Structure of Mandelbrot set's real slice

Periodic part
chaotic part = Main antenn

Chaotic part consist of chaotic bands deliminated by primary separators ( Misiurewicz points )^[1]

ordering and sequences of hyperbolic componnets edit

Chaotic bands from B0 to B10

ordering edit

ordering of hyperbolic componnets^[2]

Sharkovsky ordering shows
- ordering of hyperbolic componnets along real axis ( real slice
  - order of chaotic bands and inside periodic part
  - inside chaotic band
    - period of the biggest island inside chaotic band ( first number )
    - sequence of smaller islands periods ( next numbers)
other orders inside chotic bands

sequences edit

Sharkovsky sequence inside chaotic bands edit

Separators edit

primary separator edit

band-merging point = point merging 2 chaotic bands $B_{i-1}$ and $B_{i}$ are Misiurewicz points $M_{k,p}$

  $m_{i}=M_{2^{i},2^{i-1}}$

with

$k=2^{i}$ = preperiod of critical value
$p=2^{i-1}$ = period of critical value = period of critical point

Examples: ^[3]

$c=m_{0}=M_{1,1}\ \ =-2$ = tip of main antenna , external angle = 1/2^[4]
$c=m_{1}=M_{2,1}\ \ =-1.543689012692076...$ , external angles 5 and 7/12
$c=m_{2}=M_{4,2}\ \ =-1.430357632451307...$ , external angles 33 and 47/80
$c=m_{3}=M_{8,4}\ \ =-1.407405118164702...$ , external angles 1795 and 2557/4352
$c=m_{4}=M_{16,8}\ =-1.402492176358564...$
$c=m_{5}=M_{32,16}=-1.401441494253588...$
$c=m_{6}=M_{64,32}=-1.401216504309415..$
$c=m_{7}=M_{128,64}=-1.401168320839301..$
$c=m_{8}=M_{256,128}=-1.401158001505211..$
$c=m_{9}=M_{512,256}=-1.401155791424613..$
$c=m_{10}=M_{1024,512}=-1.401155318093230..$
$c=m_{11}=M_{2048,1024}=-1.401155216720152..$
...
$c=m_{\infty }=M_{\infty ,\infty }=-1.4011551890......$ = Feigenbaum point = MF = the Myrberg-Feigenbaum point

So the Myrberg-Feigenbaum point is a limit of a series of band-merging points $m_{n}$ :

\lim _{n\to \infty }m_{n}=m_{\infty }=c_{F}

In the text form:

double m[12] = {
-2.0,
-1.543689012692076,
-1.430357632451307,
-1.407405118164702,
-1.402492176358564,
-1.401441494253588,
-1.401216504309415,
-1.401168320839301,
-1.401158001505211,
-1.401155791424613,
-1.401155318093230,
-1.401155216720152  

};

const complex double cf = -1.401155189093314712; //the Feigenbaum point -1.401155 = m[infinity]

Differences $d=m_{i}-m_{i+1}$ or width of the band:

|m[ 0]-m[ 1]| = 0.4563109873079241 = 4.5631098730792408e-01
|m[ 1]-m[ 2]| = 0.1133313802407689 = 1.1333138024076894e-01
|m[ 2]-m[ 3]| = 0.0229525142866049 = 2.2952514286604941e-02
|m[ 3]-m[ 4]| = 0.0049129418061380 = 4.9129418061379937e-03
|m[ 4]-m[ 5]| = 0.0010506821049761 = 1.0506821049760529e-03
|m[ 5]-m[ 6]| = 0.0002249899441731 = 2.2498994417308182e-04
|m[ 6]-m[ 7]| = 0.0000481834701138 = 4.8183470113816185e-05
|m[ 7]-m[ 8]| = 0.0000103193340901 = 1.0319334090125309e-05
|m[ 8]-m[ 9]| = 0.0000022100805979 = 2.2100805978642057e-06
|m[ 9]-m[10]| = 0.0000004733313832 = 4.7333138319949342e-07
|m[10]-m[11]| = 0.0000001013730779 = 1.0137307793200989e-07
|m[11]- MF| = 0.0000000276268373 = 2.762684e-08

Ratio $r_{i-1}={\frac {m_{i-1}-m_{i-2}}{m_{i}-m_{i-1}}}$ tends to first Feigenbaum constant

r = 4.0263428040716152e+00 
r = 4.9376455592452890e+00 
r = 4.6718473762357968e+00 
r = 4.6759545849978759e+00 
r = 4.6699069544538263e+00 
r = 4.6694425212966957e+00 
r = 4.6692421907265809e+00 
r = 4.6692116568498836e+00 
r = 4.6692035988087657e+00 
r = 4.6692020490583603e+00

secondary separator edit

tree separators ( tree is a subset of band )

  $m_{i,j}=M_{(j+1)2^{i}-1,2^{i}}$

Chaotic bands edit

B0 edit

First chotic band = B0

Mandelbrot set - real slice chotic band 0

primary separators ( Misiurewicz points )

$c=m_{0}=M_{1,1}\ \ =-2$ = tip of main antenna , external angle = 1/2^[5]
$c=m_{1}=M_{2,1}\ \ =-1.543689012692076...$ , external angles 5 and 7/12

m_{0}\prec B_{0}\prec m_{1}

0 Sharkovsky sequence edit

m_{0}\prec (2k+1)\prec m_{1}

m_{0}\prec 3\prec 5\prec 7\prec ...\prec m_{1}

Bs edit

s-th chotic band = $B_{s}$

m_{s}\prec B_{s}\prec m_{s+1}

s-th Sharkovsky sequence edit

m_{s}\prec (2k+1)*2^{s}\prec m_{s+1}

m_{s}\prec 3*2^{s}\prec 5*2^{s}\prec 7*2^{s}\prec ...\prec m_{s+1}

Islands edit

Islands

Wakes_along_the_main_antenna_in_the_Mandelbrot_set

real edit

real component centers of Mandelbrot Set (period less than 16) by Jay R. Hill

probably computed using :

FINDPERC.EXE : uses 80-bit floating point arithmetic to achieve 19 digit results.
FINDPERM : uses 57 digits with the extended arithmetic
package MFLOAT by Friedrich Kaufmann. It displays results to 37 digits.

