ISBN 963 8361 28 X HU ISSN 0328 - 2091
UBV OBSERVATIONS OF THE RS CVn BINARY HK LACERTAE BETWEEN 1978-1985 Abstract We report 524 UBV observations of the RS CVn binary HK Lac made between 1978-1985. Our starspot modelling results published previ- ously for 12 light curves (using V colour) are summarized. Three ad- ditional modelled light curves are presented which have not been published before. Nine UBV light and colour curves obtained between 1982-85 in 16 American and 2 Hungarian observatories, are given. Light curve mod- elling made for the V and B light curves separately show that the resulting model parameters agree well within the error of the mod- elling procedure. Introduction and Observations We have previously published two detailed papers on HK Lac describing its light variation on the basis of starspot modelling (Olah et al., 1985, 1986, hereafter Paper I and Paper II, respectively). The observations we used were only published in part so we have compiled a complete presentation here for future use by other investigators. The magnitudes presented here are individual values, but when performing the light curve modelling for Paper II, we formed nightly means if we had more than one value per night. The DeltaV magnitudes used in Paper I are individual values and that table (Table VII in Paper I) is repeated here in full. Observations have been secured altogether in 18 observatories in the standard UBV system, the observers and observatories are listed in Table I. No systematic differences have been found between the photometric results of the different observatories. Table III gives UBV magnitudes of HK Lac with respect to HD 208728 (C1). The DeltaV magnitudes of this table have already been published in Paper I. We repeat in Table III only those measurements which can be supplemented with the corresponding DeltaB and DeltaU magnitudes. In the beginning of this table UBV magni- tudes observed by K.O. between 1976-1978 (Olah, 1979) are given. The UBV magnitude differences (with respect to HD 210731 (C2) of Table IV have not been presented before. From this table the DeltaV observations made between J.D. 2445195-2446068 were used in modelling the light curves of Paper II. Additional 100 observations gathered between J.D. 2446181-2446367 which have not been cited before in details, close Table IV. To complete the lists of observations, Table V gives the rest of DeltaV observations from Paper I. Table I. Observer Observatory Telescope Aperture Boyd, L. J. Fairborn 10 inch Burke, E.W. Jr. Kitt Peak 16 inch Chambliss, C.R. Kutztown 15 inch Eaton, J.A. Kitt Peak 16 inch Fried, R.E. Braeside 16 inch Genet, R.M. Fairborn 10 inch Henry, G.W. Dyer 24 inch Kitt Peak 16 inch Cloudcroft 48 inch Landis, H.J. Landis 8 inch Lines, H.C. Lines 20 inch Lines, R.D. Lines 20 inch Louth, H. Louth 11 inch Miles, R. Mouldsworth 11 inch Nielsen, P. Nielsen 4 inch Olah, K. Konkoly 24 inch Piszkesteto 20 inch Renner, T.R. Scuppernong 10 inch Stelzer, H.J. Stelzer 14 inch Troeger, J.C. Sky Lights 8 inch Wasatonic, R.P. Pulpit Rock 20 inch Wasson, N.F. Sunset Hills 8 inch All magnitude tables (III-V) contain some sporadic observations which have never been used for starspot modelling since they did not form appropri- ate light curves. Magnitude differences between HD 208728 (C1) and HD 210721 (C2), were published in the Inf. Bull. Var. Stars (Olah, 1979). Results Most of our starspot modelling results have already been published in Papers I and II. The main goal of those papers was, using solar analogies, to identify stable active longitudes on the surface of the star. Two different methods were used to determine the position of the corotating latitude situat- ed about 30 degrees above and below the equator. We found complex but possible 7 year cyclic variations in the median brightness of the star. In the present paper we show that spot models made in different colours of the same light curve give the same result within the error of the determi- nation of the parameters. From UBV