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Fourier Analysis of SMN (ProShares UltraShort Basic Mate)


SMN (ProShares UltraShort Basic Mate) appears to have interesting cyclic behaviour every 44 weeks (40.7749*sine), 41 weeks (32.73*sine), and 48 weeks (30.1569*cosine).

SMN (ProShares UltraShort Basic Mate) has an average price of 198.05 (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 2/2/2007 to 3/20/2017 for SMN (ProShares UltraShort Basic Mate), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0198.045   0 
1156.4764 205.9915 (1*2π)/530530 weeks
2-5.23711 157.2481 (2*2π)/530265 weeks
3-39.76278 42.36351 (3*2π)/530177 weeks
418.77774 1.0793 (4*2π)/530133 weeks
559.85299 33.27365 (5*2π)/530106 weeks
639.97233 80.17207 (6*2π)/53088 weeks
7-18.85162 77.70435 (7*2π)/53076 weeks
8-37.6279 23.40961 (8*2π)/53066 weeks
9-6.40516 -6.52297 (9*2π)/53059 weeks
1019.61439 .11393 (10*2π)/53053 weeks
1130.15689 23.5182 (11*2π)/53048 weeks
1210.77295 40.77493 (12*2π)/53044 weeks
13-7.12452 32.72996 (13*2π)/53041 weeks
14-12.26373 14.97381 (14*2π)/53038 weeks
15-1.71555 5.23178 (15*2π)/53035 weeks
165.38437 6.35481 (16*2π)/53033 weeks
1712.83185 9.26434 (17*2π)/53031 weeks
1811.55999 17.94352 (18*2π)/53029 weeks
196.64591 19.34662 (19*2π)/53028 weeks
201.48283 18.23759 (20*2π)/53027 weeks
21-1.58108 14.17126 (21*2π)/53025 weeks
22-.64518 8.24077 (22*2π)/53024 weeks
237.57016 8.21377 (23*2π)/53023 weeks
2410.4146 17.61672 (24*2π)/53022 weeks
25-.23692 24.88595 (25*2π)/53021 weeks
26-11.70938 14.96751 (26*2π)/53020 weeks
27-9.91519 1.31444 (27*2π)/53020 weeks
283.64826 -4.13296 (28*2π)/53019 weeks
2912.63339 6.6685 (29*2π)/53018 weeks
306.35073 19.45837 (30*2π)/53018 weeks
31-8.89168 18.0828 (31*2π)/53017 weeks
32-13.22507 1.76 (32*2π)/53017 weeks
331.3534 -7.47691 (33*2π)/53016 weeks
3411.75058 .98378 (34*2π)/53016 weeks
3510.02946 11.56261 (35*2π)/53015 weeks
36.73604 13.22395 (36*2π)/53015 weeks
37-2.53148 7.54685 (37*2π)/53014 weeks
38-.54947 3.59634 (38*2π)/53014 weeks
393.72267 2.51278 (39*2π)/53014 weeks
406.40925 7.4305 (40*2π)/53013 weeks
413.19714 9.59237 (41*2π)/53013 weeks
421.43774 9.03287 (42*2π)/53013 weeks
43-.11626 7.95093 (43*2π)/53012 weeks
44-.29211 7.81532 (44*2π)/53012 weeks
45-1.97902 6.51947 (45*2π)/53012 weeks
46-1.41863 4.51962 (46*2π)/53012 weeks
47-1.13737 2.63785 (47*2π)/53011 weeks
481.14998 2.90682 (48*2π)/53011 weeks
492.03198 3.85973 (49*2π)/53011 weeks
501.01622 5.55181 (50*2π)/53011 weeks
51-1.5768 3.91543 (51*2π)/53010 weeks
52-.16387 -.22982 (52*2π)/53010 weeks
534.74099 -1.11586 (53*2π)/53010 weeks
548.8919 4.6501 (54*2π)/53010 weeks
