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Fourier Analysis of TMS (TMS International Corp. Class A)


TMS (TMS International Corp. Class A) appears to have interesting cyclic behaviour every 37 weeks (11841.88*sine), 26 weeks (8104.963*sine), and 25 weeks (7666.09*cosine).

TMS (TMS International Corp. Class A) has an average price of 54,512.01 (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 2/22/2010 to 3/13/2017 for TMS (TMS International Corp. Class A), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
054,512.01   0 
1-22,701.67 -43,513.13 (1*2π)/368368 weeks
2-1,288.507 74,921.02 (2*2π)/368184 weeks
330,380.07 8,261.202 (3*2π)/368123 weeks
4-11,671.61 -3,061.644 (4*2π)/36892 weeks
5-20,986.97 -2,739.834 (5*2π)/36874 weeks
62,165.041 17,243.2 (6*2π)/36861 weeks
719,560.23 -13,086.01 (7*2π)/36853 weeks
8-3,469.149 -1,507.11 (8*2π)/36846 weeks
91,412.356 9,605.498 (9*2π)/36841 weeks
102,690.194 11,841.88 (10*2π)/36837 weeks
112,697.462 -1,484.713 (11*2π)/36833 weeks
12-4,587.428 -49.60252 (12*2π)/36831 weeks
13-1,897.216 -647.7517 (13*2π)/36828 weeks
141,592.125 8,104.963 (14*2π)/36826 weeks
157,666.09 -2,219.77 (15*2π)/36825 weeks
16-6,068.285 -51.03609 (16*2π)/36823 weeks
17-2,758.479 3,164.791 (17*2π)/36822 weeks
18781.0023 3,721.916 (18*2π)/36820 weeks
195,506.764 -6,045.232 (19*2π)/36819 weeks
20-4,340.547 -863.4766 (20*2π)/36818 weeks
213,122.842 4,338.183 (21*2π)/36818 weeks
221,238.92 3,531.804 (22*2π)/36817 weeks
233,030.238 -1,038.537 (23*2π)/36816 weeks
24-5,937.219 -710.4609 (24*2π)/36815 weeks
25664.6133 3,355.849 (25*2π)/36815 weeks
261,380.128 749.585 (26*2π)/36814 weeks
273,566.125 -1,791.304 (27*2π)/36814 weeks
28-5,534.216 -582.6334 (28*2π)/36813 weeks
29932.4352 5,906.053 (29*2π)/36813 weeks
301,792.07 -1,779.045 (30*2π)/36812 weeks
31-80.15739 -2,422.729 (31*2π)/36812 weeks
32-3,051.579 88.19474 (32*2π)/36812 weeks
333,231.889 4,115.012 (33*2π)/36811 weeks
341,792.381 -1,148.347 (34*2π)/36811 weeks
35-579.5257 486.5107 (35*2π)/36811 weeks
36-3,372.329 877.9861 (36*2π)/36810 weeks
371,615.043 3,381.396 (37*2π)/36810 weeks
38919.7206 -2,952.795 (38*2π)/36810 weeks
39-540.3578 390.755 (39*2π)/3689 weeks
40-1,083.878 79.93961 (40*2π)/3689 weeks
411,352.001 3,822.089 (41*2π)/3689 weeks
422,003.604 -2,219.161 (42*2π)/3689 weeks
43-1,952.228 171.3708 (43*2π)/3689 weeks
44-602.354 1,181.125 (44*2π)/3688 weeks
452,065.04 2,797.633 (45*2π)/3688 weeks
461,568.732 -2,513.384 (46*2π)/3688 weeks
47-2,747.235 1,465.372 (47*2π)/3688 weeks
48675.9058 1,420.14 (48*2π)/3688 weeks
49746.5167 822.8662 (49*2π)/3688 weeks
501,252.912 -1,947.447 (50*2π)/3687 weeks
51-1,380.583 517.0762 (51*2π)/3687 weeks