light curves observed between 1982-85 the V colour has already been fitted by two spots. Here we supplement by giving model results from the B data. For spot modelling we used the equations developed by Budding (1977) combined with a grid-search method to find the proper parameters. As orbital inclination we found i = 60deg (Paper I). Limb darkening coefficients were 0.75 (V), 0.85 (B), 0.91 (U), from Manduca et al. (1977). The time of 0 longi- tude was the time of maximum + 180 degrees. We took the flux ratios 0.4 (V), 0.36 (B), 0.33 (U) from Planck functions assuming that the spots were 2000 OK cooler than the surrounding photosphere. The 1.0 intensity was given by the local maximum. The overall light variation was considered to be produced by spotted belts around the star situated parallel to the equator. In most of the cases we fitted the light curves by two spots. For modelling details see Paper I. Table II lists the J.D. intervals, epochs and the resulting spot parame- ters. When both V and B models are available, we give them separately in addition to their average values. The modelling results made separately for the V and B light curves agree reasonably well. Typical uncertainties in the parameters are as follows: +/- 2-3 degrees in longitude, +/- 5-8 degrees in Table II Resulting spot parameters No. J.D. (2440000+) epoch Period lambda_1 lambda_2 beta_1 beta_2 gamma1 gamma2 color interval 1 3355-3455 3348.3 25.042 314 80 55 -6 22.9 23.3 V 2 3634-3721 3617.6 23.385 322 72 51 -7.5 23.0 26.0 V 3 3722-3806 3709.8 25.203 335 63 49 26 24.0 19.7 V 4 3855-4094 3812.1 24.282 317 63 48 6 26.8 30.7 V 5 4496-4561 4445.1 24.174 296 57 38 27.5 22.5 26.6 V 6 4865-4968 4840.8 24.243 310 70 40 26.5 18.6 15.9 V 270 50 12 46 18.2 27.9 V 276 52 3 42 17.9 25.9 B 7 5195-5279 5180.8 23.724 273 51 8 44 18.1 26.9 mean 318 52 57 23 24.2 28.1 V 320 54 59 25 23.6 28.0 B 8 5471-5622 5448.0 24.397 319 53 58 24 23.9 28.1 mean 335 60 53 17 27.0 28.0 V 335 61 50 14 26.9 28.0 B 9 5628-5687 5618.4 24.397 335 61 52 16 27.0 28.0 mean 339 -- 45 -- 37.2 ---- V 337 -- 52 -- 41.8 ---- B 10 5697-5713 5695.1 24.429 338 -- 49 -- 39.5 ---- mean 304 18 7 53 26.0 19.9 V 305 2 31 58 22.4 19.0 B 11 5820-5899 5819.3 24.461 304 10 19 56 24.2 19.5 mean 303 8 11 63 21.3 21.3 V 315 18 27 60 21.0 22.6 B 12 5970-6028 5965.0 24.461 309 13 19 62 21.2 22.0 mean 345 56 48 29 23.3 19.1 V 341 59 52 52 23.1 21.1 B 13 6030-6068 6010.9 24.461 343 58 50 41 23.2 20.1 mean 321 51 43 34 29.2 22.1 V 325 59 45 27 29.7 21.2 B 14 6181-6282 6159.8 24.389 323 55 44 31 29.5 21.7 mean 308 40 36 50 27.9 22.0 V 307 41 31 45 28.0 22.0 B 15 6283-6338 6257.7 24.501 308 41 33 48 28.0 22.0 mean latitude and +/- 0.5 degree in radius. The latitude parameter is the most un- certain one of all the fitted parameters. In two cases (model 11 and 13) one can find larger discrepancies in one of the latitude and the corresponding radius results obtained from the V and B light curves. Except model 10 (see below) these two light curves had far the smallest number of observations: 18 (model 11) and 15 (model 13) data points were fitted. This shows, obviously, that more observational data give less uncertain parameters. The last 9 light curves are displayed in Figures 1-9, together with the colour curves. The U measurements were not modelled, the curve is drawn with the resulted average parameters (determined by B and V light curves) and using the above mentioned limb darkening coefficient and flux ratio. The models of No. 10, 14 and 15 from Table V have not been published before, but the model parameters were used in a recent paper (Olah et al., 1988). Model No. 10 (Figure 4), is very uncertain because of the few observa- tional points, but is the only light curve of the star which could be fitted by one single spot. Interesting new results about starspot proper motion on HK Lac, and also a figure of the positions of the activity centers on the star, were given in the above mentioned paper (Olah et al., 1988). Budapest - Szabadsaghegy, 1988. April 8.
