SN 1991bg Ia in NGC 4374 (M84) in the Virgo Cluster


Geoffrey Chaucer with an astrolabe.

OBJ:  SN 1991bg Ia in NGC 4374 (M84) (E1 galaxy {leibundgut1993}) in the Virgo cluster which in
         Leda is
         Leda:  NGC 4374.
DISCOVERY:  1991dec3.78 by Kosai et al. (1991)
MAX:  1991dec13.0 (JD 2448603.5 in B which we estimate by subtracting 2.0 days from
           the Vmax date of {filippenko1992} and {turatto1996}:  1991dec13.0 +/- 1.0. is what
           filippenko1992}.
           {leibundgut1993} had 1991dec14.7 +/- 0.5. and
           gave JD 2448605.3 for Vmax, but if 14.7 is right,
           then they meant JD 2448605.2.
           SN 1999by which was similar to 91bg had Bmax 2.0 days before Vmax
           {garnavich2004}.
           See the US Navy Observatory 
           Julian Date Converter.
           This day of the year 348.
SUPERNOVA of the YEAR:  M = 59.

COMMENT:   This is the prototype cool SN Ia.


        Spectrum               Date                  Phase relative to Bmax      Wavelength Range
        leibundgut1993         1991dec13.49          0.5                         4658.4808772--7064.6622
        filippenko1992         1991dec13             0.6                         3300.000--8680.000
        leibundgut1993         1991dec31.56         18.56                        3187.75--7889.925982 (observer)
        turatto1996            1992jan02            20.35                        4099.9981956649--7811.29438878776 (rest???)
        leibundgut1993         1992jan07.34

REF:
       \citet{branch2006b} The Max paper
       with the subtypes defined.

       CfA List of Supernovae
       where SN 1991bg is noted.

       CfA Supernova Archive
       This has 9 SN 1991bg spectra which probably are some of the ones I have, but in different versions.

       \citet{conley2006} General value
         of 19.4 days for Ia rise time in B.
         But 91bg may well have had a shorter rise.

       \citet{filippenko1992d}
       Specifically on SN 1991bg.

       \citet{leibundgut1993}
       Specifically on SN 1991bg.

       SUSPECT Index.

       SUSPECT Index:  SN 1991bg Ia.
       There are 26 SN 1991bg spectra.

       \citet{turatto1996}
       Specifically on SN 1991bg.

HEADER: Header Common header information for this supernovae.
        The common header may (or may not) be updated relative to the header information above
        (D. J. Jeffery (2007jan01)).

REP:  F_lambda (erg/cm2/s/A) vs. lambda (ang)  (iformat = 1)
COR:  not deredshifted (heliocentric velocity 917 +/- 19 km/s from
      Leda:  NGC 4374
      not dereddened (Galactic foreground 0.18/4=.045 reddening from
      Leda:  NGC 4374
        but derived from
     Schlegel et al. (1998)
      not smoothed ????, not photometric ????
      Derived bolometric maximum is ??? (see above).