553.88152 9.82502 (55*2π)/53010 weeks
56-1.70035 8.10903 (56*2π)/5309 weeks
57-2.51844 3.60961 (57*2π)/5309 weeks
58.43658 .86445 (58*2π)/5309 weeks
593.22651 3.30148 (59*2π)/5309 weeks
601.10393 4.09819 (60*2π)/5309 weeks
611.32265 2.79553 (61*2π)/5309 weeks
622.48651 1.98669 (62*2π)/5309 weeks
633.79855 4.01123 (63*2π)/5308 weeks
641.39496 5.9951 (64*2π)/5308 weeks
65.50581 4.10475 (65*2π)/5308 weeks
66.9094 2.82088 (66*2π)/5308 weeks
673.90839 3.65156 (67*2π)/5308 weeks
681.3188 8.09534 (68*2π)/5308 weeks
69-4.53636 5.80641 (69*2π)/5308 weeks
70-4.59895 -.72219 (70*2π)/5308 weeks
711.35957 -4.47787 (71*2π)/5307 weeks
726.69273 -.02532 (72*2π)/5307 weeks
735.00195 4.65109 (73*2π)/5307 weeks
742.38464 6.48436 (74*2π)/5307 weeks
75-2.96481 4.51188 (75*2π)/5307 weeks
76-1.5392 -2.12195 (76*2π)/5307 weeks
774.51386 -2.29463 (77*2π)/5307 weeks
787.69478 2.20303 (78*2π)/5307 weeks
794.51495 7.82543 (79*2π)/5307 weeks
80-.99552 6.14818 (80*2π)/5307 weeks
81-2.71817 1.94259 (81*2π)/5307 weeks
82.85393 -2.59811 (82*2π)/5306 weeks
836.36524 -.17342 (83*2π)/5306 weeks
846.32524 4.92016 (84*2π)/5306 weeks
851.83925 7.28816 (85*2π)/5306 weeks
86-2.07583 4.27385 (86*2π)/5306 weeks
87-.4543 .18612 (87*2π)/5306 weeks
882.80307 .38261 (88*2π)/5306 weeks
893.67739 2.90092 (89*2π)/5306 weeks
901.72078 3.98413 (90*2π)/5306 weeks
911.4693 2.90107 (91*2π)/5306 weeks
921.4497 4.02946 (92*2π)/5306 weeks
93-.65708 3.3907 (93*2π)/5306 weeks
94-1.19222 .50259 (94*2π)/5306 weeks
951.53996 -1.56835 (95*2π)/5306 weeks
964.36243 -.0146 (96*2π)/5306 weeks
974.24264 3.23446 (97*2π)/5305 weeks
981.31292 4.6422 (98*2π)/5305 weeks
99-1.37364 2.13959 (99*2π)/5305 weeks
100.73202 -1.556 (100*2π)/5305 weeks
1014.70441 -1.20506 (101*2π)/5305 weeks
1026.85029 2.89915 (102*2π)/5305 weeks
1033.57384 6.20091 (103*2π)/5305 weeks
104-.84693 5.32108 (104*2π)/5305 weeks
105-1.95175 .61344 (105*2π)/5305 weeks
1062.25214 -1.7503 (106*2π)/5305 weeks
1076.08954 1.22441 (107*2π)/5305 weeks
1084.53526 5.84276 (108*2π)/5305 weeks
109.42877 6.35878 (109*2π)/5305 weeks
110-2.82254 3.73262 (110*2π)/5305 weeks
111-1.77772 -.9965 (111*2π)/5305 weeks
1121.92146 -1.76822 (112*2π)/5305 weeks
1133.93303 .37354 (113*2π)/5305 weeks
1143.51898 2.65704 (114*2π)/5305 weeks
1151.52182 3.0939 (115*2π)/5305 weeks
116.72477 1.6109 (116*2π)/5305 weeks
1171.74946 .14996 (117*2π)/5305 weeks
1183.7881 1.02232 (118*2π)/5304 weeks
1193.41955 3.53846 (119*2π)/5304 weeks
1201.01463 3.34364 (120*2π)/5304 weeks
121.26658 1.83604 (121*2π)/5304 weeks
1221.43673 .78479 (122*2π)/5304 weeks
1231.96456 1.49988 (123*2π)/5304 weeks
1241.68957 1.36817 (124*2π)/5304 weeks
1252.1678 1.23437 (125*2π)/5304 weeks
