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Fourier Analysis of YRCW (YRC Worldwide, Inc.)


YRCW (YRC Worldwide, Inc.) appears to have interesting cyclic behaviour every 133 weeks (18563.76*sine), 114 weeks (10079.91*sine), and 64 weeks (6906.342*cosine).

YRCW (YRC Worldwide, Inc.) has an average price of 137,891.4 (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 7/9/1986 to 1/17/2017 for YRCW (YRC Worldwide, Inc.), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0137,891.4   0 
1-60,725.19 27,384.44 (1*2π)/15931,593 weeks
214,127.45 103,996.4 (2*2π)/1593797 weeks
331,810.69 -11,602.59 (3*2π)/1593531 weeks
4-29,667.03 4,352.881 (4*2π)/1593398 weeks
515,893.76 29,414.63 (5*2π)/1593319 weeks
69,580.549 10,540.66 (6*2π)/1593266 weeks
7-9,122.072 7,411.667 (7*2π)/1593228 weeks
89,075.418 10,091.39 (8*2π)/1593199 weeks
9-7,156.386 13,573.83 (9*2π)/1593177 weeks
105,558.997 2,544.754 (10*2π)/1593159 weeks
112,281.864 1,955.617 (11*2π)/1593145 weeks
12-636.6075 18,563.76 (12*2π)/1593133 weeks
134,328.446 -728.1736 (13*2π)/1593123 weeks
14-2,949.009 10,079.91 (14*2π)/1593114 weeks
15-1,881.843 9,491.22 (15*2π)/1593106 weeks
161,429.107 -866.8416 (16*2π)/1593100 weeks
17-3,878.219 8,133.377 (17*2π)/159394 weeks
18211.8092 4,308.2 (18*2π)/159389 weeks
191,776.348 178.8898 (19*2π)/159384 weeks
20-4,173.27 6,180.263 (20*2π)/159380 weeks
211,608.147 2,645.325 (21*2π)/159376 weeks
22-34.65379 3,981.261 (22*2π)/159372 weeks
23-2,199.015 -1,745.303 (23*2π)/159369 weeks
24488.7583 1,339.901 (24*2π)/159366 weeks
256,906.342 8,352.987 (25*2π)/159364 weeks
26-1,345.152 -2,168.495 (26*2π)/159361 weeks
27-2,461.522 5,467.206 (27*2π)/159359 weeks
284,607.15 5,371.393 (28*2π)/159357 weeks
29-13.6854 1,288.345 (29*2π)/159355 weeks
30-2,298.522 4,673.838 (30*2π)/159353 weeks
31-631.1019 1,551.913 (31*2π)/159351 weeks
322,571.103 3,330.481 (32*2π)/159350 weeks
331,272.839 3,207.035 (33*2π)/159348 weeks
34-3,125.892 5,838.842 (34*2π)/159347 weeks
35-3,291.162 2,036.312 (35*2π)/159346 weeks
36854.9172 591.9915 (36*2π)/159344 weeks
37-1,043.555 246.1984 (37*2π)/159343 weeks
38172.4571 3,108.537 (38*2π)/159342 weeks
39360.6192 3,283.727 (39*2π)/159341 weeks
40-301.3355 382.673 (40*2π)/159340 weeks
41-1,166.754 3,546.108 (41*2π)/159339 weeks
42-822.2664 3,160.375 (42*2π)/159338 weeks
43-2,495.931 1,700.547 (43*2π)/159337 weeks
44-702.8101 271.2781 (44*2π)/159336 weeks
45-4,283.354 780.3165 (45*2π)/159335 weeks
46668.4922 -1,353.074 (46*2π)/159335 weeks
471,823.694 301.3977 (47*2π)/159334 weeks
48-333.1649 -277.2189 (48*2π)/159333 weeks
49-138.8405 3,269.028 (49*2π)/159333 weeks
50-724.6649 265.7303 (50*2π)/159332 weeks
51345.8344 -1,024.324 (51*2π)/159331 weeks
52716.7839 -276.4897 (52*2π)/159331 weeks
53989.6671 2,144.947 (53*2π)/159330 weeks
541,144.97 209.6713 (54*2π)/159330 weeks