OBSERVATIONS: From (1) 1) David Jeffery's old catalog: these came from leibundgut1993 and filippenko1992d. The leibundgut1993 ones are those in the CfA supernova archive. 2) SUSPECT: These are the turatto1996 and gomze1996 spectra. 3) David Branch: he has all the filippenko group spectra in fnu format with duplication in /home/branch/synow/91bg. No information on redshift correction. He's also has some of mine somewhere too maybe. 4) Eddie Baron: none. SPECTRUM LOG: JD times for the SN 1991bg spectra of all kinds of people. Bmax estimate 1991dec13.0 (JD 2448603.5). JD Bmax Heliocentric velocity (Leda, 2007jul06) 8603.5 946. Heliocentric velocity Z redshift 946.0000000000 0.0031555163 Index JD of some kind Observer phase Rest phase 1 8603.9900000000 0.4900000000 0.4884586607 ! leibundgut1993 1991dec13.49 2 8604.0800000000 0.5800000000 0.5781755576 ! filippenko1992 1991dec13.58 3300.000--8680.000 (rest) 3 8622.0600000000 18.5600000000 18.5016178426 ! leibundgut1993 1991dec31.56 3187.75 --7889.925982 (observer) 4 8623.0100000000 19.5100000000 19.4486295317 ! filippenko1992 1992jan01.51 3240.000--9910.000 (rest) 5 8623.8500000000 20.3500000000 20.2859872358 ! turatto1996 1992jan02.35 4099.9981956649--7811.29438878776 (observer) 6 0.0000000000****************************** ! The wavelength calibration is 7 0.0000000000****************************** ! in error somehow. 8 8694.9700000000 91.4700000000 91.1822728481 ! filippenko1992 1992mar13.47 3701.2869--9794.8690 (observer) &specnamelist aname='sn1991bg Ia 1991_12_31' ebv=.045 ! epoch=18.5016178426 ! This parameter needs to updated for the particular spectrum. idifmake=0 iformat=1 ! This spectrum is observer-frame from the telluric line. ismooth=1 ! Smoothing is needed. itick=1 itickln=4 t_rise=19.4d0 ! \citep{conley2006}, Just an average rise time. v_helio=946. ymin2=1.d-16 ymax2=3.5d-15 ymin3=.4 ymax3=2.8 wlammin1=3187.75 wlammax1=7889.925982 wlammin2=3187.75 wlammax2=7889.925982 wlammin3=3500. ! This is as far as I'd trust to the blue. wlammax3=7889.925982 ! The red end may be good by comparison to other spectra. /
./figure/sn1991bg_1991_12_31.gif Postscript plot of the spectrum.
./figure/sn1991bg_1991_12_31.dif.gif Postscript plot of the spectrum with local normalization.
Information from someone and somewhere. This is exactly the cfa supernova archive spectrum sn1991bg-19911231-mmt.flm, except the last point. #Image: 91bg.31dec91.mmt Wcs: world OBJ: SN Ia 1991bg in NGC 4374. A peculiar subluminous Ia. DATE: Dec. 31 1991 (day 18.56). Given V_max on Dec. 14.7 and P. Hoeflich's estimate of 13 days for the rise time of a fitted model. The explosion happened on Dec. 1. Thus this is day 13+17=30 after explosion. From JD analysis 622.06-592.2=29.86=30 days after explosion. OBS: Ron Marzke (what a guy) REP: F_lambda (cgs-A) vs. lambda (ang) COR: not deredshifted, not dereddened. REF: Leibundgut et al. 1993, AJ, 105, 302 COMMENT: I've removed the following bad points 3249.771862 -1.053209E-17 7891.07453500001 2.040076E-22 from the end. DAY: 29.86 END: 3177.976651012584625 0.856503323520362 3179.036153136800749 0.896180295688654 3180.096008487254949 0.933510921352288 3181.156217181717238 0.914592803135126 3182.216779337984917 0.900600430349554 3183.277695073897576 0.914825196308319 3184.338964507335277 0.898785879507720 3185.400587756213554 0.896354562302326 3186.462564938497053 0.898383069796979 3187.524896172179979 0.850558607680608 3188.587581575298827 0.779583969598266 3189.650621265926929 0.750226299936180 3190.714015362186274 0.760401534292698 3191.777763982228407 0.761597949104220 3192.841867244247624 0.744124331550211 3193.906325266473686 0.711338028204293 3194.971138167187746 0.667277164271566 3196.036306064697783 0.640094102357124 3197.101829077356342 0.662343769969854 3198.167707323551440 0.694677008276657 3199.233940921720205 0.681080666842168 3200.300529990330688 0.638232011368574 3201.367474647891868 0.644770504520047 3202.434775012950922 0.706472771584173 3203.502431204101867 0.768305471392883 3204.570443339971007 0.810689736537905 3205.638811539226026 0.848677542211432 3206.707535920571445 0.883157303360655 3207.776616602760441 0.905695715370784 3208.846053704576661 0.919125632668103 3209.915847344846952 0.932557165954435 3210.985997642433631 0.903799238623410 3212.056504716249037 0.825920285291436 3213.127368685234615 0.807804166502947 3214.198589668375462 0.842952649361242 3215.270167784693058 0.844160554641647 3216.342103153258449 0.791276358793892 3217.414395893171786 0.755150631164572 3218.487046123576420 0.747232882553510 3219.560053963656628 0.726174501845779 3220.633419532631706 0.690028079131309 3221.707142949770969 0.653856194370419 3222.781224334373746 0.605119564800714 3223.855663805782569 0.536377860612639 3224.930461483376803 0.470630557929036 3226.005617486584015 0.426235322401377 3227.081131934863151 0.401109218976720 3228.157004947715905 0.424972177673256 3229.233236644680346 0.496085235076965 3230.309827145344570 0.524771062370419 3231.386776569325775 0.516075985133354 3232.464085036285724 0.527661587776092 3233.541752665922104 0.559983398709805 3234.619779577981717 0.609003888267754 3235.698165892242741 0.607710552111087 3236.776911728525192 0.601208756915720 3237.856017206686829 0.614744387019270 3238.935482446634524 0.623517158096344 3240.015307568306525 0.621705001133684 3241.095492691682011 0.632987880236188 3242.176037936779267 0.677190136690148 3243.256943423665234 0.766672834458624 3244.338209272436870 0.892080793214292 3245.419835603235242 0.898773525223543 3246.501822536237341 0.890291634974055 3247.584170191671546 0.863544359746640 3248.666878689793975 0.897665399243466 3249.749948150906675 0.913725125769615 3250.833378695346255 0.864170170135128 3251.917170443502073 0.814098988149663 3253.001323515791228 0.776478615860417 3254.085838032674474 0.758647710536902 3255.170714114654857 0.773395049093341 3256.255951882269983 0.787105954727594 3257.341551456108846 0.800491816970003 3258.427512956789542 0.855052040950054 3259.513836504975643 0.946420454156827 3260.600522221365736 1.017249597978172 3261.687570226709340 1.035867578984876 3262.774980641785987 1.017680208304514 3263.862753587419775 0.978475822976984 3264.950889184470725 0.937479928375994 3266.039387553849338 0.943570036463393 3267.128248816496125 0.962515182852754 3268.217473093396620 0.917649857008055 3269.307060505571826 0.868110056109714 3270.397011174093677 0.887516428973499 3271.487325220065031 0.944422804711796 3272.578002764631037 1.022384552259357 3273.669043928975043 1.097154859571893 3274.760448834330873 1.121868716162273 3275.852217601961911 1.134415561290087 3276.944350353176560 1.156455725470064 3278.036847209318694 1.165173768644205 3279.129708291783572 1.158456562932003 3280.222933721997833 1.138553478215861 3281.316523621429951 1.114587194493469 3282.410478111587054 1.105775322339491 3283.504797314026291 1.119594042782277 3284.599481350335282 1.126262033917678 3285.694530342145299 1.096729223562541 3286.789944411128999 1.081225144589487 3287.885723678995419 1.106974080828659 3288.981868267504524 1.117433845468374 3290.078378298446751 1.158987554434017 3291.175253893656645 1.273586806713011 3292.272495175006043 1.399164991920900 3293.370102264416801 1.474470121547727 3294.468075283842609 1.530780044267438 3295.566414355280358 1.597868496673761 3296.665119600763774 1.592509462682936 3297.764191142378422 1.549342156510946 3298.863629102240338 1.524941852435982 3299.963433602508303 1.473891501199357 3301.063604765380205 1.407515302892047 3302.164142713103956 1.398228205085263 3303.265047567958391 1.439777751106151 3304.366319452265543 1.465978158734306 3305.467958488386103 1.485036534012961 3306.569964798730780 1.535847471861956 3307.672338505742118 1.588014026490577 3308.775079731904952 1.596308552187041 3309.878188599743680 1.574369086968793 3310.981665231832267 1.553132451378447 3312.085509750776509 1.532577194536478 3313.189722279224497 1.505429208933790 3314.294302939864338 1.480712037357904 3315.399251855433249 1.459072971446628 3316.504569148700284 1.424512187767009 3317.610254942478605 1.386291890316480 3318.716309359618208 1.351300801647481 3319.822732523021841 1.275909197237407 3320.929524555620901 1.165684442977623 3322.036685580393168 1.106340440646471 3323.144215720355533 1.138752617939573 3324.252115098564445 1.203459668314518 3325.360383838126381 1.254071071317728 3326.469022062178738 1.280124453066848 3327.578029893903476 1.311212883486135 3328.687407456520759 1.387835593505951 3329.797154873301224 1.469947956484237 3330.907272267546432 1.510261263950975 3332.017759762603418 1.513442653487787 3333.128617481856054 1.483839710973864 3334.239845548739140 1.436031748237524 3335.351444086720221 1.405944658725166 3336.463413219309587 1.378060503508584 3337.575753070055725 1.327130015223059 3338.688463762558968 1.275387186725230 3339.801545420450566 1.245264242944069 3340.914998167406338 1.242656115711699 3342.028822127139392 1.274133320394876 3343.143017423415586 1.335080359606593 3344.257584180030335 1.388640457926498 3345.372522520824532 1.401738366437953 3346.487832569676812 1.380178785557863 3347.603514450517196 1.344670080852116 3348.719568287307084 1.322344936417311 3349.835994204052440 1.314541876445897 3350.952792324797429 1.280394649986344 3352.069962773637144 1.233951230428884 3353.187505674698514 1.217799763683568 3354.305421152152576 1.245612999120162 3355.423709330209022 1.314152208732843 3356.542370333129384 1.371169522714090 3357.661404285205208 1.350689909239328 3358.780811310773970 1.263755728208649 3359.900591534213618 1.190919172672384 3361.020745079941662 1.155770974380706 3362.141272072426091 1.139270018065650 3363.262172636166270 1.143491552395494 3364.383446895707038 1.165284514912078 3365.505094975630527 1.184723342177375 3366.627117000571616 1.232938164104417 3367.749513095195653 1.308753389831738 3368.872283384213915 1.367446020308592 3369.995427992374516 1.429242064656374 3371.118947044478773 1.478481771830351 3372.242840665358017 1.475130793166773 3373.367108979889963 1.395671923093153 3374.491752112989161 1.311448231035856 3375.616770189623821 1.306454389475070 3376.742163334791712 1.362624728702579 3377.867931673536987 1.422059905328709 3378.994075330941087 1.428444796793940 3380.120594432138205 1.395056111511999 3381.247489102293912 1.355615535603424 3382.374759466618343 1.319573401908249 3383.502405650360743 1.301736524978090 3384.630427778822195 1.292389751890084 3385.758825977333800 1.250088623511109 3386.887600371274857 1.195516756976975 3388.016751086060140 1.173784694842238 3389.146278247157625 1.168507427350014 3390.276181980067577 1.180316762209965 3391.406462410334825 1.239413403883882 3392.537119663545582 1.318737272758590 3393.668153865325166 1.355711855702426 3394.799565141351195 1.373893086127292 3395.931353617332206 1.403696862703057 3397.063519419022668 1.417518219963475 3398.196062672215248 1.433911841403607 3399.328983502755364 1.468731271712029 3400.462282036519355 1.477638879575574 3401.595958399429037 1.439079541639257 3402.730012717445334 1.376664015470453 3403.864445116581464 1.315310818456095 3404.999255722881117 1.274222476748166 3406.134444662435271 1.248490670544368 3407.270012061372199 1.213292219791972 3408.405958045872922 1.189987216571200 3409.542282742149837 1.205169880014017 3410.678986276462183 1.224609938761145 3411.816068775106487 1.226824624229012 3412.953530364431572 1.220559868854278 3414.091371170819457 1.202388911234257 3415.229591320696727 1.187677783714533 3416.368190940528166 1.179168592060223 3417.507170156832672 1.135173104247711 3418.646529096159156 1.073207162447765 3419.786267885103825 1.063657009603639 3420.926386650300628 1.097821195772742 3422.066885518435811 1.131707899677077 3423.207764616228815 1.160368981986765 3424.349024070443647 1.177518642584350 3425.490664007883424 1.178758960401352 3426.632684555403557 1.154124151007014 3427.775085839892654 1.094069587348336 3428.917867988283433 1.026674130119268 3430.061031127552269 0.994078440433850 3431.204575384713280 0.997407775848825 3432.348500886834245 0.993147956060367 3433.492807761014319 0.968130574955565 3434.637496134398589 0.973481109732272 3435.782566134171702 1.019290848906600 3436.928017887570149 1.052255706280908 3438.073851521862707 1.099505180516240 3439.220067164364991 1.143451025023506 3440.366664942430361 1.164195244844445 3441.513644983465383 1.148955178888412 3442.661007414908454 1.109765482379127 3443.808752364245265 1.070866121663478 3444.956879958999252 1.040662780416837 3446.105390326746601 1.019426768664045 3447.254283595096240 0.997590457124553 3448.403559891703480 0.973441697217215 3449.553219344262288 0.964426077854808 3450.703262080518471 0.962133535675011 3451.853688228251940 0.947478350483130 3453.004497915288084 0.948257830630514 3454.155691269490035 0.981979488942405 3455.307268418776403 1.020007785098162 3456.459229491095812 1.040759719940390 3457.611574614444180 1.041725348295454 3458.764303916856989 1.045648804111529 3459.917417526421559 1.068170906134247 3461.070915571257956 1.077659685187868 3462.224798179533082 1.062288184716329 3463.379065479456131 1.046585285712935 3464.533717599275406 1.028684060924618 3465.688754667292415 1.004766135894811 3466.844176811841407 0.988328324020602 3467.999984161302564 0.978987946197437 3469.156176844095171 0.966907836188416 3470.312754988692632 0.949064927237728 3471.469718723599726 0.925367932956415 3472.627068177367619 0.904796138201250 3473.784803478587946 0.911709540242887 3474.942924755904642 0.940388688440960 3476.101432137993925 0.967719791723455 3477.260325753579764 0.989869326211755 3478.419605731423871 1.012942818977915 3479.579272200342530 1.039976150647393 3480.739325289183398 1.062970077245230 3481.899765126842340 1.070368463351812 3483.060591842252506 1.064137732160655 3484.221805564402530 1.065284970869209 3485.383406422312419 1.061759970298955 3486.545394545048566 1.032741329979231 3487.707770061717383 0.984351872755672 3488.870533101479396 1.081049810325364 3490.033683793526507 1.096631051192653 3491.197222267097004 1.045498140990612 3492.361148651470103 0.989476787979565 3493.525463075978223 0.973518857258216 3494.690165669986072 0.981963838901140 3495.855256562904287 0.972111258908977 3497.020735884184887 0.959173665569704 3498.186603763331732 0.981371837436090 3499.352860329882787 1.008956542951744 3500.519505713421950 1.011514425552664 3501.686540043576315 1.010420275691968 3502.853963450012998 1.030425995263965 3504.021776062453227 1.042765590029787 3505.189978010649611 1.040498280303685 3506.358569424402504 1.060244824345074 3507.527550433552278 1.091878158912918 3508.696921167992514 1.097695319394461 3509.866681757649985 1.084267441536042 3511.036832332497852 1.110476681962338 3512.207373022549291 1.187848885574489 3513.378303957871594 1.255735504338761 3514.549625268564341 1.281656271904845 3515.721337084775314 1.295773989336856 3516.893439536689584 1.312845498972245 3518.065932754549522 1.303104074581319 3519.238816868627509 1.274183347886943 3520.412092009244589 1.256812853397799 3521.585758306760454 1.255608250960446 3522.759815891590279 1.246456382783545 3523.934264894180615 1.205747734067460 3525.109105445026671 1.166965294483410 3526.284337674662311 1.155873777538420 3527.459961713675511 1.144526499492740 3528.635977692688357 1.121357034819786 3529.812385742369315 1.106741309158215 3530.989185993425963 1.103184325611946 3532.166378576622265 1.109278342098765 3533.343963622752653 1.119105336122956 3534.521941262660675 1.111535944060715 3535.700311627228530 1.078435055336952 3536.879074847393895 