period index root
  2      1 -1.000000000000000000
  3      1 -1.754877666246692760
  4      1 -1.940799806529484750
  4      2 -1.310702641336832880
  5      1 -1.985424253054205310
  5      2 -1.860782522204854870
  5      3 -1.625413725123303730
  6      1 -1.996376137711193750
  6      2 -1.966773216392928680
  6      3 -1.907280091065301960
  6      4 -1.772892903381623790
  6      6 -1.476014642728429890
  7      1 -1.999095682327018470
  7      2 -1.991814172549122210
  7      3 -1.977179587006257380
  7      4 -1.953705894284396240
  7      5 -1.927147709363950260
  7      6 -1.884803571586681790
  7      7 -1.832315202751229190
  7     10 -1.674066091474787970
  7     11 -1.574889139752300960
  8      1 -1.999774048693727320
  8      2 -1.997962915597714310
  8      3 -1.994332966715534900
  8      4 -1.988793274309471250
  8      5 -1.981655786276044430
  8      6 -1.972199838366875690
  8      7 -1.960758987197428950
  8      8 -1.941782090318198160
  8     10 -1.917098277113422000
  8     11 -1.896917994678832840
  8     12 -1.870003880828765360
  8     13 -1.851730049410641290
  8     14 -1.810001385728012070
  8     19 -1.711079470013152140
  8     22 -1.521817231671250990
  8     23 -1.381547484432061460
  9      1 -1.999943521765674000
  9      2 -1.999491438016398090
  9      3 -1.998586588842206870
  9      4 -1.997223024696578670
  9      5 -1.995419032661308130
  9      6 -1.993130254878976070
  9      7 -1.990376381055951220
  9      8 -1.987004347515046850
  9      9 -1.983810249999715080
  9     10 -1.979457504855952090
  9     11 -1.974780858900119900
  9     12 -1.969419120730898370
  9     13 -1.964024336820145270
  9     14 -1.957325050535698610
  9     15 -1.949574903249391220
  9     18 -1.932243966576093880
  9     19 -1.922285778246295770
  9     20 -1.911444631473453430
  9     21 -1.903116773015596850
  9     22 -1.890775424360235070
  9     23 -1.878382601500096120
  9     26 -1.841288561509692930
  9     27 -1.822756322492292640
  9     28 -1.785865646410673530
  9     38 -1.690142263118863300
  9     39 -1.656132562574207450
  9     42 -1.595680963439745770
  9     43 -1.555282700768583180
 10      1 -1.999985881140392100
 10      2 -1.999872911766329140
 10      3 -1.999646917733272930
 10      4 -1.999307504280607550
 10      5 -1.998855765981215220
 10      6 -1.998288907350478770
 10      7 -1.997608093863517390
 10      8 -1.996804552742464270
 10      9 -1.995924151930753200
 10     10 -1.994889199350771110
 10     11 -1.993747864246046470
 10     12 -1.992479382178490760
 10     13 -1.991120876123003380
 10     14 -1.989600586912049630
 10     15 -1.987940574280532540
 10     16 -1.985482320973162620
 10     18 -1.982719408297867730
 10     19 -1.980577173424231090
 10     20 -1.978293354476982960
 10     21 -1.976042168611755780
 10     22 -1.973497417321997840
 10     23 -1.970857889101421060
 10     24 -1.967742776293466570
 10     25 -1.965821785502075820
 10     26 -1.962378689702482390
 10     27 -1.959098046552301780
 10     28 -1.955423327026315770
 10     29 -1.951899996873747210
 10     30 -1.946873454179581380
 10     35 -1.935390734772530910
 10     36 -1.929320330944947580
 10     37 -1.925034238501073900
 10     38 -1.919635489318563350
 10     39 -1.914479863678402620
 10     42 -1.899832337791560340
 10     43 -1.894002022860501320
 10     44 -1.887172206397703060
 10     45 -1.882407933753996170
 10     46 -1.874314683806341270
 10     47 -1.861558413753725570
 10     51 -1.846627211198968380
 10     52 -1.835158845261234550
 10     53 -1.829509623956445570
 10     54 -1.816294855238395870
 10     55 -1.802436134811709390
 10     74 -1.721915099588692480
 10     75 -1.701700891209301220
 10     78 -1.629432500446322830
 10     86 -1.536243271282310500
 10     87 -1.501716839409633130
 10     90 -1.447008840607475070
 11      1 -1.999996470335008680
 11      2 -1.999968231709747580
 11      3 -1.999911750208503700
 11      4 -1.999826999612340710
 11      5 -1.999714045769217260
 11      6 -1.999572711292138060
 11      7 -1.999403065044500460
 11      8 -1.999204566491225700
 11      9 -1.998980020902538600
 11     10 -1.998724654904751430
 11     11 -1.998441414477602890
 11     12 -1.998129024076289590
 11     13 -1.997789739591220190
 11     14 -1.997419190865984310
 11     15 -1.997018796675792250
 11     16 -1.996572112247164520
 11     17 -1.996178289863562060
 11     18 -1.995673667316987960
 11     19 -1.995158050516975210
 11     20 -1.994612320312243470
 11     21 -1.994046774294736830
 11     22 -1.993442193455161600
 11     23 -1.992810279386047150
 11     24 -1.992132473419578720
 11     25 -1.991491196324180660
 11     26 -1.990750707290041020
 11     27 -1.989994261107521120
 11     28 -1.989195014772458840
 11     29 -1.988381342856646010
 11     30 -1.987484171114959340
 11     31 -1.986467602520304380
 11     34 -1.984400062463938130
 11     35 -1.983262197775561640
 11     36 -1.982173393685911000
 11     37 -1.981135356645495560
 11     38 -1.980017288110872010
 11     39 -1.978887819382171960
 11     40 -1.977643304770228910
 11     41 -1.976716792680409560
 11     42 -1.975406229576063050
 11     43 -1.974149564294258260
 11     44 -1.972824987746817520
 11     45 -1.971566130691004370
 11     46 -1.970142650136013340
 11     47 -1.968653636464047760
 11     50 -1.964858951761163740
 11     51 -1.963211626815652330
 11     52 -1.961521263299723720
 11     53 -1.959989860019309700
 11     54 -1.958208072391217650
 11     55 -1.956414775411862780
 11     56 -1.954165857400134740
 11     57 -1.953255117397111030
 11     58 -1.950735248729150630
 11     59 -1.948330193383247060
 11     60 -1.944985211053557280
 11     69 -1.937494133795147620
 11     70 -1.933711217574897610
 11     71 -1.930830967476639730
 11     74 -1.923587538548829290
 11     75 -1.921000946645860180
 11     76 -1.918185148739355740
 11     77 -1.916003483251741820
 11     78 -1.912969655532352200
 11     79 -1.909605827581144710
 11     82 -1.905032905698242700
 11     83 -1.901492571473506980
 11     84 -1.898089027919550120
 11     85 -1.895754220010477820
 11     86 -1.892340207089897870
 11     87 -1.889147135040407790
 11     90 -1.880248365087264960
 11     91 -1.876492993166419600
 11     92 -1.871708441054241560
 11     93 -1.868080148990981150
 11    100 -1.853761460474161530