521,441.509 1,365.075 (52*2π)/3687 weeks
531,329.489 1,197.586 (53*2π)/3687 weeks
541,235.667 -919.5596 (54*2π)/3687 weeks
55-1,755.095 895.9265 (55*2π)/3687 weeks
56699.2737 1,590.15 (56*2π)/3687 weeks
571,099.705 830.2307 (57*2π)/3686 weeks
58839.7946 -1,976.436 (58*2π)/3686 weeks
59-2,547.152 1,024.242 (59*2π)/3686 weeks
602,294.447 1,466.247 (60*2π)/3686 weeks
61515.282 -1,005.225 (61*2π)/3686 weeks
62665.6189 -499.5169 (62*2π)/3686 weeks
63-1,233.291 439.0597 (63*2π)/3686 weeks
641,479.146 1,607.116 (64*2π)/3686 weeks
65624.0381 -647.0419 (65*2π)/3686 weeks
66190.2748 -754.246 (66*2π)/3686 weeks
67-1,783.055 194.7684 (67*2π)/3685 weeks
681,498.6 1,865.158 (68*2π)/3685 weeks
691,097.155 -1,711.451 (69*2π)/3685 weeks
70-1,252.784 -1,005.013 (70*2π)/3685 weeks
71-1,409.297 1,226.342 (71*2π)/3685 weeks
722,481.563 357.5058 (72*2π)/3685 weeks
73-415.5237 -2,798.32 (73*2π)/3685 weeks
74-602.6076 823.504 (74*2π)/3685 weeks
75472.0542 -29.57677 (75*2π)/3685 weeks
76595.3215 664.5626 (76*2π)/3685 weeks
77350.8926 -1,109.69 (77*2π)/3685 weeks
78-1,081.498 -430.5821 (78*2π)/3685 weeks
79-724.7888 691.3969 (79*2π)/3685 weeks
801,617.399 532.9054 (80*2π)/3685 weeks
81-259.6715 -2,018.729 (81*2π)/3685 weeks
82-1,657.164 751.0281 (82*2π)/3684 weeks
83-114.37 672.5496 (83*2π)/3684 weeks
841,019.976 -197.0668 (84*2π)/3684 weeks
85-524.033 -2,260.921 (85*2π)/3684 weeks
86-1,295.491 1,260.82 (86*2π)/3684 weeks
871,270.798 932.6027 (87*2π)/3684 weeks
88388.263 -113.2289 (88*2π)/3684 weeks
89-1,412.491 -699.566 (89*2π)/3684 weeks
90-1,400.271 1,479.511 (90*2π)/3684 weeks
91883.2114 -123.7179 (91*2π)/3684 weeks
92-97.49815 -529.0066 (92*2π)/3684 weeks
93-501.1498 78.05998 (93*2π)/3684 weeks
94-515.7697 1,678.801 (94*2π)/3684 weeks
95-149.3366 369.2798 (95*2π)/3684 weeks
96-912.9628 561.2938 (96*2π)/3684 weeks
97-356.4044 -1,122.587 (97*2π)/3684 weeks
98-1,403.529 674.3816 (98*2π)/3684 weeks
991,551.817 891.2907 (99*2π)/3684 weeks
100264.4213 16.73801 (100*2π)/3684 weeks
101-906.4952 422.5453 (101*2π)/3684 weeks
102-1,381.787 1,982.531 (102*2π)/3684 weeks
103964.6592 151.1829 (103*2π)/3684 weeks
104-847.5271 -687.0886 (104*2π)/3684 weeks
105164.8993 277.2986 (105*2π)/3684 weeks
106-476.1158 1,389.004 (106*2π)/3683 weeks
1071,502.817 1,166.15 (107*2π)/3683 weeks
108-1,049.811 -434.3456 (108*2π)/3683 weeks
109-460.1432 840.8524 (109*2π)/3683 weeks
110-252.6289 306.6327 (110*2π)/3683 weeks
1111,684.565 920.0846 (111*2π)/3683 weeks
112503.8122 -489.6441 (112*2π)/3683 weeks
113-679.2779 1,600.692 (113*2π)/3683 weeks
114-270.2556 1,849.745 (114*2π)/3683 weeks
1151,016.803 274.68 (115*2π)/3683 weeks
116-930.1304 -1,582.331 (116*2π)/3683 weeks