1262.22147 1.67362 (126*2π)/5304 weeks
1272.17764 1.32524 (127*2π)/5304 weeks
1283.02392 1.0785 (128*2π)/5304 weeks
1293.42187 2.61497 (129*2π)/5304 weeks
1301.83531 3.37481 (130*2π)/5304 weeks
131.9878 2.90875 (131*2π)/5304 weeks
132.75977 1.4841 (132*2π)/5304 weeks
1332.48644 1.53029 (133*2π)/5304 weeks
1341.62797 3.03908 (134*2π)/5304 weeks
135.53599 1.93946 (135*2π)/5304 weeks
136.90169 .7437 (136*2π)/5304 weeks
1372.46717 .80258 (137*2π)/5304 weeks
1382.04724 2.43358 (138*2π)/5304 weeks
1391.02784 1.81254 (139*2π)/5304 weeks
1401.69691 1.39651 (140*2π)/5304 weeks
1412.08514 1.67164 (141*2π)/5304 weeks
1422.00804 2.6181 (142*2π)/5304 weeks
143.24239 2.62768 (143*2π)/5304 weeks
144-.14356 1.0242 (144*2π)/5304 weeks
145.9496 -.57952 (145*2π)/5304 weeks
1463.24301 .39492 (146*2π)/5304 weeks
1472.63792 2.13259 (147*2π)/5304 weeks
1481.68293 2.14026 (148*2π)/5304 weeks
1491.38619 1.69405 (149*2π)/5304 weeks
1501.28112 1.26613 (150*2π)/5304 weeks
1511.77046 .69081 (151*2π)/5304 weeks
1522.91412 .86424 (152*2π)/5303 weeks
1533.01757 2.76819 (153*2π)/5303 weeks
1541.41752 3.12121 (154*2π)/5303 weeks
155.75888 2.71544 (155*2π)/5303 weeks
156-.05141 1.93717 (156*2π)/5303 weeks
157.35482 .57777 (157*2π)/5303 weeks
1581.69906 .30909 (158*2π)/5303 weeks
1592.25849 1.70436 (159*2π)/5303 weeks
1601.30934 2.62448 (160*2π)/5303 weeks
161-.16406 2.11487 (161*2π)/5303 weeks
162-.49107 .54361 (162*2π)/5303 weeks
163.79199 -.64482 (163*2π)/5303 weeks
1642.26911 -.03458 (164*2π)/5303 weeks
1652.30375 1.08979 (165*2π)/5303 weeks
1661.34204 1.74973 (166*2π)/5303 weeks
167.57254 1.04926 (167*2π)/5303 weeks
168.77904 -.27571 (168*2π)/5303 weeks
1692.42694 -.94894 (169*2π)/5303 weeks
1704.10399 .36799 (170*2π)/5303 weeks
1713.853 2.82047 (171*2π)/5303 weeks
1721.4685 4.05279 (172*2π)/5303 weeks
173-.54933 2.4614 (173*2π)/5303 weeks
174-.15726 .27266 (174*2π)/5303 weeks
1751.66385 -.29609 (175*2π)/5303 weeks
1762.62418 1.16561 (176*2π)/5303 weeks
1771.75025 2.18926 (177*2π)/5303 weeks
178.34325 1.87283 (178*2π)/5303 weeks
179.53159 .8473 (179*2π)/5303 weeks
180.90859 .40809 (180*2π)/5303 weeks
1811.98808 .73381 (181*2π)/5303 weeks
1821.63782 1.93869 (182*2π)/5303 weeks
183.22648 1.93179 (183*2π)/5303 weeks
184-.91392 .74458 (184*2π)/5303 weeks
185-.43526 -1.44845 (185*2π)/5303 weeks
1861.90523 -2.1123 (186*2π)/5303 weeks
1874.13147 -1.13202 (187*2π)/5303 weeks
1884.86318 2.31913 (188*2π)/5303 weeks
1891.61961 3.79646 (189*2π)/5303 weeks
190-.28855 2.18956 (190*2π)/5303 weeks
191-.03117 .03483 (191*2π)/5303 weeks
1921.77907 -.26207 (192*2π)/5303 weeks
1932.12894 1.02869 (193*2π)/5303 weeks