 11    101 -1.849920890504228130
 11    102 -1.843795221773942920
 11    103 -1.838682168652191830
 11    106 -1.825696028265308230
 11    107 -1.819821501761180350
 11    108 -1.811769417172880500
 11    109 -1.808205447658229440
 11    110 -1.796054807927162150
 11    147 -1.732006272869656130
 11    150 -1.695239312097040780
 11    151 -1.684517123596237970
 11    154 -1.663112608365032910
 11    155 -1.648713821405736690
 11    166 -1.604313501059346050
 11    167 -1.586804684708466700
 11    170 -1.563629631087201180
 11    171 -1.547903761803955020
 12      1 -1.999999117587260820
 12      2 -1.999992058194425320
 12      3 -1.999977939093294230
 12      4 -1.999956758546406900
 12      5 -1.999928520516907940
 12      6 -1.999893213728352300
 12      7 -1.999850842236313150
 12      8 -1.999801372159398660
 12      9 -1.999744977573602180
 12     10 -1.999681361196536870
 12     11 -1.999610705772966920
 12     12 -1.999532931591664470
 12     13 -1.999448178159224800
 12     14 -1.999356173857820970
 12     15 -1.999257007353280670
 12     16 -1.999149746318768050
 12     17 -1.999040172549457130
 12     18 -1.998918689425355610
 12     19 -1.998791118960928310
 12     20 -1.998656364602012690
 12     21 -1.998515059138383320
 12     22 -1.998366020382166820
 12     23 -1.998209966745463170
 12     24 -1.998045797619839560
 12     25 -1.997878407120788970
 12     26 -1.997699713581369300
 12     27 -1.997514661455194640
 12     28 -1.997321668110368990
 12     29 -1.997122425527586520
 12     30 -1.996912951848569980
 12     31 -1.996692284798253200
 12     32 -1.996379698285911190
 12     34 -1.996049041875495070
 12     35 -1.995799524491821550
 12     36 -1.995546208217139120
 12     37 -1.995290333633020690
 12     38 -1.995024299424194510
 12     39 -1.994752157724171150
 12     40 -1.994468338311266000
 12     41 -1.994196280539621360
 12     42 -1.993897700834003610
 12     43 -1.993596318489312970
 12     44 -1.993285559762791820
 12     45 -1.992973069476001450
 12     46 -1.992645724083767440
 12     47 -1.992309541878952950
 12     48 -1.991929121793397660
 12     49 -1.991700418739953850
 12     50 -1.991304294293602250
 12     51 -1.990937061962790200
 12     52 -1.990561687511709180
 12     53 -1.990189291729953400
 12     54 -1.989797914696203210
 12     55 -1.989400474495348860
 12     56 -1.988979896182892350
 12     57 -1.988605079892900020
 12     58 -1.988161256617442870
 12     59 -1.987715995936635080
 12     60 -1.987243879034155150
 12     61 -1.986752494228893930
 12     62 -1.986136191235151480
 12     67 -1.984753209551034390
 12     68 -1.984088702632017470
 12     69 -1.983540841872044280
 12     70 -1.982988615349141780
 12     71 -1.982449683309683530
 12     72 -1.981880085194780060
 12     73 -1.981431958985322020
 12     74 -1.980853663192828480
 12     75 -1.980300030250933620
 12     76 -1.979729378401139660
 12     77 -1.979183607438254600
 12     78 -1.978591171694646240
 12     79 -1.977985134233276210
 12     82 -1.976364477321859740
 12     83 -1.975726245926107480
 12     84 -1.975081487961333710
 12     85 -1.974479154356912780
 12     86 -1.973821883630731810
 12     87 -1.973168645674608590
 12     88 -1.972443394067073310
 12     89 -1.971956620639514910
 12     90 -1.971207317826686790
 12     91 -1.970506316020478710
 12     92 -1.969766673874645700
 12     93 -1.969063069240782970
 12     94 -1.968223161521319060
 12     95 -1.966808803425221040
 12     99 -1.965318943530410270
 12    100 -1.964412302186846800
 12    101 -1.963641270444242080
 12    102 -1.962790403216217370
 12    103 -1.961962210760019850
 12    104 -1.961002493823277540
 12    105 -1.960517451508275110
 12    106 -1.959533985762773850
 12    107 -1.958661628575311190
 12    108 -1.957738162895568380
 12    109 -1.956906866402774140
 12    110 -1.955921061804021570
 12    111 -1.954885643528039000
 12    114 -1.952493902282131290
 12    115 -1.951328308699483840
 12    116 -1.950113621874738610
 12    117 -1.949020027566269450
 12    118 -1.947616978282750130
 12    119 -1.946040258941837180
 12    120 -1.942519046352060340
 12    138 -1.936323613582675850
 12    139 -1.934544936920119570
 12    140 -1.932880761211511300
 12    141 -1.931619426517274190
 12    142 -1.930068671898056470
 12    143 -1.928487858679416940
 12    146 -1.925845936126932800
 12    147 -1.924314273608037780
 12    148 -1.922842861534029360
 12    149 -1.921733096087524110
 12    150 -1.920300759000663660
 12    151 -1.918955506209422470
 12    154 -1.915201572806543990
 12    155 -1.913757361466214350
 12    156 -1.912103324745894690
 12    157 -1.910742135737493880
 12    158 -1.907397618358110370
 12    164 -1.903839831363751100
 12    165 -1.902437049527024580
 12    166 -1.900627919859425650
 12    167 -1.899025573524404280
 12    170 -1.894811910350530710
 12    171 -1.893205684645489570
 12    172 -1.891398749834893900
 12    173 -1.890145185112852020
 12    174 -1.888167413897888940
 12    175 -1.885836225640821480
 12    178 -1.883801191013467910
 12    179 -1.881338223859112010
 12    180 -1.879089532912819080
 12    181 -1.877675388360729820
 12    182 -1.875374111087519000
 12    183 -1.873180865043625740
 12    186 -1.865723323816962500
 12    199 -1.856438079483190820
 12    202 -1.848042511645563640
 12    203 -1.845283918954318180
 12    204 -1.842107555871598930
 12    205 -1.840467028507122740
 12    206 -1.836970543993694430
 12    211 -1.827586466122061330
 12    212 -1.823606190692988170
 12    213 -1.821915822765622860
 12    214 -1.817969082849710430
 12    215 -1.814483842175301100
 12    218 -1.804949143729163450
 12    219 -1.799753675058546030
 12    220 -1.789175045986018750
 12    221 -1.778266821111081960
 12    294 -1.725978693774019480
 12    295 -1.717972319411030950
 12    298 -1.704840650473635820
 12    299 -1.698845700782579910
 12    302 -1.678767891298070120
 12    307 -1.669642176971863640
 12    310 -1.641278502145420340
 12    331 -1.612971248577386260
 12    342 -1.541094106491382820
 12    343 -1.530056455961480150
 12    346 -1.512452670794389080
 12    347 -1.480925450162162270
 12    359 -1.416977731250212230
 13      1 -1.999999779397058820
 13      2 -1.999998014567262920
 13      3 -1.999994484884841200
 13      4 -1.999989190234989400
 13      5 -1.999982130856013370
 13      6 -1.999973306030850830