551,199.651 2,078.547 (55*2π)/159329 weeks
56586.1068 618.5558 (56*2π)/159328 weeks
57-1,216.796 2,487.828 (57*2π)/159328 weeks
581,697.528 1,932.609 (58*2π)/159327 weeks
59-384.0622 -792.0751 (59*2π)/159327 weeks
60-34.94285 2,005.231 (60*2π)/159327 weeks
611,760.234 2,427.542 (61*2π)/159326 weeks
62-1,164.361 1,711.613 (62*2π)/159326 weeks
63-419.5912 700.2709 (63*2π)/159325 weeks
64442.3874 1,894.802 (64*2π)/159325 weeks
65-1,234.248 1,364.613 (65*2π)/159325 weeks
66-889.4404 1,962.388 (66*2π)/159324 weeks
67-885.9069 -1,432.513 (67*2π)/159324 weeks
68-424.6606 836.726 (68*2π)/159323 weeks
692,197.408 1,619.976 (69*2π)/159323 weeks
70-3,495.879 -115.2271 (70*2π)/159323 weeks
711,407.624 196.2721 (71*2π)/159322 weeks
72431.4377 1,188.014 (72*2π)/159322 weeks
73-734.5154 -587.7887 (73*2π)/159322 weeks
74-967.8676 1,190.012 (74*2π)/159322 weeks
751,339.666 -1,369.802 (75*2π)/159321 weeks
76829.1047 114.9568 (76*2π)/159321 weeks
771,715.516 1,949.087 (77*2π)/159321 weeks
78-1,218.369 -536.6183 (78*2π)/159320 weeks
791,385.773 1,620.522 (79*2π)/159320 weeks
801,800.629 586.8661 (80*2π)/159320 weeks
81-847.3191 330.7338 (81*2π)/159320 weeks
821,335.801 2,372.894 (82*2π)/159319 weeks
83-401.4034 1,436.165 (83*2π)/159319 weeks
84194.329 233.1665 (84*2π)/159319 weeks
85-296.2011 913.3655 (85*2π)/159319 weeks
86-627.2742 681.7992 (86*2π)/159319 weeks
871,717.733 1,166.512 (87*2π)/159318 weeks
88-724.5075 156.7122 (88*2π)/159318 weeks
89259.1297 1,294.262 (89*2π)/159318 weeks
90-47.52354 1,264.901 (90*2π)/159318 weeks
91-822.9571 673.388 (91*2π)/159318 weeks
92191.7916 2.26363 (92*2π)/159317 weeks
93482.6725 -305.6599 (93*2π)/159317 weeks
94-1,046.07 1,434.961 (94*2π)/159317 weeks
951,879.387 866.0901 (95*2π)/159317 weeks
96-451.9601 -1,270.264 (96*2π)/159317 weeks
97-614.4456 1,796.31 (97*2π)/159316 weeks
982,054.053 1,210.702 (98*2π)/159316 weeks
99-553.1929 -879.5369 (99*2π)/159316 weeks
100-248.1545 2,195.778 (100*2π)/159316 weeks
101541.6168 551.6403 (101*2π)/159316 weeks
102-884.8397 299.5926 (102*2π)/159316 weeks
103801.6569 -479.804 (103*2π)/159315 weeks
104-686.4421 854.0211 (104*2π)/159315 weeks
1051,596.917 569.684 (105*2π)/159315 weeks
106436.4332 32.02318 (106*2π)/159315 weeks
107-116.4892 783.7225 (107*2π)/159315 weeks
108247.9394 1,416.613 (108*2π)/159315 weeks
1091,386.144 783.3582 (109*2π)/159315 weeks
110-1,045.706 114.8767 (110*2π)/159314 weeks
111440.7234 1,563.551 (111*2π)/159314 weeks
112-693.5876 1,094.804 (112*2π)/159314 weeks
113464.2213 -315.6935 (113*2π)/159314 weeks
114-1,076.697 242.5745 (114*2π)/159314 weeks
1151,142.927 158.0728 (115*2π)/159314 weeks
116-97.41116 911.778 (116*2π)/159314 weeks
117890.1361 810.8907 (117*2π)/159314 weeks
118-1,716.309 -84.50462 (118*2π)/159314 weeks
1191,091.274 322.976 (119*2π)/159313 weeks
120451.2119 95.54374 (120*2π)/159313 weeks
