The best known packings of equal spheres in a cube (complete up to N = 1000)

Last update: 25-Jun-2013

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Download

You may download ASCII files which contain all the values of radius, ratio etc. by using the links given in the table header below.
All coordinates of all packings are packed as ASCII files here.

Results

The table below summarizes the current status of the search.
Please use the links in the following table to view a picture for a certain configuration.
Furthermore, note that for certain values of N several distinct optimal configurations exist; however, only one is shown here.
Proven optimal packings are indicated by a radius in bold face type.

Legend:
N
the number of spheres; colors correspond to active researchers in the past, see "References" at the bottom of the page
radius
of the spheres in the cube
distance
packing of spheres in a cube is equivalent to distributing points in a cube; the latter are then the sphere centers. "distance" is here the greatest distance of these points
ratio
= 1/radius
density
ratio of total volume occupied by the spheres to container volume (for an infinite face-centered cubic packing you get the well-known value ρ = Pi/(3*sqrt(2))=0.74048048969)
contacts
number of contacts between circles and container and between the circles themselves, respectively
reference
for the best known packing so far
records
the sequence of N 's that establish density records

N radius distance ratio density contacts reference
1 0.500000000000000000000000000000 2.0000000000000000000000000000 0.523598775598298873077107230547 6
2 0.316987298107780676618138414624 1.732050807568877293527446341513 3.1547005383792515290182975610 0.266835854698717846813154146222 7
3 0.292893218813452475599155637895 1.414213562373095048801688724208 3.4142135623730950488016887242 0.315745968789368655515266902370 12 [1]
4 0.292893218813452475599155637895 1.414213562373095048801688724208 3.4142135623730950488016887242 0.420994625052491540687022536493 18 [1]
5 0.263932022500210303590826331269 1.118033988749894848204586834368 3.7888543819998317571273389350 0.385065731603426372426879737383 18 [1]
6 0.257359312880714853594933827371 1.060660171779821286601266543158 3.8856180831641267317355849656 0.428409926205119550630692291401 24 [1]
7 0.250136153876702043245287439440 1.001089824548965412749095030329 3.9978227237511750232878353022 0.458897881424660233818284390341 24 [1]
8 0.250000000000000000000000000000 1.000000000000000000000000000000 4.0000000000000000000000000000 0.523598775598298873077107230547 36 [1]
9 0.232050807568877293527446341506 0.866025403784438646763723170754 4.3094010767585030580365951220 0.471064494277334769836183318298 32 [1]
10 0.214285714285714285714285714286 0.750000000000000000000000000002 4.6666666666666666666666666667 0.412162301491372290760405108595 34 [1]
11 0.207622238388108088730418254084 0.710116382461775600785317878806 4.8164397405768296255408591189 0.412385039078370149623107996518 36 [5]
12 0.207106785524038967661929205346 0.707106806467300680044012011318 4.8284270236231810904193540608 0.446532259382081368788112965940 39 [5]
13 0.207106781186547524400844362105 0.707106781186547524400844362106 4.8284271247461900976033774484 0.483743250603770225988619412586 57 [4]
14 0.207106781186547524400844362105 0.707106781186547524400844362106 4.8284271247461900976033774484 0.520954269880983320295436290477 66 [8]
15 0.192307692307692307692307692308 0.625000000000000000000000000002 5.2000000000000000000000000000 0.446858308714979693682101072954 48 [5]
16 0.188796768447000008806390589866 0.606667120726368989360705454550 5.2967008292873672639551249767 0.451016324213052363644471724448 51 [6]
17 0.188685238868306387497346180781 0.606091526731326449486438024663 5.2998316455372217805372736898 0.478356091363763350579916296576 75 [5]
18 0.187680601147476864319898426192 0.600925212577331548853203544579 5.3282011773513747321100504007 0.498447327616997838743066186291 69 [4]
19 0.183185303161713528511335899512 0.578209612716350230440445415905 5.4589532169904122346658571280 0.489231140531370863516114858692 40 [6]
20 0.178407199722670498295402364957 0.554761174904471922549534791066 5.6051549576164797798117644013 0.475724737051231515120745813908 46 [6]
21 0.177219044407182163032127767345 0.549038105676657970145584756130 5.6427344100918363913699284553 0.489597369040547684858558280996 66 [5]
22 0.173273103227763925774353580229 0.530330085889910643300633271580 5.7712361663282534634711699312 0.479407418832445701801718545594 72 [5]
23 0.171816783367860445192850051509 0.523539214256802820070084344422 5.8201531910825955578377318568 0.488667209462063681869063221683 68 [5]
24 0.170540688701054438818560595676 0.517638090205041524697797675248 5.8637033051562731469989727989 0.498636296697434606326250885024 57 [6]
25 0.167804075634883619081459335660 0.505135865094028788102082046699 5.9593308220704323204322405506 0.494807338849210244286083444805 68 [6]
26 0.166905167286093734462460173062 0.501074021251623174966689379220 5.9914262467733577733049367126 0.506373890289133339962259413696 90 [5]
27 0.166666666666666666666666666667 0.500000000000000000000000000001 6.0000000000000000000000000000 0.523598775598298873077107230550 108 [4]
28 0.160191005918776726965553308878 0.471414849839103640395636809119 6.2425477277234912833960847616 0.482126525769403531694353687393 80 [7]
29 0.160188620508520367600361869474 0.471404520791031682933896241405 6.2426406871192851464050661726 0.499323023283416642625421303555 138 [6]
30 0.160188620508520367600361869474 0.471404520791031682933896241405 6.2426406871192851464050661726 0.516541058569051699267677210574 144 [6]
31 0.160188620508520367600361869474 0.471404520791031682933896241405 6.2426406871192851464050661726 0.533759093854686755909933117593 150 [6]
32 0.160188620508520367600361869474 0.471404520791031682933896241403 6.2426406871192851464050661726 0.550977129140321812552189024607 156 [4]
33 0.154605431908113458803268257572 0.447619754885616000062572316853 6.4680780465354498015739562139 0.510830470115208714724244643660 78 [31]
34 0.152117093470357826262144416884 0.437265213711776134156736434357 6.5738831658314861697902543645 0.501304476053766416425117254793 89 [31]
35 0.151668522645211722883250253537 0.435414346693485346395937183080 6.5933259094191531084669989858 0.511496920125610039028025464645 130 [7]
36 0.149378180763194405658757891822 0.426037892018084161007462986485 6.6944181197739692761545629773 0.502634862800194792045989472040 118 [31]
37 0.149061631334124593491369826337 0.424751593565548676230014374321 6.7086344825951906471538325016 0.513319713166235273893735842965 108 [7]
38 0.149038769067752685693797458665 0.424658782600760990374054970688 6.7096635744851212017645422820 0.526950682001199082052162266177 120 [7]
39 0.147617379098483843586701989129 0.418912200382719575735702655364 6.7742701171577083845105452562 0.525491489892602197551019143999 114 [6]
40 0.147058823529411764705882352941 0.416666666666666666666666666666 6.8000000000000000000000000000 0.532870726234784116707823356956 152 [7]
41 0.144837878409323524702584699959 0.407807785809571339905766033723 6.9042712512946327197458390501 0.521817848599596939963392997452 100 [27]
42 0.143045425138611931482588665745 0.400738455850185035077174446876 6.9907863116278874823379812670 0.514943781725833270445991779244 121 [24]
43 0.141652316450780131858955961430 0.395292959752937441558299769175 7.0595386299063422693874325568 0.511950660652272656851519025384 115 [24]
44 0.140860610937643660647157949944 0.392217103519064119809298912222 7.0992166890620768711738345916 0.515121870167879425646624216564 127 [7]
45 0.140631937345523308925037746607 0.391331205969567090042912499527 7.1107603214130981127884301356 0.524267579579614606071552494783 163 [7]
46 0.140246869718722237549525183737 0.389841971935222245249972032046 7.1302839201016771831185958683 0.531527784153556883866709639688 133 [24]
47 0.139958859837643585218718460156 0.388730187262852088784813869658 7.1449567477187908027183728499 0.539743790761371827222108621968 136 [24]
48 0.139958844038428028961026945453 0.388730126323020031391610191835 7.1449575542752651213595466567 0.551227514527583660429372951318 184 [6]
49 0.136426759340618099952131723523 0.375238725196586185387205120062 7.3299402905502553606085128281 0.521174764236338017305232414522 140 [28]
50 0.135954512641663590961947158274 0.373454739483808408472531690647 7.3554013071688770746778761899 0.526307423600463993079822746299 138 [7]
51 0.135023077845862978090586437561 0.369949631469685208313976891575 7.4061413497147544768991034524 0.525875327965038185181047832145 131 [24]
52 0.133820037890438853775788550699 0.365448827728044445325518968785 7.4727224395102924413168470857 0.521981845434466730971571917555 138 [7]
53 0.133230838599655268343340284059 0.363255291396290339106320603082 7.5057697640476119951801199464 0.525023524874578323684066164616 142 [7]
54 0.132203229521778740003053671001 0.359446412076658051995325222327 7.5641117362814739494807795401 0.522647120970089079733083892679 159 [24]
55 0.131220272864170084341106694224 0.355822902422829467292032420138 7.6207736668489406695839345107 0.520540000701974563414689542214 148 [28]
56 0.130661065057563874410482351159 0.353770081342570208426772520565 7.6533893211374119620371932393 0.523257206240241269143654969326 158 [24]
57 0.130622145185501770981979216365 0.353627439985811513706393750775 7.6556697073062129797486254749 0.532125290724566979167593878757 213 [24]
58 0.130602161880930003786122951566 0.353554212839849660955194253986 7.6568410935777620589662392225 0.541212353063956864170567561832 202 [24]
59 0.130601937481870721275104439800 0.353553390593273762265353277805 7.6568542494923801941678573488 0.550540762723330593953062687237 8 [27]
60 0.130601937481870721257384103459 0.353553390593273762200422181054 7.6568542494923801952067548968 0.559871962091522637690475137013 288 [7]
61 0.130601937481870721257384103459 0.353553390593273762200422181054 7.6568542494923801952067548968 0.569203161459714681651983055964 297 [7]
62 0.130601937481870721257384103459 0.353553390593273762200422181054 7.6568542494923801952067548968 0.578534360827906725613490974914 306 [7]
63 0.130601937481870721257384103459 0.353553390593273762200422181052 7.6568542494923801952067548968 0.587865560196098769574998893858 318 [4]
64 0.126743552193897270549733562135 0.339561588122216004343919795137 7.8899477148167716912093512776 0.545815931129724941052263735001 172 [28]
65 0.126182631397946433581712956126 0.337551547885068626151940036335 7.9250209709628432818543192689 0.547016851657182669396844905268 175 [24]
66 0.125739648702998446145768439109 0.335968392770559100573823832582 7.9529409403873540080104543247 0.549603225501246189543226851593 199 [24]
67 0.124481087806075488201234438680 0.331490861748638866611537150224 8.0333488212913374301332534962 0.541344260395592933667757574932 175 [7]
68 0.123435656366815640818905541847 0.327794329053777135329546731618 8.1013868231743719248792696061 0.535697246664581152446526135764 194 [28]
69 0.123140054764804721591458806538 0.326752833039749018840130273394 8.1208344588605382827007773089 0.539679258630250003025024948976 199 [24]
70 0.123037729238609389915888192279 0.326392689088213155242352915300 8.1275882299540910005182293051 0.546136963248697157818529000762 192 [28]