 13      7 -1.999962715997427380
 13      8 -1.999950358622764070
 13      9 -1.999936244749900350
 13     10 -1.999920355797937180
 13     11 -1.999902703145052300
 13     12 -1.999883281786830700
 13     13 -1.999862100392188940
 13     14 -1.999839141984026040
 13     15 -1.999814412072751620
 13     16 -1.999787853668707650
 13     17 -1.999759822287990670
 13     18 -1.999729726986660350
 13     19 -1.999697925778814780
 13     20 -1.999664351452618790
 13     21 -1.999629043325972380
 13     22 -1.999591927797102650
 13     23 -1.999553049495826010
 13     24 -1.999512340492577180
 13     25 -1.999470102641411210
 13     26 -1.999425837033743530
 13     27 -1.999379848633972050
 13     28 -1.999332039942962510
 13     29 -1.999282515332690260
 13     30 -1.999231030875014680
 13     31 -1.999177539673828520
 13     32 -1.999120129219865650
 13     33 -1.999071123104258280
 13     34 -1.999010155601063610
 13     35 -1.998949560665576310
 13     36 -1.998887385802144270
 13     37 -1.998823719285646910
 13     38 -1.998758095004111650
 13     39 -1.998690762171753370
 13     40 -1.998621384712255170
 13     41 -1.998551378625902050
 13     42 -1.998478427148903620
 13     43 -1.998403963335860260
 13     44 -1.998327590466323910
 13     45 -1.998249774943241320
 13     46 -1.998169716662974620
 13     47 -1.998087787126349670
 13     48 -1.998002281800938210
 13     49 -1.997923284282567990
 13     50 -1.997834145816585540
 13     51 -1.997744971336148670
 13     52 -1.997653960242822880
 13     53 -1.997561783969082660
 13     54 -1.997467123465330480
 13     55 -1.997370755734261560
 13     56 -1.997271706916242310
 13     57 -1.997173904259916700
 13     58 -1.997070795451303500
 13     59 -1.996966242723546650
 13     60 -1.996858879449535870
 13     61 -1.996749306397858200
 13     62 -1.996633602482708120
 13     63 -1.996503976487468170
 13     66 -1.996249586645907680
 13     67 -1.996112735562520350
 13     68 -1.995986053390446330
 13     69 -1.995862298918904640
 13     70 -1.995736651119407800
 13     71 -1.995610300564670430
 13     72 -1.995480902211787300
 13     73 -1.995356858817844030
 13     74 -1.995224212280947220
 13     75 -1.995091510137129610
 13     76 -1.994956451454225050
 13     77 -1.994821486063741190
 13     78 -1.994682438227252630
 13     79 -1.994541298568581160
 13     80 -1.994388919368511080
 13     81 -1.994277084474347430
 13     82 -1.994121004548257950
 13     83 -1.993972531591739310
 13     84 -1.993822261456267240
 13     85 -1.993673063820117630
 13     86 -1.993519332990714400
 13     87 -1.993364464708878100
 13     88 -1.993204581704255110
 13     89 -1.993055583611996970
 13     90 -1.992891588058554200
 13     91 -1.992728508853559510
 13     92 -1.992561950624025510
 13     93 -1.992396002267897220
 13     94 -1.992221924957425350
 13     95 -1.992038422454623780
 13     98 -1.991588651436407940
 13     99 -1.991397367403519550
 13    100 -1.991211276846009670
 13    101 -1.991030385326110740
 13    102 -1.990843802348540540
 13    103 -1.990657006716107380
 13    104 -1.990463163290922980
 13    105 -1.990289330253915720
 13    106 -1.990091439211542080
 13    107 -1.989896712673324520
 13    108 -1.989697969824023740
 13    109 -1.989502567905885850
 13    110 -1.989297971157129010
 13    111 -1.989090080172714770
 13    112 -1.988843594433844470
 13    113 -1.988743533046821600
 13    114 -1.988491280630593060
 13    115 -1.988271912766547740
 13    116 -1.988049247424621930
 13    117 -1.987831001341904130
 13    118 -1.987600353036893210
 13    119 -1.987366010037147550
 13    120 -1.987114420002861210
 13    121 -1.986892000177792390
 13    122 -1.986612617967636560
 13    123 -1.986311940477874130
 13    124 -1.985919339165349980
 13    133 -1.984979711741364010
 13    134 -1.984566953715764840
 13    135 -1.984242709478445480
 13    136 -1.983931742354021170
 13    137 -1.983690743848291260
 13    138 -1.983399555928720700
 13    139 -1.983125957249840210
 13    140 -1.982850299322924640
 13    141 -1.982588461724877370
 13    142 -1.982311383418081680
 13    143 -1.982032257410464090
 13    146 -1.981278362488297320
 13    147 -1.980995003176886390
 13    148 -1.980711159871871300
 13    149 -1.980443082412393760
 13    150 -1.980157965190628880
 13    151 -1.979875529205254370
 13    152 -1.979572646383293700
 13    153 -1.979342288121985900
 13    154 -1.979034142791775490
 13    155 -1.978741138060588350
 13    156 -1.978438008832349510
 13    157 -1.978146473271400110
 13    158 -1.977819189687716740
 13    159 -1.977429866576216250
 13    162 -1.976933792791600370
 13    163 -1.976536329679920850
 13    164 -1.976195819946017180
 13    165 -1.975889954061085450
 13    166 -1.975564902982367480
 13    167 -1.975246651042623630
 13    168 -1.974901395935832960
 13    169 -1.974660509384451990
 13    170 -1.974311879376944280
 13    171 -1.973987492860424630
 13    172 -1.973653152767076860
 13    173 -1.973340807516330430
 13    174 -1.972996804631849620
 13    175 -1.972646446628845460
 13    178 -1.971749779050545060
 13    179 -1.971387719952259770
 13    180 -1.971024466023662080
 13    181 -1.970690905077556960
 13    182 -1.970323349153749290
 13    183 -1.969959340032184960
 13    184 -1.969549385121737370
 13    185 -1.969288214958784310
 13    186 -1.968856705812902680
 13    187 -1.968445358953126280
 13    188 -1.967982056263112120
 13    189 -1.967459948447780180
 13    196 -1.966112673852083820
 13    197 -1.965573546660818290
 13    198 -1.965082296652303900
 13    199 -1.964639125688107330
 13    200 -1.964155514102714490
 13    201 -1.963894361986566830
 13    202 -1.963421086839842490
 13    203 -1.963003753315637050
 13    204 -1.962572166902528510
 13    205 -1.962184348857040730
 13    206 -1.961741443062427960
 13    207 -1.961288784271196030
 13    210 -1.960227346566223470
 13    211 -1.959763260380314710
 13    212 -1.959301047545957320
 13    213 -1.958895059188797130
 13    214 -1.958432274613339490
 13    215 -1.957980614374257190
 13    216 -1.957446035104258440
 13    217 -1.957204450588352620
 13    218 -1.956655054242284760
 13    219 -1.956173541130666800
 13    220 -1.955656893396317580
 13    221 -1.955182038301438880
 13    222 -1.954564688867107360
 13    227 -1.952838372356932960
 13    228 -1.952167769491066290