1.036137958000561 3538.058231054127191 1.009544834818113 3539.237780378445223 1.011353005491582 3540.417722951408905 1.028261570602265 3541.598058904119625 1.042755918579975 3542.778788367732886 1.041369143945908 3543.959911473437842 1.017803986698469 3545.141428352470029 0.978961291210286 3546.323339136104551 0.946208237112633 3547.505643955673804 0.950064740638584 3548.688342942540203 0.983691281698726 3549.871436228114817 1.018664329712402 3551.054923943849190 1.027941035443634 3552.238806221248979 1.039666216897444 3553.423083191853038 1.084691125358211 3554.607754987247972 1.146431635830971 3555.792821739060400 1.194984071722639 3556.978283578971059 1.230399331071424 3558.164140638694789 1.256036811647727 3559.350393049993272 1.253967352717855 3560.537040944668661 1.253366590430474 3561.724084454578588 1.267335273368233 3562.911523711612062 1.263418100609570 3564.099358847707663 1.232823074336885 3565.287589994843074 1.191046057564754 3566.476217285051462 1.155593898978389 3567.665240850398732 1.129333134609725 3568.854660822998994 1.101749548765619 3570.044477335005467 1.085463740001214 3571.234690518628668 1.072858126245704 3572.425300506109124 1.038217988536238 3573.616307429738299 1.011181238954109 3574.807711421849490 1.004336392123258 3575.999512614817831 0.997251694450439 3577.191711141072119 1.012815778148058 3578.384307133076163 1.038238018963085 3579.577300723340159 1.028148190136483 3580.770692044415682 1.012689495026412 3581.964481228908426 1.034249082268945 3583.158668409458187 1.065118904779069 3584.353253718752967 1.081996031680946 3585.548237289520330 1.097256984904003 3586.743619254543773 1.111984571734816 3587.939399746639538 1.115395370273885 3589.135578898672065 1.090949468918363 3590.332156843546727 1.062207711189199 3591.529133714224372 1.067926734955859 3592.726509643698137 1.073536003425904 3593.924284765009816 1.055897844083801 3595.122459211242131 1.040749762256133 3596.321033115532828 1.016558095963173 3597.520006611053304 0.979625822701991 3598.719379831022707 0.943832539404173 3599.919152908700653 0.902640202821497 3601.119325977403150 0.874820872922465 3602.319899170478948 0.867086904364228 3603.520872621324997 0.859550018465105 3604.722246463379179 0.861959958302972 3605.924020830134850 0.856112376172889 3607.126195855118567 0.839024000037071 3608.328771671905997 0.840948999648256 3609.531748414111917 0.841385274580606 3610.735126215408854 0.845126653922119 3611.938905209501172 0.876802635490702 3613.143085530141889 0.902619541711114 3614.347667311129953 0.910903219575205 3615.552650686302513 0.908026151501118 3616.758035789554924 0.892469259218184 3617.963822754815283 0.876516287923700 3619.170011716059889 0.864640149098326 3620.376602807305062 0.864847300450487 3621.583596162625327 0.871669217867535 3622.790991916126586 0.859625459998463 3623.998790201963857 0.842833397389924 3625.206991154333082 0.837150683437488 3626.415594907487048 0.822704395051967 3627.624601595710374 0.817661239693319 3628.834011353338155 0.850220740036310 3630.043824314744597 0.888870808496538 3631.254040614361202 0.902012196466046 3632.464660386653122 0.910335588911921 3633.675683766132806 0.931237322582638 3634.887110887355448 0.958427885407837 3636.098941884930809 0.981951171190434 3637.311176893503671 1.011221405540247 3638.523816047766559 1.047564738127587 3639.736859482453838 1.060620720635696 3640.950307332354896 1.048463007808081 3642.164159732293683 1.043448333224227 3643.378416817143261 1.038388595791890 3644.593078721816710 1.020010099758015 3645.808145581283952 0.998717291633734 3647.023617530549473 0.982131176310644 3648.239494704664594 0.974684727878204 3649.455777238723840 0.976755036262395 3650.672465267876760 0.990423602516650 3651.889558927307462 1.007788106281202 3653.107058352248714 1.026795726963162 3654.324963677977394 1.061792535344216 3655.543275039813579 1.110319591883515 3656.761992573132375 1.162367130201583 3657.981116413342988 1.207109314588624 3659.200646695903288 1.234962836015036 3660.420583556313431 1.258221601991339 3661.640927130129512 1.278531898654920 3662.861677552940819 1.293805206942255 3664.082834960387117 1.313185556411989 3665.304399488148192 1.325144407699433 3666.526371271961125 1.318122185156565 3667.748750447597104 1.302641761997427 3668.971537150875520 1.282625355670940 3670.194731517658511 1.265408505592050 3671.418333683863239 1.249250772288828 3672.642343785441881 1.220037939977283 3673.866761958396637 1.192300213599913 3675.091588338768815 1.180287840914493 3676.316823062658386 1.178115911262390 3677.542466266198971 1.178805925224988 3678.768518085572850 1.188762761922844 3679.994978657004140 1.203033630930879 3681.221848116774254 1.204883347203025 3682.449126601197804 1.200805069298029 3683.676814246639424 1.197262574570207 3684.904911189504674 1.184530456811201 3686.133417566256412 1.163511989858169 3687.362333513391604 1.140704760441147 3688.591659167456783 1.118309398466726 3689.821394665043499 1.087731241062133 3691.051540142784688 1.061417452923025 3692.282095737371947 1.051901268081898 3693.513061585528703 1.046103953864289 3694.744437824029774 1.037749200767038 3695.976224589689991 1.040301744421911 3697.208422019383306 1.042332126167104 3698.441030250016411 1.025339621495861 3699.674049418545110 1.013224498839167 3700.907479661968409 1.024493977174308 3702.141321117341249 1.020307678758441 3703.375573921754039 1.004442850827302 3704.610238212344939 1.006607665161718 3705.845314126296216 1.009837943660745 3707.080801800845165 1.009170661476623 3708.316701373265005 1.024059461859266 3709.553012980877611 1.054294682751099 3710.789736761047152 1.078026490443626 3712.026872851195094 1.098207014262250 3713.264421388777009 1.130381667958390 3714.502382511298947 1.159643792387788 3715.740756356307429 1.164974814453102 3716.979543061407639 1.155258795845737 3718.218742764238868 1.156552124504581 3719.458355602489519 1.156798965992967 3720.698381713891195 1.157150466731737 3721.938821236231433 1.174293148660407 3723.179674307333698 1.191346480747546 3724.420941065070110 1.195781472777980 3725.662621647355536 1.193824152497698 3726.904716192162141 1.202870265548077 3728.147224837496651 1.237811614798378 3729.390147721415815 1.269500390469851 3730.633484982021400 1.272948946306976 3731.877236757458832 1.262656287114919 3733.121403185930376 1.248085796769991 3734.365984405672407 1.236309251656665 3735.610980554972684 1.229814105674808 3736.856391772159441 1.232840731095491 3738.102218195619571 1.238135464052698 3739.348459963774076 1.227290342721808 3740.595117215095343 1.211869200053582 3741.842190088095776 1.214619268208198 3743.089678721347354 1.223133574271719 3744.337583253456160 1.215327405484481 3745.585903823078297 1.189480912708067 3746.834640568911254 1.164990560886186 3748.083793629712545 1.137792743046324 3749.333363144272425 1.102695560331081 3750.583349251432082 1.063179896007647 3751.833752090074995 1.016125809474017 3753.084571799142395 0.971290026622934 3754.335808517610531 0.936010825769121 3755.587462384505670 0.904550733789508 3756.839533538896831 0.880631528169378 3758.092022119910325 0.856852268494108 3759.344928266707939 0.822560219717594 3760.598252118501932 0.786561899949986 3761.851993814545494 0.763837541790849 3763.106153494152295 0.751521039430026 3764.360731296668291 0.733599687010705 3765.615727361492191 0.715183294761280 3766.871141828063173 0.697475899768695 3768.126974835879992 0.675399359700775 3769.383226524475504 0.658377301077874 3770.639897033433954 0.654751992097416 3771.896986502384152 0.648202811043501 3773.154495070999928 0.635094517295229 3774.412422879011956 0.634820985074735 3775.670770066185469 0.641291965906719 3776.929536772337542 0.643879605806990 3778.188723137327088 0.637356001589487 3779.448329301071681 0.618603918449750 3780.708355403523001 0.592820430514625 3781.968801584684570 0.570905713226651 3783.229667984601747 0.569758346136011 3784.490954743379007 0.576658173341708 3785.752662001154931 0.562072669217147 3787.014789898119034 0.548856227642215 3788.277338574504938 0.539174861878179 3789.540308170602202 0.533378197537303 3790.803698826738128 0.550808976070245 3792.067510683288674 0.573772671980461 3793.331743880673912 0.579343465619112 3794.596398559371664 0.569532566605009 3795.861474859895679 0.558126948974956 3797.126972922809273 0.553229186925693 3798.392892888720326 0.537050928239987 3799.659234898293562 0.520716679700471 3800.925999092230086 0.517424127607052 3802.193185611281933 0.502855372282286 3803.460794596243431 0.480217029430877 3804.728826187967115 0.465731759371126 3805.997280527342355 0.456840962472235 3807.266157755308086 0.456156251371392 3808.535458012850995 0.465898285887273 3809.805181441000514 0.491933964287688 3811.075328180844281 0.515157452531688 3812.345898373506316 0.525224860525797 3813.616892160161115 0.540269051567797 3814.888309682026375 0.566357930824184 3816.160151080378000 0.601285882923876 3817.432416496528276 0.635793357241784 3818.705106071839509 0.664108034583562 3819.978219947718571 0.687434950146801 3821.251758265629633 0.705174658404810 3822.525721167073243 0.730349060933108 3823.800108793601339 0.764202600489148 3825.074921286807694 0.796805654028581 3826.350158788347017 0.826887715227509 3827.625821439907668 0.855533354579344 3828.901909383230304 0.891341561521937 3830.178422760098329 0.930251904354404 3831.455361712354261 0.959403570503980 3832.732726381877001 0.971990551771636 3834.010516910595015 0.984067624029328 3835.288733440482247 1.010784989707598 3836.567376113569480 1.047416287571575 3837.846445071924791 1.070895712100504 3839.125940457666729 1.078921430639411 3840.405862412957504 1.078038721192780 3841.686211080018893 1.080036548555746 3842.966986601107692 1.113161276921537 3844.248189118532537 1.160464780593554 3845.529818774644809 1.181236063855180 3846.811875711855919 1.191526031181181 3848.094360072612744 1.206108555355814 3849.377271999413551 1.218597880391160 3850.660611634803900 1.233789809591940 3851.944379121373458 1.261438989791281 3853.228574601771015 1.301589253730040 3854.513198218680827 1.313569992880563 3855.798250114838538 1.312383392167887 3857.083730433024357 1.334180578352756 3858.369639316077155 1.349766810744800 3859.655976906871274 1.343864835760804 3860.942743348333806 1.344321459118106 3862.229938783434136 1.358889158151669 3863.517563355202583 1.366200435371324 3864.805617206704028 1.356924992759709 3866.094100481055648 1.360175274867971 3867.383013321418730 1.370837829915885 3868.672355871013679 1.371840865137630 3869.962128273095914 1.377900834343023 3871.252330670974516 1.397670915255482 3872.542963208001311 1.410014462156134 3873.834026027587242 1.414634391866585 3875.125519273180089 1.432155113323241 3876.417443088279015 1.443099817040322 3877.709797616427295 1.444323644440715 3879.002583001227322 1.445140680464272 3880.295799386318777 1.450666740508151 3881.589446915391818 1.456815978796273 3882.883525732181170 1.462463331232249 3884.178035980481582 1.470975222721092 3885.472977804122820 1.464699741610249 3886.768351346988311 1.447728409921294 3888.064156753007865 1.442033845693209 3889.360394166155857 1.446062019582417 3890.657063730466689 1.446891355039382 3891.954165590010689 1.446233263692705 3893.251699888910480 1.449900332607312 3894.549666771332795 1.463554883222072 3895.848066381503486 1.486197678133425 3897.146898863686147 1.504364584694898 3898.446164362194395 1.513635850377440 3899.745863021387777 1.525687791623099 3901.045994985684956 1.546595758859733 3902.346560399540977 1.568501758073355 3903.647559407463632 1.580942056823100 3904.948992154003918 1.587113785499898 3906.250858783773310 1.593185776112098 3907.553159441420121 1.596641014872121 3908.855894271644502 1.613952425959302 3910.159063419190261 1.637971539000004 3911.462667028862143 1.643636123468392 3912.766705245500816 1.635480784975473 3914.071178214000156 1.637463393120050 3915.376086079296783 1.657158767981243 3916.681428986388710 1.674049274211207 3917.987207080310327 1.684992704222867 3919.293420506147868 1.700527601014845 3920.600069409032130 1.718717180515149 3921.907153934154394 1.750767887357418 3923.214674226741863 1.799306913906696 3924.522630432075402 1.837777088588833 3925.831022695479078 1.861831346975673 3927.139851162337436 1.882273537701885 3928.449115978072314 1.902410706843814 3929.758817288157388 1.929408218211694 3931.068955238115450 1.957506085287249 3932.379529973512490 1.968354343218705 3933.690541639976800 1.958888142098005 3935.001990383171687 1.947233680120610 3936.313876348814574 1.953243487479598 3937.626199682665629 1.957024496212992 3938.938960530546865 1.964005490334613 3940.252159038316677 1.982927219889851 3941.565795351886209 1.989110259885118 3942.879869617210261 2.016955877440314 3944.194381980306389 2.062795365191884 3945.509332587226254 2.099426794669665 3946.824721584076542 2.117907108755688 3948.140549117006685 2.128213885711346 3949.456815332227961 2.150680416171150 3950.773520375988937 2.176381189325586 3952.090664394589112 2.181581619960282 3953.408247534374368 2.178786286345882 3954.726269941750616 2.178761940651323 3956.044731763161053 2.195486158721252 3957.363633145101630 2.227394976309820 3958.682974234111953 2.262909488541501 3960.002755176794835 2.293835188597648 3961.322976119787654 2.308560621151293 3962.643637209781900 2.330255735511347 3963.964738593513630 2.381067497863000 3965.286280417779835 2.422806764233851 3966.608262829414798 2.438176864172865 3967.930685975305096 2.453748898746178 3969.253550002383236 2.486841839922707 3970.576855057641296 2.527553000928919 3971.900601288109556 2.561253984969471 3973.224788840871042 2.602350265968433 3974.549417863057442 2.637739784229438 3975.874488501846372 2.658415787188620 3977.200000904475019 2.669846130054557 3978.525955218219224 2.656428824284319 3979.852351590406670 2.632508617751594 3981.179190168411424 2.620482166619701 3982.506471099667124 2.623780119103972 3983.834194531646517 2.631174385798263 3985.162360611873282 2.608235222431295 3986.490969487918392 2.578180312008486 3987.820021307412389 2.556100271184248 3989.149516218024473 2.541300087396854 3990.479454367475228 2.539798225745275 3991.809835903532530 2.520570408479640 3993.140660974023831 2.470846784479909 3994.471929726815233 2.430457574399137 3995.803642309824681 2.400937135600826 3997.135798871016959 2.375524387700734 3998.468399558417332 2.343467079830823 3999.801444520088353 2.306293343095699 4001.134933904146237 2.281079339408822 4002.468867858752674 2.251698155621499 4003.803246532129833 2.231629811494551 4005.138070072538994 2.212873979850858 4006.473338628293277 2.167036516416472 4007.809052347751731 2.125347374010906 4009.145211379335251 2.092472408525152 4010.481815871502022 2.069924344664096 4011.818865972763888 2.058145888827512 4013.156361831681352 2.035566742497884 4014.494303596861300 2.017432278127772 4015.832691416972011 1.991326213598862 4017.171525440719506 1.968959911333561 4018.510805816862558 1.964191663020808 4019.850532694206322 1.957402679464071 4021.190706221617802 1.946578107961212 4022.531326548000379 1.920067337370784 4023.872393822312461 1.886927563140718 4025.213908193557472 1.851730215563209 4026.555869810800232 1.817921902697746 4027.898278823143755 1.812337347271273 4029.241135379744719 1.805370055916536 4030.584439629805274 1.781704836645042 4031.928191722589418 1.770359903348050 4033.272391807399345 1.767284099426383 4034.617040033590001 1.767962958843571 4035.962136550562718 1.777764473809962 4037.307681507781581 1.792641904283975 4038.653675054746600 1.788388366536220 4040.000117341013265 1.772521354932611 