71 0.123029495260108833411823691895 0.326363717355019377977552753033 8.1281321839596352062825305686 0.553827714565103651388494612090 202 [24]
72 0.123027579246856645375052517365 0.326356975932252703569620474818 8.1282587702834118781406511382 0.561601865590241996390372558799 315 [24]
73 0.121787558898588281805759130210 0.322008336224806690471434466121 8.2110193277844872328605052354 0.552357488411101402328771769016 201 [24]
74 0.121338760477507576980121392507 0.320441460104342346099426873903 8.2413896109097704306960950094 0.553756696936473605022017125720 201 [24]
75 0.121321447243951955120787808530 0.320381089346006738993940207719 8.2425657022472702763364590832 0.560999688103833389001664784854 201 [24]
76 0.120183555428448647905536180377 0.316425360581795413860577234018 8.3206058968304578255166363986 0.552633674326334702101722648206 184 [24]
77 0.119055120033309745814179732258 0.312525843748628153841596684405 8.3994707637959271628496412132 0.544281491411501066339301833242 249 [24]
78 0.118546035457300935508803608738 0.310774160125503610025810430685 8.4355414851489464604873897305 0.544307495936209012465190234298 212 [28]
79 0.118014005111223125177457028297 0.308948513009188581150121016930 8.4735705652692915583962960562 0.543896606506104405231578498907 231 [28]
80 0.117788131720054479915866130763 0.308174971777125134075652402875 8.4898196906347660621298425468 0.547624911879789046688435101586 234 [31]
81 0.117097826866012569527637211147 0.305816563817299083193946649361 8.5398681321749462319479018459 0.544778719257497850206851685381 237 [28]
82 0.116833115824453777868360608909 0.304914439763868528613313475757 8.5592170759405083579725243577 0.547772643047056825480779907961 306 [24]
83 0.11628516041895784 0.30305098584647762 8.59954955900780 0.54668806244074162 [30]
84 0.116283622527162899015929568587 0.303045763365663224743219012332 8.5996632910744435610745473796 0.553252714427328719246181669954 255 [27]
85 0.116283622527162899015929568587 0.303045763365663224743219012332 8.5996632910744435610745473796 0.559839056265749299237207642215 292 [27]
86 0.116283622527162899015929568587 0.303045763365663224743219012332 8.5996632910744435610745473796 0.566425398104169879228233614477 387 [27]
87 0.116283622527162899015929568587 0.303045763365663224743219012332 8.5996632910744435610745473796 0.573011739942590459219259586738 408 [27]
88 0.115521432463999509608513951182 0.300462606288665774426601772290 8.6564023547027494642201008015 0.568275559153308581278574088040 338 [31]
89 0.113769756020378567236974295678 0.294564596620199871439459956241 8.7896822053558668982863860385 0.548983252851931792729496118071 236 [28]
90 0.113282348330133080002307754446 0.292932965022346437858862646788 8.8275006189468286086796630608 0.548047055413839547619720253735 251 [24]
91 0.112825882631227847852400102019 0.291408639084632965955099750725 8.8632145096396603398676866149 0.547464824935975169300611938211 256 [31]
92 0.112501402436970813748889460007 0.290327250587459799510215296630 8.8887780804355078966820742690 0.548719312571929204782555288040 251 [28]
93 0.112377874545726467438435800962 0.289916047527022045973379764321 8.8985487939007139552756609060 0.552858510480727376147712067057 243 [24]
94 0.112059610672800520390188722519 0.288857808456459520078494905514 8.9238218301495786823284245310 0.554068921570735702062946133158 [29]
95 0.111760641276069087137149634920 0.287865304649701420432878322160 8.9476938265754786903432159062 0.555493357136876952763922111076 [29]
96 0.11165576298837838 0.28751749697018669 8.95609839775206563 0.55976182028352371 [30]
97 0.111549039238116230729755354203 0.287163761982544260806231889419 8.9646670812230597958988011647 0.563972393641469203048923004492 221 [28]
98 0.111518995642259881967158256699 0.287064217790081429083027024090 8.9670821929555843752227121440 0.569326282758774967321823488704 280 [24]
99 0.111387457101684639571115939167 0.286628569090808688359550770570 8.9776715082660403001577716344 0.573102987205336104739443994026 288 [24]
100 0.111382347512479750227357863499 0.286611652351681559449894454738 8.9780833528217365165192364463 0.578812244763156874778608325788 340 [31]
101 0.110240604605984488395300868556 0.282842712475321017818381107303 9.0710678118479250425574031187 0.566806396072810700369521403152 14 [31]
102 0.110240604605881656306005409178 0.282842712474982559277239594058 9.0710678118563865060859090728 0.572418340586781233457562554315 14 [31]
103 0.110240604605771200956705296110 0.282842712474619009760337744843 9.0710678118654752440084436210 0.578030285100600443415634932218 516 [4]
104 0.110240604605771200956705296110 0.282842712474619009760337744843 9.0710678118654752440084436210 0.583642229616140253545883815055 522 [4]
105 0.110240604605771200956705296110 0.282842712474619009760337744843 9.0710678118654752440084436210 0.589254174131680063676132697892 531 [4]
106 0.110240604605771200956705296110 0.282842712474619009760337744843 9.0710678118654752440084436210 0.594866118647219873806381580729 542 [4]
107 0.110240604605771200956705296110 0.282842712474619009760337744843 9.0710678118654752440084436210 0.600478063162759683936630463566 549 [4]
108 0.110240604605771200956705296110 0.282842712474619009760337744842 9.0710678118654752440084436210 0.606090007678299494066879346399 558 [4]
109 0.10803724109568319 0.27563139262946274 9.25606753614107872 0.57575214283184305 307 [30]
110 0.107351687751265221334223234275 0.273404174683578149338902686781 9.3151772547536332422981834626 0.570043403591332641537597199758 [29]
111 0.106941670183376412904632662949 0.272075827099933748042636722891 9.3508919234688123125007150399 0.568659731424354101524264192519 323 [24]
112 0.106596144936939921438574825419 0.270958567296838646631830718233 9.3812022994975977227594957771 0.568239118501435976756366850492 309 [24]
113 0.106015030670236449830990992236 0.269083947163228889884260008738 9.4326247295115710357687295962 0.563987375597636967443858551600 319 [24]
114 0.105638674774892988622921118486 0.267872806022732938707799834377 9.4662300727542707316760823617 0.562940239853321911570444032153 339 [24]
115 0.105139320062404106634646927986 0.266269409451000315492470955083 9.5111895283939701573851291872 0.559863225596092975002279257651 329 [24]
116 0.105020769143720196890610392111 0.265889345412022096838660670743 9.5219260737988588704372486963 0.562823447919202064693822567595 351 [24]
117 0.104862565393023965043484822020 0.265382513042141027646523575124 9.5362915855816503174786828708 0.565113790776855993736326304529 333 [24]
118 0.104825223479775015134210424464 0.265262941129062867109435302828 9.5396887009064193371376512991 0.569335163220245327553870887294 350 [24]
119 0.104807213897334002029276796620 0.265205281024807060080694079557 9.5413279564856094411454935521 0.573864156233627816904912468700 345 [24]
120 0.104799209238670891294951835980 0.265179654718761825150209026857 9.5420567317696912678179911287 0.578553962545588357479927073936 333 [24]
121 0.104794644945186055341346762105 0.265165042944955321650316635789 9.5424723326565069269423398625 0.583299026102383995476920834177 612 [24]
122 0.104794644945186055341346762105 0.265165042944955321650316635789 9.5424723326565069269423398625 0.588119679210668160728796212972 549 [24]
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318 0.077867647557479019928881136957 0.184462638570403702017611572722 12.8423039781937287074796135523 0.628907672222718924632454674440 1667 [31]
319 0.077867647557479019928881136957 0.184462638570403702017611572722 12.8423039781937287074796135523 0.630885369305180304898594469014 1674 [31]
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330 0.075652168339158149744613921034 0.178278673047687008412458243249 13.2183917784996551824481807214 0.598503493816364285809569216464 835 [26]
331 0.075651838670568089735796779112 0.178277757663801228234831551083 13.2184493803855717256403024315 0.600309292816075030017864005351 839 [26]
332 0.075485773612752219576366990660 0.177816829026344684180139517407 13.2475293308918887085248677341 0.598166412998213940654763330945 911 [31]
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349 0.075110552411167422504419313672 0.176776695296636881103214887700 13.3137084989847603902212667746 0.619465186669589833239997516774 20 [31]
350 0.075110552411167422503341538752 0.176776695296636881100229874973 13.3137084989847603904123075891 0.621240158551164589182423701450 20 [31]
351 0.075110552411167422503334756401 0.176776695296636881100211090527 13.3137084989847603904135097936 0.623015130432739345151347569079 661 [4]
352 0.075110552411167422503334756401 0.176776695296636881100211090527 13.3137084989847603904135097936 0.624790102314314101120439727396 714 [4]
353 0.075110552411167422503334756401 0.176776695296636881100211090527 13.3137084989847603904135097936 0.626565074195888857089531885712 492 [4]
354 0.075110552411167422503334756401 0.176776695296636881100211090527 13.3137084989847603904135097936 0.628340046077463613058624044029 721 [4]
355 0.075110552411167422503334756401 0.176776695296636881100211090527 13.3137084989847603904135097936 0.630115017959038369027716202345 699 [4]
356 0.075110552411167422503334756401 0.176776695296636881100211090527 13.3137084989847603904135097936 0.631889989840613124996808360662 1049 [4]
357 0.075110552411167422503334756401 0.176776695296636881100211090527 13.3137084989847603904135097936 0.633664961722187880965900518978 1804 [4]
358 0.075110552411167422503334756401 0.176776695296636881100211090527 13.3137084989847603904135097936 0.635439933603762636934992677295 1920 [4]
359 0.075110552411167422503334756401 0.176776695296636881100211090527 13.3137084989847603904135097936 0.637214905485337392904084835611 1928 [4]
360 0.075110552411167422503334756401 0.176776695296636881100211090527 13.3137084989847603904135097936 0.638989877366912148873176993928 1935 [4]
361 0.075110552411167422503334756401 0.176776695296636881100211090526 13.3137084989847603904135097937 0.640764849248486904842269152234 1943 [4]
362 0.075110552411167422503334756401 0.176776695296636881100211090526 13.3137084989847603904135097937 0.642539821130061660811361310551 1955 [4]
363 0.075110552411167422503334756401 0.176776695296636881100211090526 13.3137084989847603904135097937 0.644314793011636416780453468867 1961 [4]
364 0.075110552411167422503334756401 0.176776695296636881100211090526 13.3137084989847603904135097937 0.646089764893211172749545627184 1968 [4]
365 0.075110552411167422503334756401 0.176776695296636881100211090526 13.3137084989847603904135097937 0.647864736774785928718637785500 1974 [4]
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570 0.063894413220094973169222611575 0.146511338439563220436488404870 15.6508206211290031777316128921 0.622805047037851391104863206462 1952 [31]
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573 0.063825431502544478269635619614 0.146330015806313136330987669977 15.6677358297238270398042873806 0.624057360801786402798455585457 1567 [31]
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581 0.063813232033087541882319517721 0.146297954728255721839522568083 15.6707311029394973804950398191 0.632407433467161433295122119144 818 [31]
582 0.063813232033087345054964559607 0.146297954728255204577626993631 15.6707311029395457157455040511 0.633495914419766864721203740373 713 [31]