 13    229 -1.951636609615316180
 13    230 -1.951027748059039160
 13    231 -1.950437006069502970
 13    232 -1.949693257414629020
 13    233 -1.949457312249734050
 13    234 -1.948667769124337720
 13    235 -1.947986099526642220
 13    236 -1.947220298252152950
 13    237 -1.946509125078109440
 13    238 -1.945538362441865100
 13    239 -1.944287944810346280
 13    274 -1.938260257511659750
 13    275 -1.936884606921352580
 13    276 -1.935790867387698630
 13    277 -1.935007886149670170
 13    278 -1.934113362608295730
 13    279 -1.933311861224671770
 13    282 -1.931205915440248190
 13    283 -1.930460477500059410
 13    284 -1.929653057166209850
 13    285 -1.928974106575291940
 13    286 -1.927901860177768390
 13    291 -1.926424724060414610
 13    292 -1.925367563060475990
 13    293 -1.924716597963723500
 13    294 -1.923938657990586440
 13    295 -1.923234355081571430
 13    298 -1.921346486271202680
 13    299 -1.920660837085426220
 13    300 -1.919921059930409490
 13    301 -1.919347791451423580
 13    302 -1.918570071017347720
 13    303 -1.917738122089322460
 13    306 -1.916460480737417940
 13    307 -1.915605571578263260
 13    308 -1.914783551436252340
 13    309 -1.914176388545304330
 13    310 -1.913354783255979230
 13    311 -1.912569773785826680
 13    314 -1.910170723617192530
 13    315 -1.908931826214812890
 13    326 -1.905725916148711160
 13    327 -1.904445920013786190
 13    330 -1.901926250252122750
 13    331 -1.901073297570601080
 13    332 -1.900155142848305620
 13    333 -1.899508494661992780
 13    334 -1.898556818390603400
 13    335 -1.897507583789435760
 13    338 -1.896337282007117960
 13    339 -1.895284527237429950
 13    340 -1.894321987246244820
 13    341 -1.893684626800101830
 13    342 -1.892757718194488580
 13    343 -1.891910190181937590
 13    346 -1.889609554042126680
 13    347 -1.888684772079146760
 13    348 -1.887578010914632450
 13    349 -1.886728606088137900
 13    356 -1.882869577588283460
 13    357 -1.881982841275756750
 13    358 -1.880765351482615140
 13    359 -1.879722423783904770
 13    362 -1.877031185176452370
 13    363 -1.875962656797656920
 13    364 -1.874716784041837120
 13    365 -1.873903882652548330
 13    366 -1.872461845002545990
 13    367 -1.870512163360348920
 13    370 -1.869504434719225040
 13    371 -1.866997262675337630
 13    372 -1.863875372522171900
 13    397 -1.858436592603852310
 13    398 -1.855016237203271160
 13    403 -1.848961758462986960
 13    404 -1.847086917881278570
 13    405 -1.846176964428325160
 13    406 -1.844497191069899850
 13    407 -1.843066678796390480
 13    410 -1.839465930747930130
 13    411 -1.837900071937871850
 13    412 -1.835787473973298110
 13    413 -1.834413111865540070
 13    420 -1.830263987454646830
 13    421 -1.828873568345840410
 13    422 -1.826563647163177340
 13    423 -1.824810174588801420
 13    426 -1.820706444192080710
 13    427 -1.818963820809965470
 13    428 -1.816769370104764200
 13    429 -1.815813973665414540
 13    430 -1.813204541544214450
 13    435 -1.806558617470037880
 13    436 -1.803064753925804300
 13    437 -1.801804974208399730
 13    438 -1.797872311946276710
 13    439 -1.793843439544230650
 13    586 -1.735743215639539130
 13    587 -1.729110547534052670
 13    590 -1.714755776843017460
 13    595 -1.707699703878214580
 13    598 -1.696833613455780920
 13    599 -1.693483525793746680
 13    602 -1.686614878789848990
 13    603 -1.682371529705357990
 13    614 -1.665615273358813720
 13    615 -1.660520098118306540
 13    618 -1.651601823940944280
 13    619 -1.645846421297178480
 13    662 -1.607652793309694670
 13    663 -1.600760170367417400
 13    666 -1.590604970929252350
 13    667 -1.582769344968892910
 13    678 -1.567637178918668210
 13    679 -1.559812946578950940
 13    682 -1.551071900191275510
 13    683 -1.545201781692656630
 14      1 -1.999999944849281450
 14      2 -1.999999503643104930
 14      3 -1.999998621229130370
 14      4 -1.999997297599793480
 14      5 -1.999995532769403620
 14      6 -1.999993326692368880
 14      7 -1.999990679382586930
 14      8 -1.999987590705632880
 14      9 -1.999984061337587940
 14     10 -1.999980090115991300
 14     11 -1.999975677749973990
 14     12 -1.999970823924961540
 14     13 -1.999965529180348800
 14     14 -1.999959792453355320
 14     15 -1.999953614085991390
 14     16 -1.999946990534007550
 14     17 -1.999939943924431430
 14     18 -1.999932437458235810
 14     19 -1.999924493418017710
 14     20 -1.999916107620813270
 14     21 -1.999907282517294840
 14     22 -1.999898013509485100
 14     23 -1.999888303379111940
 14     24 -1.999878147891296040
 14     25 -1.999867565843136560
 14     26 -1.999856526150501010
 14     27 -1.999845047803984050
 14     28 -1.999833124729209780
 14     29 -1.999820763422679580
 14     30 -1.999807948714237550
 14     31 -1.999794677858812310
 14     32 -1.999780842847123750
 14     33 -1.999767164702024560
 14     34 -1.999752445371167900
 14     35 -1.999737406522118410
 14     36 -1.999721937658352670
 14     37 -1.999706044438691340
 14     38 -1.999689697875459490
 14     39 -1.999672913470118910
 14     40 -1.999655670402655080
 14     41 -1.999638056390800720
 14     42 -1.999619927841466700
 14     43 -1.999601373530389960
 14     44 -1.999582368881836020
 14     45 -1.999562942847550910
 14     46 -1.999543045753531940
 14     47 -1.999522700723505550
 14     48 -1.999501806722464670
 14     49 -1.999480969823647180
 14     50 -1.999459186545477810
 14     51 -1.999437064276617060
 14     52 -1.999414496074664990
 14     53 -1.999391523501541370
 14     54 -1.999368064985777370
 14     55 -1.999344168581775340
 14     56 -1.999319774781949710
 14     57 -1.999295123478913310
 14     58 -1.999269814269226940
 14     59 -1.999244083216270320
 14     60 -1.999217847912204850
 14     61 -1.999191146830591360
 14     62 -1.999163756894241300
 14     63 -1.999135363374085880
 14     64 -1.999095903510509200
 14     66 -1.999055332805167790
 14     67 -1.999025162580165360
 14     68 -1.998995098961158360
 14     69 -1.998964860960704480
 14     70 -1.998934170273330620
 14     71 -1.998903101562350830
 14     72 -1.998871513725033070
 14     73 -1.998839916326486220
 14     74 -1.998807462073474790
 14     75 -1.998774669251661110
 14     76 -1.998741398363051330
 14     77 -1.998707799738548180