121151.3173 324.145 (121*2π)/159313 weeks
122198.3346 1,465.019 (122*2π)/159313 weeks
123-232.016 -538.5897 (123*2π)/159313 weeks
124441.8823 -575.9019 (124*2π)/159313 weeks
125944.8798 1,176.14 (125*2π)/159313 weeks
1261,775.467 322.8551 (126*2π)/159313 weeks
127-783.276 1,126.458 (127*2π)/159313 weeks
128817.887 1,789.972 (128*2π)/159312 weeks
129-200.28 -487.2998 (129*2π)/159312 weeks
130-325.0361 1,667.919 (130*2π)/159312 weeks
131960.7078 355.6743 (131*2π)/159312 weeks
132-870.3705 209.5855 (132*2π)/159312 weeks
133-56.82922 1,654.569 (133*2π)/159312 weeks
134564.1666 -563.9769 (134*2π)/159312 weeks
135-753.5037 535.5551 (135*2π)/159312 weeks
1361,007.601 1,124.607 (136*2π)/159312 weeks
137-1,106.886 159.8063 (137*2π)/159312 weeks
13873.0471 508.7741 (138*2π)/159312 weeks
139268.5705 -808.7634 (139*2π)/159311 weeks
140159.6819 1,095.456 (140*2π)/159311 weeks
141105.1167 91.82093 (141*2π)/159311 weeks
142440.2788 4.89254 (142*2π)/159311 weeks
143-133.3213 505.4697 (143*2π)/159311 weeks
144731.355 136.8364 (144*2π)/159311 weeks
145488.3665 393.9614 (145*2π)/159311 weeks
146-330.8284 852.966 (146*2π)/159311 weeks
147928.7026 -129.004 (147*2π)/159311 weeks
148291.1853 590.207 (148*2π)/159311 weeks
149247.8102 942.9055 (149*2π)/159311 weeks
150412.115 705.5782 (150*2π)/159311 weeks
15189.6492 804.5738 (151*2π)/159311 weeks
152-605.3116 394.7548 (152*2π)/159310 weeks
153248.3163 777.0083 (153*2π)/159310 weeks
154157.9624 499.5318 (154*2π)/159310 weeks
155-674.2042 -340.5912 (155*2π)/159310 weeks
156306.166 1,348.621 (156*2π)/159310 weeks
157135.6112 15.61322 (157*2π)/159310 weeks
158-1,066.518 -425.4003 (158*2π)/159310 weeks
159788.7284 652.3832 (159*2π)/159310 weeks
160195.2399 -320.3158 (160*2π)/159310 weeks
1618.09366 244.3118 (161*2π)/159310 weeks
162529.308 367.5797 (162*2π)/159310 weeks
163265.3564 89.36829 (163*2π)/159310 weeks
164-91.32442 935.6252 (164*2π)/159310 weeks
16568.08234 -368.2981 (165*2π)/159310 weeks
166629.5126 -436.2929 (166*2π)/159310 weeks
167219.1792 1,105.175 (167*2π)/159310 weeks
168965.5592 252.7574 (168*2π)/15939 weeks
169217.6549 170.7223 (169*2π)/15939 weeks
170-418.9646 1,245.31 (170*2π)/15939 weeks
171271.9513 155.8715 (171*2π)/15939 weeks
172204.6938 -283.3224 (172*2π)/15939 weeks
173293.4982 17.73783 (173*2π)/15939 weeks
174971.5873 1,228.375 (174*2π)/15939 weeks
175-111.7858 419.194 (175*2π)/15939 weeks
176-182.9509 384.2339 (176*2π)/15939 weeks
177422.3994 384.9523 (177*2π)/15939 weeks
17885.26203 227.4084 (178*2π)/15939 weeks
179107.5661 502.3701 (179*2π)/15939 weeks
180580.5224 781.7064 (180*2π)/15939 weeks
181-356.355 122.8848 (181*2π)/15939 weeks
182-228.9791 591.4262 (182*2π)/15939 weeks
183508.4633 -61.34102 (183*2π)/15939 weeks
184-69.5698 654.9495 (184*2π)/15939 weeks
185412.451 171.7794 (185*2π)/15939 weeks
186-474.9988 600.7368 (186*2π)/15939 weeks