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585 0.063813232033085825787209552099 0.146297954728251211945002287801 15.6707311029399188050829904413 0.636761357277555234426519132464 286 [31]
586 0.063813232033085825787209549822 0.146297954728251211945002281815 15.6707311029399188050829910007 0.637849838230166439955453284898 1872 [31]
587 0.063813232033085825787209549822 0.146297954728251211945002281815 15.6707311029399188050829910007 0.638938319182777645484387505519 2193 [31]
588 0.063813232033085825787209549822 0.146297954728251211945002281815 15.6707311029399188050829910007 0.640026800135388851013321726141 2729 [31]
589 0.063813232033085825787209549822 0.146297954728251211945002281815 15.6707311029399188050829910007 0.641115281088000056542255946763 3106 [31]
590 0.063813232033085825787209549822 0.146297954728251211945002281815 15.6707311029399188050829910007 0.642203762040611262071190167386 3113 [31]
591 0.063813232033085825787209549822 0.146297954728251211945002281815 15.6707311029399188050829910007 0.643292242993222467600124388009 3122 [31]
592 0.063813232033085825787209549822 0.146297954728251211945002281815 15.6707311029399188050829910007 0.644380723945833673129058608632 3143 [31]
593 0.063813232033085825787209549822 0.146297954728251211945002281815 15.6707311029399188050829910007 0.645469204898444878657992829254 3194 [31]
594 0.063813232033085825787209549822 0.146297954728251211945002281815 15.6707311029399188050829910007 0.646557685851056084186927049877 3200 [31]
595 0.063813232033085825787209549822 0.146297954728251211945002281815 15.6707311029399188050829910007 0.647646166803667289715861270500 3207 [31]
596 0.063813232033085825787209549822 0.146297954728251211945002281815 15.6707311029399188050829910007 0.648734647756278495244795491122 3214 [31]
597 0.063813232033085825787209549822 0.146297954728251211945002281815 15.6707311029399188050829910007 0.649823128708889700773729711745 3220 [31]
598 0.063813232033085825787209549822 0.146297954728251211945002281815 15.6707311029399188050829910007 0.650911609661500906302663932368 3225 [31]
599 0.063813232033085825787209549822 0.146297954728251211945002281815 15.6707311029399188050829910007 0.652000090614112111831598152991 3240 [31]
600 0.063813232033085825787209549822 0.146297954728251211945002281815 15.6707311029399188050829910007 0.653088571566723317360532373614 3246 [4]
601 0.062797016946445163282811404177 0.143633550960362253324376829501 15.9243232979175513074402350553 0.623419127463691853010654078468 1588 [31]
602 0.062766685063556315287911682777 0.143554214464833477301122699534 15.9320186972980904838549080478 0.623552002573237935862133648205 1616 [31]
603 0.062765988427004737037220065467 0.143552392461870712453780885214 15.9321955259730323850922457687 0.624567006897672644137033644165 1636 [31]
604 0.062750741995934676976202828007 0.143512517968300937020007907855 15.9360665418870307258119294557 0.625146989951187280477612029060 1670 [31]
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606 0.062671605429717208039275555091 0.143305594166365730404621293858 15.9561893004551404557495491331 0.624847006219564481317393927539 1664 [31]
607 0.062573992666848107412476682949 0.143050462519002842665343210187 15.9810802760202172098762322479 0.622958191957172358722771154459 1611 [31]
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660 0.061949671549647706571514730827 0.141421356237309504880168872421 16.1421356237309504880168872421 0.657278716106298484557016415473 3525 [4]
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663 0.061949671549647706571514730827 0.141421356237309504880168872421 16.1421356237309504880168872421 0.660266346634054386759548308271 3630 [4]
664 0.061949671549647706571514730827 0.141421356237309504880168872421 16.1421356237309504880168872421 0.661262223476639687493725605870 3642 [4]
665 0.061949671549647706571514730827 0.141421356237309504880168872421 16.1421356237309504880168872421 0.662258100319224988227902903469 3660 [4]
666 0.061949671549647706571514730827 0.141421356237309504880168872421 16.1421356237309504880168872421 0.663253977161810288962080201068 3666 [4]
667 0.060646739335517307812446345765 0.138036392955851775860916317479 16.4889326443038876415498227605 0.623213441055139072354426130374 2125 [31]
668 0.060615915806494546783203742812 0.137956557797845041065034550346 16.4973173579084554657789129883 0.623196613731216360444233120608 1803 [31]
669 0.060598218134957951246404102678 0.137910724616884007301558455348 16.5021353890786956259861898538 0.623583032118333257027783444148 1891 [31]
670 0.060583629869387875366148049352 0.137872946907690300297652431466 16.5061090290545147215975220576 0.624064220139301707823687018676 1869 [31]
671 0.060561745199243631835072719088 0.137816279164640884125648165586 16.5120736978446454492527202798 0.624318600952046474005216779503 1818 [31]
672 0.060539105099612028667929187308 0.137757661266617018952838386224 16.5182487972787791834960135148 0.624548073263005889714983146640 1895 [31]
673 0.060536779317784512258365772528 0.137751639884239254578641495443 16.5188834171463713031268790744 0.625405374561866222721761024616 1848 [31]
674 0.060518962287604899472148626836 0.137705514218817513682608921126 16.5237466440301720234469509585 0.625781793568690344672795606986 2208 [31]
675 0.060509904683154657578733854372 0.137682066849608376185365525087 16.5262200500274434521115088883 0.626428904490330927771163334086 2051 [31]
676 0.060493299377578445036236539968 0.137639083299319243108892971084 16.5307564687180092008000014180 0.626840605631377113214557912021 2110 [31]
677 0.060475934636548219151131916319 0.137594137391633800260240091228 16.5355030229769580401331052176 0.627227433146248244891666586082 2220 [31]
678 0.060421169466225890650477759733 0.137452409600474511336314256385 16.5504906448223926024218439049 0.626448947403734431906409088702 1906 [31]
679 0.060417018648301931339267688767 0.137441669062169542402268610933 16.5516277097546884713425520158 0.627243624354148895422027982895 1845 [31]
680 0.060392988442166306274367327997 0.137379493170847987582977529978 16.5582135574831282198776740029 0.627418157955136840202753595518 1876 [31]
681 0.060377232528843577711999481314 0.137338729920999639859059717173 16.5625345534391170960047266150 0.627849176907347815383042370359 1949 [31]
682 0.060313129109733103109029868159 0.137172913504587023637543982229 16.5801379361467055421859456900 0.626770526888274308631527482265 1932 [31]
683 0.060289244513501583126386417518 0.137111143544344801974042887102 16.5867064361049209077410284810 0.626944126704948600672777611069 1935 [31]
684 0.060227237082535876777889045209 0.136950812239909528325095560464 16.6037834116413505452692659632 0.625926778892476082630162872350 1947 [31]
685 0.060191867073540742067103420653 0.136859377003847907948550521698 16.6135401445219821709507834835 0.625738137465091122189517683698 3314 [24]
686 0.060191867073540742067103420653 0.136859377003847907948550521698 16.6135401445219821709507834835 0.626651623797156948645268804405 3337 [24]
687 0.060191867073540742067103420653 0.136859377003847907948550521698 16.6135401445219821709507834835 0.627565110129222775101019925111 3351 [24]
688 0.060191867073540742067103420653 0.136859377003847907948550521698 16.6135401445219821709507834835 0.628478596461288601556771045816 3373 [24]
689 0.060191867073540742067103420653 0.136859377003847907948550521698 16.6135401445219821709507834835 0.629392082793354428012522166522 3390 [24]
690 0.060191867073540742067103420653 0.136859377003847907948550521698 16.6135401445219821709507834835 0.630305569125420254468273287229 3418 [24]
691 0.060191867073540742067103420653 0.136859377003847907948550521698 16.6135401445219821709507834835 0.631219055457486080924024407934 3438 [24]
692 0.060191867073540742067103420653 0.136859377003847907948550521698 16.6135401445219821709507834835 0.632132541789551907379775528641 3474 [24]
693 0.060191867073540742067103420653 0.136859377003847907948550521698 16.6135401445219821709507834835 0.633046028121617733835526649348 3508 [24]
694 0.060191867073540742067103420653 0.136859377003847907948550521698 16.6135401445219821709507834835 0.633959514453683560291277770054 3523 [24]
695 0.060191867073540742067103420653 0.136859377003847907948550521698 16.6135401445219821709507834835 0.634873000785749386747028890760 3531 [24]
696 0.060191867073540742067103420653 0.136859377003847907948550521698 16.6135401445219821709507834835 0.635786487117815213202780011466 3549 [24]
697 0.060191867073540742067103420653 0.136859377003847907948550521698 16.6135401445219821709507834835 0.636699973449881039658531132172 3563 [24]
698 0.060191867073540742067103420653 0.136859377003847907948550521698 16.6135401445219821709507834835 0.637613459781946866114282252878 3577 [24]
699 0.060191867073540742067103420653 0.136859377003847907948550521698 16.6135401445219821709507834835 0.638526946114012692570033373585 3587 [24]
700 0.060191867073540742067103420653 0.136859377003847907948550521698 16.6135401445219821709507834835 0.639440432446078519025784494290 3601 [24]
701 0.060191867073540742067103420653 0.136859377003847907948550521698 16.6135401445219821709507834835 0.640353918778144345481535614996 3611 [24]
702 0.060191867073540742067103420653 0.136859377003847907948550521698 16.6135401445219821709507834835 0.641267405110210171937286735703 3621 [24]
703 0.060191867073540742067103420653 0.136859377003847907948550521698 16.6135401445219821709507834835 0.642180891442275998393037856408 3627 [24]
704 0.060191867073540742067103420653 0.136859377003847907948550521698 16.6135401445219821709507834835 0.643094377774341824848788977114 3636 [24]
705 0.060191867073540742067103420653 0.136859377003847907948550521698 16.6135401445219821709507834835 0.644007864106407651304540097821 3644 [24]
706 0.060191867073540742067103420653 0.136859377003847907948550521698 16.6135401445219821709507834835 0.644921350438473477760291218527 3653 [24]
707 0.060191867073540742067103420653 0.136859377003847907948550521698 16.6135401445219821709507834835 0.645834836770539304216042339234 3663 [24]
708 0.060191867073540742067103420653 0.136859377003847907948550521698 16.6135401445219821709507834835 0.646748323102605130671793459940 3673 [24]
709 0.060191867073540742067103420653 0.136859377003847907948550521698 16.6135401445219821709507834835 0.647661809434670957127544580645 3680 [24]
710 0.060191867073540742067103420653 0.136859377003847907948550521698 16.6135401445219821709507834835 0.648575295766736783583295701352 3687 [24]
711 0.060191867073540742067103420653 0.136859377003847907948550521698 16.6135401445219821709507834835 0.649488782098802610039046822057 3873 [24]
712 0.059780288091492160542569852862 0.135796481789339942268546816682 16.7279220613578554392151985179 0.637151359175493297819565441529 3074 [31]
713 0.059780288091492160542569852862 0.135796481789339942268546816682 16.7279220613578554392151985179 0.638046234679953260316503033441 3245 [31]
714 0.059780288091492160542569852862 0.135796481789339942268546816682 16.7279220613578554392151985179 0.638941110184413222813440625354 3401 [31]
715 0.059780288091492160542569852862 0.135796481789339942268546816682 16.7279220613578554392151985179 0.639835985688873185310378217267 3594 [31]