117-153.4633 1,232.082 (117*2π)/3683 weeks
1181,696.809 801.3427 (118*2π)/3683 weeks
1191,323.991 424.226 (119*2π)/3683 weeks
120-914.3392 134.5376 (120*2π)/3683 weeks
121-494.3362 1,634.06 (121*2π)/3683 weeks
122575.0198 -187.0931 (122*2π)/3683 weeks
1231,140.869 -435.6764 (123*2π)/3683 weeks
124225.0891 -833.2922 (124*2π)/3683 weeks
125335.2743 2,285.125 (125*2π)/3683 weeks
1261,429.739 820.8989 (126*2π)/3683 weeks
127-322.4021 -58.56128 (127*2π)/3683 weeks
128-1,211.986 -570.6445 (128*2π)/3683 weeks
129186.4404 1,017.208 (129*2π)/3683 weeks
1302,075.424 -1,076.93 (130*2π)/3683 weeks
13146.73184 -74.58418 (131*2π)/3683 weeks
132336.0843 848.4897 (132*2π)/3683 weeks
133-157.0224 968.254 (133*2π)/3683 weeks
134361.3803 -421.2103 (134*2π)/3683 weeks
13519.12105 -725.9319 (135*2π)/3683 weeks
136513.8105 -706.7447 (136*2π)/3683 weeks
137568.7292 1,274.394 (137*2π)/3683 weeks
1381,639.434 455.8143 (138*2π)/3683 weeks
139-888.8047 99.99832 (139*2π)/3683 weeks
140-880.2383 111.8065 (140*2π)/3683 weeks
141-404.295 309.0112 (141*2π)/3683 weeks
1421,865.584 -1,095.009 (142*2π)/3683 weeks
143-166.9637 -820.7381 (143*2π)/3683 weeks
144553.0855 1,525.894 (144*2π)/3683 weeks
145197.6127 1,210.501 (145*2π)/3683 weeks
146130.4209 34.11793 (146*2π)/3683 weeks
147-1,387.899 -806.7173 (147*2π)/3683 weeks
148-16.9621 147.8927 (148*2π)/3682 weeks
149906.0453 231.2761 (149*2π)/3682 weeks
1501,548.231 80.60037 (150*2π)/3682 weeks
151-1,155.818 244.3626 (151*2π)/3682 weeks
152-515.6424 1,901.226 (152*2π)/3682 weeks
15354.93325 -282.1646 (153*2π)/3682 weeks
154165.5324 -906.4007 (154*2π)/3682 weeks
155-190.6755 -483.6344 (155*2π)/3682 weeks
156959.8916 1,511.944 (156*2π)/3682 weeks
157918.652 871.4578 (157*2π)/3682 weeks
158-137.5174 513.8584 (158*2π)/3682 weeks
159-1,565.805 46.33632 (159*2π)/3682 weeks
16075.73112 957.9641 (160*2π)/3682 weeks
1611,298.814 -791.893 (161*2π)/3682 weeks
162682.4458 -84.3707 (162*2π)/3682 weeks
163-197.9725 1,028.641 (163*2π)/3682 weeks
164593.8303 2,106.924 (164*2π)/3682 weeks
165247.7481 -589.5619 (165*2π)/3682 weeks
166-643.5895 -118.1084 (166*2π)/3682 weeks
167692.2571 -161.3193 (167*2π)/3682 weeks
1681,447.423 893.7598 (168*2π)/3682 weeks
1691,586.024 612.8931 (169*2π)/3682 weeks
17083.54781 1,109.233 (170*2π)/3682 weeks
171-742.5336 795.0907 (171*2π)/3682 weeks
172209.2062 1,024.461 (172*2π)/3682 weeks
1731,313.129 -1,442.687 (173*2π)/3682 weeks
174255.0674 -80.65318 (174*2π)/3682 weeks
1751,484.325 1,012.084 (175*2π)/3682 weeks
176987.3031 1,460.657 (176*2π)/3682 weeks
177661.5477 142.2291 (177*2π)/3682 weeks
178-760.1757 -108.99 (178*2π)/3682 weeks
179455.3808 -157.0229 (179*2π)/3682 weeks
1801,663.67 239.4418 (180*2π)/3682 weeks