187-180.1971 24.77743 (187*2π)/15939 weeks
188705.5917 376.6154 (188*2π)/15938 weeks
189-586.0645 -513.7562 (189*2π)/15938 weeks
190116.9202 743.1823 (190*2π)/15938 weeks
191988.1585 -291.4707 (191*2π)/15938 weeks
192-585.2344 -10.43024 (192*2π)/15938 weeks
193673.0914 445.3664 (193*2π)/15938 weeks
194605.2337 -46.73092 (194*2π)/15938 weeks
19543.28604 29.69887 (195*2π)/15938 weeks
196441.9149 968.256 (196*2π)/15938 weeks
197381.4096 -564.0509 (197*2π)/15938 weeks
198353.7629 726.4973 (198*2π)/15938 weeks
199508.5714 113.5838 (199*2π)/15938 weeks
200436.8987 399.7726 (200*2π)/15938 weeks
201616.9518 875.1069 (201*2π)/15938 weeks
202-183.614 404.5548 (202*2π)/15938 weeks
203158.1622 146.8466 (203*2π)/15938 weeks
204427.9412 677.9747 (204*2π)/15938 weeks
205564.8736 75.84124 (205*2π)/15938 weeks
206-9.95698 794.0424 (206*2π)/15938 weeks
207265.9207 983.738 (207*2π)/15938 weeks
20899.84592 269.5457 (208*2π)/15938 weeks
209-573.4301 504.1961 (209*2π)/15938 weeks
21078.38147 434.3658 (210*2π)/15938 weeks
21128.63523 91.01444 (211*2π)/15938 weeks
212-171.1655 -43.51712 (212*2π)/15938 weeks
213464.7702 366.3352 (213*2π)/15937 weeks
214-159.7934 346.2478 (214*2π)/15937 weeks
215268.2683 174.0264 (215*2π)/15937 weeks
21673.33345 -93.49711 (216*2π)/15937 weeks
217134.6784 574.9769 (217*2π)/15937 weeks
218484.2261 228.2404 (218*2π)/15937 weeks
219-287.5823 285.6444 (219*2π)/15937 weeks
220153.4169 80.80113 (220*2π)/15937 weeks
221103.7538 321.5647 (221*2π)/15937 weeks
222369.5783 -4.11961 (222*2π)/15937 weeks
223-21.09792 -169.541 (223*2π)/15937 weeks
224685.5247 1,056.847 (224*2π)/15937 weeks
225-70.35073 -371.6448 (225*2π)/15937 weeks
22650.38293 316.4964 (226*2π)/15937 weeks
227517.4999 487.0229 (227*2π)/15937 weeks
228600.7138 79.15231 (228*2π)/15937 weeks
229-538.5411 393.6666 (229*2π)/15937 weeks
230450.8827 744.4984 (230*2π)/15937 weeks
231221.5019 -261.3909 (231*2π)/15937 weeks
232-95.27769 322.6429 (232*2π)/15937 weeks
233106.0332 154.553 (233*2π)/15937 weeks
234440.4408 554.7339 (234*2π)/15937 weeks
235367.3971 -329.3624 (235*2π)/15937 weeks
236-211.0208 635.9991 (236*2π)/15937 weeks
237372.0215 591.9104 (237*2π)/15937 weeks
238242.812 -78.81945 (238*2π)/15937 weeks
239-488.8461 213.5047 (239*2π)/15937 weeks
240240.333 332.7104 (240*2π)/15937 weeks
241193.2633 -345.7201 (241*2π)/15937 weeks
242484.3405 -134.0827 (242*2π)/15937 weeks
243174.8159 586.0614 (243*2π)/15937 weeks
244461.6996 98.96474 (244*2π)/15937 weeks
24579.53621 278.9527 (245*2π)/15937 weeks
24676.35556 -19.11468 (246*2π)/15936 weeks
247362.7747 -147.1349 (247*2π)/15936 weeks
248703.7538 292.1071 (248*2π)/15936 weeks
249346.5835 194.3571 (249*2π)/15936 weeks
250488.965 173.0044 (250*2π)/15936 weeks
251523.7443 410.4673 (251*2π)/15936 weeks
252486.8454 397.3564 (252*2π)/15936 weeks