716 0.059780288091492160542569852862 0.135796481789339942268546816682 16.7279220613578554392151985179 0.640730861193333147807315809178 3624 [31]
717 0.059780288091492160542569852862 0.135796481789339942268546816682 16.7279220613578554392151985179 0.641625736697793110304253401091 3631 [31]
718 0.059780288091492160542569852862 0.135796481789339942268546816682 16.7279220613578554392151985179 0.642520612202253072801190993003 3651 [31]
719 0.059780288091492160542569852862 0.135796481789339942268546816682 16.7279220613578554392151985179 0.643415487706713035298128584916 3657 [31]
720 0.059780288091492160542569852862 0.135796481789339942268546816682 16.7279220613578554392151985179 0.644310363211172997795066176828 3664 [31]
721 0.059780288091492160542569852862 0.135796481789339942268546816682 16.7279220613578554392151985179 0.645205238715632960292003768740 3673 [31]
722 0.059780288091492160542569852862 0.135796481789339942268546816682 16.7279220613578554392151985179 0.646100114220092922788941360653 3573 [31]
723 0.059780288091492160542569852862 0.135796481789339942268546816682 16.7279220613578554392151985179 0.646994989724552885285878952565 3550 [31]
724 0.059780288091492160542569852862 0.135796481789339942268546816682 16.7279220613578554392151985179 0.647889865229012847782816544477 3364 [31]
725 0.059780288091492160542569852862 0.135796481789339942268546816682 16.7279220613578554392151985179 0.648784740733472810279754136389 3617 [31]
726 0.059780288091492160542569852862 0.135796481789339942268546816682 16.7279220613578554392151985179 0.649679616237932772776691728302 2273 [31]
727 0.058742069061895289913172736513 0.133124109377503846514491893512 17.0235746879518477520883931118 0.617263701439627672592655739621 1946 [31]
728 0.058717280483190052832989968956 0.133060457358229531974183592284 17.0307615027621417356919308187 0.617330574974004953545675489680 1915 [31]
729 0.058659720173699229604117241598 0.132912681790082835937095550723 17.0474730707692955389224244556 0.616362344403669973602048511491 1986 [31]
730 0.058636886104586061002102372750 0.132854070171529433448395371156 17.0541116084571346947250898592 0.616487346270310092808446994209 1970 [31]
731 0.058595440459740292066085178673 0.132747700931702560715565424899 17.0661742987848891215070430785 0.616023749510966898482260863488 1942 [31]
732 0.058531226258185347923785573032 0.132582936188407109020912368160 17.0848974800037470577333404196 0.614840630208502029491511022313 1998 [31]
733 0.058531064606729197904556991356 0.132582521473653323626898124011 17.0849446651792495528879145934 0.615675475281541777142333350554 289 [31]
734 0.058531064606463267172112911935 0.132582521472971081966518637096 17.0849446652568734929123367842 0.616515414530002840299593231954 289 [31]
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736 0.058531064606523069903409257452 0.132582521473124505056508461908 17.0849446652394173546736446245 0.618195293045603449380049237422 289 [31]
737 0.058531064606607046705346434048 0.132582521473339946394410308911 17.0849446652149049180059801578 0.619035232305123350846277754508 291 [31]
738 0.058531064606618489087859209965 0.132582521473369301670396906647 17.0849446652115649399382158887 0.619875171562345948385397001083 289 [31]
739 0.058531064606460477616596983880 0.132582521472963925399959311151 17.0849446652576877511519696305 0.620715110814178416092501958181 679 [31]
740 0.058531064606342182608229852055 0.132582521472660441172389272528 17.0849446652922175121553197790 0.621555050067262553908762749021 353 [31]
741 0.058531064606353920678854735030 0.132582521472690555032187131067 17.0849446652887912241072180994 0.622394989324484659286931759345 355 [31]
742 0.058531064606421802298035764892 0.132582521472864704398654237891 17.0849446652689768961892724942 0.623234928583501213779062950291 640 [31]
743 0.058531064606434406548529962253 0.132582521472897040431071257898 17.0849446652652977742787361514 0.624074867840755463899212661131 638 [31]
744 0.058531064606383841251155892942 0.132582521472767315851587791891 17.0849446652800575486554426837 0.624914807095987484671089688273 856 [31]
745 0.058531064606301217841448297100 0.132582521472555346622958252211 17.0849446653041749364461145995 0.625754746350186953260098166655 353 [31]
746 0.058531064606306462168195647943 0.132582521472568800871569524784 17.0849446653026441419374562028 0.626594685607201268620360523052 663 [31]
747 0.058531064606338124912380608762 0.132582521472650031209132838390 17.0849446652934019346413820016 0.627434624865065626933601103545 681 [31]
748 0.058531064606349411277370825254 0.132582521472678986224297114619 17.0849446652901074973604780807 0.628274564122276549095677234410 668 [31]
749 0.058531064606312360652617583659 0.132582521472583933352756462998 17.0849446653009224018557449074 0.629114503377929809094270020278 662 [31]
750 0.058531064606309995663691230586 0.132582521472577866005981372135 17.0849446653016127310888208372 0.629954442634699816070705246388 734 [31]
751 0.058531064606270936722161146988 0.132582521472477660825191610838 17.0849446653130138538808917278 0.630794381890283257646274785321 289 [31]
752 0.058531064606270936722154604912 0.132582521472477660825174827232 17.0849446653130138538828013292 0.631634321147127842543062024458 292 [31]
753 0.058531064606270936722149773899 0.132582521472477660825162433334 17.0849446653130138538842114793 0.632474260403972427439904168445 236 [31]
754 0.058531064606270936722148371011 0.132582521472477660825158834244 17.0849446653130138538846209758 0.633314199660817012336857174828 287 [31]
755 0.058531064606270936722148674943 0.132582521472477660825159613977 17.0849446653130138538845322596 0.634154138917661597233865537982 356 [31]
756 0.058531064606270936722148498890 0.132582521472477660825159162316 17.0849446653130138538845836486 0.634994078174506182130858305474 380 [31]
757 0.058531064606270936722148259138 0.132582521472477660825158547235 17.0849446653130138538846536311 0.635834017431350767027848981883 356 [31]
758 0.058531064606270936722148546693 0.132582521472477660825159284952 17.0849446653130138538845696953 0.636673956688195351924856845038 359 [31]
759 0.058531064606270936722148419663 0.132582521472477660825158959059 17.0849446653130138538846067746 0.637513895945039936821851186138 358 [31]
760 0.058531064606270936722148171924 0.132582521472477660825158323487 17.0849446653130138538846790886 0.638353835201884521718841566834 295 [31]
761 0.058531064606270936722148171618 0.132582521472477660825158322703 17.0849446653130138538846791778 0.639193774458729106615840032563 297 [31]
762 0.058531064606270936722148171052 0.132582521472477660825158321251 17.0849446653130138538846793430 0.640033713715573691512838489737 295 [31]
763 0.058531064606270936722148174825 0.132582521472477660825158330931 17.0849446653130138538846782417 0.640873652972418276409837089377 319 [31]
764 0.058531064606270936722148174286 0.132582521472477660825158329548 17.0849446653130138538846783990 0.641713592229262861306835547521 358 [31]
765 0.058531064606270936722148173933 0.132582521472477660825158328643 17.0849446653130138538846785020 0.642553531486107446203834011746 289 [31]
766 0.058531064606270936722148169744 0.132582521472477660825158317895 17.0849446653130138538846797249 0.643393470742952031100832349422 3788 [24]
767 0.058531064606270936722148169744 0.132582521472477660825158317895 17.0849446653130138538846797249 0.644233409999796615997830825074 3815 [24]
768 0.058531064606270936722148169744 0.132582521472477660825158317895 17.0849446653130138538846797249 0.645073349256641200894829300726 3830 [24]
769 0.058531064606270936722148169744 0.132582521472477660825158317895 17.0849446653130138538846797249 0.645913288513485785791827776378 3851 [24]
770 0.058531064606270936722148169744 0.132582521472477660825158317895 17.0849446653130138538846797249 0.646753227770330370688826252030 3867 [24]
771 0.058531064606270936722148169744 0.132582521472477660825158317895 17.0849446653130138538846797249 0.647593167027174955585824727683 3933 [24]
772 0.058531064606270936722148169744 0.132582521472477660825158317895 17.0849446653130138538846797249 0.648433106284019540482823203335 3993 [24]
773 0.058531064606270936722148169744 0.132582521472477660825158317895 17.0849446653130138538846797249 0.649273045540864125379821678987 4029 [24]
774 0.058531064606270936722148169744 0.132582521472477660825158317895 17.0849446653130138538846797249 0.650112984797708710276820154639 4047 [24]
775 0.058531064606270936722148169744 0.132582521472477660825158317895 17.0849446653130138538846797249 0.650952924054553295173818630291 4083 [24]
776 0.058531064606270936722148169744 0.132582521472477660825158317895 17.0849446653130138538846797249 0.651792863311397880070817105943 4161 [24]
777 0.058531064606270936722148169744 0.132582521472477660825158317895 17.0849446653130138538846797249 0.652632802568242464967815581594 4194 [24]
778 0.058531064606270936722148169744 0.132582521472477660825158317895 17.0849446653130138538846797249 0.653472741825087049864814057245 4212 [24]
779 0.058531064606270936722148169744 0.132582521472477660825158317895 17.0849446653130138538846797249 0.654312681081931634761812532897 4230 [24]
780 0.058531064606270936722148169744 0.132582521472477660825158317895 17.0849446653130138538846797249 0.655152620338776219658811008550 4236 [24]
781 0.058531064606270936722148169744 0.132582521472477660825158317895 17.0849446653130138538846797249 0.655992559595620804555809484201 4249 [24]
782 0.058531064606270936722148169744 0.132582521472477660825158317895 17.0849446653130138538846797249 0.656832498852465389452807959854 4268 [24]
783 0.058531064606270936722148169744 0.132582521472477660825158317895 17.0849446653130138538846797249 0.657672438109309974349806435506 4275 [24]
784 0.058531064606270936722148169744 0.132582521472477660825158317895 17.0849446653130138538846797249 0.658512377366154559246804911159 4282 [24]
785 0.058531064606270936722148169744 0.132582521472477660825158317895 17.0849446653130138538846797249 0.659352316622999144143803386810 4289 [24]
786 0.058531064606270936722148169744 0.132582521472477660825158317895 17.0849446653130138538846797249 0.660192255879843729040801862463 4296 [24]
787 0.057589005447075341007033535483 0.130170827931777573235495378929 17.3644255919475168409109299720 0.629625163810081469279672352268 3050 [24]
788 0.057515288371078796443164796010 0.129982543711730683075746301561 17.3866814949821890260092950724 0.628007357224186666003012462027 1958 [31]
789 0.057515302753686151119318472507 0.129982580440899725495993067185 17.3866771471686303619906694633 0.628804792602995781128356090454 2118 [31]
790 0.057498654206606746878816500585 0.129940066291805677952862616865 17.3917114026139652669210271950 0.629055176021812315832527605867 2147 [31]
791 0.057452205749238243596185626847 0.129821471252625842816764498109 17.4057721015047182650886259241 0.628326264806301586719887080566 2145 [31]
792 0.057365811216482482817408133377 0.129600949655831529485392866921 17.4319856861481564032124848952 0.626286728853364150959902997818 2148 [31]
793 0.057356312222008810279000968621 0.129576708774340370202818434866 17.4348726628257525128215546104 0.626766040109754195139690259598 55 [31]
794 0.057356312222008707705264984053 0.129576708774340108446226622246 17.4348726628257836926508734666 0.627556413426408778053995693107 55 [31]