4041.347008516181631 1.758684998554035 4042.694348729914964 1.736391092594036 4044.042138131913362 1.709859769029407 4045.390376871931494 1.681798653953825 4046.739065099769050 1.659043785723183 4048.088202965288929 1.646759642716677 4049.437790618390864 1.632907646493404 4050.787828209029612 1.608769808312551 4052.138315887204499 1.587337876290097 4053.489253802978510 1.573753663081691 4054.840642106451469 1.562734067907470 4056.192480947778222 1.563085841506030 4057.544770477161819 1.566046954349952 4058.897510844853969 1.555268130482132 4060.250702201166405 1.532766703537308 4061.604344696449971 1.510857474280963 4062.958438481109170 1.495317410118022 4064.312983705594888 1.486164765964746 4065.667980520420770 1.478531830755439 4067.023429076137290 1.460933864502839 4068.379329523350407 1.435674701357772 4069.735682012711095 1.413916568484273 4071.092486694933541 1.397096425333164 4072.449743720770130 1.386380120867925 4073.807453241026906 1.369482825462790 4075.165615406555844 1.335086977215981 4076.524230368273038 1.297307374603728 4077.883298277130962 1.260725312230019 4079.242819284137113 1.220810916660545 4080.602793540345829 1.178333330735055 4081.963221196873292 1.141654118041738 4083.324102404873884 1.106022313637951 4084.685437315556555 1.072405874472039 4086.047226080177097 1.054736673103762 4087.409468850052690 1.038825522762628 4088.772165776540987 1.019165823219898 4090.135317011051484 1.002083546997711 4091.498922705041423 0.986203412360147 4092.862983010031712 0.984155980067452 4094.227498077579185 0.988153682044486 4095.592468059297971 0.988809117743338 4096.957893106846313 0.987686936330695 4098.323773371947027 0.993832363528826 4099.690109006359307 1.008148946676088 4101.056900161899648 1.016861855746550 4102.424146990432746 1.028011073431280 4103.791849643871501 1.039324734531754 4105.160008274190659 1.034739672287888 4106.528623033404074 1.029190263162717 4107.897694073580169 1.028843400895498 4109.267221546832843 1.031499447775432 4110.637205605340569 1.033499302306068 4112.007646401320017 1.036929832942775 4113.378544087042428 1.037233100354407 4114.749898814825428 1.026799942735669 4116.121710737049398 1.020986458763303 4117.493980006134734 1.023681069457662 4118.866706774555496 1.022381251379026 4120.239891194832126 1.010552758227770 4121.613533419550549 0.982455799290298 4122.987633601332163 0.953341932395373 4124.362191892854753 0.926019132584902 4125.737208446842487 0.902298047756893 4127.112683416085019 0.887610310192863 4128.488616953407472 0.871472612962035 4129.865009211691358 0.853357062273109 4131.241860343865483 0.834221573434311 4132.619170502922316 0.814143524510788 4133.996939841889798 0.810465727367172 4135.375168513855897 0.810864004792677 4136.753856671951326 0.794809819803802 4138.133004469372281 0.774389347349814 4139.512612059354069 0.757015353821599 4140.892679595185655 0.742131280990640 4142.273207230208754 0.738401239256740 4143.654195117809650 0.743699551081266 4145.035643411441015 0.747814053618944 4146.417552264592814 0.748638350311088 4147.799921830809581 0.743876575624095 4149.182752263684961 0.732990086191513 4150.566043716874447 0.729479608972049 4151.949796344072638 0.731509235993602 4153.334010299031434 0.733232934266170 4154.718685735546387 0.729905776834781 4156.103822807478537 0.710800106728507 4157.489421668729847 0.683914090146437 4158.875482473254124 0.673435647665861 4160.262005375053377 0.669752849080445 4161.648990528196009 0.666189966402119 4163.036438086785893 0.671765314531453 4164.424348204985108 0.672340437636302 4165.812721037000301 0.673165138823781 4167.201556737103601 0.677944309292455 4168.590855459607155 0.676133987075060 4169.980617358876771 0.672001020951727 4171.370842589325548 0.665599994151548 4172.761531305432072 0.650623971899356 4174.152683661713127 0.643545930621797 4175.544299812741883 0.640275879187451 4176.936379913136079 0.635765264885877 4178.328924117581664 0.644291609242645 4179.721932580800967 0.652734933964835 4181.115405457572706 0.653081830111991 4182.509342902722892 0.659226264795061 4183.903745071141202 0.673474271403717 4185.298612117758239 0.691221099275103 4186.693944197559176 0.717500268091852 4188.089741465580119 0.739034232525201 4189.486004076905374 0.747090116763703 4190.882732186684734 0.742030956824111 4192.279925950104371 0.735376036087816 4193.677585522409572 0.745587091679018 4195.075711058891102 0.766581159159646 4196.474302714904297 0.778869077333310 4197.873360645844514 0.775737025923802 4199.272885007162586 0.771661083061523 4200.672875954356641 0.765665558670119 4202.073333642990292 0.762066033147770 4203.474258228665349 0.765795989744782 4204.875649867039101 0.781874189581211 4206.277508713819770 0.790549897775793 4207.679834924775605 0.780002889649575 4209.082628655718509 0.767744671136351 4210.485890062512226 0.764047922208401 4211.889619301072344 0.768077600732597 4213.293816527376293 0.766183313156762 4214.698481897441525 0.761496087028792 4216.103615567342786 0.759933713252693 4217.509217693202118 0.761828052885064 4218.915288431204317 0.753713283398799 4220.321827937576927 0.743031549708078 4221.728836368601151 0.739979355313975 4223.136313880607304 0.733476414366496 4224.544260629990276 0.725806927576626 4225.952676773184066 0.719775044939754 4227.361562466679970 0.719719392050013 4228.770917867020216 0.721108652156353 4230.180743130796145 0.718375169813055 4231.591038414662762 0.717691665321458 4233.001803875316000 0.714237610720608 4234.413039669508180 0.710273961812962 4235.824745954037098 0.700145991370186 4237.236922885768763 0.695881194276656 4238.649570621608291 0.700398893051134 4240.062689318514458 0.699175308573948 4241.476279133497883 0.681670527207504 4242.890340223631938 0.660548162770830 4244.304872746030014 0.650659172487572 4245.719876857863710 0.652180674870040 4247.135352716350098 0.660425999139874 4248.551300478772646 0.676015540194138 4249.967720302455746 0.688617914975700 4251.384612344778361 0.686850015613984 4252.801976763169478 0.673204292851646 4254.219813715121745 0.681474848309792 4255.638123358169651 0.699904831584289 4257.056905849901341 0.713600817045623 4258.476161347956804 0.711091596986354 4259.895890010038784 0.699659888346943 4261.316091993890041 0.689449779138541 4262.736767457312453 0.679967798660679 4264.157916558152465 0.675067562099800 4265.579539454325641 0.685483694661820 4267.001636303785745 0.698081459613780 4268.424207264542929 0.700521112995138 4269.847252494656459 0.702336894168022 4271.270772152251084 0.703605098584154 4272.694766395491570 0.708720605849143 4274.119235382599982 0.716157629239264 4275.544179271849316 0.720462231448585 4276.969598221563501 0.723411139257371 4278.395492390130130 0.727794647522313 4279.821861935978632 0.725360675063770 4281.248707017593915 0.722122709309965 4282.676027793509093 0.714756626831462 4284.103824422326397 0.708730462378949 4285.532097062683533 0.697879685016851 4286.960845873278231 0.691150136036774 4288.390071012855515 0.688264993805748 4289.819772640227711 0.685860838451163 4291.249950914245346 0.686410637985391 4292.680605993817153 0.686698049866966 4294.111738037900977 0.688506095338389 4295.543347205521059 0.691852100848504 4296.975433655738925 0.697319797551120 4298.407997547676132 0.699915981343483 4299.841039040501528 0.697738703463974 4301.274558293451264 0.688482840535086 4302.708555465801510 0.684529558921657 4304.143030716883914 0.687249194434273 4305.577984206081055 0.688196421548157 4307.013416092840998 0.676309627494602 4308.449326536651824 0.656867252606720 4309.885715697058913 0.647451705144326 4311.322583733655847 0.649806278673672 4312.759930806104421 0.665430872722407 4314.197757074106448 0.685750077189185 4315.636062697418311 0.702272638362183 4317.074847835848232 0.710527638191400 4318.514112649269919 0.716080513555232 4319.953857297598006 0.726456396902256 4321.394081940803517 0.746150021415440 4322.834786738911134 0.766524018416751 4324.275971851995564 0.775395064689955 4325.717637440196995 0.775510260418503 4327.159783663694725 0.771098708336262 4328.602410682729897 0.765630095270007 4330.045518657587309 0.761341332905748 4331.489107748622700 0.754187021315654 4332.933178116230920 0.746522587587687 4334.377729920862294 0.740891790427598 4335.822763323019899 0.742556246067523 4337.268278483270478 0.746323819645903 4338.714275562223520 0.744330068279052 4340.160754720545810 0.735097356948100 4341.607716118950520 0.727650356346946 4343.055159918222671 0.728798608380648 4344.503086279182753 0.731908888366562 4345.951495362713104 0.731460692145995 4347.400387329743353 0.729928698136440 4348.849762341269525 0.728175851166933 4350.299620558328570 0.719766510689281 4351.749962142017466 0.707581231650682 4353.200787253479575 0.698754814455915 4354.652096053927380 0.695635247415018 4356.103888704612473 0.695557105958581 4357.556165366844652 0.692883574848493 4359.008926201984650 0.687889664088454 4360.462171371458680 0.682146358736311 4361.915901036734795 0.673931954300186 4363.370115359336523 0.661484453391437 4364.824814500844695 0.656962107611141 4366.279998622888343 0.663944460738422 4367.735667887162890 0.671283407502707 4369.191822455404690 0.675195952274989 4370.648462489409212 0.668571957258729 4372.105588151020129 0.654612494583349 4373.563199602150235 0.645736356679369 4375.021297004752341 0.644744000280425 4376.479880520835650 0.646813998272404 4377.938950312460292 0.649365561442265 4379.398506541756433 0.644459914855550 4380.858549370890614 0.637819515082089 4382.319078962090316 0.629810442688916 4383.780095477632130 0.623621321213104 4385.241599079860862 0.625844018569649 4386.703589931160423 0.626028432153424 4388.166068193973842 0.616727953739709 4389.629034030795083 0.604678016639628 4391.092487604185408 0.588303603960188 4392.556429076744280 0.575884337679280 4394.020858611133917 0.570484831676753 4395.485776370063832 0.565819808047215 4396.951182516310837 0.565270363207270 4398.417077212693584 0.572391603639436 4399.883460622088933 0.589482840256463 4401.350332907425582 0.602092545032122 4402.817694231695896 0.610975025272348 4404.285544757937714 0.624098716279194 4405.753884649244355 0.637814326355593 4407.222714068760069 0.642456200545626 4408.692033179698228 0.645381501708310 4410.161842145310402 0.648486785109483 4411.632141128910007 0.643092013643046 4413.102930293863210 0.630742987699649 4414.574209803586200 0.624207478205158 4416.045979821564288 0.624211841227685 4417.518240511321892 0.628967695981456 4418.990992036444368 0.634929950146172 4420.464234560566183 0.636374935053104 4421.937968247389108 0.640630837285502 4423.412193260658569 0.648431278367116 4424.886909764175471 0.666801264429179 4426.362117921793470 0.683294976005320 4427.837817897434434 0.694843361347804 4429.314009855059339 0.702500330872262 4430.790693958689189 0.711252247863534 4432.267870372396828 0.720319503667971 4433.745539260321493 0.726818483561413 4435.223700786643349 0.742656866970518 4436.702355115603496 0.754623647710096 4438.181502411492147 0.761113922384095 4439.661142838667729 0.774113257060808 4441.141276561530503 0.795473987356667 4442.621903744539850 0.814838058010492 4444.103024552205170 0.832687457184416 4445.584639149104987 0.848597415714562 4447.066747699857842 0.870746197591385 4448.549350369142303 0.889694930905331 4450.032447321687869 0.903948377039428 4451.516038722293160 0.919878874011025 4453.000124735795907 0.922020546678305 4454.484705527094775 0.925293337598447 4455.969781261138451 0.936056447437866 4457.455352102944744 0.946975431741442 4458.941418217572391 0.959923381711353 4460.427979770141064 0.967805375669115 4461.915036925822278 0.974469672877197 4463.402589849841206 0.974714349068756 4464.890638707490325 0.974840913150398 4466.379183664103948 0.989510723586443 4467.868224885075506 0.994073122630791 4469.357762535850270 0.990245773147255 4470.847796781940815 0.997810006404759 4472.338327788902461 1.004657753685132 4473.829355722349646 1.006590922546656 4475.320880747947740 1.004142884282299 4476.812903031430324 1.009661788920411 4478.305422738573725 1.020673813649016 4479.798440035212479 1.028159493662931 4481.291955087233873 1.044033123277975 4482.785968060593405 1.063206205328134 4484.280479121286589 1.080176773221636 4485.775488435370789 1.085424940028356 4487.270996168954298 1.093272719379865 4488.767002488212711 1.101386068350671 4490.263507559365280 1.099279858426938 4491.760511548690374 1.097766934981423 4493.258014622516384 1.096377289918928 4494.756016947241733 1.095913661026124 4496.254518689307588 1.097856505949179 4497.753520015212416 1.097577223084862 4499.253021091509254 1.099640439994776 4500.753022084817530 1.098135521179613 4502.253523161799421 1.098314071724879 4503.754524489178038 1.111379395775120 4505.256026233730154 1.122609244165028 4506.758028562285290 1.126413078403774 4508.260531641741181 1.129548630698854 4509.763535639039219 1.137328775137560 4511.267040721179001 1.144071623426131 4512.771047055211966 1.149735952141614 4514.275554808260495 1.152614993015328 4515.780564147485165 1.156669317996836 4517.286075240111131 1.166668660302929 4518.792088253411748 1.174650229194090 4520.298603354732222 1.176966309363186 4521.805620711456868 1.181098181943578 4523.313140491032755 1.192281520992971 4524.821162860958793 1.202353855777572 4526.329687988800288 1.203434665566439 4527.838716042167107 1.212578563930865 4529.348247188730056 1.231159117435522 4530.858281596208144 1.249362832369630 4532.368819432394957 1.264036568665178 4533.879860865120463 1.287652701356563 4535.391406062281021 1.308865523659824 4536.903455191819376 1.320502010014334 4538.416008421751030 1.327798805423795 4539.929065920132416 1.346394725806775 4541.442627855081810 1.376117228143250 4542.956694394767510 1.395149742411478 4544.471265707428756 1.403614504902944 4545.986341961345715 1.419509014642884 4547.501923324861309 1.443101094719635 4549.018009966368481 1.458969471149346 4550.534602054330207 1.466361084605452 4552.051699757253118 1.479975598455422 4553.569303243702961 1.498048015294270 4555.087412682301874 1.504960566662497 4556.606028241723834 1.513033173516195 4558.125150090714669 1.528956986825083 4559.644778398060225 1.545691596030276 4561.164913332607284 1.561569930648170 4562.685555063256288 1.580832078811373 4564.206703758976801 1.591890602376516 4565.728359588779313 1.601662429383524 4567.250522721738889 1.616115771881292 4568.773193326977889 1.623664398724341 4570.296371573692340 1.633957918914466 4571.820057631119198 1.652627919178393 4573.344251668557263 1.664485318262252 4574.868953855356267 1.661962110357115 4576.394164360937793 1.659472293351284 4577.919883354765261 1.672610696073824 4579.446111006361207 1.691036032308648 4580.972847485303646 1.700113567353184 4582.500092961237897 1.711504822814830 4584.027847603853843 1.718861226557736 4585.556111582902304 1.718041221207065 4587.084885068185031 1.726957699379300 4588.614168229575625 1.751969191390791 4590.143961236989526 1.774804930555134 4591.674264260404016 1.781330557306098 4593.205077469848220 1.770513279553999 4594.736401035421295 1.760322187414279 4596.268235127266053 1.763165291969364 4597.800579915586241 1.773780461943051 4599.333435570641996 1.775449523250172 4600.866802262746205 1.758768442322817 4602.400680162281787 1.720426424927700 4603.935069439676226 1.682363264807951 4605.469970265416123 1.656932516328433 4607.005382810041738 1.645096903865646 4608.541307244163363 1.643484888242445 4610.077743738435856 1.625718388558430 4611.614692463572283 1.586430724205704 4613.152153590342095 1.558637916045503 4614.690127289582961 1.550979708843957 4616.228613732176200 