*2π)/4251 weeks
2992.67046 -1.60606 (299*2π)/4251 weeks
3001.08455 -.88271 (300*2π)/4251 weeks
301.19644 -3.54313 (301*2π)/4251 weeks
3023.78548 -4.61072 (302*2π)/4251 weeks
3034.56644 -.87084 (303*2π)/4251 weeks
3041.27169 -.487 (304*2π)/4251 weeks
3051.07137 -2.40647 (305*2π)/4251 weeks
3061.53248 -2.12679 (306*2π)/4251 weeks
307.36176 -3.57285 (307*2π)/4251 weeks
3082.3001 -4.98467 (308*2π)/4251 weeks
3093.46473 -2.76472 (309*2π)/4251 weeks
310.87301 -2.67755 (310*2π)/4251 weeks
3111.09735 -5.83339 (311*2π)/4251 weeks
3123.92063 -5.97829 (312*2π)/4251 weeks
3134.65064 -4.93657 (313*2π)/4251 weeks
3145.04223 -4.43597 (314*2π)/4251 weeks
3156.39962 -3.06351 (315*2π)/4251 weeks
3165.44389 -.57756 (316*2π)/4251 weeks
3172.14657 -1.63243 (317*2π)/4251 weeks
3183.32333 -4.14635 (318*2π)/4251 weeks
3194.61501 -2.38133 (319*2π)/4251 weeks
3203.59924 -2.36474 (320*2π)/4251 weeks
3213.71072 -2.47404 (321*2π)/4251 weeks
3224.39773 -2.43702 (322*2π)/4251 weeks
3233.70623 -1.69175 (323*2π)/4251 weeks
3242.86557 -1.88002 (324*2π)/4251 weeks
3253.39547 -2.19755 (325*2π)/4251 weeks
3262.24816 -1.05434 (326*2π)/4251 weeks
3271.42067 -3.58318 (327*2π)/4251 weeks
3283.71789 -3.68032 (328*2π)/4251 weeks
3293.68473 -.94067 (329*2π)/4251 weeks
330.12756 -1.78138 (330*2π)/4251 weeks
3311.31785 -5.08331 (331*2π)/4251 weeks
3323.02844 -3.55976 (332*2π)/4251 weeks
3331.95143 -3.92842 (333*2π)/4251 weeks
3342.58452 -5.28894 (334*2π)/4251 weeks
3353.66292 -4.11711 (335*2π)/4251 weeks
3362.45672 -3.82201 (336*2π)/4251 weeks
3373.09132 -5.77122 (337*2π)/4251 weeks
3385.72462 -5.1144 (338*2π)/4251 weeks
3395.19741 -1.83108 (339*2π)/4251 weeks
3402.65955 -2.0883 (340*2π)/4251 weeks
3412.61572 -3.76738 (341*2π)/4251 weeks
3423.57994 -3.25316 (342*2π)/4251 weeks
3432.88024 -3.62123 (343*2π)/4251 weeks
3443.07983 -3.72007 (344*2π)/4251 weeks
3453.32233 -3.09494 (345*2π)/4251 weeks
3461.62166 -2.38733 (346*2π)/4251 weeks
347.73187 -5.81219 (347*2π)/4251 weeks
3484.02964 -5.50271 (348*2π)/4251 weeks
3493.4049 -2.67736 (349*2π)/4251 weeks
350.48947 -3.96564 (350*2π)/4251 weeks
3511.69616 -6.67992 (351*2π)/4251 weeks
3523.06178 -6.24682 (352*2π)/4251 weeks
3533.24766 -5.80056 (353*2π)/4251 weeks
3544.04737 -6.4045 (354*2π)/4251 weeks
3553.84171 -5.58483 (355*2π)/4251 weeks
3562.84641 -6.78607 (356*2π)/4251 weeks
3575.03996 -7.62054 (357*2π)/4251 weeks
3587.93293 -6.43427 (358*2π)/4251 weeks
3597.7344 -3.07039 (359*2π)/4251 weeks
3604.0465 -1.69946 (360*2π)/4251 weeks
3613.54293 -4.15468 (361*2π)/4251 weeks
3624.0491 -4.27851 (362*2π)/4251 weeks