 14     78 -1.998673617223986430
 14     79 -1.998638973746260830
 14     80 -1.998603382752777010
 14     81 -1.998569715724412030
 14     82 -1.998533230577223080
 14     83 -1.998496802935837600
 14     84 -1.998459930744523730
 14     85 -1.998422790073559700
 14     86 -1.998385038298978660
 14     87 -1.998346882957913300
 14     88 -1.998308092687099040
 14     89 -1.998269617111005710
 14     90 -1.998229907509096090
 14     91 -1.998189914285069140
 14     92 -1.998149375932539040
 14     93 -1.998108539370637510
 14     94 -1.998066884714488490
 14     95 -1.998024389278545940
 14     96 -1.997977043640656530
 14     97 -1.997948863103026750
 14     98 -1.997900608363868160
 14     99 -1.997856300542907740
 14    100 -1.997811907264013320
 14    101 -1.997767482431589890
 14    102 -1.997722379513346120
 14    103 -1.997676927241894690
 14    104 -1.997630728077940530
 14    105 -1.997585359115732280
 14    106 -1.997538244798284530
 14    107 -1.997490971877406800
 14    108 -1.997443123143856220
 14    109 -1.997395136134830840
 14    110 -1.997346266932665280
 14    111 -1.997296871794211120
 14    112 -1.997245528136246670
 14    113 -1.997200462273753940
 14    114 -1.997148105818586370
 14    115 -1.997096688087975180
 14    116 -1.997044742189386970
 14    117 -1.996992715610057080
 14    118 -1.996939652351235800
 14    119 -1.996886062241108440
 14    120 -1.996831255533841820
 14    121 -1.996777641016509220
 14    122 -1.996720914133284320
 14    123 -1.996663246068795730
 14    124 -1.996603192104159820
 14    125 -1.996539537312301810
 14    126 -1.996462674248760210
 14    131 -1.996292143926352460
 14    132 -1.996212531522951240
 14    133 -1.996145325101204480
 14    134 -1.996080692373588950
 14    135 -1.996017565957715780
 14    136 -1.995954257501753440
 14    137 -1.995894068931964160
 14    138 -1.995830851919679840
 14    139 -1.995768165743606080
 14    140 -1.995704991152231810
 14    141 -1.995642252722101260
 14    142 -1.995578287609322520
 14    143 -1.995513871388373990
 14    144 -1.995445767916989500
 14    145 -1.995392299257733450
 14    146 -1.995323378469362990
 14    147 -1.995257345947944880
 14    148 -1.995190926464489710
 14    149 -1.995125084021620230
 14    150 -1.995057906416177430
 14    151 -1.994990544161405160
 14    152 -1.994921746133318940
 14    153 -1.994856560298372200
 14    154 -1.994786774977852140
 14    155 -1.994717435004807330
 14    156 -1.994647179616772460
 14    157 -1.994577248378290860
 14    158 -1.994505055419295510
 14    159 -1.994430419658113530
 14    162 -1.994235003616787730
 14    163 -1.994158529244607570
 14    164 -1.994083522473660040
 14    165 -1.994010021732086940
 14    166 -1.993935082852639800
 14    167 -1.993860180902437620
 14    168 -1.993783560325755170
 14    169 -1.993712094299168260
 14    170 -1.993634594977357210
 14    171 -1.993557970338126800
 14    172 -1.993480437761401840
 14    173 -1.993403810956061590
 14    174 -1.993325049955261420
 14    175 -1.993245641003048570
 14    176 -1.993159082573497660
 14    177 -1.993101467525295000
 14    178 -1.993013880227481870
 14    179 -1.992932430988947880
 14    180 -1.992850527750188290
 14    181 -1.992769922103547940
 14    182 -1.992687095019985040
 14    183 -1.992604126628503580
 14    184 -1.992518666064715140
 14    185 -1.992439940112752000
 14    186 -1.992352716728743060
 14    187 -1.992266069426295370
 14    188 -1.992177028979100050
 14    189 -1.992086871630443480
 14    190 -1.991987100356510650
 14    191 -1.991816222142209720
 14    195 -1.991641342006020950
 14    196 -1.991538558168540090
 14    197 -1.991444655368957320
 14    198 -1.991350600485734500
 14    199 -1.991258020463511620
 14    200 -1.991163341972685700
 14    201 -1.991078417551542380
 14    202 -1.990983494116391440
 14    203 -1.990890624091869150
 14    204 -1.990796646113679650
 14    205 -1.990704630563102230
 14    206 -1.990609364305899080
 14    207 -1.990513370796075550
 14    208 -1.990404117955717020
 14    209 -1.990348756176104130
 14    210 -1.990238485301084010
 14    211 -1.990140488550730060
 14    212 -1.990042122316184500
 14    213 -1.989946315374884240
 14    214 -1.989847220635101950
 14    215 -1.989748355499357750
 14    216 -1.989645857824970860
 14    217 -1.989555212741355620
 14    218 -1.989451284336389730
 14    219 -1.989349537471854780
 14    220 -1.989245807029620550
 14    221 -1.989143770846709010
 14    222 -1.989035662292664620
 14    223 -1.988920183078533340
 14    226 -1.988666040040855120
 14    227 -1.988547708101623780
 14    228 -1.988435164793583690
 14    229 -1.988327635258175460
 14    230 -1.988216433767627570
 14    231 -1.988105783451232400
 14    232 -1.987990426842512270
 14    233 -1.987890575400184920
 14    234 -1.987773204599568100
 14    235 -1.987658593988944070
 14    236 -1.987541335597084520
 14    237 -1.987426547138461620
 14    238 -1.987305142387210580
 14    239 -1.987181104821226900
 14    240 -1.987025149194848090
 14    241 -1.986983729397838340
 14    242 -1.986821150340011950
 14    243 -1.986683462728355920
 14    244 -1.986539600871503150
 14    245 -1.986393117807894820
 14    246 -1.986226758767011610
 14    247 -1.986036335555756500
 14    248 -1.985762196151882600
 14    265 -1.985141994861989690
 14    266 -1.984857896047200490
 14    267 -1.984657594504809610
 14    268 -1.984479913248899030
 14    269 -1.984322457710670040
 14    270 -1.984164914165931120
 14    271 -1.984012208098155900
 14    274 -1.983613179119843630
 14    275 -1.983470180886899160
 14    276 -1.983328869471261360
 14    277 -1.983195799089393710
 14    278 -1.983056850461228870
 14    279 -1.982920211821635480
 14    280 -1.982776561164042170
 14    281 -1.982662308741334580
 14    282 -1.982518354574480820
 14    283 -1.982381068853094880
 14    284 -1.982240686302687610
 14    285 -1.982105415642333080
 14    286 -1.981957706051399750
 14    287 -1.981791634529150790
 14    290 -1.981520892521647970
 14    291 -1.981353719865481040
 14    292 -1.981204199615362240
 14    293 -1.981067111914470940
 14    294 -1.980923819809116970
 14    295 -1.980783300247901020
 14    296 -1.980634445224090600
 14    297 -1.980519949849240920
 14    298 -1.980370692614224040
 14    299 -1.980229534462502270
 14    300 -1.980085484671117710
 14    301 -1.979948861801408550