1.555721439074591 4617.767613089064071 1.556350941786383 4619.307125531242491 1.555949888915890 4620.847151229777410 1.548635615452450 4622.387690355778432 1.520009196601789 4623.928743080417007 1.491495826287882 4625.470309574915518 1.480587351717861 4627.012390010569106 1.462184710133379 4628.554984558714750 1.432431927354488 4630.098093390753093 1.406752938188638 4631.641716678134799 1.382106778869898 4633.185854592383293 1.358263875481681 4634.730507305064748 1.343198052563603 4636.275674987808088 1.340455595590565 4637.821357812292263 1.345489503253401 4639.367555950270798 1.340670773827805 4640.914269573537240 1.323987481372639 4642.461498853950616 1.308031267185416 4644.009243963419067 1.297945055522407 4645.557505073923494 1.296923277815975 4647.106282357489363 1.286514164015289 4648.655575986203075 1.271937385762594 4650.205386132207423 1.252052904930711 4651.755712967698855 1.224511957477969 4653.306556664945674 1.203027827530838 4654.857917396258927 1.196207513406496 4656.409795334012415 1.181584230713713 4657.962190650632692 1.159878767703527 4659.515103518616343 1.150813487403219 4661.068534110505425 1.145903613100295 4662.622482598902934 1.126844662497519 4664.176949156465525 1.109078689418414 4665.731933955920795 1.090847832432774 4667.287437170039993 1.075293932857302 4668.843458971657128 1.061275140462292 4670.399999533658956 1.052030109045663 4671.957059029003176 1.039581075460522 4673.514637630692050 1.024790851969675 4675.072735511790597 1.021932864573937 4676.631352845414767 1.025539476738053 4678.190489804754179 1.027858690224431 4679.750146563042108 1.027644304994722 4681.310323293572765 1.024214888302570 4682.871020169695839 1.019567210206731 4684.432237364830144 1.014168317947561 4685.993975052440874 1.005243160847046 4687.556233406052343 0.979788976597799 4689.119012599246162 0.955437751897372 4690.682312805673064 0.941839787331413 4692.246134199029257 0.934636144395107 4693.810476953070975 0.935980462839653 4695.375341241609931 0.929639939644457 4696.940727238530599 0.920610344387898 4698.506635117758378 0.905591650289419 4700.073065053284154 0.891435558379115 4701.640017219155197 0.881476156312008 4703.207491789472442 0.865423102445448 4704.775488938410490 0.853739249247428 4706.344008840183960 0.851115831412048 4707.913051669075685 0.852284496082735 4709.482617599416699 0.850530747242917 4711.052706805614434 0.849098426061861 4712.623319462117252 0.850950492381882 4714.194455743438084 0.859739267280286 4715.766115824143526 0.869036716937062 4717.338299878871112 0.875559480548631 4718.911008082303852 0.880245177301416 4720.484240609186600 0.875199560066066 4722.057997634318781 0.866671750137146 4723.632279332570761 0.862236169554903 4725.207085878859289 0.862935281745459 4726.782417448162050 0.858511261437337 4728.358274215510392 0.852249753946361 4729.934656356011146 0.855086954165289 4731.511564044811166 0.849774970126672 4733.088997457123696 0.837301384701174 4734.666956768213822 0.829612995500857 4736.245442153419390 0.833418460433726 4737.824453788123719 0.840251232491736 4739.403991847771977 0.848526400077338 4740.984056507863897 0.871159998602703 4742.564647943971977 0.884779011341221 4744.145766331712366 0.888619291243039 4745.727411846764880 0.897086530999542 4747.309584664868453 0.906051810858540 4748.892284961814767 0.906956155015837 4750.475512913469174 0.912735884388799 4752.059268695740684 0.918188604037952 4753.643552484602878 0.914361398053978 4755.228364456081181 0.904272001751570 4756.813704786277412 0.913361375791636 4758.399573651334322 0.921299824215583 4759.985971227459231 0.919431570250083 4761.572897690914942 0.929799365916295 4763.160353218036107 0.940093771270723 4764.748337985201033 0.947228551163694 4766.336852168852602 0.956673604939626 4767.925895945487355 0.970794195190875 4769.515469491676413 0.972474818288012 4771.105572984033643 0.963075221053069 4772.696206599237485 0.965281106969149 4774.287370514020040 0.972928493929526 4775.879064905186169 0.964975461270556 4777.471289949587117 0.951237107184433 4779.064045824135974 0.941405955113830 4780.657332705801309 0.940159030148993 4782.251150771624452 0.940499417097113 4783.845500198692207 0.950266740084182 4785.440381164153223 0.963663241573451 4787.035793845211629 0.971499771236535 4788.631738419146131 0.984942895575301 4790.228215063279094 1.015277300973017 4791.825223954996545 1.041850922185922 4793.422765271738172 1.052725428580253 4795.020839191019149 1.059960042878291 4796.619445890399220 1.080441856177704 4798.218585547499970 1.093782984639174 4799.818258340003922 1.106945225882796 4801.418464445647260 1.128849668320981 4803.019204042241654 1.145584714373109 4804.620477307641522 1.163232832914180 4806.222284419765856 1.192812911921596 4807.824625556588217 1.229640500007788 4809.427500896156744 1.258772789340259 4811.030910616563233 1.283301874296428 4812.634854895964963 1.304868648197599 4814.239333912573784 1.330114714380348 4815.844347844673393 1.353344217791966 4817.449896870593875 1.370346160291763 4819.055981168730796 1.374813397640252 4820.662600917531563 1.369787721358528 4822.269756295520892 1.367764415393013 4823.877447481265335 1.371833710933349 4825.485674653397837 1.375949556093857 4827.094437990605002 1.382741198939949 4828.703737671648923 1.392607108020560 4830.313573875335351 1.406324127944895 4831.923946780535516 1.409262080183029 4833.534856566173403 1.403357893800812 4835.146303411250301 1.412837787900768 4836.758287494810247 1.424466543688497 4838.370808995962761 1.429350517311066 4839.983868093871024 1.424563667224291 4841.597464967775522 1.417398896712402 4843.211599796958581 1.406272313091063 4844.826272760768916 1.387672539278160 4846.441484038608905 1.359785926037099 4848.057233809957324 1.335408705778534 4849.673522254337513 1.322381003979050 4851.290349551335567 1.307477473746844 4852.907715880599426 1.291137112088873 4854.525621421832511 1.272305867126812 4856.144066354811002 1.253487629875532 4857.763050859357463 1.230648843031209 4859.382575115358122 1.200192142443130 4861.002639302757416 1.174131173157280 4862.623243601569811 1.151886954439397 4864.244388191859798 1.129174443300681 4865.866073253752802 1.115046618378985 4867.488298967431547 1.102036221786486 4869.111065513154244 1.094574506421373 4870.734373071221853 1.085058387005640 4872.358221822003543 1.079196584090522 4873.982611945920326 1.074628242695803 4875.607543623470519 1.072576451226054 4877.233017035197918 1.074909502969235 4878.859032361709069 1.079633430224217 4880.485589783668729 1.090476748108388 4882.112689481815323 1.091532798164197 4883.740331636932751 1.094532032363702 4885.368516429868578 1.109293359241971 4886.997244041529484 1.121712944792610 4888.626514652894002 1.131177087654561 4890.256328444987048 1.147036775844595 4891.886685598899930 1.167879143715430 4893.517586295777619 1.181436283068483 4895.149030716841480 1.197851326549236 4896.781019043358356 1.217446728278285 4898.413551456660571 1.242539792755586 4900.046628138139567 1.254357008015292 4901.680249269244086 1.266973319526231 4903.314415031497447 1.285323327398308 4904.949125606469352 1.301921666809772 4906.584381175793169 1.324869360178084 4908.220181921158655 1.343397656203139 4909.856528024332874 1.358319796555383 4911.493419667126545 1.370307359156200 4913.130857031415871 1.374975346829032 4914.768840299133444 1.375493877043761 4916.407369652289162 1.383005317294503 4918.046445272933852 1.379476576898370 4919.686067343190189 1.380734538305666 4921.326236045230871 1.384517670787081 4922.966951561307724 1.385677512455875 4924.608214073718045 1.391705425347424 4926.250023764823709 1.401854888907774 4927.892380817042977 1.400218773076159 4929.535285412870508 1.401991350694157 4931.178737734846436 1.413880256632570 4932.822737965575470 1.411130402649683 4934.467286287719617 1.409221261612684 4936.112382884017279 1.409348156919877 4937.758027937250517 1.403708811878733 4939.404221630271422 1.397565242622475 4941.050964145982107 1.398083145823017 4942.698255667366539 1.402194587609133 4944.346096377450522 1.417716083599557 4945.994486459328073 1.420114349257225 4947.643426096148687 1.425172434389226 4949.292915471138258 1.435796469058569 4950.942954767568153 1.441459022192283 4952.593544168775225 1.446058547654119 4954.244683858159988 1.449851194106947 4955.896374019174800 1.451799660221006 4957.548614835353874 1.449081024723101 4959.201406490272348 1.438042712169920 4960.854749167574482 1.424052089624873 4962.508643050960018 1.408617631641585 4964.163088324204182 1.382448165562796 4965.818085171131315 1.355057249618641 4967.473633775627604 1.321060628177081 4969.129734321639262 1.296650430551533 4970.786386993186170 1.274420094740591 4972.443591974338233 1.236811969826821 4974.101349449227200 1.202089778227126 4975.759659602043030 1.167470479465766 4977.418522617054805 1.135051978452788 4979.077938678573446 1.106910104929349 4980.737907970979904 1.076595858123066 4982.398430678708792 1.048993064179253 4984.059506986273846 1.021801924128107 4985.721137078233369 0.984474135691654 4987.383321139213876 0.958270739235223 4989.046059353896453 0.931535706575827 4990.709351907040400 0.901713590741889 4992.373198983450493 0.876907385450181 4994.037600767998811 0.853719027736483 4995.702557445614730 0.832025658135196 4997.368069201302205 0.814149902275067 4999.034136220114306 0.794206716825940 5000.700758687167763 0.786748979421998 5002.367936787644794 0.782091383028079 5004.035670706781275 0.763291389844834 5005.703960629891299 0.746349866968922 5007.372806742336252 0.733312392127246 5009.042209229542095 0.723704147393595 5010.712168276992998 0.713643968619643 5012.382684070251344 0.698187326408846 5014.053756794924084 0.689913398064927 5015.725386636685471 0.676037842864408 5017.397573781267965 0.649880696862517 5019.070318414480425 0.633062547012293 5020.743620722177184 0.630185106456647 5022.417480890281695 0.627493708062582 5024.091899104772892 0.625616007366939 5025.766875551708836 0.621295722712244 5027.442410417190331 0.616132064641643 5029.118503887390034 0.610173289814872 5030.795156148533351 0.612989917956313 5032.472367386927544 0.618595495726045 5034.150137788923530 0.617254440455352 5035.828467540939528 0.616113843631397 5037.507356829451965 0.618326502434303 5039.186805841014575 0.616031702809516 5040.866814762227477 0.602644556356109 5042.547383779758093 0.597633898358318 5044.228513080332050 0.601981006389802 5045.910202850750466 0.603204489782914 5047.592453277863569 0.599751937059758 5049.275264548587074 0.602748364726141 5050.958636849896720 0.603266195374865 5052.642570368841916 0.598775368504744 5054.327065292523002 0.594068794996195 5056.012121808105803 0.603208720069250 5057.697740102817988 0.606249830287795 5059.383920363945435 0.604308284542946 5061.070662778852238 0.605901074693298 5062.757967534949785 0.612524606687265 5064.445834819714946 0.619853368492427 5066.134264820683711 0.625674679456639 5067.823257725471194 0.630693320480208 5069.512813721736165 0.635233749860715 5071.202932997207427 0.630725447205578 5072.893615739671986 0.638897809955041 5074.584862136993252 0.652937380621463 5076.276672377081923 0.662069371088973 5077.969046647916912 0.669037548154961 5079.661985137535339 0.664293751802113 5081.355488034050722 0.655460825483248 5083.049555525626602 0.649982055511882 5084.744187800491090 0.648256908925319 5086.439385046932330 0.650858230212330 5088.135147453314858 0.657039442418177 5089.831475208053234 0.655550257359549 5091.528368499627504 0.652362534558213 5093.225827516575919 0.660121914721832 5094.923852447514946 0.671045851497567 5096.622443481110167 0.684960028404803 5098.321600806092647 0.707962323022950 5100.021324611253476 0.726693737997613 5101.721615085461053 0.737027041365551 5103.422472417631070 0.746386023584942 5105.123896796747431 0.760750856253843 5106.825888411852247 0.773770508449713 5108.528447452065848 0.782838200862323 5110.231574106557673 0.785375582897014 5111.935268564562648 0.791980865537734 5113.639531015380271 0.791697022873135 5115.344361648368249 0.781251175936409 5117.049760652962505 0.772217771736502 5118.755728218646254 0.771089421972503 5120.462264534971837 0.760487208239266 5122.169369791548888 0.757104888537504 5123.877044178067081 0.754768176614613 5125.585287884261561 0.747413995224734 5127.294101099937507 0.743686519269603 5129.003484014958303 0.743880498737577 5130.713436819265553 0.752903112112782 5132.423959702849061 0.767649335504762 5134.135052855766844 0.777989728519834 5135.846716468135128 0.785745227369148 5137.558950730148354 0.792962412324246 5139.271755832050985 0.794088901863156 5140.985131964152970 0.790604558587037 5142.699079316826101 0.791261604035734 5144.413598080518568 0.792749217445581 5146.128688445727676 0.790038700044349 5147.844350603018029 0.788965017896011 5149.560584743013351 0.789171023532616 5151.277391056418310 0.787635685540692 5152.994769733983048 0.787089582854842 5154.712720966526831 0.784563863042169 5156.431244944929858 0.795138388850372 5158.150341860147819 0.803019687088619 5159.870011903186423 0.805735399118385 5161.590255265120504 0.804467733045140 5163.311072137088559 0.800718154466455 5165.032462710287291 0.796639769239984 5166.754427175992532 0.794038455596365 5168.476965725527407 0.787874962530244 5170.200078550286889 0.782413915780115 5171.923765841721433 0.780626210008420 5173.648027791363347 0.776773522772512 5175.372864590790414 0.772436216304842 5177.098276431653176 0.772776223375213 5178.824263505657655 0.780007165507136 5180.550826004589908 0.778254721577749 5182.277964120286924 0.779141749746754 5184.005678044652086 0.781444697027264 5185.733967969646983 0.786548504413406 5187.462834087316878 0.786905833387273 5189.192276589750691 0.785575281099964 5190.922295669110099 0.783290949709840 5192.652891517613170 0.783968321724162 5194.384064327558917 0.786801337041659 5196.115814291295464 0.792593969407742 5197.848141601238240 0.799818306397670 5199.581046449864516 0.801546921061516 5201.314529029727964 0.802434407697157 5203.048589533434097 0.802639706305253 5204.783228153654818 0.806939693339370 5206.518445083123879 0.821229326512663 5208.254240514652338 0.834690628479512 5209.990614641102184 0.839647049458396 5211.727567655403618 0.842400769973145 5213.465099750545050 0.845866544641623 5215.203211119597654 0.856840745008355 5216.941901955678986 0.873164598255871 5218.681172451977545 0.890647785745996 5220.421022801744584 0.904956088890514 5222.161453198292293 0.908066437549623 5223.902463835011986 0.901333500742162 5225.644054905344092 0.909157192014874 5227.386226602799070 0.912725894997146 5229.128979120945587 0.922019888289941 5230.872312653434165 0.933371235443216 5232.616227393962617 0.940092986023965 5234.360723536299702 0.950614752233694 5236.105801274272380 0.954294979214467 5237.851460801789472 0.960254921914480 5239.597702312807087 0.979722929062074 5241.344526001354097 0.977589199103562 5243.091932061513944 0.980621070012703 5244.839920687454651 0.987084182195753 5246.588492073392445 0.990316536170652 5248.337646413612674 0.993793390183183 5250.087383902459806 0.985856348617372 5251.837704734360159 0.985910122218385 5253.588609103789167 0.992889311059124 5255.340097205291386 0.993785361334585 5257.092169233470486 0.997709643109945 5258.844825383013813 0.994097525448956 5260.598065848653277 0.988376340569522 5262.351890825193550 0.984731804598599 5264.106300507501146 0.985641759602066 5265.861295090518979 0.991296781366192 5267.616874769240894 0.984901971254394 5269.373039738733496 0.976476800997803 5271.129790194117959 0.979464013149878 5272.887126330601859 0.986531439534418 