1812,154.527 -720.8453 (181*2π)/3682 weeks
182-288.1136 1,012.61 (182*2π)/3682 weeks
183778.0044 1,399.651 (183*2π)/3682 weeks
184-27.93516   (184*2π)/3682 weeks
185778.0044 -1,399.651 (185*2π)/3682 weeks
186-288.1136 -1,012.61 (186*2π)/3682 weeks
1872,154.527 720.8453 (187*2π)/3682 weeks
1881,663.67 -239.4418 (188*2π)/3682 weeks
189455.3808 157.0229 (189*2π)/3682 weeks
190-760.1757 108.99 (190*2π)/3682 weeks
191661.5477 -142.2291 (191*2π)/3682 weeks
192987.3031 -1,460.657 (192*2π)/3682 weeks
1931,484.325 -1,012.084 (193*2π)/3682 weeks
194255.0674 80.65318 (194*2π)/3682 weeks
1951,313.129 1,442.687 (195*2π)/3682 weeks
196209.2062 -1,024.461 (196*2π)/3682 weeks
197-742.5336 -795.0907 (197*2π)/3682 weeks
19883.54781 -1,109.233 (198*2π)/3682 weeks
1991,586.024 -612.8931 (199*2π)/3682 weeks
2001,447.423 -893.7598 (200*2π)/3682 weeks
201692.2571 161.3193 (201*2π)/3682 weeks
202-643.5895 118.1084 (202*2π)/3682 weeks
203247.7481 589.5619 (203*2π)/3682 weeks
204593.8303 -2,106.924 (204*2π)/3682 weeks
205-197.9725 -1,028.641 (205*2π)/3682 weeks
206682.4458 84.3707 (206*2π)/3682 weeks
2071,298.814 791.893 (207*2π)/3682 weeks
20875.73112 -957.9641 (208*2π)/3682 weeks
209-1,565.805 -46.33632 (209*2π)/3682 weeks
210-137.5174 -513.8584 (210*2π)/3682 weeks
211918.652 -871.4578 (211*2π)/3682 weeks
212959.8916 -1,511.944 (212*2π)/3682 weeks
213-190.6755 483.6344 (213*2π)/3682 weeks
214165.5324 906.4007 (214*2π)/3682 weeks
21554.93325 282.1646 (215*2π)/3682 weeks
216-515.6424 -1,901.226 (216*2π)/3682 weeks
217-1,155.818 -244.3626 (217*2π)/3682 weeks
2181,548.231 -80.60037 (218*2π)/3682 weeks
219906.0453 -231.2761 (219*2π)/3682 weeks
220-16.9621 -147.8927 (220*2π)/3682 weeks
221-1,387.899 806.7173 (221*2π)/3682 weeks
222130.4209 -34.11793 (222*2π)/3682 weeks
223197.6127 -1,210.501 (223*2π)/3682 weeks
224553.0855 -1,525.894 (224*2π)/3682 weeks
225-166.9637 820.7381 (225*2π)/3682 weeks
2261,865.584 1,095.009 (226*2π)/3682 weeks
227-404.295 -309.0112 (227*2π)/3682 weeks
228-880.2383 -111.8065 (228*2π)/3682 weeks
229-888.8047 -99.99832 (229*2π)/3682 weeks
2301,639.434 -455.8143 (230*2π)/3682 weeks
231568.7292 -1,274.394 (231*2π)/3682 weeks
232513.8105 706.7447 (232*2π)/3682 weeks
23319.12105 725.9319 (233*2π)/3682 weeks
234361.3803 421.2103 (234*2π)/3682 weeks
235-157.0224 -968.254 (235*2π)/3682 weeks
236336.0843 -848.4897 (236*2π)/3682 weeks
23746.73184 74.58418 (237*2π)/3682 weeks
2382,075.424 1,076.93 (238*2π)/3682 weeks
239186.4404 -1,017.208 (239*2π)/3682 weeks
240-1,211.986 570.6445 (240*2π)/3682 weeks
241-322.4021 58.56128 (241*2π)/3682 weeks
2421,429.739 -820.8989 (242*2π)/3682 weeks
243335.2743 -2,285.125 (243*2π)/3682 weeks