795 0.057356312222008669400180342410 0.129576708774340010695975949901 17.4348726628257953364307329664 0.628346786743065464704886358808 55 [31]
796 0.057356312222008670379250441030 0.129576708774340013194452286954 17.4348726628257950388181104646 0.629137160059723440903690406024 55 [31]
797 0.057356312222008671385910720093 0.129576708774340015763335649067 17.4348726628257947328187688011 0.629927533376381418092488858754 55 [31]
798 0.057356312222008685492265170878 0.129576708774340051761159346294 17.4348726628257904448427107490 0.630717906693039827516344326745 55 [31]
799 0.057356312222008669347287088414 0.129576708774340010560998338303 17.4348726628257953525089484657 0.631508280009697238880823352866 220 [31]
800 0.057356312222008669309225735683 0.129576708774340010463870063945 17.4348726628257953640786399700 0.632298653326355181600627232158 3120 [24]
801 0.057069268186840375740526806975 0.128844679512808707237924828061 17.5225656780121526139453994662 0.623631489091423516971572531777 2040 [31]
802 0.057055411748154953230562086726 0.128809366366419973808708969935 17.5268211964544766400188896022 0.623955344713997791103451214268 2042 [31]
803 0.057043037901732207475443304360 0.128777833475111954677323913066 17.5306231362133208468946556713 0.624326966421639006078208681529 2055 [31]
804 0.057030074202568724297952592237 0.128744799322219436758445978755 17.5346080814841097675797146321 0.624678369426781448896327124537 2054 [31]
805 0.057020707254359809737224278698 0.128720931628515740611495800565 17.5374885397188735623421166651 0.625147198018025957910871111898 2068 [31]
806 0.056998038726805455918700419099 0.128663174679841605874942127877 17.5444633243093092910751435173 0.625177568925971253502314686449 2019 [31]
807 0.056993183936507771807010201798 0.128650805969403968441850680074 17.5459577958310235174344996925 0.625793290985059798660126430957 1786 [31]
808 0.056992119514288443071593588896 0.128648094141807538434991380678 17.5462854956515680835041460627 0.626533642039714517855149200573 1693 [31]
809 0.056991835237605583666387710450 0.128647369892545698512919518712 17.5463730169573202560980830493 0.627299667957461430209529924889 1688 [31]
810 0.056985204349746179788122177130 0.128630476700227857893829645816 17.5484147404738427045326017294 0.627855868888642306860932682756 1491 [31]
811 0.056962601890588273032970877791 0.128572897307691596494483409546 17.5553778586301975649124236280 0.627883280683735684961438245082 526 [31]
812 0.056959450361781703936323533204 0.128564869306645004436799983209 17.5563491861040455367843539644 0.628553151348367548584908705744 26 [31]
813 0.056959450361781703936322927386 0.128564869306645004436798439998 17.5563491861040455367845406929 0.629327231584018247536347872434 26 [31]
814 0.056959450361781703936212533232 0.128564869306645004436517231056 17.5563491861040455368185669748 0.630101311819668946484143462230 26 [31]
815 0.056959450361781703936212521918 0.128564869306645004436517202236 17.5563491861040455368185704621 0.630875392055319645435597807991 26 [31]
816 0.056959450361781703936212508673 0.128564869306645004436517168497 17.5563491861040455368185745445 0.631649472290970344387052088588 26 [31]
817 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.632423552526621043338506655630 813 [4]
818 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.633197632762271742289961376139 362 [4]
819 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.633971712997922441241416096648 875 [4]
820 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.634745793233573140192870817156 882 [4]
821 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.635519873469223839144325537665 646 [4]
822 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.636293953704874538095780258174 912 [4]
823 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.637068033940525237047234978683 1142 [4]
824 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.637842114176175935998689699191 1210 [4]
825 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.638616194411826634950144419700 1048 [4]
826 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.639390274647477333901599140209 1275 [4]
827 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.640164354883128032853053860717 1224 [4]
828 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.640938435118778731804508581226 1275 [4]
829 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.641712515354429430755963301735 1188 [4]
830 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.642486595590080129707418022244 1280 [4]
831 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.643260675825730828658872742752 1183 [4]
832 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.644034756061381527610327463261 1060 [4]
833 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.644808836297032226561782183770 1642 [4]
834 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.645582916532682925513236904279 1557 [4]
835 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.646356996768333624464691624787 1467 [4]
836 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.647131077003984323416146345296 1742 [4]
837 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.647905157239635022367601065805 1657 [4]
838 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.648679237475285721319055786313 1748 [4]
839 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.649453317710936420270510506822 1669 [4]
840 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.650227397946587119221965227331 1881 [4]
841 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.651001478182237818173419947840 1560 [4]
842 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.651775558417888517124874668348 1879 [4]
843 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.652549638653539216076329388857 2483 [4]
844 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.653323718889189915027784109366 2837 [4]
845 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.654097799124840613979238829874 2984 [4]
846 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.654871879360491312930693550383 2917 [4]
847 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.655645959596142011882148270892 3210 [4]
848 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.656420039831792710833602991401 2903 [4]
849 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.657194120067443409785057711909 2947 [4]
850 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.657968200303094108736512432418 3062 [4]
851 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.658742280538744807687967152927 3664 [4]
852 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.659516360774395506639421873436 3806 [4]
853 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.660290441010046205590876593944 3887 [4]
854 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.661064521245696904542331314453 3951 [4]
855 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.661838601481347603493786034962 4096 [4]
856 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.662612681716998302445240755470 4626 [4]
857 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.663386761952649001396695475982 4722 [4]
858 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.664160842188299700348150196491 4729 [4]
859 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.664934922423950399299604916999 4736 [4]
860 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.665709002659601098251059637508 4743 [4]
861 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.666483082895251797202514358017 4762 [4]
862 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.667257163130902496153969078526 4768 [4]
863 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.668031243366553195105423799034 4781 [4]
864 0.056959450361781703936212504060 0.128564869306645004436517156746 17.5563491861040455368185759663 0.668805323602203894056878519544 4788 [4]
865 0.056156773481307844658496053043 0.126523894307853857428827117027 17.8072908753003170179009539388 0.641669147770983638227090145443 1978 [31]
866 0.056154991435925812537449412137 0.126519371294944249944072791218 17.8078559791256295054839057923 0.642349806102414930310091832429 1861 [31]
867 0.056140201356690653283231385138 0.126481833967138666841579139688 17.8125474407622946828413707909 0.642583551760174107999698630783 2025 [31]
868 0.056128012575057355280636431019 0.126450900631679140272182249277 17.8164156206804394317562486766 0.642905777270775350049419425444 1978 [31]
869 0.056106912473384981671269525184 0.126397355692142680038512837946 17.8231158321955882806592127455 0.642920830459460550412315150016 1770 [31]
870 0.056071806417837649423518430642 0.126308279646266405178227588271 17.8342747253079126719063931127 0.642453212049619020875258466087 2126 [31]
871 0.055949689012166998852504362332 0.125998535813884438182882218705 17.8732003279327753210471166361 0.638998435786468612814589161499 2190 [31]
872 0.055797709737818520954404934931 0.125613286921337221385306319739 17.9218825413943631734026765561 0.634533001425841559390092906611 2241 [31]
873 0.055759822943043844867261140129 0.125517289571705853724648943668 17.9340598161772337952006893632 0.633967524220520016984229761374 2283 [31]
874 0.055733670838415080213518668538 0.125451035066274592183202863965 17.9424750775744414212515540607 0.633801097595291523610815284359 2338 [31]
875 0.055716324325719934748361094866 0.125407093207195676855772005976 17.9480612208723366293489201601 0.633933986183002575323089423626 2245 [31]
876 0.055698446850663686946609710769 0.125361809914588834345724346471 17.9538219922210323303118917881 0.634047757152465598346340098985 2291 [31]
877 0.055688027900021744326379410706 0.125335420598324385463192882051 17.9571810622442518420396134723 0.634415401519018207710980015336 2285 [31]
878 0.055663055758705725099353009481 0.125272175721850997591869243763 17.9652372003238356814305940026 0.634284732859348991278527781765 2270 [31]
879 0.055644148592601269984039631904 0.125224295834882684809669605448 17.9713415568904059788964221811 0.634360290676203543401532003218 2240 [31]
880 0.055644148446431840738504768261 0.125224295464743769072749206236 17.9713416040986176505349873295 0.635081969733590576119090001697 2195 [31]
881 0.055609934599387289434184941416 0.125137663798256945159409805362 17.9823984186274875696363265032 0.634631567404083205194575199979 2235 [31]
882 0.055592226301537126202514510074 0.125092830485132914924075536644 17.9881265156734688892754826584 0.634745154363583600358732799420 2385 [31]
883 0.055541080512676902017145268078 0.124963361240995525354352793147 18.0046911361718340106434506418 0.633712518047204901217653055284 2196 [31]
884 0.055518541079436331451335847978 0.124906314909658427131072766412 18.0120006858464227908549495329 0.633658127781404225581464173104 2287 [31]
885 0.055492923046045800317630476676 0.124841483798905245218382806140 18.0203158368543703368368165655 0.633497178015874437170154373260 2271 [31]
886 0.055470027839216034700251427886 0.124783549621155445482501946254 18.0277537068950772197524722077 0.633428329242550851479235416105 4254 [24]
887 0.055470027839216034700251427886 0.124783549621155445482501946254 18.0277537068950772197524722077 0.634143259636729802778873379328 4281 [24]