5274.645048343438248 0.996805697902770 5276.403556427952935 1.004724805533371 5278.162650779533578 1.008843781253017 5279.922331593632407 1.008668140732092 5281.682599065778049 1.005101837712215 5283.443453391550975 1.007077094492952 5285.204894766602592 1.008921261557318 5286.966923386642520 1.002241847469786 5288.729539447462230 0.999587064012820 5290.492743144902306 1.010807277584646 5292.256534674876093 1.024974886882339 5294.020914233353324 1.042919373890509 5295.785882016387404 1.057536023639735 5297.551438220079945 1.068346688522349 5299.317583040604404 1.075808287779644 5301.084316674194270 1.089036041168526 5302.851639317163063 1.098150114009351 5304.619551165875237 1.110561383111287 5306.388052416765277 1.112903576854154 5308.157143266328603 1.111561328039403 5309.926823911140673 1.105875050680273 5311.697094547826055 1.104982784323115 5313.467955373083896 1.105150148120830 5315.239406583670643 1.106303739922986 5317.011448376424596 1.107206944160045 5318.784080948233168 1.110971729521133 5320.557304496056531 1.112776825532091 5322.331119216913066 1.108379110577549 5324.105525307905737 1.097303265994562 5325.880522966184799 1.084014922094980 5327.656112388971451 1.071118980289220 5329.432293773553283 1.059998361634546 5331.209067317279732 1.055254159898898 5332.986433217579361 1.042517632278721 5334.764391671933481 1.025917925551305 5336.542942877891619 1.004912401772291 5338.322087033065145 0.986129576758710 5340.101824335149104 0.976472064408720 5341.882154981885833 0.970834127047388 5343.663079171088611 0.958552771164406 5345.444597100634383 0.950955467194080 5347.226708968479215 0.943654177907680 5349.009414972631930 0.938786433887882 5350.792715311167740 0.936029100081643 5352.576610182228251 0.930796017191869 5354.361099784034195 0.926675333117132 5356.146184314857237 0.927592192648079 5357.931863973039071 0.925071233533127 5359.718138956983239 0.927803808831980 5361.505009465176954 0.932730078923275 5363.292475696154725 0.929255086401058 5365.080537848523818 0.928103575919846 5366.869196120953347 0.931396418567840 5368.658450712192462 0.938682926594812 5370.448301821043060 0.947446991109270 5372.238749646377983 0.957249762950195 5374.029794387128277 0.966853614875451 5375.821436242312302 0.981110653658341 5377.613675410993892 0.994134384952638 5379.406512092312369 1.011059323396811 5381.199946485465262 1.025697823794189 5382.993978789734683 1.034158450606900 5384.788609204451859 1.037646358209168 5386.583837929018955 1.049214424002146 5388.379665162907258 1.050906420126818 5390.176091105648084 1.055891866917309 5391.973115956854599 1.058897789908255 5393.770739916189996 1.062468719935134 5395.568963183390224 1.067892441286336 5397.367785958253990 1.073711351873295 5399.167208440660943 1.088477532170068 5400.967230830539847 1.109193134132675 5402.767853327895864 1.115889913976596 5404.569076132790542 1.129891589662503 5406.370899445370924 1.145853877640661 5408.173323465834983 1.153677541300673 5409.976348394451634 1.171932293213260 5411.779974431551636 1.188385355522433 5413.584201777548515 1.201498641438132 5415.389030632906724 1.212559518381399 5417.194461198163481 1.226978273201829 5419.000493673915116 1.241147746043353 5420.807128260844365 1.259032954444280 5422.614365159682166 1.289604741791920 5424.422204571232214 1.321458264330357 5426.230646696361873 1.347685184318853 5428.039691736017630 1.379606180502094 5429.849339891201453 1.415947275596899 5431.659591362983520 1.447684787685469 5433.470446352497675 1.488965331793185 5435.281905060961435 1.531249017713658 5437.093967689643250 1.557474967192566 5438.906634439882509 1.577398122937397 5440.719905513086815 1.603796894690023 5442.533781110723794 1.609633338424506 5444.348261434349297 1.613411272275012 5446.163346685563738 1.615065358987809 5447.979037066045748 1.610740807236000 5449.795332777530348 1.600519938823053 5451.612234021842596 1.605699807499412 5453.429741000852118 1.604700626568415 5455.247853916505846 1.597859503741268 5457.066572970808920 1.600967606560426 5458.885898365853791 1.615231624903653 5460.705830303782932 1.626182265388723 5462.526368986808848 1.652773420628014 5464.347514617209526 1.685303923741510 5466.169267397344811 1.706356378450730 5467.991627529627294 1.729494785791341 5469.814595216540511 1.761304344193368 5471.638170660630749 1.766854867835322 5473.462354064528881 1.767336425067147 5475.287145630916712 1.782615474754216 5477.112545562547893 1.789138547664285 5478.938554062240655 1.779681282044453 5480.765171332895079 1.761382254309389 5482.592397577462179 1.750326382570103 5484.420232998969368 1.734443503965257 5486.248677800501355 1.726870486176483 5488.077732185231071 1.735292681468240 5489.907396356381469 1.734535038722545 5491.737670517248262 1.733235371886859 5493.568554871189917 1.725884651335394 5495.400049621647668 1.730189761689759 5497.232154972117314 1.753616750432173 5499.064871126165599 1.773088014805794 5500.898198287427476 1.794750732345921 5502.732136659599746 1.808866901032342 5504.566686446465610 1.831122372025813 5506.401847851858292 1.851980710661712 5508.237621079682867 1.877240376329343 5510.074006333910802 1.918290592854122 5511.911003818595418 1.964766228788899 5513.748613737840969 1.995291954368092 5515.586836295828107 2.010206232969615 5517.425671696795689 2.022173150207336 5519.265120145071705 2.038295978847023 5521.105181845034167 2.063139073899197 5522.945857001133845 2.066354023123016 5524.787145817883356 2.067952431383349 5526.629048499882629 2.070767041436100 5528.471565251782522 2.069275282409189 5530.314696278306656 2.071401660426566 5532.158441784240495 2.072440369658834 5534.002801974457725 2.086024964245413 5535.847777053881146 2.096495798136473 5537.693367227507224 2.102934809499702 5539.539572700396093 2.097190040268562 5541.386393677693377 2.103748639651036 5543.233830364596542 2.122322478362297 5545.081882966374906 2.129575410024265 5546.930551688361447 2.118366187232966 5548.779836735978279 2.097779859770437 5550.629738314692077 2.084334498405784 5552.480256630050462 2.074833838166278 5554.331391887658356 2.073487101230297 5556.183144293210717 2.068546589657364 5558.035514052451617 2.068662683974393 5559.888501371199709 2.066983369610219 5561.742106455342764 2.060256465648406 5563.596329510830401 2.056705045046081 5565.451170743699549 2.068496476939318 5567.306630360038071 2.071156177192206 5569.162708566007495 2.078717288821332 5571.019405567834838 2.092575190318645 5572.876721571828966 2.088034144683266 5574.734656784352410 2.075138562634848 5576.593211411844095 2.067894137522741 5578.452385660804794 2.064271880664110 5580.312179737818951 2.069022693298143 5582.172593849525583 2.063063213918227 5584.033628202636464 2.052704507267928 5585.895283003928853 2.063893445618161 5587.757558460264590 2.073902975872222 5589.620454778556450 2.068305266732563 5591.483972165794512 2.065938361395241 5593.348110829028883 2.072611288273814 5595.212870975397891 2.073138436645753 5597.078252812091705 2.069210214934721 5598.944256546375073 2.056503646304345 5600.810882385575496 2.051880433874727 5602.678130537107791 2.050192597880445 5604.546001208438611 2.031699280806251 5606.414494607108281 2.004554718182872 5608.283610940721701 1.998938172408931 5610.153350416971080 2.006988699873262 5612.023713243597740 2.006113609107408 5613.894699628420312 2.001253071606285 5615.766309779326548 1.999244332229075 5617.638543904266953 1.994067398297326 5619.511402211279346 1.994738092668065 5621.384884908454296 1.989826219308430 5623.258992203955131 1.984633568726772 5625.133724306009753 1.971563061016369 5627.009081422935196 1.953071529766826 5628.885063763097605 1.916742046671183 5630.761671534939524 1.882058279004015 5632.638904946967159 1.842787133031052 5634.516764207773122 1.801626174010531 5636.395249526003681 1.759625963077498 5638.274361110377868 1.703573345787664 5640.154099169682013 1.647253452281197 5642.034463912787032 1.590525545307774 5643.915455548614773 1.522935588200260 5645.797074286166207 1.462400608341306 5647.679320334504155 1.406026446607781 5649.562193902777835 1.346201740872966 5651.445695200189220 1.295726536999278 5653.329824436017589 1.234832363002710 5655.214581819604973 1.178422969211136 5657.099967560378900 1.124435117717550 5658.985981867821465 1.072416770144853 5660.872624951491161 1.032371413013584 5662.759897021007419 0.995500600917585 5664.647798286079706 0.956072250646641 5666.536328956468424 0.928559572170281 5668.425489242010372 0.895111941019141 5670.315279352606922 0.856091361603789 5672.205699498246759 0.827049065882805 5674.096749888969498 0.797560671342820 5675.988430734892063 0.783214602762133 5677.880742246202317 0.771345479204113 5679.773684633150879 0.759069734367493 5681.667258106075678 0.746613606749309 5683.561462875368306 0.728059834835666 5685.456299151495841 0.720584487346455 5687.351767144990845 0.731746180267366 5689.247867066470462 0.747296689621173 5691.144599126608227 0.771186466587933 5693.041963536152252 0.798583027183955 5694.939960505914314 0.816857773375993 5696.838590246794411 0.842397640381845 5698.737852969746200 0.868343090226271 5700.637748885797919 0.897087029563128 5702.538278206045106 0.925289952105460 5704.439441141667885 0.957973232999573 5706.341237903900947 0.988676356219466 5708.243668704055381 1.019691958278041 5710.146733753505941 1.045702019415061 5712.050433263717423 1.077702881950821 5713.954767446203732 1.104371542756281 5715.859736512559721 1.125046444356486 5717.765340674442086 1.155234987171131 5719.671580143596657 1.188181166373647 5721.578455131821102 1.213597863119197 5723.485965850990397 1.233243409418648 5725.394112513045002 1.255969603301110 5727.302895330012689 1.272342780305144 5729.212314513975798 1.289122786556548 5731.122370277089431 1.300570555038893 5733.033062831578718 1.305005210740219 5734.944392389752466 1.309969132980534 5736.856359163976776 1.311584650689980 5738.768963366690514 1.323556871132936 5740.682205210406210 1.332407941079469 5742.596084907700060 1.336764136622707 5744.510602671238303 1.333594018276109 5746.425758713737196 1.330461850936358 5748.341553247993033 1.320548530934351 5750.257986486866685 1.324279211272386 5752.175058643305420 1.339886328189959 5754.092769930312897 1.345639070878027 5756.011120560966447 1.346370527816780 5757.930110748412517 1.338245154782713 5759.849740705882141 1.331618919433184 5761.770010646661831 1.320703773513269 5763.690920784115406 1.322516370922679 5765.612471331671259 1.328785290064052 5767.534662502846913 1.337861273213729 5769.457494511213554 1.341525217489276 5771.380967570418761 1.339656864507470 5773.305081894175601 1.347554188289444 5775.229837696287177 1.350142255662958 5777.155235190608437 1.362500306591184 5779.081274591073452 1.380968571775672 5781.007956111679960 1.400440034553082 5782.935279966514827 1.410946974996822 5784.863246369721310 1.419392730041688 5786.791855535515424 1.434710692113693 5788.721107678184126 1.446965858973812 5790.651003012097135 1.446214395876881 5792.581541751684199 1.447307280669574 5794.512724111447824 1.449390249959290 5796.444550305965095 1.444278671793724 5798.377020549875851 1.433760823239016 5800.310135057912703 1.433081883885942 5802.243894044860099 1.439530732442160 5804.178297725578886 1.443594802364634 5806.113346314996306 1.436702213954600 5808.049040028132367 1.450529942497023 5809.985379080056191 1.470461601466081 5811.922363685916935 1.484163454797027 5813.859994060929239 1.491058801321151 5815.798270420396875 1.488491676054654 5817.737192979679094 1.497692807050241 5819.676761954210633 1.495782838988332 5821.616977559493534 1.497727435413484 5823.557840011118969 1.485906609446605 5825.499349524732679 1.470221777279597 5827.441506316057712 1.450297664571937 5829.384310600884419 1.438058196863845 5831.327762595090462 1.434937570775905 5833.271862514608074 1.441442926458185 5835.216610575451341 1.445874441002073 5837.162006993696195 1.439502692785232 5839.108051985507700 1.429144896298005 5841.054745767110035 1.424301217509701 5843.002088554800139 1.421179167959323 5844.950080564945893 1.431564331065018 5846.898722014000668 1.436291257754023 5848.848013118475137 1.438817726640281 5850.797954094957277 1.438686580249583 5852.748545160100548 1.434634429934875 5854.699786530650272 1.432860789080376 5856.651678423404519 1.432808820449425 5858.604221055240487 1.431869393312657 5860.557414643106313 1.431102580205830 5862.511259404018347 1.418525733075911 5864.465755555082069 1.408056633070517 5866.420903313458439 1.400998490550478 5868.376702896385723 1.385704453975761 5870.333154521169490 1.392309347696571 5872.290258405203531 1.397066361127447 5874.248014765938933 1.393076521434854 5876.206423820905002 1.387625588897341 5878.165485787696525 1.385222600118418 5880.125200883996513 1.391572643013739 5882.085569327548910 1.392100429750773 5884.046591336169513 1.393282209543700 5886.008267127745967 1.392960511690495 5887.970596920252319 1.378019501014875 5889.933580931719916 1.371656073666067 5891.897219380258321 1.363810538275788 5893.861512484043487 1.352518018846023 5895.826460461341412 1.347503380264799 5897.792063530474479 1.352088910896665 5899.758321909843289 1.358819280170229 5901.725235817914836 1.353078990157740 5903.692805473247063 1.349852927304381 5905.661031094452483 1.354113133686702 5907.629912900221825 1.348864832767530 5909.599451109315851 1.337343282617893 5911.569645940582632 1.344976039814659 5913.540497612928448 1.346090626750349 5915.512006345334157 1.339821356792193 5917.484172356858835 1.326869044962726 5919.456995866625221 1.318475551683418 5921.430477093847003 1.308238898151946 5923.404616257794260 1.291922043068236 5925.379413577817104 1.285396726802507 5927.354869273329314 1.284974352211913 5929.330983563839254 1.286018529139089 5931.307756668909860 1.275765883181663 5933.285188808181374 1.263312646625933 5935.263280201363159 1.256322830747066 5937.242031068253709 1.245938051293979 5939.221441628709727 1.235343416547977 5941.201512102666129 1.240549719107581 5943.182242710123319 1.236768943934350 5945.163633671176285 1.239062103015784 5947.145685205970949 1.228189881743615 5949.128397534737815 1.229360490661747 5951.111770877771050 1.236951838394326 5953.095805455456684 1.233573916997039 5955.080501488238951 1.242327825212459 5957.065859196638485 1.238679551542895 5959.051878801244129 1.231089643296582 5961.038560522737498 1.226131752782660 5963.025904581854775 1.214456469364784 5965.013911199412178 1.214566277812530 5967.002580596294138 1.211964608213721 5968.991912993473306 1.199755361017563 5970.981908611984181 1.185919493992556 5972.972567672934019 1.174509806719706 5974.963890397502837 1.176481942495049 5976.955877006960691 1.179205785502985 5978.948527722634026 1.169722652908625 5980.941842765925685 1.159067157816096 5982.935822358318546 1.127960751112344 5984.930466721358243 1.094501102175023 5986.925776076684997 1.088547003332723 5988.921750645991779 1.084804084824007 5990.918390651056143 1.076396232104739 5992.915696313718399 1.064762307941187 5994.913667855915264 1.051137795059088 5996.912305499636204 1.045494523199431 5998.911609466953450 1.038864753631398 6000.911579980005627 1.037887274748611 6002.912217261022306 1.045229672729847 6004.913521532293089 1.036203327399152 6006.915493016182154 1.041017461656317 6008.918131935126439 1.037904353795724 6010.921438511652923 1.039037747176381 6012.925412968345881 1.044458712552778 6014.930055527868717 1.044583034300994 6016.935366412952135 1.048849130194857 6018.941345846424156 1.045036023541315 6020.947994051161004 1.043545608549800 6022.955311250127124 1.043118242965193 6024.963297666348808 1.029578858150681 