1941.98679 1.85213 (194*2π)/5303 weeks
195.01869 2.43635 (195*2π)/5303 weeks
196-.59883 .27836 (196*2π)/5303 weeks
197.07085 -.78778 (197*2π)/5303 weeks
1981.97308 -1.56059 (198*2π)/5303 weeks
1993.54369 .11537 (199*2π)/5303 weeks
2002.64281 2.36923 (200*2π)/5303 weeks
201-.01054 2.29762 (201*2π)/5303 weeks
202-.66962 -.38092 (202*2π)/5303 weeks
2031.81698 -1.66866 (203*2π)/5303 weeks
2043.38909 .02583 (204*2π)/5303 weeks
2053.04518 2.12136 (205*2π)/5303 weeks
206.37814 2.84479 (206*2π)/5303 weeks
207-.69401 .22947 (207*2π)/5303 weeks
2081.08535 -1.35338 (208*2π)/5303 weeks
2093.2179 -.20608 (209*2π)/5303 weeks
2102.31717 2.01643 (210*2π)/5303 weeks
211.41961 1.55055 (211*2π)/5303 weeks
212.5231 -.12439 (212*2π)/5303 weeks
2131.96214 -.15566 (213*2π)/5302 weeks
2142.44295 .90701 (214*2π)/5302 weeks
2151.70999 2.17805 (215*2π)/5302 weeks
216-.12456 1.84911 (216*2π)/5302 weeks
217-.14197 -.00334 (217*2π)/5302 weeks
218.99307 -.34519 (218*2π)/5302 weeks
2191.61777 .60987 (219*2π)/5302 weeks
220.4479 1.19545 (220*2π)/5302 weeks
221-.10779 .11963 (221*2π)/5302 weeks
222.25802 -.92729 (222*2π)/5302 weeks
2231.45866 -1.3547 (223*2π)/5302 weeks
2242.4106 -.41364 (224*2π)/5302 weeks
2252.21547 .83708 (225*2π)/5302 weeks
226.77866 1.42253 (226*2π)/5302 weeks
227-.4492 -.13513 (227*2π)/5302 weeks
228.54904 -1.75216 (228*2π)/5302 weeks
2292.36044 -1.75979 (229*2π)/5302 weeks
2303.66695 -.27228 (230*2π)/5302 weeks
2312.33042 1.64369 (231*2π)/5302 weeks
232.99291 1.29377 (232*2π)/5302 weeks
233.11738 .3644 (233*2π)/5302 weeks
2341.07321 -1.0497 (234*2π)/5302 weeks
2352.2479 -.50205 (235*2π)/5302 weeks
2362.5137 .32993 (236*2π)/5302 weeks
2371.84576 1.63885 (237*2π)/5302 weeks
238-.14958 1.51084 (238*2π)/5302 weeks
239-.87047 -.43357 (239*2π)/5302 weeks
240.38322 -2.61454 (240*2π)/5302 weeks
2413.06075 -2.33754 (241*2π)/5302 weeks
2423.90241 .09294 (242*2π)/5302 weeks
2432.74771 1.5816 (243*2π)/5302 weeks
244.88206 1.92751 (244*2π)/5302 weeks
245-.85426 .20308 (245*2π)/5302 weeks
246.19731 -2.2375 (246*2π)/5302 weeks
2473.30428 -2.59928 (247*2π)/5302 weeks
2484.5917 .65144 (248*2π)/5302 weeks
2492.20595 2.61871 (249*2π)/5302 weeks
250-.19264 1.96199 (250*2π)/5302 weeks
251-1.23881 -.85981 (251*2π)/5302 weeks
2521.35108 -3.1014 (252*2π)/5302 weeks
2534.4203 -1.56183 (253*2π)/5302 weeks
2543.65775 1.77668 (254*2π)/5302 weeks
255.92369 2.49104 (255*2π)/5302 weeks
256-1.24852 .65306 (256*2π)/5302 weeks
257-.7086 -2.47766 (257*2π)/5302 weeks
2582.87296 -3.78251 (258*2π)/5302 weeks
2595.57626 -.52859 (259*2π)/5302 weeks
2603.38142 2.6411 (260*2π)/5302 weeks
261.49363 2.05876 (261*2π)/5302 weeks
262-.68754 -.02824 (262*2π)/5302 weeks