244225.0891 833.2922 (244*2π)/3682 weeks
2451,140.869 435.6764 (245*2π)/3682 weeks
246575.0198 187.0931 (246*2π)/3681 weeks
247-494.3362 -1,634.06 (247*2π)/3681 weeks
248-914.3392 -134.5376 (248*2π)/3681 weeks
2491,323.991 -424.226 (249*2π)/3681 weeks
2501,696.809 -801.3427 (250*2π)/3681 weeks
251-153.4633 -1,232.082 (251*2π)/3681 weeks
252-930.1304 1,582.331 (252*2π)/3681 weeks
2531,016.803 -274.68 (253*2π)/3681 weeks
254-270.2556 -1,849.745 (254*2π)/3681 weeks
255-679.2779 -1,600.692 (255*2π)/3681 weeks
256503.8122 489.6441 (256*2π)/3681 weeks
2571,684.565 -920.0846 (257*2π)/3681 weeks
258-252.6289 -306.6327 (258*2π)/3681 weeks
259-460.1432 -840.8524 (259*2π)/3681 weeks
260-1,049.811 434.3456 (260*2π)/3681 weeks
2611,502.817 -1,166.15 (261*2π)/3681 weeks
262-476.1158 -1,389.004 (262*2π)/3681 weeks
263164.8993 -277.2986 (263*2π)/3681 weeks
264-847.5271 687.0886 (264*2π)/3681 weeks
265964.6592 -151.1829 (265*2π)/3681 weeks
266-1,381.787 -1,982.531 (266*2π)/3681 weeks
267-906.4952 -422.5453 (267*2π)/3681 weeks
268264.4213 -16.73801 (268*2π)/3681 weeks
2691,551.817 -891.2907 (269*2π)/3681 weeks
270-1,403.529 -674.3816 (270*2π)/3681 weeks
271-356.4044 1,122.587 (271*2π)/3681 weeks
272-912.9628 -561.2938 (272*2π)/3681 weeks
273-149.3366 -369.2798 (273*2π)/3681 weeks
274-515.7697 -1,678.801 (274*2π)/3681 weeks
275-501.1498 -78.05998 (275*2π)/3681 weeks
276-97.49815 529.0066 (276*2π)/3681 weeks
277883.2114 123.7179 (277*2π)/3681 weeks
278-1,400.271 -1,479.511 (278*2π)/3681 weeks
279-1,412.491 699.566 (279*2π)/3681 weeks
280388.263 113.2289 (280*2π)/3681 weeks
2811,270.798 -932.6027 (281*2π)/3681 weeks
282-1,295.491 -1,260.82 (282*2π)/3681 weeks
283-524.033 2,260.921 (283*2π)/3681 weeks
2841,019.976 197.0668 (284*2π)/3681 weeks
285-114.37 -672.5496 (285*2π)/3681 weeks
286-1,657.164 -751.0281 (286*2π)/3681 weeks
287-259.6715 2,018.729 (287*2π)/3681 weeks
2881,617.399 -532.9054 (288*2π)/3681 weeks
289-724.7888 -691.3969 (289*2π)/3681 weeks
290-1,081.498 430.5821 (290*2π)/3681 weeks
291350.8926 1,109.69 (291*2π)/3681 weeks
292595.3215 -664.5626 (292*2π)/3681 weeks
293472.0542 29.57677 (293*2π)/3681 weeks
294-602.6076 -823.504 (294*2π)/3681 weeks
295-415.5237 2,798.32 (295*2π)/3681 weeks
2962,481.563 -357.5058 (296*2π)/3681 weeks
297-1,409.297 -1,226.342 (297*2π)/3681 weeks
298-1,252.784 1,005.013 (298*2π)/3681 weeks
2991,097.155 1,711.451 (299*2π)/3681 weeks
3001,498.6 -1,865.158 (300*2π)/3681 weeks
301-1,783.055 -194.7684 (301*2π)/3681 weeks
302190.2748 754.246 (302*2π)/3681 weeks
303624.0381 647.0419 (303*2π)/3681 weeks
3041,479.146 -1,607.116 (304*2π)/3681 weeks
305-1,233.291 -439.0597 (305*2π)/3681 weeks