888 0.055470027839216034700251427886 0.124783549621155445482501946254 18.0277537068950772197524722077 0.634858190030908754078511342552 4316 [24]
889 0.055470027839216034700251427886 0.124783549621155445482501946254 18.0277537068950772197524722077 0.635573120425087705378149305776 4342 [24]
890 0.055470027839216034700251427886 0.124783549621155445482501946254 18.0277537068950772197524722077 0.636288050819266656677787268999 4367 [24]
891 0.055470027839216034700251427886 0.124783549621155445482501946254 18.0277537068950772197524722077 0.637002981213445607977425232223 4391 [24]
892 0.055470027839216034700251427886 0.124783549621155445482501946254 18.0277537068950772197524722077 0.637717911607624559277063195446 4414 [24]
893 0.055470027839216034700251427886 0.124783549621155445482501946254 18.0277537068950772197524722077 0.638432842001803510576701158670 4436 [24]
894 0.055470027839216034700251427886 0.124783549621155445482501946254 18.0277537068950772197524722077 0.639147772395982461876339121894 4453 [24]
895 0.055470027839216034700251427886 0.124783549621155445482501946254 18.0277537068950772197524722077 0.639862702790161413175977085117 4495 [24]
896 0.055470027839216034700251427886 0.124783549621155445482501946254 18.0277537068950772197524722077 0.640577633184340364475615048341 4523 [24]
897 0.055470027839216034700251427886 0.124783549621155445482501946254 18.0277537068950772197524722077 0.641292563578519315775253011564 4542 [24]
898 0.055470027839216034700251427886 0.124783549621155445482501946254 18.0277537068950772197524722077 0.642007493972698267074890974788 4560 [24]
899 0.055470027839216034700251427886 0.124783549621155445482501946254 18.0277537068950772197524722077 0.642722424366877218374528938012 4578 [24]
900 0.055470027839216034700251427886 0.124783549621155445482501946254 18.0277537068950772197524722077 0.643437354761056169674166901235 4596 [24]
901 0.055470027839216034700251427886 0.124783549621155445482501946254 18.0277537068950772197524722077 0.644152285155235120973804864459 4617 [24]
902 0.055470027839216034700251427886 0.124783549621155445482501946254 18.0277537068950772197524722077 0.644867215549414072273442827682 4632 [24]
903 0.055470027839216034700251427886 0.124783549621155445482501946254 18.0277537068950772197524722077 0.645582145943593023573080790906 4646 [24]
904 0.055470027839216034700251427886 0.124783549621155445482501946254 18.0277537068950772197524722077 0.646297076337771974872718754130 4660 [24]
905 0.055470027839216034700251427886 0.124783549621155445482501946254 18.0277537068950772197524722077 0.647012006731950926172356717353 4674 [24]
906 0.055470027839216034700251427886 0.124783549621155445482501946254 18.0277537068950772197524722077 0.647726937126129877471994680577 4685 [24]
907 0.055470027839216034700251427886 0.124783549621155445482501946254 18.0277537068950772197524722077 0.648441867520308828771632643800 4706 [24]
908 0.055470027839216034700251427886 0.124783549621155445482501946254 18.0277537068950772197524722077 0.649156797914487780071270607024 4720 [24]
909 0.055470027839216034700251427886 0.124783549621155445482501946254 18.0277537068950772197524722077 0.649871728308666731370908570247 4730 [24]
910 0.055470027839216034700251427886 0.124783549621155445482501946254 18.0277537068950772197524722077 0.650586658702845682670546533471 4740 [24]
911 0.055470027839216034700251427886 0.124783549621155445482501946254 18.0277537068950772197524722077 0.651301589097024633970184496695 4750 [24]
912 0.055470027839216034700251427886 0.124783549621155445482501946254 18.0277537068950772197524722077 0.652016519491203585269822459918 4757 [24]
913 0.055470027839216034700251427886 0.124783549621155445482501946254 18.0277537068950772197524722077 0.652731449885382536569460423142 4763 [24]
914 0.055470027839216034700251427886 0.124783549621155445482501946254 18.0277537068950772197524722077 0.653446380279561487869098386365 4773 [24]
915 0.055470027839216034700251427886 0.124783549621155445482501946254 18.0277537068950772197524722077 0.654161310673740439168736349589 4780 [24]
916 0.055470027839216034700251427886 0.124783549621155445482501946254 18.0277537068950772197524722077 0.654876241067919390468374312813 4787 [24]
917 0.055470027839216034700251427886 0.124783549621155445482501946254 18.0277537068950772197524722077 0.655591171462098341768012276036 4794 [24]
918 0.055470027839216034700251427886 0.124783549621155445482501946254 18.0277537068950772197524722077 0.656306101856277293067650239260 5040 [24]
919 0.055120302302885600478352648055 0.123899343099295413143029461654 18.1421356237309504880168872421 0.644672126222635688712340415902 3592 [31]
920 0.055120302302885600478352648055 0.123899343099295413143029461654 18.1421356237309504880168872421 0.645373619287078164978621526259 3644 [31]
921 0.055120302302885600478352648055 0.123899343099295413143029461654 18.1421356237309504880168872421 0.646075112351520641244902636613 3656 [31]
922 0.055120302302885600478352648055 0.123899343099295413143029461654 18.1421356237309504880168872421 0.646776605415963117511183746968 3682 [31]
923 0.055120302302885600478352648055 0.123899343099295413143029461654 18.1421356237309504880168872421 0.647478098480405593777464857322 3701 [31]
924 0.055120302302885600478352648055 0.123899343099295413143029461654 18.1421356237309504880168872421 0.648179591544848070043745967677 3832 [31]
925 0.055120302302885600478352648055 0.123899343099295413143029461654 18.1421356237309504880168872421 0.648881084609290546310027078032 3839 [31]
926 0.055120302302885600478352648055 0.123899343099295413143029461654 18.1421356237309504880168872421 0.649582577673733022576308188387 3886 [31]
927 0.055120302302885600478352648055 0.123899343099295413143029461654 18.1421356237309504880168872421 0.650284070738175498842589298741 3919 [31]
928 0.055120302302885600478352648055 0.123899343099295413143029461654 18.1421356237309504880168872421 0.650985563802617975108870409094 4075 [31]
929 0.055120302302885600478352648055 0.123899343099295413143029461654 18.1421356237309504880168872421 0.651687056867060451375151519449 4133 [31]
930 0.055120302302885600478352648055 0.123899343099295413143029461654 18.1421356237309504880168872421 0.652388549931502927641432629805 4451 [31]
931 0.055120302302885600478352648055 0.123899343099295413143029461654 18.1421356237309504880168872421 0.653090042995945403907713740158 4741 [31]
932 0.055120302302885600478352648055 0.123899343099295413143029461654 18.1421356237309504880168872421 0.653791536060387880173994850515 4747 [31]
933 0.055120302302885600478352648055 0.123899343099295413143029461654 18.1421356237309504880168872421 0.654493029124830356440275960869 4754 [31]
934 0.055120302302885600478352648055 0.123899343099295413143029461654 18.1421356237309504880168872421 0.655194522189272832706557071222 4761 [31]
935 0.055120302302885600478352648055 0.123899343099295413143029461654 18.1421356237309504880168872421 0.655896015253715308972838181577 4768 [31]
936 0.055120302302885600478352648055 0.123899343099295413143029461654 18.1421356237309504880168872421 0.656597508318157785239119291931 3028 [31]
937 0.054056513690627580830230951765 0.121218305346265289897287814822 18.4991582276861089026863398808 0.619972318829358081822994988447 1561 [24]
938 0.054056513690627580830230937602 0.121218305346265289897287779212 18.4991582276861089026863447277 0.620633975519677567502634836782 1943 [24]
939 0.054056513690627580830230929761 0.121218305346265289897287759496 18.4991582276861089026863474113 0.621295632209997053182274902045 1949 [24]
940 0.054056513690627580830230921904 0.121218305346265289897287739743 18.4991582276861089026863500999 0.621957288900316538861914966227 2140 [24]
941 0.054056513690627580830230915671 0.121218305346265289897287724070 18.4991582276861089026863522332 0.622618945590636024541555085899 1982 [24]
942 0.054056513690627580830230910331 0.121218305346265289897287710644 18.4991582276861089026863540606 0.623280602280955510221195236034 1951 [24]
943 0.054056513690627580830230905833 0.121218305346265289897287699334 18.4991582276861089026863555999 0.623942258971274995900835414919 1955 [24]
944 0.054056513690627580830230899175 0.121218305346265289897287682597 18.4991582276861089026863578781 0.624603915661594481580475518639 1894 [24]
945 0.054056513690627580830230895524 0.121218305346265289897287673416 18.4991582276861089026863591278 0.625265572351913967260115726162 1999 [24]
946 0.054056513690627580830230869984 0.121218305346265289897287609202 18.4991582276861089026863678680 0.625927229042233452939755173077 829 [24]
947 0.054056513690627580830230868286 0.121218305346265289897287604932 18.4991582276861089026863684491 0.626588885732552938619395447188 420 [24]
948 0.054056513690627580830230868286 0.121218305346265289897287604932 18.4991582276861089026863684491 0.627250542422872424299035780291 558 [24]
949 0.054056513690627580830230868286 0.121218305346265289897287604932 18.4991582276861089026863684491 0.627912199113191909978676113392 601 [24]
950 0.054056513690627580830230868286 0.121218305346265289897287604932 18.4991582276861089026863684491 0.628573855803511395658316446493 617 [24]
951 0.054056513690627580830230868286 0.121218305346265289897287604932 18.4991582276861089026863684491 0.629235512493830881337956779595 628 [24]
952 0.054056513690627580830230868286 0.121218305346265289897287604932 18.4991582276861089026863684491 0.629897169184150367017597112696 862 [24]
953 0.054056513690627580830230868286 0.121218305346265289897287604932 18.4991582276861089026863684491 0.630558825874469852697237445799 993 [24]
954 0.054056513690627580830230868286 0.121218305346265289897287604932 18.4991582276861089026863684491 0.631220482564789338376877778901 1219 [24]
955 0.054056513690627580830230868286 0.121218305346265289897287604932 18.4991582276861089026863684491 0.631882139255108824056518112002 1286 [24]
956 0.054056513690627580830230868286 0.121218305346265289897287604932 18.4991582276861089026863684491 0.632543795945428309736158445104 1309 [24]
957 0.054056513690627580830230868286 0.121218305346265289897287604932 18.4991582276861089026863684491 0.633205452635747795415798778204 1364 [24]
958 0.054056513690627580830230868286 0.121218305346265289897287604932 18.4991582276861089026863684491 0.633867109326067281095439111307 1590 [24]
959 0.054056513690627580830230868286 0.121218305346265289897287604932 18.4991582276861089026863684491 0.634528766016386766775079444408 1725 [24]
960 0.054056513690627580830230868286 0.121218305346265289897287604932 18.4991582276861089026863684491 0.635190422706706252454719777509 1864 [24]
961 0.054056513690627580830230868286 0.121218305346265289897287604932 18.4991582276861089026863684491 0.635852079397025738134360110610 1959 [24]
962 0.054056513690627580830230868286 0.121218305346265289897287604932 18.4991582276861089026863684491 0.636513736087345223814000443712 1981 [24]
963 0.054056513690627580830230868286 0.121218305346265289897287604932 18.4991582276861089026863684491 0.637175392777664709493640776813 2094 [24]
964 0.054056513690627580830230868286 0.121218305346265289897287604932 18.4991582276861089026863684491 0.637837049467984195173281109916 2295 [24]
965 0.054056513690627580830230868286 0.121218305346265289897287604932 18.4991582276861089026863684491 0.638498706158303680852921443016 2313 [24]