263.38267 -2.21144 (263*2π)/5302 weeks
2643.10147 -2.84287 (264*2π)/5302 weeks
2655.35967   (265*2π)/5302 weeks
2663.10147 2.84287 (266*2π)/5302 weeks
267.38267 2.21144 (267*2π)/5302 weeks
268-.68754 .02824 (268*2π)/5302 weeks
269.49363 -2.05876 (269*2π)/5302 weeks
2703.38142 -2.6411 (270*2π)/5302 weeks
2715.57626 .52859 (271*2π)/5302 weeks
2722.87296 3.78251 (272*2π)/5302 weeks
273-.7086 2.47766 (273*2π)/5302 weeks
274-1.24852 -.65306 (274*2π)/5302 weeks
275.92369 -2.49104 (275*2π)/5302 weeks
2763.65775 -1.77668 (276*2π)/5302 weeks
2774.4203 1.56183 (277*2π)/5302 weeks
2781.35108 3.1014 (278*2π)/5302 weeks
279-1.23881 .85981 (279*2π)/5302 weeks
280-.19264 -1.96199 (280*2π)/5302 weeks
2812.20595 -2.61871 (281*2π)/5302 weeks
2824.5917 -.65144 (282*2π)/5302 weeks
2833.30428 2.59928 (283*2π)/5302 weeks
284.19731 2.2375 (284*2π)/5302 weeks
285-.85426 -.20308 (285*2π)/5302 weeks
286.88206 -1.92751 (286*2π)/5302 weeks
2872.74771 -1.5816 (287*2π)/5302 weeks
2883.90241 -.09294 (288*2π)/5302 weeks
2893.06075 2.33754 (289*2π)/5302 weeks
290.38322 2.61454 (290*2π)/5302 weeks
291-.87047 .43357 (291*2π)/5302 weeks
292-.14958 -1.51084 (292*2π)/5302 weeks
2931.84576 -1.63885 (293*2π)/5302 weeks
2942.5137 -.32993 (294*2π)/5302 weeks
2952.2479 .50205 (295*2π)/5302 weeks
2961.07321 1.0497 (296*2π)/5302 weeks
297.11738 -.3644 (297*2π)/5302 weeks
298.99291 -1.29377 (298*2π)/5302 weeks
2992.33042 -1.64369 (299*2π)/5302 weeks
3003.66695 .27228 (300*2π)/5302 weeks
3012.36044 1.75979 (301*2π)/5302 weeks
302.54904 1.75216 (302*2π)/5302 weeks
303-.4492 .13513 (303*2π)/5302 weeks
304.77866 -1.42253 (304*2π)/5302 weeks
3052.21547 -.83708 (305*2π)/5302 weeks
3062.4106 .41364 (306*2π)/5302 weeks
3071.45866 1.3547 (307*2π)/5302 weeks
308.25802 .92729 (308*2π)/5302 weeks
309-.10779 -.11963 (309*2π)/5302 weeks
310.4479 -1.19545 (310*2π)/5302 weeks
3111.61777 -.60987 (311*2π)/5302 weeks
312.99307 .34519 (312*2π)/5302 weeks
313-.14197 .00334 (313*2π)/5302 weeks
314-.12456 -1.84911 (314*2π)/5302 weeks
3151.70999 -2.17805 (315*2π)/5302 weeks
3162.44295 -.90701 (316*2π)/5302 weeks
3171.96214 .15566 (317*2π)/5302 weeks
318.5231 .12439 (318*2π)/5302 weeks
319.41961 -1.55055 (319*2π)/5302 weeks
3202.31717 -2.01643 (320*2π)/5302 weeks
3213.2179 .20608 (321*2π)/5302 weeks
3221.08535 1.35338 (322*2π)/5302 weeks
323-.69401 -.22947 (323*2π)/5302 weeks
324.37814 -2.84479 (324*2π)/5302 weeks
3253.04518 -2.12136 (325*2π)/5302 weeks
3263.38909 -.02583 (326*2π)/5302 weeks
3271.81698 1.66866 (327*2π)/5302 weeks
328-.66962 .38092 (328*2π)/5302 weeks
329-.01054 -2.29762 (329*2π)/5302 weeks
3302.64281 -2.36923 (330*2π)/5302 weeks