306665.6189 499.5169 (306*2π)/3681 weeks
307515.282 1,005.225 (307*2π)/3681 weeks
3082,294.447 -1,466.247 (308*2π)/3681 weeks
309-2,547.152 -1,024.242 (309*2π)/3681 weeks
310839.7946 1,976.436 (310*2π)/3681 weeks
3111,099.705 -830.2307 (311*2π)/3681 weeks
312699.2737 -1,590.15 (312*2π)/3681 weeks
313-1,755.095 -895.9265 (313*2π)/3681 weeks
3141,235.667 919.5596 (314*2π)/3681 weeks
3151,329.489 -1,197.586 (315*2π)/3681 weeks
3161,441.509 -1,365.075 (316*2π)/3681 weeks
317-1,380.583 -517.0762 (317*2π)/3681 weeks
3181,252.912 1,947.447 (318*2π)/3681 weeks
319746.5167 -822.8662 (319*2π)/3681 weeks
320675.9058 -1,420.14 (320*2π)/3681 weeks
321-2,747.235 -1,465.372 (321*2π)/3681 weeks
3221,568.732 2,513.384 (322*2π)/3681 weeks
3232,065.04 -2,797.633 (323*2π)/3681 weeks
324-602.354 -1,181.125 (324*2π)/3681 weeks
325-1,952.228 -171.3708 (325*2π)/3681 weeks
3262,003.604 2,219.161 (326*2π)/3681 weeks
3271,352.001 -3,822.089 (327*2π)/3681 weeks
328-1,083.878 -79.93961 (328*2π)/3681 weeks
329-540.3578 -390.755 (329*2π)/3681 weeks
330919.7206 2,952.795 (330*2π)/3681 weeks
3311,615.043 -3,381.396 (331*2π)/3681 weeks
332-3,372.329 -877.9861 (332*2π)/3681 weeks
333-579.5257 -486.5107 (333*2π)/3681 weeks
3341,792.381 1,148.347 (334*2π)/3681 weeks
3353,231.889 -4,115.012 (335*2π)/3681 weeks
336-3,051.579 -88.19474 (336*2π)/3681 weeks
337-80.15739 2,422.729 (337*2π)/3681 weeks
3381,792.07 1,779.045 (338*2π)/3681 weeks
339932.4352 -5,906.053 (339*2π)/3681 weeks
340-5,534.216 582.6334 (340*2π)/3681 weeks
3413,566.125 1,791.304 (341*2π)/3681 weeks
3421,380.128 -749.585 (342*2π)/3681 weeks
343664.6133 -3,355.849 (343*2π)/3681 weeks
344-5,937.219 710.4609 (344*2π)/3681 weeks
3453,030.238 1,038.537 (345*2π)/3681 weeks
3461,238.92 -3,531.804 (346*2π)/3681 weeks
3473,122.842 -4,338.183 (347*2π)/3681 weeks
348-4,340.547 863.4766 (348*2π)/3681 weeks
3495,506.764 6,045.232 (349*2π)/3681 weeks
350781.0023 -3,721.916 (350*2π)/3681 weeks
351-2,758.479 -3,164.791 (351*2π)/3681 weeks
352-6,068.285 51.03609 (352*2π)/3681 weeks
3537,666.09 2,219.77 (353*2π)/3681 weeks
3541,592.125 -8,104.963 (354*2π)/3681 weeks
355-1,897.216 647.7517 (355*2π)/3681 weeks
356-4,587.428 49.60252 (356*2π)/3681 weeks
3572,697.462 1,484.713 (357*2π)/3681 weeks
3582,690.194 -11,841.88 (358*2π)/3681 weeks
3591,412.356 -9,605.498 (359*2π)/3681 weeks
360-3,469.149 1,507.11 (360*2π)/3681 weeks
36119,560.23 13,086.01 (361*2π)/3681 weeks
3622,165.041 -17,243.2 (362*2π)/3681 weeks
363-20,986.97 2,739.834 (363*2π)/3681 weeks
364-11,671.61 3,061.644 (364*2π)/3681 weeks
36530,380.07 -8,261.202 (365*2π)/3681 weeks
366-1,288.507 -74,921.02 (366*2π)/3681 weeks

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