6026.971953522950571 1.016613836437494 6028.981279043107861 1.000986657635159 6030.991274450080709 0.999170905049103 6033.001939967194630 1.011826997131585 6035.013275817869726 1.015610697766727 6037.025282225582487 1.023692253942913 6039.037959413888530 1.036352144098783 6041.051307606411683 1.041193303143026 6043.065327026870364 1.042595099416013 6045.080017899037557 1.050374057272637 6047.095380446769923 1.060689007849029 6049.111414893994151 1.054669629011339 6051.128121464709693 1.039454656156536 6053.145500383006947 1.036998842722204 6055.163551873030883 1.054148149789193 6057.182276159012872 1.053628743246194 6059.201673465247950 1.049060047312272 6061.221744016124831 1.047000753995296 6063.242488036091345 1.045425720949200 6065.263905749673540 1.044600093551030 6067.285997381467496 1.041444895169617 6069.308763156162968 1.036944114883970 6071.332203298504282 1.035817718714238 6073.356318033319440 1.015391055968461 6075.381107585502832 1.016182286958061 6077.406572180045259 1.021807680329350 6079.432712041989362 1.027843204392414 6081.459527396464182 1.030603428768708 6083.487018468663337 1.035815823345412 6085.515185483877758 1.038266485776538 6087.544028667452039 1.032169448059336 6089.573548244813537 1.013154164599469 6091.603744441458730 1.011333221740386 6093.634617482976864 0.996917397175630 6095.666167595013576 0.983524797570552 6097.698395003298174 0.973571540117540 6099.731299933626360 0.968076094028032 6101.764882611889334 0.962034433295171 6103.799143264033773 0.954280991595578 6105.834082116090940 0.948160628448142 6107.869699394162126 0.942803757887224 6109.905995324423202 0.932332971287074 6111.942970133139170 0.925603744620155 6113.980624046636876 0.926349671757803 6116.018957291322295 0.929092967623907 6118.057970093667791 0.925055395423511 6120.097662680245776 0.906710239012116 6122.138035277681411 0.902167996322932 6124.179088112682621 0.900281698606947 6126.220821412027362 0.909172678443774 6128.263235402586361 0.904603125885436 6130.306330311289457 0.898421356906685 6132.350106365146530 0.890690259725238 6134.394563791237488 0.873134197696149 6136.439702816736826 0.865278135495621 6138.485523668876340 0.854460228618855 6140.532026574970587 0.830356723334929 6142.579211762399609 0.816537016172717 6144.627079458642584 0.801040138320758 6146.675629891235076 0.789758163747657 6148.724863287791777 0.772124872654932 6150.774779876000139 0.753884500476908 6152.825379883641290 0.745349053589155 6154.876663538552748 0.724295651103520 6156.928631068656614 0.710919018856129 6158.981282701940472 0.708839638518505 6161.034618666491042 0.687187248929972 6163.088639190449612 0.664179795658139 6165.143344502042055 0.656159926906567 6167.198734829560635 0.661856535826330 6169.254810401396753 0.658833485303564 6171.311571445995469 0.644430201823428 6173.369018191886425 0.645333715358886 6175.427150867673845 0.643638862058314 6177.485969702034708 0.631052434720762 6179.545474923737856 0.646065575199476 6181.605666761610337 0.645564539733238 6183.666545444564690 0.625609403716589 6185.728111201578940 0.608653096977352 6187.790364261729337 0.599555656766596 6189.853304854148519 0.592799148355972 6191.916933208052797 0.581598605367678 6193.981249552727604 0.571047764621276 6196.046254117553872 0.568563412889741 6198.111947131969828 0.564268865454988 6200.178328825497374 0.560529739751857 6202.245399427729353 0.564028789156076 6204.313159168350467 0.579695245676020 6206.381608277107262 0.591987185683153 6208.450746983827230 0.598270335862269 6210.520575518407895 0.623463834892690 6212.591094110843187 0.648700103973924 6214.662302991183424 0.675544260940100 6216.734202389563507 0.698293474461757 6218.806792536189278 0.711486495326806 6220.880073661360257 0.716547217595886 6222.954045995434171 0.730336429512842 6225.028709768853332 0.737865130371816 6227.104065212129171 0.745309781673818 6229.180112555869528 0.749509703304676 6231.256852030739537 0.742919796073153 6233.334283867488921 0.746149048539637 6235.412408296935610 0.748462775264855 6237.491225549996670 0.755340958608863 6239.570735857645559 0.770378765060181 6241.650939450937585 0.788621952575660 6243.731836561006276 0.789499765586878 6245.813427419057916 0.787678828923180 6247.895712256391562 0.793584305637060 6249.978691304366293 0.801607811825245 6252.062364794424866 0.811375083264518 6254.146732958078246 0.811989230446412 6256.231796026937445 0.814573131204438 6258.317554232669863 0.809054439894141 6260.404007807026574 0.797389715075049 6262.491156981826862 0.784883090983211 6264.579001988991877 0.789706931790224 6266.667543060497337 0.798794120838346 6268.756780428401726 0.787447507126061 6270.846714324838103 0.785818332626212 6272.937344982033210 0.787729816279634 6275.028672632272901 0.786442222543969 6277.120697507927616 0.782457654634471 6279.213419841436917 0.794663181492591 6281.306839865339498 0.813653639874066 6283.400957812230445 0.824972150999200 6285.495773914790334 0.822975271169337 6287.591288405768864 0.825909920006684 6289.687501518014869 0.843336671453932 6291.784413484434481 0.843385065131599 6293.882024538017504 0.843798812067925 6295.980334911825594 0.854748300492688 6298.079344839016812 0.857276054104521 6300.179054552808338 0.851691846443116 6302.279464286501934 0.840036947053876 6304.380574273474849 0.844780165965262 6306.482384747179822 0.850872030157356 6308.584895941161449 0.849669938442810 6310.688108089027082 0.853213363633014 6312.792021424466839 0.863107688315783 6314.896636181241774 0.864746689067702 6317.001952593212991 0.867473227474086 6319.107970894295249 0.868604192459015 6321.214691318492441 0.873821982343933 6323.322114099877581 0.895813014119558 6325.430239472620997 0.914696598692679 6327.539067670953955 0.935608823811748 6329.648598929189575 0.949990039675047 6331.758833481713737 0.964317268144270 6333.869771563010545 0.973680506269897 6335.981413407621403 0.979526864747469 6338.093759250174116 0.986309507935800 6340.206809325366521 1.008904058332158 6342.320563867995588 1.016084370569112 6344.435023112914678 1.008597837163215 6346.550187295066280 1.015026982981858 6348.666056649461098 1.030484963853272 6350.782631411208058 1.052665542671327 6352.899911815476116 1.058262432236887 6355.017898097518810 1.063739692473491 6357.136590492661526 1.077251752388641 6359.255989236326968 1.077782432103027 6361.376094563997867 1.074126920658245 6363.496906711241536 1.088492089668770 6365.618425913697138 1.087938791445654 6367.740652407102061 1.082591019696765 6369.863586427252812 1.070198904644710 6371.987228210030480 1.062150557363551 6374.111577991396189 1.063670732838730 6376.236636007381094 1.064555168549228 6378.362402494116395 1.084009405127979 6380.488877687792410 1.096561060850694 6382.616061824683129 1.115686288771766 6384.743955141136212 1.122174761813655 6386.872557873597543 1.152114762644450 6389.001870258572126 1.179672747134398 6391.131892532649545 1.204669232685231 6393.262624932493054 1.217542202033491 6395.394067694864134 1.238851767787882 6397.526221056581562 1.240084282903035 6399.659085254553247 1.242554265065984 6401.792660525756219 1.254598529644621 6403.926947107267551 1.264085900887137 6406.061945236225256 1.260246060067882 6408.197655149849197 1.252672440844291 6410.334077085435638 1.243689444502411 6412.471211280376338 1.235776509507625 6414.609057972124901 1.253072469551435 6416.747617398219518 1.268417889362274 6418.886889796272953 1.284290487631801 6421.026875403993472 1.304393124148468 6423.167574459150273 1.322598180584436 6425.308987199600779 1.342582697085707 6427.451113863271530 1.358436805078428 6429.593954688190934 1.365645517461953 6431.737509912444693 1.387221710595526 6433.881779774206734 1.392154840668787 6436.026764511728288 1.381096093565913 6438.172464363335166 1.385780656176754 6440.318879567450495 1.397410755376232 6442.466010362559246 1.395165592324087 6444.613856987231884 1.394599450861872 6446.762419680110725 1.400709820912818 6448.911698679938127 1.412669416074025 6451.061694225516476 1.427584951689596 6453.212406555734560 1.440166110624659 6455.363835909553018 1.468239509499660 6457.515982526033440 1.487328509610162 6459.668846644295627 1.501564213110582 6461.822428503548508 1.506297162303590 6463.976728343070135 1.510533701664732 6466.131746402243152 1.514344897777853 6468.287482920503862 1.550067839732668 6470.443938137381338 1.584005665998760 6472.601112292473772 1.589226678168176 6474.759005625482132 1.597516611585950 6476.917618376162864 1.603419726034820 6479.076950784364271 1.608941832860024 6481.237003090004691 1.606069155523821 6483.397775533103413 1.616859956618253 6485.559268353737934 1.619256359682659 6487.721481792077611 1.609660225564663 6489.884416088358194 1.590707869068898 6492.048071482920932 1.584452658792617 6494.212448216165285 1.585812316363416 6496.377546528578023 1.584361166971129 6498.543366660716856 1.582130821030169 6500.709908853243178 1.587467776842333 6502.877173346878408 1.592986044129313 6505.045160382427639 1.590047385168955 6507.213870200778729 1.598505783625564 6509.383303042893203 1.601090907280841 6511.553459149832634 1.597873604998601 6513.724338762719526 1.592496283130903 6515.895942122760971 1.588647405881001 6518.068269471241365 1.585431699626707 6520.241321049541511 1.585610594826637 6522.415097099107697 1.583863371637207 6524.589597861468064 1.581994434806903 6526.764823578228970 1.589258312422448 6528.940774491094089 1.596485819343229 6531.117450841829850 1.605288869909763 6533.294852872289994 1.605170151806403 6535.472980824399201 1.607080295666156 6537.651834940187655 1.601376716771988 6539.831415461741926 1.603824984621341 6542.011722631237717 1.599994857428765 6544.192756690924398 1.599759596768779 6546.374517883154112 1.607529159908905 6548.557006450335393 1.589915835881862 6550.740222634969541 1.583143267487067 6552.924166679628797 1.584332518452910 6555.108838826986357 1.576324562665232 6557.294239319777262 1.559745776970380 6559.480368400823863 1.538382148145331 6561.667226313022184 1.529637091960241 6563.854813299371017 1.521803648057714 6566.043129602927365 1.512742769894426 6568.232175466838271 1.516297167059599 6570.421951134324445 1.532536348133608 6572.612456848707552 1.522632588947699 6574.803692853370194 1.512985425528057 6576.995659391783192 1.520870018567940 6579.188356707498315 1.525601502983613 6581.381785044142816 1.524689677451876 6583.575944645443087 1.519371857640799 6585.770835755188273 1.516694755283991 6587.966458617255739 1.497771933465463 6590.162813475595613 1.466855958360956 6592.359900574262610 1.442344032422659 6594.557720157368749 1.430811516716671 6596.756272469117903 1.430586038247934 6598.955557753786707 1.417930363591231 6601.155576255752749 1.419174482728847 6603.356328219455463 1.417585740651863 6605.557813889425233 1.397785095852385 6607.760033510262474 1.390969516334668 6609.962987326672192 1.388763116579291 6612.166675583421238 1.381115005165090 6614.371098525362868 1.385361515594201 6616.576256397426732 1.380611987703815 6618.782149444643437 1.371165056665419 6620.988777912106343 1.372142161248040 6623.196142044996122 1.370560992304463 6625.404242088567116 1.367097843683136 6627.613078288179167 1.337895791264474 6629.822650889252145 1.317956983437683 6632.032960137292321 1.310287791692788 6634.244006277883273 1.291823496436007 6636.455789556711352 1.261053564573489 6638.668310219522937 1.244359173040900 6640.881568512153535 1.236305383021646 6643.095564680520511 1.211748123930603 6645.310298970616714 1.189854538477085 6647.525771628537768 1.189941228090846 6649.741982900441144 1.188975717470729 6651.958933032570712 1.175716183046105 6654.176622271248561 1.171458857138695 6656.395050862898643 1.152521778727859 6658.614219054004934 1.141634566552707 6660.834127091142363 1.120750354455791 6663.054775220961346 1.110542160662161 6665.276163690213252 1.109295571490499 6667.498292745712206 1.097763148263476 6669.721162634361463 1.099776887092235 6671.944773603140675 1.100567664594068 6674.169125899130449 1.071581896453758 6676.394219769474148 1.059218651493814 6678.620055461404263 1.051597466046401 6680.846633222229684 1.035713580910684 6683.073953299362074 1.015547230596104 6685.302015940273122 0.993763656395858 6687.530821392526377 0.989887809255817 6689.760369903759965 0.978739845209335 6691.990661721714787 0.967686411014636 6694.221697094195406 0.949060203712210 6696.453476269092789 0.944858645848318 6698.685999494377029 0.935024334248002 6700.919267018118262 0.923565914639199 6703.153279088453019 0.923020418504959 6705.388035953602412 0.926133045354976 6707.623537861867590 0.901187822815688 6709.859785061650655 0.875393444843620 6712.096777801416465 0.851851868321548 6714.334516329719918 0.848629217391613 6716.573000895199584 0.840298361650301 6718.812231746567704 0.840698549083930 6721.052209132642020 0.837273171199107 6723.292933302302117 0.828281081011748 6725.534404504516715 0.803437945069963 6727.776622988332747 0.791151222870052 6730.019589002897192 0.785001747664016 6732.263302797424330 0.776947512969213 6734.507764621213937 0.768909563278711 6736.752974723644002 0.773909851587185 6738.998933354196197 0.769578187224582 6741.245640762414041 0.777466316391914 6743.493097197932912 0.774075549909623 6745.741302910461854 0.767178220157392 6747.990258149817237 0.765875852072037 6750.239963165873633 0.775512267267679 6752.490418208600204 0.780964480138096 6754.741623528039781 0.797293615828150 6756.993579374340698 0.808957136735702 6759.246285997713130 0.809654047854273 6761.499743648456388 0.813585005997523 6763.753952576949814 0.816460605537846 6766.008913033674617 0.827878769178550 6768.264625269173848 0.822733876970200 6770.521089534082421 0.814717662657934 6772.778306079112554 0.811405873851132 6775.036275155080148 0.805422434323812 6777.294997012862041 0.796503245857360 6779.554471903428748 0.781871183063075 6781.814700077825364 0.765847142715695 6784.075681787202484 0.761809545692495 6786.337417282774368 0.756405321715202 6788.599906815843497 0.763696620295647 6790.863150637797844 0.766508834522604 6793.127149000102690 0.769230670623820 6795.391902154326999 0.762096306833886 6797.657410352103398 0.761744418521539 6799.923673845153644 0.758596664637117 6802.190692885278622 0.761439567276728 6804.458467724383809 0.763108690442108 6806.726998614437434 0.765757710694306 6808.996285807497770 0.770791644355500 6811.266329555700395 0.767920988648445 6813.537130111288207 0.760643439478931 6815.808687726563221 0.752022637358800 6818.081002653921132 0.734442197229253 6820.354075145835850 0.740431620633914 6822.627905454883148 0.741918872856109 6824.902493833705194 0.729422343683455 6827.177840535034193 0.710506687260485 6829.453945811677841 0.716900170074245 6831.730809916552971 0.721754750832141 6834.008433102634626 0.725553666553444 6836.286815622994254 0.709670270898998 6838.565957730778791 0.694417701084532 6840.845859679238856 0.684575126679635 6843.126521721689642 0.672957708468258 6845.407944111539109 0.674672634343548 6847.690127102271617 0.682366830055884 6849.973070947477026 0.655435072465049 6852.256775900807042 0.640794075617943 6854.541242216009778 0.624305145278327 6856.826470146912470 0.633491704910477 6859.112459947422394 0.642066997093026 6861.399211871554144 0.640200547526821 6863.686726173382340 0.625180028122454 6865.975003107076191 0.607346505273616 6868.264042926882212 0.604511496205627 6870.553845887150601 0.629710929937631 6872.844412242298858 0.641888229888143 6875.135742246831796 0.652251542265977 6877.427836155337900 0.664291070203937 6879.720694222505699 0.679800847468174 6882.014316703091026 0.685298743166311 6884.308703851940663 