3313.54369 -.11537 (331*2π)/5302 weeks
3321.97308 1.56059 (332*2π)/5302 weeks
333.07085 .78778 (333*2π)/5302 weeks
334-.59883 -.27836 (334*2π)/5302 weeks
335.01869 -2.43635 (335*2π)/5302 weeks
3361.98679 -1.85213 (336*2π)/5302 weeks
3372.12894 -1.02869 (337*2π)/5302 weeks
3381.77907 .26207 (338*2π)/5302 weeks
339-.03117 -.03483 (339*2π)/5302 weeks
340-.28855 -2.18956 (340*2π)/5302 weeks
3411.61961 -3.79646 (341*2π)/5302 weeks
3424.86318 -2.31913 (342*2π)/5302 weeks
3434.13147 1.13202 (343*2π)/5302 weeks
3441.90523 2.1123 (344*2π)/5302 weeks
345-.43526 1.44845 (345*2π)/5302 weeks
346-.91392 -.74458 (346*2π)/5302 weeks
347.22648 -1.93179 (347*2π)/5302 weeks
3481.63782 -1.93869 (348*2π)/5302 weeks
3491.98808 -.73381 (349*2π)/5302 weeks
350.90859 -.40809 (350*2π)/5302 weeks
351.53159 -.8473 (351*2π)/5302 weeks
352.34325 -1.87283 (352*2π)/5302 weeks
3531.75025 -2.18926 (353*2π)/5302 weeks
3542.62418 -1.16561 (354*2π)/5301 weeks
3551.66385 .29609 (355*2π)/5301 weeks
356-.15726 -.27266 (356*2π)/5301 weeks
357-.54933 -2.4614 (357*2π)/5301 weeks
3581.4685 -4.05279 (358*2π)/5301 weeks
3593.853 -2.82047 (359*2π)/5301 weeks
3604.10399 -.36799 (360*2π)/5301 weeks
3612.42694 .94894 (361*2π)/5301 weeks
362.77904 .27571 (362*2π)/5301 weeks
363.57254 -1.04926 (363*2π)/5301 weeks
3641.34204 -1.74973 (364*2π)/5301 weeks
3652.30375 -1.08979 (365*2π)/5301 weeks
3662.26911 .03458 (366*2π)/5301 weeks
367.79199 .64482 (367*2π)/5301 weeks
368-.49107 -.54361 (368*2π)/5301 weeks
369-.16406 -2.11487 (369*2π)/5301 weeks
3701.30934 -2.62448 (370*2π)/5301 weeks
3712.25849 -1.70436 (371*2π)/5301 weeks
3721.69906 -.30909 (372*2π)/5301 weeks
373.35482 -.57777 (373*2π)/5301 weeks
374-.05141 -1.93717 (374*2π)/5301 weeks
375.75888 -2.71544 (375*2π)/5301 weeks
3761.41752 -3.12121 (376*2π)/5301 weeks
3773.01757 -2.76819 (377*2π)/5301 weeks
3782.91412 -.86424 (378*2π)/5301 weeks
3791.77046 -.69081 (379*2π)/5301 weeks
3801.28112 -1.26613 (380*2π)/5301 weeks
3811.38619 -1.69405 (381*2π)/5301 weeks
3821.68293 -2.14026 (382*2π)/5301 weeks
3832.63792 -2.13259 (383*2π)/5301 weeks
3843.24301 -.39492 (384*2π)/5301 weeks
385.9496 .57952 (385*2π)/5301 weeks
386-.14356 -1.0242 (386*2π)/5301 weeks
387.24239 -2.62768 (387*2π)/5301 weeks
3882.00804 -2.6181 (388*2π)/5301 weeks
3892.08514 -1.67164 (389*2π)/5301 weeks
3901.69691 -1.39651 (390*2π)/5301 weeks
3911.02784 -1.81254 (391*2π)/5301 weeks
3922.04724 -2.43358 (392*2π)/5301 weeks
3932.46717 -.80258 (393*2π)/5301 weeks
394.90169 -.7437 (394*2π)/5301 weeks
395.53599 -1.93946 (395*2π)/5301 weeks
3961.62797 -3.03908 (396*2π)/5301 weeks
3972.48644 -1.53029 (397*2π)/5301 weeks