References:
Budding, E., 1977, Astrophys. Space Sci. 48.207
Manduca, A., Bell, R.A., Gustaffson, B., 1977, Astron. Astrophys. 61.809
Olah, K., 1979, Inf. Bull. Var. Stars No. 1717 (IBVS N°.1717)
Olah, K., Eaton, J.A., Hall, D.S., Henry, G.W., Burke, E.W. Jr., Chambliss, C.R., Fried, R.E., Landis, H.J., Louth, H., Renner, T.R., Stelzer, H.J., Wasatonic, R.P., 1985, Astrophys. Space Sci. 108.137 (Paper I)
Olah, K., Gesztelyi, L., Holl, A., 1988, Proc. Xth European Regional Astr. Meeting (in press) 1987eram....5...95O
Olah, K., Hall, D.S., Boyd, L.J., Genet, R.M., Fried, R.E., Lines, R.D., Lines, H.C., Louth, H., Miles, R., Nielsen, P., Stelzer, H.J., Troeger, J.C., Wasson, N.F., 1986, Astrophys. Letters 25.133 (Paper II)
Figure 1: Light and colour curves of HK Lac (model 7)
Figure 2: Light and colour curves of HK Lac (model 8)
Figure 3: Light and colour curves of HK Lac (model 9)
Figure 4: Light and colour curves of HK Lac (model 10)
Figure 5: Light and colour curves of HK Lac (model 11)
Figure 6: Light and colour curves of HK Lac (model 12)
Figure 7: Light and colour curves of HK Lac (model 13)
Figure 8: Light and colour curves of HK Lac (model 14)
Figure 9: Light and colour curves of HK Lac (model 15)
091-t3.txt Table III UBV magnitudes of HK Lac with respect to HD 208728 (C1) J.D. Delta U Delta B Delta V 3045.437 ---- -.013 .100 3048.522 ---- -.011 .126 3073.303 ---- .002 .107 3076.286 -.095 -.002 .112 3077.230 -.053 .018 .122 3079.217 -.042 .037 .180 3108.254 -.025 .093 .192 3368.503 -.090 .024 .130 3385.525 ---- -.056 .086 3432.316 -.138 -.017 .115 3434.322 -.113 -.012 .117 3438.356 -.112 -.007 .113 3455.286 -.107 .014 .152 3482.276 -.137 -.024 .124 3514.222 -.188 -.029 .088 3713.473 -.002 .096 .199 3727.547 -.167 -.034 .078 3739.464 -.025 .065 .177 3740.412 -.077 .059 .162 3742.456 -.038 .009 .111 3747.497 ---- -.101 .039 3766.378 -.063 .016 .122 3777.461 -.152 -.048 .077 3797.304 -.225 -.113 .022 3879.209 ---- -.011 .091 3881.232 ---- .039 .157 4034.950 ---- .092 .223 4035.945 ---- .063 .197 4036.937 ---- .018 .158 4038.954 ---- -.061 .081 4043.947 ---- -.121 .018 4045.942 ---- -.097 .040 4048.944 ---- -.073 .066 4069.878 ---- -.115 .034 4086.810 ---- -.019 .125 4091.849 ---- -.138 -.008 4172.369 -.185 -.081 .044 4474.785 ---- .058 .139 4483.688 ---- -.102 -.011 4497.717 ---- .061 .152 4502.390 -.259 -.122 .029 4502.708 ---- -.094 .009 4511.375 -.115 -.041 .085 4514.350 -.092 -.004 .115 4533.439 -.206 -.078 .050 4541.244 -.082 .004 .109 4561.250 -.108 -.015 .082 4605.265 -.247 -.118 -.017 4613.257 -.150 -.039 .067 4621.344 ---- .022 .114 4628.246 -.247 -.144 -.013 4633.242 ---- -.073 .048 4635.231 -.130 -.038 .074 4638.246 -.153 -.049 .085 4783.522 -.127 -.024 .084 4787.536 -.004 .075 .169 4811.464 -.056 .069 .170 4813.422 -.042 .081 .184 4822.412 -.172 -.043 .063 4854.459 -.142 -.032 .067 4873.453 -.148 -.044 .054