253345.0894 599.6967 (253*2π)/15936 weeks
254379.0588 254.0821 (254*2π)/15936 weeks
255339.9099 650.701 (255*2π)/15936 weeks
256380.5348 560.3645 (256*2π)/15936 weeks
257-45.39182 471.6612 (257*2π)/15936 weeks
258700.0356 793.6191 (258*2π)/15936 weeks
259-482.2298 750.3197 (259*2π)/15936 weeks
260-123.7319 202.8588 (260*2π)/15936 weeks
261-202.6311 691.0414 (261*2π)/15936 weeks
26229.76663 -219.6198 (262*2π)/15936 weeks
26351.83832 118.7012 (263*2π)/15936 weeks
264-19.35852 468.9794 (264*2π)/15936 weeks
265393.3342 -40.30128 (265*2π)/15936 weeks
266205.1243 455.2467 (266*2π)/15936 weeks
267-261.3453 343.4257 (267*2π)/15936 weeks
268397.6906 -50.44585 (268*2π)/15936 weeks
269-67.5325 540.3244 (269*2π)/15936 weeks
270341.962 131.852 (270*2π)/15936 weeks
271-74.98586 57.40872 (271*2π)/15936 weeks
272269.6614 487.8387 (272*2π)/15936 weeks
273152.8947 177.2344 (273*2π)/15936 weeks
274133.9652 180.7091 (274*2π)/15936 weeks
275149.5208 582.4439 (275*2π)/15936 weeks
276121.0369 -113.0863 (276*2π)/15936 weeks
277-136.2047 608.9029 (277*2π)/15936 weeks
278483.0943 298.9405 (278*2π)/15936 weeks
279-94.7561 -34.72469 (279*2π)/15936 weeks
280-204.4467 791.424 (280*2π)/15936 weeks
281-48.97214 33.46582 (281*2π)/15936 weeks
282148.4412 6.89515 (282*2π)/15936 weeks
283-141.5619 138.8025 (283*2π)/15936 weeks
284-303.5395 178.2713 (284*2π)/15936 weeks
285419.8077 -103.4641 (285*2π)/15936 weeks
28661.99421 -66.25463 (286*2π)/15936 weeks
287-185.2201 -91.83588 (287*2π)/15936 weeks
288408.6766 387.3485 (288*2π)/15936 weeks
289145.4699 -581.1805 (289*2π)/15936 weeks
29014.61821 99.55488 (290*2π)/15935 weeks
291731.8608 79.48471 (291*2π)/15935 weeks
292-79.01159 -462.8653 (292*2π)/15935 weeks
293893.0117 388.9855 (293*2π)/15935 weeks
294429.1452 -236.5519 (294*2π)/15935 weeks
295509.6189 363.0018 (295*2π)/15935 weeks
296559.335 92.92384 (296*2π)/15935 weeks
297612.2462 734.3972 (297*2π)/15935 weeks
298642.4814 -285.9788 (298*2π)/15935 weeks
29938.5169 1,215.605 (299*2π)/15935 weeks
300688.7565 333.5064 (300*2π)/15935 weeks
301-14.97647 287.7187 (301*2π)/15935 weeks
302348.9802 357.5567 (302*2π)/15935 weeks
303297.6881 665.1191 (303*2π)/15935 weeks
304396.4137 755.1674 (304*2π)/15935 weeks
305-64.47798 304.9733 (305*2π)/15935 weeks
306-253.2864 632.1359 (306*2π)/15935 weeks
307-122.8907 509.6743 (307*2π)/15935 weeks
308327.0897 1.31245 (308*2π)/15935 weeks
309-416.8681 95.3495 (309*2π)/15935 weeks
310410.5443 294.6751 (310*2π)/15935 weeks
311173.0673 696.9437 (311*2π)/15935 weeks
312-139.1419 80.33099 (312*2π)/15935 weeks
313-189.3396 181.4739 (313*2π)/15935 weeks
314-308.0605 143.5936 (314*2π)/15935 weeks
315494.3529 -165.8256 (315*2π)/15935 weeks
316352.5276 -40.99294 (316*2π)/15935 weeks
317-81.15564 375.3865 (317*2π)/15935 weeks
318507.3779 71.53165 (318*2π)/15935 weeks
31988.69916 390.4744 (319*2π)/15935 weeks