398.75977 -1.4841 (398*2π)/5301 weeks
399.9878 -2.90875 (399*2π)/5301 weeks
4001.83531 -3.37481 (400*2π)/5301 weeks
4013.42187 -2.61497 (401*2π)/5301 weeks
4023.02392 -1.0785 (402*2π)/5301 weeks
4032.17764 -1.32524 (403*2π)/5301 weeks
4042.22147 -1.67362 (404*2π)/5301 weeks
4052.1678 -1.23437 (405*2π)/5301 weeks
4061.68957 -1.36817 (406*2π)/5301 weeks
4071.96456 -1.49988 (407*2π)/5301 weeks
4081.43673 -.78479 (408*2π)/5301 weeks
409.26658 -1.83604 (409*2π)/5301 weeks
4101.01463 -3.34364 (410*2π)/5301 weeks
4113.41955 -3.53846 (411*2π)/5301 weeks
4123.7881 -1.02232 (412*2π)/5301 weeks
4131.74946 -.14996 (413*2π)/5301 weeks
414.72477 -1.6109 (414*2π)/5301 weeks
4151.52182 -3.0939 (415*2π)/5301 weeks
4163.51898 -2.65704 (416*2π)/5301 weeks
4173.93303 -.37354 (417*2π)/5301 weeks
4181.92146 1.76822 (418*2π)/5301 weeks
419-1.77772 .9965 (419*2π)/5301 weeks
420-2.82254 -3.73262 (420*2π)/5301 weeks
421.42877 -6.35878 (421*2π)/5301 weeks
4224.53526 -5.84276 (422*2π)/5301 weeks
4236.08954 -1.22441 (423*2π)/5301 weeks
4242.25214 1.7503 (424*2π)/5301 weeks
425-1.95175 -.61344 (425*2π)/5301 weeks
426-.84693 -5.32108 (426*2π)/5301 weeks
4273.57384 -6.20091 (427*2π)/5301 weeks
4286.85029 -2.89915 (428*2π)/5301 weeks
4294.70441 1.20506 (429*2π)/5301 weeks
430.73202 1.556 (430*2π)/5301 weeks
431-1.37364 -2.13959 (431*2π)/5301 weeks
4321.31292 -4.6422 (432*2π)/5301 weeks
4334.24264 -3.23446 (433*2π)/5301 weeks
4344.36243 .0146 (434*2π)/5301 weeks
4351.53996 1.56835 (435*2π)/5301 weeks
436-1.19222 -.50259 (436*2π)/5301 weeks
437-.65708 -3.3907 (437*2π)/5301 weeks
4381.4497 -4.02946 (438*2π)/5301 weeks
4391.4693 -2.90107 (439*2π)/5301 weeks
4401.72078 -3.98413 (440*2π)/5301 weeks
4413.67739 -2.90092 (441*2π)/5301 weeks
4422.80307 -.38261 (442*2π)/5301 weeks
443-.4543 -.18612 (443*2π)/5301 weeks
444-2.07583 -4.27385 (444*2π)/5301 weeks
4451.83925 -7.28816 (445*2π)/5301 weeks
4466.32524 -4.92016 (446*2π)/5301 weeks
4476.36524 .17342 (447*2π)/5301 weeks
448.85393 2.59811 (448*2π)/5301 weeks
449-2.71817 -1.94259 (449*2π)/5301 weeks
450-.99552 -6.14818 (450*2π)/5301 weeks
4514.51495 -7.82543 (451*2π)/5301 weeks
4527.69478 -2.20303 (452*2π)/5301 weeks
4534.51386 2.29463 (453*2π)/5301 weeks
454-1.5392 2.12195 (454*2π)/5301 weeks
455-2.96481 -4.51188 (455*2π)/5301 weeks
4562.38464 -6.48436 (456*2π)/5301 weeks
4575.00195 -4.65109 (457*2π)/5301 weeks
4586.69273 .02532 (458*2π)/5301 weeks
4591.35957 4.47787 (459*2π)/5301 weeks
460-4.59895 .72219 (460*2π)/5301 weeks
461-4.53636 -5.80641 (461*2π)/5301 weeks
4621.3188 -8.09534 (462*2π)/5301 weeks
4633.90839 -3.65156 (463*2π)/5301 weeks
464.9094 -2.82088 (464*2π)/5301 weeks