 14    302 -1.979802394391235180
 14    303 -1.979654413074846510
 14    306 -1.979259695835952980
 14    307 -1.979109140592709300
 14    308 -1.978958507266460100
 14    309 -1.978817058408266850
 14    310 -1.978665776914326280
 14    311 -1.978515886085850840
 14    312 -1.978353919699903470
 14    313 -1.978232489016609860
 14    314 -1.978065255503476880
 14    315 -1.977903834339121230
 14    316 -1.977730393097605550
 14    317 -1.977548904934786590
 14    318 -1.977185565418327380
 14    324 -1.976812905294283720
 14    325 -1.976627791323942480
 14    326 -1.976448809360218180
 14    327 -1.976281004652376570
 14    328 -1.976104404744912110
 14    329 -1.975980256794389070
 14    330 -1.975806734683449640
 14    331 -1.975646223694345990
 14    332 -1.975482484741425350
 14    333 -1.975329796125692170
 14    334 -1.975163927232344120
 14    335 -1.974996408015570680
 14    338 -1.974564953021598630
 14    339 -1.974395797671780800
 14    340 -1.974227247384884100
 14    341 -1.974071948194395880
 14    342 -1.973904046336329350
 14    343 -1.973739096662368280
 14    344 -1.973558842819211900
 14    345 -1.973435955493763920
 14    346 -1.973253429339273910
 14    347 -1.973083819431326410
 14    348 -1.972907669794066690
 14    349 -1.972740885252284680
 14    350 -1.972548771267590000
 14    351 -1.972301936925606800
 14    354 -1.972099362170400950
 14    355 -1.971849590814444630
 14    356 -1.971652687000830540
 14    357 -1.971480701921515690
 14    358 -1.971296544419418460
 14    359 -1.971117652479066670
 14    360 -1.970921211565174620
 14    361 -1.970794621971850520
 14    362 -1.970596954671429170
 14    363 -1.970415918780043580
 14    364 -1.970228863824534350
 14    365 -1.970055888438403040
 14    366 -1.969863012621806620
 14    367 -1.969666038292439270
 14    370 -1.969168260435901080
 14    371 -1.968960768736546970
 14    372 -1.968750436405351270
 14    373 -1.968555698193588620
 14    374 -1.968334498588442700
 14    375 -1.968107571123952230
 14    376 -1.967832867918118720
 14    377 -1.967647690502132290
 14    378 -1.967250302569876160
 14    391 -1.966327483267411280
 14    392 -1.965916974565233180
 14    393 -1.965731729445262340
 14    394 -1.965441109130642520
 14    395 -1.965200779925640150
 14    396 -1.964963527281978860
 14    397 -1.964755203777971010
 14    398 -1.964524999168059580
 14    399 -1.964294986486702570
 14    402 -1.963756404744781960
 14    403 -1.963531482034853580
 14    404 -1.963309690957174840
 14    405 -1.963113928802032780
 14    406 -1.962895772273366300
 14    407 -1.962684116339055380
 14    408 -1.962442338269747820
 14    409 -1.962315117157472020
 14    410 -1.962070768871570950
 14    411 -1.961853750746750800
 14    412 -1.961625298391762480
 14    413 -1.961414768600139690
 14    414 -1.961155729140230970
 14    419 -1.960362576892650700
 14    420 -1.960098595710888030
 14    421 -1.959883348585628130
 14    422 -1.959646765602406240
 14    423 -1.959420616730964610
 14    424 -1.959159955121737950
 14    425 -1.959036328411693490
 14    426 -1.958775220991762310
 14    427 -1.958548729659928240
 14    428 -1.958312661205590150
 14    429 -1.958102847973194800
 14    430 -1.957859221739880780
 14    431 -1.957609548843569450
 14    434 -1.957038610136172340
 14    435 -1.956781755899286050
 14    436 -1.956526115865375300
 14    437 -1.956303255778516020
 14    438 -1.956045969222128440
 14    439 -1.955793751149312670
 14    440 -1.955488288061836390
 14    441 -1.955358061750299000
 14    442 -1.955032085366485200
 14    443 -1.954733314433029820
 14    444 -1.954370332478722000
 14    445 -1.953721580092951690
 14    453 -1.953043384373758520
 14    454 -1.952658282608317420
 14    455 -1.952334036753504130
 14    456 -1.951964326012690370
 14    457 -1.951836264420761380
 14    458 -1.951477286894205710
 14    459 -1.951180708612767180
 14    460 -1.950869812955405930
 14    461 -1.950599592086105170
 14    462 -1.950275353730205820
 14    463 -1.949938706994839430
 14    466 -1.949204652177764540
 14    467 -1.948845753736719580
 14    468 -1.948484676220402200
 14    469 -1.948174419648125040
 14    470 -1.947799993066469070
 14    471 -1.947428156873450630
 14    472 -1.946937734464085660
 14    473 -1.946809262989177820
 14    474 -1.946271044717636470
 14    475 -1.945801025445699330
 14    476 -1.945247329270462750
 14    477 -1.944696181861109370
 14    478 -1.943762692862965120
 14    547 -1.938847112257878880
 14    548 -1.937806631324786460
 14    549 -1.937210511380442490
 14    550 -1.936590753058155470
 14    551 -1.936064174381500320
 14    554 -1.934763697402604530
 14    555 -1.934332520496416430
 14    556 -1.933888228275309520
 14    557 -1.933534954375642650
 14    558 -1.933094662802479630
 14    559 -1.932644885868921040
 14    562 -1.931849249886687850
 14    563 -1.931413328765830210
 14    564 -1.930994608660057170
 14    565 -1.930668248022459400
 14    566 -1.930260432068765520
 14    567 -1.929872467752803650
 14    570 -1.928726788541386680
 14    571 -1.928228270711204060
 14    572 -1.927176104005788460
 14    582 -1.926101625716711440
 14    583 -1.925611186843377780
 14    586 -1.924503085674265740
 14    587 -1.924130557842427760
 14    588 -1.923738958659116820
 14    589 -1.923435908833199230
 14    590 -1.923037674828473760
 14    591 -1.922621489477265330
 14    594 -1.921952806061505450
 14    595 -1.921540481913382940
 14    596 -1.921148087292329940
 14    597 -1.920854842581835950
 14    598 -1.920475965247496840
 14    599 -1.920122169087242060
 14    602 -1.919141395318818190
 14    603 -1.918770144596616080
 14    604 -1.918353117342264020
 14    605 -1.918007604676204970
 14    606 -1.917374301497376950
 14    611 -1.916828878782212450
 14    612 -1.916184756793865740
 14    613 -1.915831448689605470
 14    614 -1.915396249458068550
 14    615 -1.915004982324275610
 14    618 -1.913954309703880600
 14    619 -1.913562879362455140
 14    620 -1.913132786424482530
 14    621 -1.912804166342478810
 14    622 -1.912337758520783850
 14    623 -1.911822218870022270
 14    626 -1.911055297867218850
 14    627 -1.910464418879767560
 14    628 -1.909849015228005420
 14    629 -1.909345459577653460
 14    630 -1.908434525478168420
 14    651 -1.906234307314068560
 14    652 -1.905298404786475180