320288.3492 -134.7448 (320*2π)/15935 weeks
321552.7795 214.0903 (321*2π)/15935 weeks
322228.1209 682.9604 (322*2π)/15935 weeks
323414.9098 507.1516 (323*2π)/15935 weeks
32488.89096 125.9931 (324*2π)/15935 weeks
325-78.61794 974.7089 (325*2π)/15935 weeks
326384.8451 52.63963 (326*2π)/15935 weeks
327-266.6895 635.2629 (327*2π)/15935 weeks
328114.3861 421.6179 (328*2π)/15935 weeks
329-119.1087 454.6244 (329*2π)/15935 weeks
330-263.5292 437.7475 (330*2π)/15935 weeks
331-364.9971 -99.59424 (331*2π)/15935 weeks
332-70.22903 321.3005 (332*2π)/15935 weeks
333293.4045 -92.72598 (333*2π)/15935 weeks
334-364.4774 263.8709 (334*2π)/15935 weeks
33532.83725 197.345 (335*2π)/15935 weeks
336-86.10597 -110.4173 (336*2π)/15935 weeks
337101.4593 24.19602 (337*2π)/15935 weeks
338201.1426 242.1928 (338*2π)/15935 weeks
339-295.6768 -97.2326 (339*2π)/15935 weeks
340222.1272 145.6924 (340*2π)/15935 weeks
34180.15623 -29.55674 (341*2π)/15935 weeks
342219.9873 -413.5332 (342*2π)/15935 weeks
343335.7442 483.4245 (343*2π)/15935 weeks
344364.4954 253.7394 (344*2π)/15935 weeks
34581.52959 -150.2606 (345*2π)/15935 weeks
34636.91813 830.3121 (346*2π)/15935 weeks
347215.6839 -368.0118 (347*2π)/15935 weeks
34848.21785 408.8156 (348*2π)/15935 weeks
34947.65731 301.1776 (349*2π)/15935 weeks
350220.0791 -129.8917 (350*2π)/15935 weeks
35184.51943 405.1527 (351*2π)/15935 weeks
352-161.738 31.63829 (352*2π)/15935 weeks
353310.4975 316.6492 (353*2π)/15935 weeks
35459.85492 -202.5484 (354*2π)/15935 weeks
355-138.326 75.12772 (355*2π)/15934 weeks
356557.0041 499.2784 (356*2π)/15934 weeks
35768.89983 -347.6035 (357*2π)/15934 weeks
358-67.83328 434.5467 (358*2π)/15934 weeks
359531.4929 314.0502 (359*2π)/15934 weeks
360-195.9326 -18.50638 (360*2π)/15934 weeks
361-47.17923 500.2225 (361*2π)/15934 weeks
36266.7088 -229.3607 (362*2π)/15934 weeks
363-1.5116 84.12764 (363*2π)/15934 weeks
36480.53981 -69.35795 (364*2π)/15934 weeks
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370259.5281 224.6977 (370*2π)/15934 weeks
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39272.09547 -55.13191 (392*2π)/15934 weeks
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45589.27705 -23.40503 (455*2π)/15934 weeks
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4826.03236 299.6206 (482*2π)/15933 weeks
483104.7982 203.4827 (483*2π)/15933 weeks
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485118.8672 129.8 (485*2π)/15933 weeks
486405.1925 178.1187 (486*2π)/15933 weeks
487228.5665 93.14663 (487*2π)/15933 weeks
488184.18 234.2489 (488*2π)/15933 weeks
489-74.97906 56.12525 (489*2π)/15933 weeks
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491370.8184 130.219 (491*2π)/15933 weeks
492264.5009 208.8979 (492*2π)/15933 weeks
493-167.264 436.8049 (493*2π)/15933 weeks
494338.3552 182.4321 (494*2π)/15933 weeks
495-12.51076 -92.6163