966 0.054056513690627580830230868286 0.121218305346265289897287604932 18.4991582276861089026863684491 0.639160362848623166532561776118 3001 [24]
967 0.054056513690627580830230868286 0.121218305346265289897287604932 18.4991582276861089026863684491 0.639822019538942652212202109221 3408 [24]
968 0.054056513690627580830230868286 0.121218305346265289897287604932 18.4991582276861089026863684491 0.640483676229262137891842442322 3453 [24]
969 0.054056513690627580830230868286 0.121218305346265289897287604932 18.4991582276861089026863684491 0.641145332919581623571482775424 3462 [24]
970 0.054056513690627580830230868286 0.121218305346265289897287604932 18.4991582276861089026863684491 0.641806989609901109251123108524 3489 [24]
971 0.054056513690627580830230868286 0.121218305346265289897287604932 18.4991582276861089026863684491 0.642468646300220594930763441626 3504 [24]
972 0.054056513690627580830230868286 0.121218305346265289897287604932 18.4991582276861089026863684491 0.643130302990540080610403774728 3972 [24]
973 0.054056513690627580830230868286 0.121218305346265289897287604932 18.4991582276861089026863684491 0.643791959680859566290044107829 4051 [24]
974 0.054056513690627580830230868286 0.121218305346265289897287604932 18.4991582276861089026863684491 0.644453616371179051969684440932 4064 [24]
975 0.054056513690627580830230868286 0.121218305346265289897287604932 18.4991582276861089026863684491 0.645115273061498537649324774032 4273 [24]
976 0.054056513690627580830230868286 0.121218305346265289897287604932 18.4991582276861089026863684491 0.645776929751818023328965107134 4283 [24]
977 0.054056513690627580830230868286 0.121218305346265289897287604932 18.4991582276861089026863684491 0.646438586442137509008605440235 4314 [24]
978 0.054056513690627580830230868286 0.121218305346265289897287604932 18.4991582276861089026863684491 0.647100243132456994688245773337 4494 [24]
979 0.054056513690627580830230868286 0.121218305346265289897287604932 18.4991582276861089026863684491 0.647761899822776480367886106439 4533 [24]
980 0.054056513690627580830230868286 0.121218305346265289897287604932 18.4991582276861089026863684491 0.648423556513095966047526439541 4724 [24]
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376786 0.007735195147788253543600394244 0.015713484026367722764463208047 129.2792206135785543921519851789 0.730461265418989539407384521005 2236146 [4]
389344 0.007651493790068344573073660702 0.015540808377726319217600974991 130.6934341759516494409536739031 0.730568236335025712957681902009 2310948 [4]
402179 0.007569584479929375117570040335 0.015371886547533641834800964394 132.1076477383247444897553626273 0.730674784269150811518265484288 2387406 [4]
415292 0.007489410275280319159162544891 0.015206597444871989772061169078 133.5218613006978395385570513515 0.730777287486202699740943628873 2465526 [4]
428688 0.007410916621183548482417859411 0.015044825131628670731932858768 134.9360748630709345873587400757 0.730879393375718537738424774266 2545338 [4]
442368 0.007334051226058075453627420414 0.014886458551295737355807249729 136.3502884254440296361604287999 0.730977703023270627606054529356 2626848 [4]
456337 0.007258763945507766696600939740 0.014731391274719740091684257544 137.7645019878171246849621175241 0.731075638966294655328513060002 2710086 [4]
470596 0.007185006673232179214083331894 0.014579521261578299472182357982 139.1787155501902197337638062483 0.731170007199629885728468432521 2795058 [4]
485150 0.007112733238521314037834070765 0.014430750636460153559200905349 140.5929291125633147825654949725 0.731264023517023138328385772760 2881794 [4]
500000 0.007041899309875314309182936203 0.014284985478516111604057461861 142.0071426749364098313671836968 0.731354682675485237388693859157 2970300 [4]
515151 0.006972462304326340512110865794 0.014142135623730950488016887242 143.4213562373095048801688724210 0.731445010046662075225141185833 3060606 [4]
530604 0.006904381302072879690605479025 0.014002114478941535136650383408 144.8355697996825999289705611452 0.731532174562475423867132435372 3152718 [4]
546364 0.006837616966066895547864461155 0.013864838846795049498055771806 146.2497833620556949777722498694 0.731619025914698142645571248211 3246666 [4]
562432 0.006772131466221777600950972876 0.013730228760903835425259113827 147.6639969244287900265739385936 0.731702894005339595994020506192 3342456 [4]
578813 0.006707888407934246581994434405 0.013598207330510529315400853117 149.0782104868018850753756273178 0.731786466189064617647744155443 3440118 [4]
595508 0.006644852764636441083379176088 0.013468700594029476655254178326 150.4924240491749801241773160420 0.731867221361287113327174547636 3539658 [4]
612522 0.006582990814115545450105884136 0.013341637380878255177374421927 151.9066376115480751729790047662 0.731947696639303830918210307454 3641106 [4]
629856 0.006522270078357699406909264152 0.013216949181056963072912978731 153.3208511739211702217806934904 0.732025509028818896988502534290 3744468 [4]
647515 0.006462659266690716226658479773 0.013094570021973102303719340039 154.7350647362942652705823822146 0.732103056402886372355272291887 3849774 [4]
665500 0.006404128222016472780511157123 0.012974436352046743566987969947 156.1492782986673603193840709389 0.732178083970278474294675743389 3957030 [4]
683816 0.006346647869938851684914273420 0.012856486930664500443651715675 157.5634918610404553681857596631 0.732252860365578033210352903164 4066266 [4]
702464 0.006290190170606930368414134605 0.012740662724081937376591790308 158.9777054234135504169874483873 0.732325249966132413315432151385 4177488 [4]
721449 0.006234728073105830229061917442 0.012626906806902634364300792180 160.3919189857866454657891371115 0.732397401291001927087683209923 4290726 [4]
740772 0.006180235472239356956003400401 0.012515164268788451759306979860 161.8061325481597405145908258357 0.732467289633685490161539443262 4405986 [4]
760438 0.006126687167559367229621075672 0.012405382126079781129839374774 163.2203461105328355633925145599 0.732536951729691540744431511473 4523298 [4]
780448 0.006074058824506765885661128461 0.012297509238026913467840771515 164.6345596729059306121942032841 0.732604466238457212157201070401 4642668 [4]
800807 0.006022326937538242368849260146 0.012191496227354267662083523485 166.0487732352790256609958920083 0.732671765733819373186608315343 4764126 [4]
821516 0.005971468795121360440921954436 0.012087295404898248280356313882 167.4629867976521207097975807325 0.732737025322645970411012670904 4887678 [4]
842580 0.005921462446488479232818534315 0.011984860698077076684760073934 168.8772003600252157585992694567 0.732802080400291820154031811393 5013354 [4]
864000 0.005872286670047260075125395797 0.011884147582967185284047804405 170.2914139223983108074009581810 0.732865196171872840127877598689 5141160 [4]
885781 0.005823920943352250515912024132 0.011785113019775792073347406035 171.7056274847714058562026469052 0.732928117261922826446614812262 5271126 [4]
907924 0.005776345414548278601851367430 0.011687715391513182221501559704 173.1198410471445009050043356294 0.732989193138636718525702573164 5403258 [4]
930434 0.005729540875202176990787730962 0.011591914445681106957390891182 174.5340546095175959538060243536 0.733050083543853305089024942433 5537586 [4]
953312 0.005683488734444724367112041815 0.011497671238805650803265761985 175.9482681718906910026077130778 0.733109216838550162850880845671 5674116 [4]
976563 0.005638170994349674321952953096 0.011404948083653992329045876808 177.3624817342637860514094018020 0.733168173300201699020948337793 5812878 [4]
1000188 0.005593570226481369810542504337 0.011313708498984760390413509794 178.7766952966368811002110905262 0.733225455233398208117544792799 5953878 [4]
1024192 0.005549669549546742350668161120 0.011223917161691230546045148605 180.1909088590099761490127792504 0.733282568444056442958329123480 6097146 [4]



Updates

Please note that the results are taken from a running search. For updates look at the list below.

08-Feb-2012: First raw presentation from N=1 to N=600.
13-Feb-2012: First improvements for N=47, 55, 56 and 57 by David W. Cantrell [24].
13-Feb-2012: All parameters are displayed at 30 decimal places.
13-Feb-2012: The packings for N=14, 63, 172, 365, 666, 1099, 1688, 2457, 3430, 4631, 6084, 7813, 9842, 12195, 14896, 17969 ...
13-Feb-2012: Extension up to N=1000 and improvements for N=43, 47, 51, 68, 73, 74, 77, 79, 81, 82, 84, 85, 86, 87, 92, 93, 94, 95, 97, 99, 109–122, 124, 126–139 any many others by E. Specht [31].
13-Feb-2012: Further improvements for N=65, 68, 180, 416 and 567 by David W. Cantrell [24].
14-Feb-2012: More improvements for N=43 and 51 by David W. Cantrell [24].
14-Feb-2012: One improvement for N=57 by Eckard Specht [31].
15-Feb-2012: Now all spheres are colored in the usual manner. All of these images were made by POV-Ray.
20-Feb-2012: Again, one improvement for N=57 by Eckard Specht [31].
20-Feb-2012: The case N=12 was a hard nut to crack, it was done by David W. Cantrell [24].
20-Feb-2012: Two improvements for N=47 and 71 by David W. Cantrell [24].
24-Feb-2012: Six improvements for N=56, 57, 72, 76, 77 and 79 by program Packntile created by Tomaz and Nevenka Kristan [26].
25-Feb-2012: David Cantrell has found new regular lattice packings for N=126, 221, 405, 550, 726, 750, 787, 800, 936, 968 and 1008. Furthermore he improved the cases N=46, 71 and 72 [24].
29-Feb-2012: Many, many new record packings, namely for N=41, 42, 55, 58, 59, 64, 65, 66, 68, 69, 71, 73, 74, 75, 76, 77, 78, 79, 83, 84, 85, 86, 87, 89, 90, 92, 93, 94, 95, 96, 97, 99, 101, 102, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 134, 135, 136, 137, 138, 139, 140, 145, 150, 155, 160, 165, 175 and 195 are found by Liang Yu from WenQi Huang's group [27]. That's overwhelming!
01-Mar-2012: A symmetric better packing for N=98 by David W. Cantrell [24].
01-Mar-2012: Three improvements for N=58, 71 and 82 by program Packntile [26].
01-Mar-2012: Some better packings for N=42, 55, 64 and 65 by David W. Cantrell [24].
01-Mar-2012: A remarkable improvement for N=54 by WenQi Huang and Liang Yu [27].
08-Mar-2012: One better packing for N=55 by Eckard Specht [31].
08-Mar-2012: A couple of improvements for N=73, 77, 81, 90, 99, 112 and 176 by program Packntile [26].
08-Mar-2012: More better packings for N=54, 55, 56, 57, 58, 66, 68, 69, 75 and 99 by David W. Cantrell [24].
22-Mar-2012: A couple of new records for N=42, 54, 55, 71, 73, 81 and 82 by WenQi Huang and Liang Yu [27].
29-Mar-2012: More improvements for N=74, 93, 96, 97, 122, 178, 258 and 437 by program Packntile [26].
30-Mar-2012: In [4], Michael Goldberg mentioned more packings, i.e. for N=256, 500 and 864. Many thanks to David W. Cantrell who has kindly calculated the coordinates.
31-Mar-2012: To continue this work, I have (re)calculated all these cubic close-packed Goldberg packings up to 39754, namely for N=32, 63, 108, 172, 256, 365, 500, 666, 864, 1099, 1372, 1688, 2048, 2457, 2916, 3430, 4000, 4631, 5324, 6084, 6912, 7813, 8788, 9842, 10976, 12195, 13500, 14896, 16384, 17969, 19652, 21438, 23328, 25327, 27436, 29660, 32000, 34461, 37044 and 39754. More will follow ...
01-Apr-2012: ... more packings for N=42592, 45563, 48668, 51912, 55296, 58825, 62500, 66326, 70304, 74439, 78732, 83188, 87808, 92597, 97556, 102690, 108000, 113491, 119164 and 125024 by Eckard Specht [31].