3634.88893 -6.31282 (363*2π)/4251 weeks
3649.31609 -4.44948 (364*2π)/4251 weeks
3657.92848 2.50862 (365*2π)/4251 weeks
366.26959 2.60388 (366*2π)/4251 weeks
367-1.66513 -3.5597 (367*2π)/4251 weeks
3681.22169 -4.30937 (368*2π)/4251 weeks
3691.65874 -4.21187 (369*2π)/4251 weeks
3702.85589 -5.35407 (370*2π)/4251 weeks
3713.01245 -3.04822 (371*2π)/4251 weeks
372-.26553 -.45889 (372*2π)/4251 weeks
373-3.42726 -5.25172 (373*2π)/4251 weeks
374.63457 -7.67949 (374*2π)/4251 weeks
375-.62436 -6.42441 (375*2π)/4251 weeks
376.90894 -9.61258 (376*2π)/4251 weeks
3773.97294 -6.58067 (377*2π)/4251 weeks
378.91673 -3.18309 (378*2π)/4251 weeks
379-3.01535 -6.24071 (379*2π)/4251 weeks
380-2.68303 -10.02188 (380*2π)/4251 weeks
381-.08905 -12.11646 (381*2π)/4251 weeks
3821.95612 -11.74721 (382*2π)/4251 weeks
3835.21272 -12.67268 (383*2π)/4251 weeks
3847.81366 -6.67686 (384*2π)/4251 weeks
385.56182 -3.93312 (385*2π)/4251 weeks
386-1.56077 -10.29886 (386*2π)/4251 weeks
3872.50433 -11.32387 (387*2π)/4251 weeks
3882.76548 -9.81712 (388*2π)/4251 weeks
3893.29034 -9.77197 (389*2π)/4251 weeks
3904.8511 -8.56144 (390*2π)/4251 weeks
3912.40626 -3.46142 (391*2π)/4251 weeks
392-6.08199 -5.80369 (392*2π)/4251 weeks
393-6.32825 -14.44825 (393*2π)/4251 weeks
394.3648 -17.90121 (394*2π)/4251 weeks
3951.71421 -14.12558 (395*2π)/4251 weeks
3962.27805 -16.72248 (396*2π)/4251 weeks
3974.86178 -13.12997 (397*2π)/4251 weeks
398-.55685 -12.81036 (398*2π)/4251 weeks
399.73051 -17.16819 (399*2π)/4251 weeks
4006.46115 -15.90026 (400*2π)/4251 weeks
4014.10026 -10.2991 (401*2π)/4251 weeks
402-2.77784 -11.91506 (402*2π)/4251 weeks
403-3.17059 -13.88608 (403*2π)/4251 weeks
404-4.81851 -20.18946 (404*2π)/4251 weeks
405-1.13889 -22.82706 (405*2π)/4251 weeks
406.85927 -22.51691 (406*2π)/4251 weeks
4073.61594 -19.06579 (407*2π)/4251 weeks
408-3.2432 -19.18558 (408*2π)/4251 weeks
409-2.96167 -22.68449 (409*2π)/4251 weeks
410-5.77218 -22.18482 (410*2π)/4251 weeks
411-14.73214 -27.68127 (411*2π)/4251 weeks
412-16.8433 -45.27722 (412*2π)/4251 weeks
4132.40518 -53.27817 (413*2π)/4251 weeks
4147.91999 -42.57035 (414*2π)/4251 weeks
415.17248 -41.70785 (415*2π)/4251 weeks
416-8.4816 -46.48129 (416*2π)/4251 weeks
417-15.63535 -64.18238 (417*2π)/4251 weeks
418-5.73052 -92.47851 (418*2π)/4251 weeks
41922.82255 -103.105 (419*2π)/4251 weeks
42027.39962 -91.37326 (420*2π)/4251 weeks
42124.25697 -113.3701 (421*2π)/4251 weeks
42228.21802 -154.7357 (422*2π)/4251 weeks
42364.50101 -233.585 (423*2π)/4251 weeks



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