091-t4.txt Table IV UBV magnitudes of HK Lac with respect to HD 210731 (C2) J.D. Delta U Delta B Delta V 2440000+ 5195.585 ---- ---- -.541 5210.509 ---- ---- -.509 5213.855 .583 -.088 -.571 5218.451 .584 -.077 -.563 5219.479 ---- -.050 -.539 5221.426 .658 -.025 -.517 5223.451 .645 -.009 -.509 5224.444 .645 -.018 -.518 5225.465 .662 -.018 -.501 5226.482 .630 -.024 -.510 5228.505 .635 .014 -.471 5228.835 .715 .040 -.445 5228.840 ---- ---- -.451 5229.426 .678 .047 -.449 5230.449 .710 .079 -.429 5230.672 ---- ---- -.417 5231.806 .760 .073 -.422 5234.810 .691 .009 -.488 5239.437 .572 -.096 -.596 5243.773 .608 -.056 -.538 5244.765 .632 -.039 -.532 5245.578 ---- ---- -.509 5245.743 .649 -.026 -.516 5246.499 ---- -.051 -.535 5247.778 .648 -.024 -.514 5250.824 .639 -.013 -.493 5253.595 ---- ---- -.419 5254.796 .754 .076 -.416 5256.780 .752 .077 -.418 5257.763 .690 .025 -.456 5259.415 .654 .009 -.488 5259.547 ---- ---- -.461 5261.361 .591 -.049 -.533 5261.824 .603 -.062 -.541 5265.563 ---- ---- -.590 5270.721 .667 -.014 -.507 5275.761 .684 .011 -.499 5279.717 .780 .108 -.391 5306.644 .760 .104 -.387 5310.688 ---- ---- -.508 5311.506 ---- ---- -.542 5316.674 .594 -.067 -.544 5319.668 .648 -.030 -.516 5322.673 .723 .008 -.477 5325.475 ---- ---- -.344 5471.557 .724 .087 -.399 5473.539 .834 .168 -.336 5475.542 .815 .158 -.353 5493.489 .663 .002 -.472 5508.471 .522 -.120 -.593 5521.510 .708 .095 -.385 5525.910 .812 .127 -.376 5526.539 .780 .109 -.388 5528.515 .659 .011 -.478 5529.930 .616 -.049 -.527 5531.944 .569 -.097 -.570 5532.517 .533 -.112 -.585 5532.902 .564 -.107 -.581 5533.487 .546 -.095 -.579 5534.750 ---- ---- -.592 5539.817 ---- ---- -.483 5541.475 .638 -.021 -.492 5542.517 .672 .027 -.458 5545.732 ---- ---- -.369 5546.519 .810 .158 -.346 5547.515 .807 .151 -.347 5547.721 ---- ---- -.349 5548.711 ---- ---- -.356 5560.963 ---- ---- -.542 5566.565 .674 .027 -.450 5572.862 .818 .149 -.343 5574.884 .765 .101 -.392 5580.741 ---- ---- -.581 5581.718 ---- ---- -.578 5581.853 .556 -.104 -.586 5582.732 ---- ---- -.586 5582.741 ---- ---- -.579 5583.726 ---- ---- -.574 5583.781 ---- -.080 -.572 5585.716 ---- ---- -.514 5586.705 ---- ---- -.523 5586.846 .638 -.042 -.523 5587.724 ---- ---- -.520 5588.444 .626 -.014 -.502 5588.886 .657 -.008 -.494 5589.889 .691 .012 -.464 5591.709 ---- ---- -.432 5595.695 ---- ---- -.339 5596.699 ---- ---- -.337 5596.786 .849 .167 -.342 5597.364 .803 .153 -.344 5599.695 ---- ---- -.403 5601.372 .676 .029 -.464 5601.670 ---- ---- -.474 5603.328 .589 -.070 -.552 5604.334 .539 -.098 -.580 5605.462 .529 -.114 -.593 5606.494 .502 -.125 -.595 5606.710 ---- ---- -.587 5607.418 .529 -.114 -.591 5618.669 ---- ---- -.371 5619.627 ---- ---- -.352 5619.718 ---- ---- -.334 5621.629 ---- ---- -.347 5622.392 .788 .134 -.359 5628.615 ---- ---- -.599 5630.624 ---- ---- -.619 5631.621 ---- ---- -.610 5632.640 ---- ---- -.595 5633.622 ---- ---- -.576 5635.354 .537 -.096 -.575 5635.627 ---- ---- -.557 5636.331 .531 -.093 -.568 5636.585 ---- ---- -.523 5641.707 .795 .106 -.395 5642.643 ---- ---- -.378 5643.636 ---- ---- -.352 5645.736 .851 .164 -.345 5646.597 ---- ---- -.365 5647.746 .789 .109 -.386 5648.323 .751 .093 -.402 5649.347 .668 .033 -.460 5649.637 ---- ---- -.471 5650.608 ---- ---- -.515 5651.290 .582 -.068 -.545 5652.664 .501 -.096 -.597 5653.352 .510 -.127 -.605 5653.627 .469 -.126 -.608 5654.632 .499 -.128 -.610 5654.652 ---- ---- -.628 5655.664 .484 -.114 -.598 5657.660 .539 -.121 -.572 5658.587 .509 -.080 -.592 5662.710 .636 -.008 -.476 5665.625 .714 .104 -.405 5665.682 .748 .085 -.409 5666.589 .669 .095 -.417 5667.606 .763 .150 -.356 5667.612 ---- ---- -.376 5667.673 .792 .132 -.358 5668.583 .766 .169 -.341 5673.616 .643 .054 -.450 5674.647 .603 .008 -.489 5675.629 .560 -.045 -.521 5676.579 .527 -.080 -.564 5677.608 .490 -.105 -.597 5678.615 .492 -.123 -.603 5679.637 .484 -.131 -.607 5681.665 .513 -.121 -.587 5683.595 .539 -.076 -.566 5684.571 .569 -.045 -.547 5685.571 .569 -.019 -.528 5686.578 .586 0.000 -.515 5687.581 .644 .032 -.481 5697.577 .722 .124 -.402 5698.574 .671 .040 -.446 5699.569 .630 .011 -.496 5700.610 .575 -.050 -.522 5703.582 .527 -.079 -.526 5704.596 .503 -.122 -.588 5710.598 .567 -.041 -.536 5711.580 .622 -.006 -.528 5713.571 .712 .079 -.422 5820.981 .662 .060 -.450 5823.972 .611 -.004 -.500 5824.965 .613 -.028 -.501 5825.963 .614 -.024 -.530 5826.963 .576 -.045 -.532 5827.956 .544 -.041 -.541 5828.955 .563 -.050 -.550 5829.965 .569 -.059 -.565 5830.951 .580 -.053 -.549 5831.947 .540 -.052 -.545 5832.945 .579 -.052 -.552 5836.935 .687 .061 -.463 5837.930 .732 .108 -.397 5838.929 .767 .134 -.380 5862.907 .686 .080 -.406 5871.929 .642 .001 -.481 5872.955 .643 -.020 -.489 5873.944 .621 -.033 -.522 5970.752 .598 .008 -.505 5971.724 .572 -.015 -.507 5972.752 .603 -.034 -.527 5973.774 .594 -.053 -.540 5983.769 .661 .058 -.462 5984.691 .712 .086 -.417 5986.710 .736 .142 -.386 5987.714 .748 .145 -.373 5990.735 .690 .081 -.429 5991.767 .642 .067 -.465 5992.738 .644 .022 -.479 5993.737 .597 -.003 -.505 5994.749 .583 -.004 -.505 5997.698 .549 -.058 -.550 5999.676 .530 -.071 -.553 6000.702 .522 -.064 -.555 6001.668 .538 -.064 -.549 6002.671 .540 -.068 -.546 6004.674 .580 -.037 -.534 6005.655 .598 -.020 -.518 6006.657 .635 .013 -.497 6007.656 .676 .043 -.466 6008.656 .706 .077 -.423 6009.691 .722 .095 -.406 6010.648 .747 .121 -.381 6012.653 .738 .139 -.382 6013.757 .706 .093 -.395 6014.645 .693 .071 -.417 6015.711 .687 .068 -.451 6016.713 .632 .038 -.475 6021.653 .526 -.035 -.550 6022.635 .560 -.065 -.535 6024.634 .519 -.072 -.545 6025.644 .551 -.077 -.560 6028.662 .598 -.048 -.532 6030.626 .634 .008 -.485 6031.633 .660 .040 -.464 6032.619 .689 .070 -.442 6034.629 .737 .100 -.411 6036.626 .788 .145 -.360 6039.676 .699 .077 -.433 6043.623 .573 -.023 -.533 6046.664 .550 -.079 -.558 6051.589 .542 -.066 -.556 6055.611 .625 .009 -.486 6056.619 .679 .042 -.456 6058.625 .766 .060 -.422 6060.614 .745 .108 -.390 6064.608 .678 .030 -.449 6068.576 .584 -.032 -.535 6181.567 .741 .083 -.383 6187.977 .727 .103 -.430 6190.979 .624 -.001 -.515 6197.956 .494 -.088 -.577 6198.954 .538 -.084 -.573 6199.954 .535 -.064 -.547 6204.950 .706 .096 -.426 6205.938 .773 .134 -.370 6206.929 .776 .152 -.351 6207.926 .698 .132 -.358 6208.928 .728 .149 -.359 6209.916 .734 .131 -.365 6210.915 .696 .105 -.389 6211.524 .696 .068 -.422 6211.912 .697 .102 -.413 6213.533 .645 .005 -.486 6213.904 .640 .036 -.467 6218.900 .526 -.083 -.570 6221.938 .500 -.103 -.596 6222.889 .498 -.100 -.561 6223.890 .526 -.081 -.581 6224.881 .623 -.059 -.554 6225.875 .664 -.012 -.509 6226.872 .694 .046 -.448 6228.497 .731 .087 -.420 6229.865 .736 .141 -.371 6230.862 .738 .140 -.371 6231.867 .770 .152 -.350 6233.895 .738 .143 -.363 6234.901 .734 .124 -.384 6235.846 .723 .098 -.415 6236.873 .673 .057 -.447 6237.892 .662 .041 -.454 6238.850 .662 .015 -.498 6241.874 .553 -.066 -.564 6242.873 .513 -.111 -.591 6243.878 .503 -.090 -.594 6244.931 .520 -.103 -.593 6245.872 .459 -.112 -.603 6248.840 .549 -.059 -.554 6249.916 .606 -.035 -.517 6250.845 .612 .022 -.466 6251.912 .546 .037 -.453 6252.932 .708 .083 -.403 6259.851 .705 .114 -.386 6267.829 .495 -.102 -.588 6269.848 .462 -.116 -.605 6270.828 .494 -.114 -.597 6271.827 .535 -.101 -.577 6272.793 .605 -.065 -.547 6277.948 .769 .147 -.372 6281.880 .770 .150 -.367 6282.784 .786 .139 -.367 6283.399 .736 .074 -.429 6283.784 .711 .100 -.406 6285.995 .662 .030 -.493 6286.832 .623 .015 -.493 6287.886 .605 -.036 -.523 6288.952 .595 -.067 -.563 6289.833 .568 -.067 -.560 6290.782 .533 -.087 -.575 6291.771 .520 -.095 -.579 6292.767 .481 -.110 -.598 6293.479 .519 -.125 -.607 6293.771 .479 -.129 -.603 6296.771 .514 -.105 -.581 6298.876 .592 -.026 -.522 6299.366 .675 .025 -.482 6299.810 .645 .023 -.482 6300.761 .686 .072 -.434 6301.796 .745 .093 -.412 6304.833 .782 .142 -.362 6306.780 .699 .114 -.381 6307.761 .751 .106 -.404 6308.883 .669 .044 -.447 6309.398 .679 .055 -.458 6312.753 .567 -.053 -.544 6313.753 .546 -.054 -.544 6314.744 .542 -.062 -.560 6316.737 .518 -.110 -.595 6317.747 .473 -.117 -.613 6320.743 .522 -.097 -.598 6321.784 .529 -.093 -.572 6322.737 .546 -.057 -.539 6325.752 .717 .086 -.422 6327.786 .745 .138 -.387 6328.825 .747 .128 -.387 6329.723 .763 .121 -.377 6330.729 .713 .119 -.409 6331.729 .708 .082 -.428 6332.754 .656 .036 -.453 6333.720 .611 .028 -.467 6334.784 .619 -.013 -.518 6338.736 .548 -.081 -.572 6356.327 .741 .087 -.426 6359.330 .659 .006 -.503 6364.314 .587 -.059 -.556 6365.367 .568 -.080 -.571 6366.354 .549 -.092 -.580 6367.330 .524 -.103 -.593
091-t5.txt Table V V observations of HK Lac with respect to HD 208728 (C1) J.D. Delta V 2440000+ 3633.960 0.131 3650.807 0.081 3659.834 0.164 3662.871 0.195 3676.842 0.075 3714.820 0.212 3718.762 0.139 3721.775 0.068 3722.786 0.048 3723.777 0.037 3726.783 0.053 3727.753 0.093 3747.719 0.038 3770.737 0.052 3790.727 0.168 3794.687 0.081 3795.719 0.056 3806.698 0.148 3834.629 0.178 3849.680 0.039 3855.623 0.152 3870.614 -0.005 3871.621 -0.013 3872.607 -0.005 3873.603 0.009 3876.615 0.068 3877.635 0.087 3878.568 0.103 3879.619 0.130 3902.608 0.112 3903.635 0.129 3906.600 0.179 4078.769 0.183 4094.771 0.017 4136.641 0.066 4160.618 0.074 4169.576 0.036 4177.620 0.229 4182.547 0.187 4194.563 0.021 4196.541 0.037 4209.669 0.062 4210.566 0.031 4217.676 0.018 4227.667 0.232 4451.840 0.099 4453.818 0.031 4454.868 -0.004 4458.838 -0.019 4459.823 -0.004 4496.856 0.159 4498.730 0.136 4499.700 0.109 4500.861 0.068 4501.707 0.039 4503.721 -0.014 4504.842 -0.028 4505.706 -0.030 4506.717 -0.017 4509.804 0.049 4510.814 0.072 4511.701 0.084 4512.704 0.100 4513.703 0.107 4514.806 0.110 4526.694 0.030 4528.672 -0.011 4529.638 -0.016 4530.644 -0.011 4531.650 0.002 4532.652 0.021 4534.639 0.075 4535.646 0.090 4535.666 0.082 4536.619 0.099 4536.644 0.100 4537.638 0.112 4539.652 0.122 4540.721 0.118 4541.640 0.123 4542.610 0.125 4543.640 0.165 4544.658 0.156 4545.632 0.154 4546.642 0.163 4547.640 0.136 4549.610 0.068 4554.585 -0.020 4554.668 -0.025 4555.647 -0.001 4816.806 0.098 4828.678 0.031 4854.769 0.062 4865.544 0.128 4866.546 0.110 4867.534 0.114 4868.543 0.120 4869.539 0.110 4869.588 0.093 4870.531 0.106 4871.527 0.098 4872.710 0.087 4873.725 0.076 4874.681 0.072 4875.558 0.062 4876.557 0.045 4877.548 0.047 4877.703 0.055 4878.520 0.057 4880.558 0.078 4880.616 0.067 4881.564 0.113 4883.536 0.128 4884.664 0.117 4889.519 0.123 4891.534 0.118 4893.535 0.115 4893.544 0.094 4897.514 0.084 4898.512 0.077 4900.564 0.039 4905.561 0.086 4905.644 0.068 4907.525 0.104 4914.691 0.128 4915.499 0.132 4916.496 0.136 4917.503 0.133 4918.682 0.120 4920.503 0.106 4921.496 0.095 4923.493 0.061 4926.513 0.059 4927.538 0.051 4931.506 0.119 4933.521 0.144 4934.557 0.146 4937.570 0.142 4944.507 0.133 4947.517 0.085 4954.603 0.098 4955.516 0.106 4956.607 0.109 4959.634 0.125 4960.603 0.129 4967.647 0.137 4968.607 0.139