02-Apr-2012: ... even more packings for N=131072, 137313, 143748, 150382, 157216, 164255, 171500, 186624, 194509, 202612, 210938, 219488, 275684, 285894 and 389344 by Eckard Specht [31].
04-Apr-2012: ... even more packings for N=178956, 228267, 237276, 246520, 256000, 265721, 296352, 307063, 318028, 329252, 340736, 352485, 364500, 376786, 402179, 415292, 428688, 442368, 456337, 530604, 546364 and 562432 by Eckard Specht [31].
04-Apr-2012: Here comes a bundle of new records for N=74, 90, 93, 96, 97 and 112 by WenQi Huang and Liang Yu [27].
06-Apr-2012: More better packings for N=42, 54, 55, 73, 74, 76, 77, 78, 79, 81, 82 and 89 by David W. Cantrell [24].
06-Apr-2012: More packings for N=470596, 485150, 500000, 515151, 578813, 595508, 612522, 629856, 647515, 665500, 683816, 702464, 721449, 740772, 760438, 780448, 800807, 821516, 842580, 864000, 885781, 907924, 930434, 953312 and 976563 by Eckard Specht [31].
06-Apr-2012: David W. Cantrell sent me better packings for N=121, 190 and 280 [24].
06-Apr-2012: Seven improvements for N=550, 600, 726, 936, 1183, 1575 and 1920 by Eckard Specht [31].
09-Apr-2012: The last of Goldberg's packings (up to one million of spheres) for N=1000188 and 1024192 are now shown here [31].
09-Apr-2012: As it is easy to see there are many candidate packings which are derived from higher packings (i.e. from a "root" packing with a higher number of spheres) only by omitting one or more spheres. If they have exactly the same radius as the root packing and were not discovered before I have decided to give the credits who owns them for the associated root packing. According to this rule David W. Cantrell and I have calculated some improvements compared to the old packings shown here for N=146, 174, 179, 188, 189, 201, 235, 236, 237, 238, 239, 240, 241, 255, 257, 361–364, 408–415, 489–499, 564–566, 653–665, 721–725 and 857–863.
09-Apr-2012: They same once more for N=619–628, 630, 636, 637, 641–652 and 707–720.
09-Apr-2012: Here are derivatives from two more roots: N=793–799 by David W. Cantrell and N=895–935 by Eckard Specht.
09-Apr-2012: David W. Cantrell sent me four packings, namely for N=220, 445, 786 and 1008, which are members of a particularly nice family in which spheres are grouped in pyramids in four corners of the cube and in a tetrahedron in the middle of the cube. I have calculated all derivatives from these roots in the ranges N=211–219, 428–444, 733–785, 937–1007 which are better than the previous ones.
11-Apr-2012: Three improvements for N=69, 125 and 199 by program Packntile [26].
12-Apr-2012: The range between N=501 and 600 was reconsidered, improvements for N=501–538, 551–563, 568–582 and 593–599 were found by Eckard Specht [31].
13-Apr-2012: Six improvements for N=64, 69, 122, 125, 132 and 146 by WenQi Huang and Liang Yu [27].
15-Apr-2012: The range between N=200 and 299 was reconsidered, nearly for all of the non-regular packings and its derivatives improvements were found by Eckard Specht [31].
15-Apr-2012: A new family of packings was discovered by David W. Cantrell [24] which typical roots are N=122, 395, 538, 711 and 918. Their derivatives are N= 394–385, 537–530, 710–685 and 917–886. David sent me two (may be the final) improvements for N=64 and 69.
16-Apr-2012: Several better packings were found for N=93, 94, 149, 150, 151, 152, 153, 154, 156, 157, 158, 159, 163, 164, 179, 181, 182, 183, 188, 189, 193, 194 by Eckard Specht [31].
21-Apr-2012: A third new family of packings was discovered by David W. Cantrell [24] which roots are N=n^2 (n+1) / 2. Improvements were found for N=405 (and 404 as its derivative) and the new packing for N=1470. David sent me two improvements for N=92 and 93.
21-Apr-2012: A couple of new records for N=92, 338, 339, 340, 341, 342, 343, 344, 346, 347, 397, 398 and 399 by Eckard Specht [31].
22-Apr-2012: Two new records for N=68 and 75 by WenQi Huang and Liang Yu [27].
22-Apr-2012: Improvements for N=163, 306, 311, 338, 339, 340, 341, 342, 343, 344, 346, 459, 462, 463, 466, 467, 468, 470, 471, 472, 474, 477, 479, 584, 586, 602, 605, 619, 620, 621, 622, 623, 624, 625, 626, 627, 628, 630, 632, 634, 635, 636, 637, 638, 639, 673, 788, 812 and 879 by Eckard Specht [31]. Now all packings shown here fulfill the unproven conjecture that the radius r(N) as a function of N is a monoton decreasing function (but not a strictly monoton decreasing function!).
24-Apr-2012: Three improvements for N=236, 330 and 331 by program Packntile [26].
21-May-2012: Two improvements for N=75 and 92 by David W. Cantrell [24].
21-May-2012: Three improvements for N=78, 79 and 89 by WenQi Huang and Liang Yu [27].
21-May-2012: Further improvements for N=147, 148, 151, 152 and 153 by WenQi Huang and Liang Yu [27].
21-May-2012: Eight improvements for N=149, 154, 179, 181, 235, 237, 238 and 326 by program Packntile [26].
21-May-2012: The last improvement for today for N=179 by WenQi Huang and Liang Yu [27].
01-Jun-2012: Welcome to the list of players in this 3D game! 19 nice improvements arrived for N=42, 49, 51, 55, 64, 68, 70, 71, 75, 78, 79, 81, 89, 90, 95, 96, 97, 98 and 99 by Marco Locatelli, Mirko Maischberger and Fabio Schoen [28].
03-Jun-2012: Six improvements for N=149, 156, 157, 158, 159 abd 173 by WenQi Huang and Liang Yu [27].
03-Jun-2012: Many new records for N=101, 102, 109, 112, 115, 116, 119, 123, 124, 131, 132, 133, 134, 135, 137, 139, 140, 161, 165, 174, 175, 176, 177, 178, 182, 183, 184, 185, 186, 187, 191, 192, 197, 198, 201, 202, 203, 204, 205, 206, 207, 208, 213, 222, 223, 224, 225, 226, 227, 228, 229, 230, 232, 233, 234, 239, 240, 241, 257, 258, 259, 261, 262, 263, 264, 265, 266, 267, 268, 271, 272, 273, 275, 281, 282, 283, 289, 290, 291, 292, 293, 294, 295, 297 and 298 by Eckard Specht [31].
16-Jun-2012: Twenty-three improvements for N=42, 51, 71, 75, 90, 95, 96, 97, 98, 99, 109, 111, 112, 113, 114, 115, 116, 117, 118, 119 and 120 by David W. Cantrell [24]. Davids packings are well fine-tuned, many of them without rattlers. So it is very hard to beat these records.
14-Aug-2012: Twenty-two improvements for N=127, 129, 130, 131, 132, 134, 135, 136, 137, 138, 145, 146, 147, 148, 149, 150, 151, 154, 155, 156, 409 and 413 by David W. Cantrell [24].
14-Aug-2012: One improvement for N=340 by Eckard Specht [31].
15-Oct-2012: Three tiny improvements for N=92, 94 and 97 by Marco Locatelli, Mirko Maischberger and Fabio Schoen [28].
02-Nov-2012: Lots of slightly improvements for N=300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 321, 322, 323, 324, 325, 327, 328, 329, 332, 333, 334, 335, 336, 337, 338, 339, 341, 342, 343, 344, 345, 346, 349, 366, 367, 368, 369, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 384, 396, 397, 406, 407, 408, 410, 411, 412, 414, 417, 418, 419, 420, 421, 422, 423, 424, 425, 426, 427, 446, 447, 448, 449, 450, 451, 452, 453, 454, 455, 456, 457, 458, 460, 461, 462, 463, 464, 465, 466, 467, 468, 470, 471, 472, 474, 477, 478, 501, 502, 503, 504, 505, 506, 507, 508, 509, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 551, 552, 553, 554, 555, 556, 557, 558, 559, 560, 561, 562, 563, 568, 569, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 580, 581, 582, 583, 584, 585, 601, 602, 603, 604, 605, 606, 607, 608, 609, 610, 611, 612, 613, 614, 615, 616, 617, 618, 619, 620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 631, 632, 639, 667, 668, 669, 670, 671, 672, 673, 674, 675, 676, 677, 678, 679, 680, 681, 682, 683, 684, 727, 728, 729, 730, 731, 732, 733, 734, 735, 736, 737, 738, 739, 740, 741, 742, 743, 744, 745, 746, 747, 748, 749, 750, 751, 752, 753, 754, 755, 756, 757, 758, 759, 760, 761, 762, 763, 764, 765, 788, 789, 790, 791, 792, 793, 794, 795, 796, 79,7 798 and 799 by Eckard Specht [31].
25-Jun-2013: Two improvements for N=507 and 619 by program Packntile [26] dated from June 2012.
25-Jun-2014: Three improvements for N=83, 94, 95 by István Kolossváry. It was my failure to update packomania much too late in June 2018, it is really embarrassing, sorry!
13-Sep-2014: One improvement for N=110 again by István Kolossváry. The method used to get these results are published in [10].
29-Jun-2018: Three improvements for N=83, 96 and 109 by Francesco Bagattini, Fabio Schoen and Luca Tigli [30].

References

[1]   J. Schaer, On the densest packing of spheres in a cube, Canadian Mathematical Bulletin 9 (1966) 3, 265–270.
[2]   J. Schaer, The densest packing of five spheres in a cube, Canadian Mathematical Bulletin 9 (1966) 3, 271–274.
[3]   J. Schaer, The densest packing of six spheres in a cube, Canadian Mathematical Bulletin 9 (1966) 3, 275–280.
[4]   M. Goldberg, On the densest packing of equal spheres in a cube, Math. Mag. 44 (1971) 4, 199–208.
[5]   Th. Gensane, Dense Packings of Equal Spheres in a Cube, The Electronic Journal of Combinatorics 11 (2004) #R33, 211–227.
[6]   D. Boll, Optimal Packing Of Circles And Spheres.
[7]   H. Pfoertner, Densest Packings of Equal Spheres in a Cube, April 13, 2005.
[8]   A. Joós, On the packing of fourteen congruent Spheres in a cube, Geom. Dedicata 140 (2009) 3, 49–80.
[9]   M. Tatarevic, On limits of dense packing of equal spheres in a cube, The Electronic Journal of Combinatorics 22(1) (2015) #P1.35.
[10]   I. Kolossváry, K.J. Bowers, Global optimization of additive potential energy functions: Predicting binary Lennard-Jones clusters, Phys. Rev. E 82 (2010), 056711.
[24]   , private communication, February–April 2012.
[26]   , Results of Pack'n'tile contest, January–June 2012.
[27]   , private communication, February–April 2012.
[28]   , private communication, June-October 2012.
[29]   István Kolossváry, private communication, June 2014, September 2014.
[30]   F. Bagattini, F. Schoen, L. Tigli, Clustering methods for the optimization of atomic structure, J. Chem. Phys 148(14) (2018), 144102, and private communication, June 2018.
[31]   , program scu, April 2010–November 2012.

Datenschutzerklärung der Otto-von-Guericke-Universität Magdeburg nach DSGVO

©  E. Specht    29-Jun-2018