0.694043858095358 6886.603855923980518 0.705780407018291 6888.899773174239272 0.714729106762503 6891.196455857814726 0.711731012460961 6893.493904229891086 0.695454042324159 6895.792118545735320 0.692856492527714 6898.091099060718079 0.688218421281017 6900.390846030274588 0.680832533309954 6902.691359709931930 0.673897242919880 6904.992640355296317 0.672774250201549 6907.294688222078548 0.679372195339534 6909.597503566055821 0.698384561990363 6911.901086643096278 0.703235156419192 6914.205437709146281 0.708957611526514 6916.510557020259512 0.717454148157600 6918.816444832552406 0.730826563411792 6921.123101402235079 0.746877629256287 6923.430526985595861 0.754470827243607 6925.738721839029495 0.753553532880155 6928.047686218995295 0.758589744126912 6930.357420382044438 0.755134419062313 6932.667924584813591 0.749241400174900 6934.979199084018546 0.755415889255668 6937.291244136482419 0.775541444245473 6939.604059999091987 0.783162338961814 6941.917646928825889 0.773543039067880 6944.232005182743706 0.758353769254615 6946.547135018008703 0.760417441083427 6948.863036691852358 0.768105592075474 6951.179710461595278 0.773736218419959 6953.497156584639924 0.784275420663239 6955.815375318494262 0.781802039512457 6958.134366920729917 0.779233283609834 6960.454131649014016 0.772713090594436 6962.774669761090991 0.770668689122717 6965.095981514810774 0.780362633450003 6967.418067168092421 0.792368331032732 6969.740926978944117 0.794076807212658 6972.064561205454083 0.784820506803775 6974.388970105818771 0.764814795512662 6976.714153938299205 0.763346383612428 6979.040112961247360 0.769265882997850 6981.366847433097064 0.769468487634915 6983.694357612388558 0.762486057709854 6986.022643757727565 0.778115343723203 6988.351706127810758 0.775240809584394 6990.681544981417574 0.782377233950330 6993.012160577432951 0.801394674915702 6995.343553174806402 0.815782967504541 6997.675723032582027 0.838439925190394 7000.008670409889419 0.836635004840865 7002.342395565938205 0.834668017354941 7004.676898760044423 0.832247252806173 7007.012180251592326 0.829946320729330 7009.348240300056204 0.816781626163831 7011.685079164990384 0.814814595774826 7014.022697106059240 0.799061365532639 7016.361094382990814 0.772350484538421 7018.700271255606822 0.757831909802877 7021.040227983808109 0.744895601981255 7023.380964827604657 0.742215211936481 7025.722482047071935 0.749910610115177 7028.064779902377268 0.757582207488570 7030.407858653768926 0.756017632388792 7032.751718561604321 0.758066022413498 7035.096359886304526 0.770266502798887 7037.441782888385205 0.766361849373889 7039.787987828442056 0.767593134948398 7042.134974967178096 0.776630344978286 7044.482744565363646 0.781833443345452 7046.831296883860887 0.773581347552553 7049.180632183613852 0.755149919727940 7051.530750725672988 0.736814539449199 7053.881652771156951 0.735846597890490 7056.233338581275348 0.725278498994128 7058.585808417321459 0.730987386452824 7060.939062540693158 0.748616680592284 7063.293101212857437 0.753779807081662 7065.647924695373149 0.751682178506358 7068.003533249881002 0.752022202890915 7070.359927138128114 0.751500287731295 7072.717106621930725 0.756099422990120 7075.075071963197843 0.762475447466650 7077.433823423923968 0.763830344207904 7079.793361266185457 0.767983544386480 7082.153685752168712 0.763430964168203 7084.514797144123804 0.775256108959012 7086.876695704398117 0.784537321250972 7089.239381695415432 0.782416060059429 7091.602855379712310 0.793735182062492 7093.967117019889884 0.811267140916535 7096.332166878642965 0.826804569614189 7098.698005218747312 0.828262999737457 7101.064632303089638 0.824061888425675 7103.432048394620324 0.820557936861544 7105.800253756386155 0.800781368863678 7108.169248651513044 0.805484034516971 7110.539033343238771 0.808597858206373 7112.909608094863870 0.813047013300862 7115.280973169785284 0.801941439379548 7117.653128831482718 0.803713657965579 7120.026075343541379 0.813672216595825 7122.399812969616505 0.818383698463218 7124.774341973456103 0.824847096200716 7127.149662618889124 0.831065926656085 7129.525775169854569 0.840558854599210 7131.902679890357831 0.839785768316624 7134.280377044499801 0.832389591026443 7136.658866896461404 0.827160940737273 7139.038149710533617 0.813798549882553 7141.418225751074715 0.812879352312184 7143.799095282536655 0.822415185452926 7146.180758569454156 0.826416108915281 7148.563215876471077 0.831420080158812 7150.946467468295850 0.823852703058046 7153.330513609736045 0.799687203687086 7155.715354565685629 0.797685023223106 7158.100990601118610 0.809824517082561 7160.487421981120860 0.836276051888796 7162.874648970843737 0.859544931888416 7165.262671835535002 0.867388020005715 7167.651490840524275 0.867225916223191 7170.041106251248493 0.902496639794603 7172.431518333213717 0.928651339625027 7174.822727352022412 0.963907864414874 7177.214733573356170 0.972385391513030 7179.607537263008453 0.972297439969252 7182.001138686839113 0.981921331345809 7184.395538110803500 0.975373449918084 7186.790735800938819 0.965374244515447 7189.186732023392324 0.958479678044479 7191.583527044379480 0.930198167493898 7193.981121130211250 0.889235818689313 7196.379514547277722 0.859483548127687 7198.778707562082673 0.863916818846623 7201.178700441196270 0.888235173726337 7203.579493451283270 0.911805663697651 7205.981086859093011 0.920543273450737 7208.383480931482154 0.933913573125499 7210.786675935376479 0.943410880601200 7213.190672137798174 0.964797063723735 7215.595469805849461 0.995309493667846 7218.001069206746251 1.019058424731178 7220.407470607769028 1.026205112549759 7222.814674276295591 1.019785617757269 7225.222680479793780 1.013976638185283 7227.631489485812381 1.021120277760861 7230.041101562010226 1.021382898558150 7232.451516976117091 1.023703778342254 7234.862735995954608 1.011952344793601 7237.274758889429904 0.997835045618941 7239.687585924559244 1.010440736265488 7242.101217369428014 1.011707238233399 7244.515653492218007 1.016790146950414 7246.930894561191053 1.018831641261017 7249.346940844723576 0.990318083675824 7251.763792611255667 0.984378309658597 7254.181450129328368 0.969277592758147 7256.599913667562760 0.981716196844290 7259.019183494690878 1.006504774223451 7261.439259879513884 0.993600854445173 7263.860143090928432 0.988750716878191 7266.281833397913942 1.003734169531981 7268.704331069563523 1.014192401958447 7271.127636375034854 1.034305610562892 7273.551749583584751 1.051693232477430 7275.976670964550067 1.062074239271814 7278.402400787383158 1.062823493079391 7280.828939321602775 1.052056290893794 7283.256286836822255 1.074539551387451 7285.684443602739520 1.089819933639357 7288.113409889166178 1.085391133675671 7290.543185965979319 1.076091491964999 7292.973772103154261 1.094568235011253 7295.405168570748174 1.087345855483996 7297.837375638931007 1.085592006331933 7300.270393577940922 1.089727314050763 7302.704222658113395 1.094566881857759 7305.138863149873032 1.080534469250457 7307.574315323729934 1.071392712347889 7310.010579450302430 1.078043631614941 7312.447655800280700 1.063728024819818 7314.885544644450420 1.035218488495760 7317.324246253680030 0.989215654903316 7319.763760898952569 0.985306515129714 7322.204088851317465 0.989972099757353 7324.645230381921465 1.002841404827317 7327.087185761995897 1.005095952129808 7329.529955262883050 1.003619020959831 7331.973539155996150 0.981448363959700 7334.417937712842104 0.979272144526687 7336.863151205016038 1.026559970538181 7339.309179904220400 1.061052713843153 7341.756024082231306 1.089702234796136 7344.203684010917641 1.083640231526562 7346.652159962236510 1.057983771489087 7349.101452208255068 1.051292993721759 7351.551561021108682 1.036893054579909 7354.002486673032763 1.044371957316917 7356.454229436343667 1.053293939252455 7358.906789583473255 1.041641846634947 7361.360167386920693 1.018274017997767 7363.814363119282461 1.011352752167756 7366.269377053240532 0.990482124430196 7368.725209461588747 1.038048768929756 7371.181860617190978 1.045900169395480 7373.639330793006593 1.049980835963304 7376.097620262081364 1.033360202935508 7378.556729297573838 1.040419636227513 7381.016658172709867 1.059408735439833 7383.477407160816256 1.061493826316323 7385.938976535308029 1.054581748168124 7388.401366569686616 1.080179841428207 7390.864577537565310 1.063286519827737 7393.328609712627440 1.047305824589718 7395.793463368653647 1.051241327465955 7398.259138779509158 1.076021117220253 7400.725636219171975 1.112078673854727 7403.192955961691951 1.086886784974824 7405.661098281214436 1.055876068928564 7408.130063451970273 1.072674254247817 7410.599851748303990 1.056082621124068 7413.070463444628331 1.067740576426280 7415.541898815456079 1.082732373346339 7418.014158135384605 1.061666028985716 7420.487241679123144 1.060731854245786 7422.961149721451875 1.029481422361054 7425.435882537249199 1.041088446088642 7427.911440401478103 1.068143626170494 7430.387823589216168 1.064141653697270 7432.865032375608280 1.075279116714421 7435.343067035900276 1.059446722001516 7437.821927845422579 1.001026569419735 7440.301615079618387 1.003915305236547 7442.782129014001839 0.993061825592353 7445.263469924184392 0.980785391752325 7447.745638085863902 0.947675130226441 7450.228633774851914 0.914212962289337 7452.712457267029095 0.907882261302645 7455.197108838375243 0.877313643648176 7457.682588764963839 0.821313925014179 7460.168897322952034 0.827632721681390 7462.656034788609759 0.832134051887360 7465.144001438279702 0.814879126642335 7467.632797548400958 0.778119869891095 7470.122423395500846 0.742360635844971 7472.612879256217639 0.713949012142889 7475.104165407263281 0.682999646479951 7477.596282125445214 0.664356858597910 7480.089229687659099 0.680242948793548 7482.583008370913376 0.682898549542275 7485.077618452287425 0.638166622182456 7487.573060208959760 0.617694211399621 7490.069333918195298 0.637053534507043 7492.566439857371734 0.660822350136099 7495.064378303937701 0.663190899454798 7497.563149535442790 0.648031651749297 7500.062753829520261 0.632796792419373 7502.563191463918884 0.612840366347143 7505.064462716457456 0.597470613045783 7507.566567865054822 0.604185396605998 7510.069507187716226 0.615690585210012 7512.573280962559693 0.595149728527561 7515.077889467776004 0.591093917240190 7517.583332981654166 0.602252753695532 7520.089611782569591 0.623994871763428 7522.596726149012284 0.617722120243848 7525.104676359544101 0.646130455840172 7527.613462692825124 0.659050419562880 7530.123085427601836 0.648282702969458 7532.633544842737138 0.649356429784847 7535.144841217163048 0.651364524680471 7537.656974829912542 0.631504087082840 7540.169945960111363 0.609217360706048 7542.683754886969837 0.589878356482786 7545.198401889818342 0.604582446892576 7547.713887248050924 0.612342596312663 7550.230211241168945 0.590608255320599 7552.747374148753806 0.613749700516580 7555.265376250507870 0.622372159479826 7557.784217826199892 0.633442475704658 7560.303899155701401 0.638171279604639 7562.824420518969418 0.631314356487386 7565.345782196078289 0.595653131854364 7567.867984467170572 0.552457163614843 7570.391027612490689 0.516002105297240 7572.914911912369462 0.482136879204325 7575.439637647254131 0.477567993299290 7577.965205097661965 0.454087043750386 7580.491614544212098 0.449793849407193 7583.018866267607336 0.457527180444750 7585.546960548670540 0.473276566058948 7588.075897668291873 0.492221047103473 7590.605677907466088 0.535858010271481 7593.136301547270705 0.592330508099935 7595.667768868903295 0.615521966970732 7598.200080153627823 0.641250029452389 7600.733235682813756 0.659188465662284 7603.267235737915144 0.706101589478632 7605.802080600502450 0.736477820697278 7608.337770552217989 0.751462854458894 7610.874305874805032 0.788487793700666 7613.411686850092337 0.843356882936195 7615.949913760026902 0.893552022607074 7618.488986886626662 0.932354797496186 7621.028906512010508 0.976293235749839 7623.569672918391916 1.011806931579622 7626.111286388069857 1.048363532937630 7628.653747203462444 1.083138144772539 7631.197055647056914 1.095568595456798 7633.741212001443273 1.140569300232322 7636.286216549297933 1.157779167659180 7638.832069573414628 1.207780003643448 7641.378771356657126 1.243333141451604 7643.926322181993783 1.268820724767798 7646.474722332477540 1.297881777121840 7649.023972091278665 1.370769873584153 7651.574071741641092 1.441192461858698 7654.125021566907890 1.489517104852720 7656.676821850510350 1.550286670291246 7659.229472875997089 1.553368769478216 7661.782974926989482 1.599308589318599 7664.337328287208948 1.623750613171498 7666.892533240465127 1.662610482179668 7669.448590070684986 1.695780361384038 7672.005499061867340 1.748607482590062 7674.563260498112868 1.752052271150567 7677.121874663609560 1.752929892307138 7679.681341842663642 1.726309913967201 7682.241662319653187 1.713199804927053 7684.802836379056316 1.738501876013332 7687.364864305442097 1.703339110024260 7689.927746383495105 1.698757285496287 7692.491482897972674 1.711912817420129 7695.056074133733091 1.716863812213230 7697.621520375732871 1.720766630934389 7700.187821909012200 1.761469719583884 7702.754979018732229 1.755445842260443 7705.322991990124137 1.809117730063453 7707.891861108523699 1.821824568730148 7710.461586659352179 1.836783081530929 7713.032168928149986 1.875926544031078 7715.603608200530289 1.854009414070066 7718.175904762208120 1.776226118309374 7720.749058898986732 1.741279454033549 7723.323070896788522 1.688396164561505 7725.897941041605009 1.644405777264162 7728.473669619534121 1.608541147713218 7731.050256916761100 1.587677912380541 7733.627703219586692 1.619398210658243 7736.206008814388042 1.609510762982274 7738.785173987642338 1.566570248290298 7741.365199025915899 1.525331677682672 7743.946084215894189 1.522712143886073 7746.527829844334519 1.546138105315323 7749.110436198096977 1.547425086694140 7751.693903564130778 1.578056166414334 7754.278232229502464 1.560713132130180 7756.863422481353155 1.551818493321052 7759.449474606924923 1.490518354852337 7762.036388893548974 1.493095228925835 7764.624165628676565 1.533238580891364 7767.212805099831712 1.600572841624488 7769.802307594638478 1.650904829786452 7772.392673400813692 1.581178706997994 7774.983902806190599 1.522917375042642 7777.575996098676114 1.525603026312593 7780.168953566279924 1.518070125462467 7782.762775497109033 1.499620958393656 7785.357462179357753 1.490143498747400 7787.953013901339546 1.414808647733285 7790.549430951443355 1.333680531665997 7793.146713618157264 1.256493298079339 7795.744862190063031 1.234389121382237 7798.343876955857013 1.293872470648200 7800.943758204312871 1.306588443032791 7803.544506224305223 1.281126470576869 7806.146121304798726 1.259629422910494 7808.748603734876269 1.239181794997867 7811.351953803696233 1.231663313719982 7813.956171800519769 1.204111395562503 7816.561258014694431 1.201990822885428 7819.167212735692374 1.174272140787641 7821.774036253054874 1.149358714796022 7824.381728856430527 1.098900465323539 7826.990290835552514 1.057868224173553 7829.599722480279524 0.994668256689465 7832.210024080538460 0.960642496373743 7834.821195926364453 0.928632259636352 7837.433238307878128 0.910076893948541 7840.046151515323800 0.944254604088472 7842.659935839016725 0.928060114596554 7845.274591569376753 0.918227039175928 7847.890118996913770 0.918180041632005 7850.506518412257719 0.926192937614908 7853.123790106112210 0.918228261795267 7855.741934369284536 0.934649128094591 7858.360951492680215 0.941079896591966 7860.980841767292077 0.949339560037405 7863.601605484236643 0.945280791231409