465.50581 -4.10475 (465*2π)/5301 weeks
4661.39496 -5.9951 (466*2π)/5301 weeks
4673.79855 -4.01123 (467*2π)/5301 weeks
4682.48651 -1.98669 (468*2π)/5301 weeks
4691.32265 -2.79553 (469*2π)/5301 weeks
4701.10393 -4.09819 (470*2π)/5301 weeks
4713.22651 -3.30148 (471*2π)/5301 weeks
472.43658 -.86445 (472*2π)/5301 weeks
473-2.51844 -3.60961 (473*2π)/5301 weeks
474-1.70035 -8.10903 (474*2π)/5301 weeks
4753.88152 -9.82502 (475*2π)/5301 weeks
4768.8919 -4.6501 (476*2π)/5301 weeks
4774.74099 1.11586 (477*2π)/5301 weeks
478-.16387 .22982 (478*2π)/5301 weeks
479-1.5768 -3.91543 (479*2π)/5301 weeks
4801.01622 -5.55181 (480*2π)/5301 weeks
4812.03198 -3.85973 (481*2π)/5301 weeks
4821.14998 -2.90682 (482*2π)/5301 weeks
483-1.13737 -2.63785 (483*2π)/5301 weeks
484-1.41863 -4.51962 (484*2π)/5301 weeks
485-1.97902 -6.51947 (485*2π)/5301 weeks
486-.29211 -7.81532 (486*2π)/5301 weeks
487-.11626 -7.95093 (487*2π)/5301 weeks
4881.43774 -9.03287 (488*2π)/5301 weeks
4893.19714 -9.59237 (489*2π)/5301 weeks
4906.40925 -7.4305 (490*2π)/5301 weeks
4913.72267 -2.51278 (491*2π)/5301 weeks
492-.54947 -3.59634 (492*2π)/5301 weeks
493-2.53148 -7.54685 (493*2π)/5301 weeks
494.73604 -13.22395 (494*2π)/5301 weeks
49510.02946 -11.56261 (495*2π)/5301 weeks
49611.75058 -.98378 (496*2π)/5301 weeks
4971.3534 7.47691 (497*2π)/5301 weeks
498-13.22507 -1.76 (498*2π)/5301 weeks
499-8.89168 -18.0828 (499*2π)/5301 weeks
5006.35073 -19.45837 (500*2π)/5301 weeks
50112.63339 -6.6685 (501*2π)/5301 weeks
5023.64826 4.13296 (502*2π)/5301 weeks
503-9.91519 -1.31444 (503*2π)/5301 weeks
504-11.70938 -14.96751 (504*2π)/5301 weeks
505-.23692 -24.88595 (505*2π)/5301 weeks
50610.4146 -17.61672 (506*2π)/5301 weeks
5077.57016 -8.21377 (507*2π)/5301 weeks
508-.64518 -8.24077 (508*2π)/5301 weeks
509-1.58108 -14.17126 (509*2π)/5301 weeks
5101.48283 -18.23759 (510*2π)/5301 weeks
5116.64591 -19.34662 (511*2π)/5301 weeks
51211.55999 -17.94352 (512*2π)/5301 weeks
51312.83185 -9.26434 (513*2π)/5301 weeks
5145.38437 -6.35481 (514*2π)/5301 weeks
515-1.71555 -5.23178 (515*2π)/5301 weeks
516-12.26373 -14.97381 (516*2π)/5301 weeks
517-7.12452 -32.72996 (517*2π)/5301 weeks
51810.77295 -40.77493 (518*2π)/5301 weeks
51930.15689 -23.5182 (519*2π)/5301 weeks
52019.61439 -.11393 (520*2π)/5301 weeks
521-6.40516 6.52297 (521*2π)/5301 weeks
522-37.6279 -23.40961 (522*2π)/5301 weeks
523-18.85162 -77.70435 (523*2π)/5301 weeks
52439.97233 -80.17207 (524*2π)/5301 weeks
52559.85299 -33.27365 (525*2π)/5301 weeks
52618.77774 -1.0793 (526*2π)/5301 weeks
527-39.76278 -42.36351 (527*2π)/5301 weeks
528-5.23711 -157.2481 (528*2π)/5301 weeks

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