 14    653 -1.904784362513578360
 14    654 -1.904135526180684780
 14    655 -1.903495214017661830
 14    658 -1.902752630726683060
 14    659 -1.902180756506843660
 14    660 -1.901666751088358250
 14    661 -1.901320834729774510
 14    662 -1.900842489513325490
 14    663 -1.900409101975750900
 14    666 -1.899250315608976960
 14    667 -1.898802251847459760
 14    668 -1.898284018241063630
 14    669 -1.897879451321189430
 14    676 -1.895963233924724060
 14    677 -1.895560027600515110
 14    678 -1.895036869306184830
 14    679 -1.894585133854304030
 14    682 -1.893425878535148140
 14    683 -1.892990381723943540
 14    684 -1.892506611814020010
 14    685 -1.892172131098194550
 14    686 -1.891655134596309550
 14    687 -1.891068343617213670
 14    690 -1.890483236770906820
 14    691 -1.889878819473058250
 14    692 -1.889327766965617570
 14    693 -1.888966618626104640
 14    694 -1.888418632276790950
 14    695 -1.887903316216598040
 14    698 -1.886293568921892030
 14    699 -1.884847358114919980
 14    711 -1.883328267558645300
 14    714 -1.881626755272862280
 14    715 -1.881062045058783690
 14    716 -1.880445559227508080
 14    717 -1.880050278256470840
 14    718 -1.879406752269899760
 14    719 -1.878649421753561980
 14    722 -1.878119160801547900
 14    723 -1.877353584959888590
 14    724 -1.876693598301199070
 14    725 -1.876293636361769810
 14    726 -1.875656817984735270
 14    727 -1.875080207662324120
 14    730 -1.873512343395894320
 14    731 -1.872846583477733140
 14    732 -1.872005422384874320
 14    733 -1.871373482409366460
 14    740 -1.868504491312580180
 14    741 -1.867681541115989320
 14    742 -1.866352991422473180
 14    743 -1.864997458512127290
 14    794 -1.857226000199673510
 14    795 -1.855744968593255980
 14    796 -1.854207799563460980
 14    797 -1.853271907817385930
 14    804 -1.850326268968556300
 14    805 -1.849570973433470140
 14    806 -1.848465562114005780
 14    807 -1.847619181345964200
 14    810 -1.845670962855900670
 14    811 -1.844912140274683340
 14    812 -1.844026981571453730
 14    813 -1.843561399228632500
 14    814 -1.842596031522865480
 14    819 -1.839962109329970890
 14    820 -1.838930348486507220
 14    821 -1.838434629476678050
 14    822 -1.837416474691728940
 14    823 -1.836485288494735740
 14    826 -1.832413646409658830
 14    842 -1.828112053649822730
 14    843 -1.827100348488180830
 14    844 -1.825952639510425610
 14    845 -1.825438925122554170
 14    846 -1.824224431130188570
 14    851 -1.821295869539552380
 14    852 -1.820068515079604780
 14    853 -1.819577286962882860
 14    854 -1.818436032590136700
 14    855 -1.817475296883476670
 14    858 -1.815051415323738370
 14    859 -1.813912507021792650
 14    860 -1.812219918731991830
 14    861 -1.811192888899089420
 14    868 -1.808814740120561550
 14    869 -1.807720863175156600
 14    870 -1.805682859549362850
 14    871 -1.804187671881200290
 14    874 -1.800605211123667990
 14    875 -1.798907876829344250
 14    876 -1.796498928278923010
 14    877 -1.795596041478110730
 14    878 -1.791959222729839520
 14   1171 -1.739717601451463260
 14   1174 -1.727337454527380830
 14   1175 -1.724573334524673260
 14   1178 -1.719324721366147410
 14   1179 -1.716649494320694670
 14   1190 -1.705985003375647170
 14   1191 -1.703701482841706200
 14   1194 -1.699819183456152310
 14   1195 -1.697957750767596830
 14   1198 -1.691791187875565450
 14   1203 -1.688485963674945080
 14   1206 -1.680548784886868490
 14   1207 -1.674512571992340340
 14   1227 -1.667700411924743470
 14   1230 -1.657710272497178540
 14   1235 -1.654607695995066950
 14   1238 -1.643386879903734840
 14   1239 -1.638450753506089530
 14   1322 -1.616138817876333490
 14   1323 -1.610591956500734480
 14   1334 -1.575583880548504000
 14   1366 -1.542775192277610740
 14   1367 -1.539018371902009570
 14   1370 -1.533141904231423680
 14   1371 -1.526188608447815360
 14   1382 -1.517498827477666100
 14   1383 -1.507456393419337000
 14   1386 -1.494808873464007780
 14   1431 -1.457680525957156930
 14   1434 -1.436411564771381880
15    1  -1.9999999862123214
15    2  -1.9999998759108646
15    3  -1.9999996553078370
15    4  -1.9999993244027419
15    5  -1.9999988831964370
15    6  -1.9999983316860241
15    7  -1.9999976698723114
15    8  -1.9999968977468248
15    9  -1.9999950226142833
15   10  -1.9999960153517302
15   11  -1.9999939195786911
15   12  -1.9999927062251734
15   13  -1.9999913825873044
15   14  -1.9999899485985244
15   15  -1.9999884042800535
15   16  -1.9999867494105252
15   17  -1.9999849853712743
15   18  -1.9999831098643579
15   19  -1.9999811242808065
15   20  -1.9999790283593020
15   21  -1.9999768222527283
15   22  -1.9999745056735727
15   23  -1.9999720787953770
15   24  -1.9999668945212412
15   25  -1.9999695413534386
15   26  -1.9999641363574199
15   27  -1.9999612680475185
15   28  -1.9999582892119732
15   29  -1.9999552002561281
15   30  -1.9999486889731040
15   31  -1.9999520002328282
15   32  -1.9999452598828638
15   33  -1.9999417573492966
15   34  -1.9999381075245966
15   35  -1.9999343548361763
15   36  -1.9999304925346626
15   37  -1.9999265209755102
15   38  -1.9999224383490952
15   39  -1.9999182456226583
15   40  -1.9999139414976181
15   41  -1.9999095314431723
15   42  -1.9999050065041870
15   43  -1.9999003722158313
15   44  -1.9998907727984596
15   45  -1.9998956270453463
15   46  -1.9998858063758074
15   47  -1.9998807292205045
15   48  -1.9998755350983013
15   49  -1.9998702615291153
15   50  -1.9998648463478643
15   51  -1.9998479595272383
15   52  -1.9998593271563554
15   53  -1.9998536973527015
15   54  -1.9998421085958566
15   55  -1.9998361475529465
15   56  -1.9998300727003961
15   57  -1.9998238989425550
15   58  -1.9998176013989324
15   59  -1.9998111947380779
15   60  -1.9997771038062719
15   61  -1.9998046738555277
15   62  -1.9997980411665455
15   63  -1.9997912830361366
15   64  -1.9997843816388838
15   65  -1.9997561442696492
15   66  -1.9997709866502882
15   67  -1.9997634877132517
15   68  -1.9997487225334099
15   69  -1.9997335799311162
15   70  -1.9997412067769649
15   71  -1.9997258466612557
15   72  -1.9997179982331859
15   73  -1.9997100662454734
15   74  -1.9997019981422817
15   75  -1.9996938260620192
15   76  -1.9996855413542101
15   77  -1.9996771533666269
15   78  -1.9996686461707847
15   79  -1.9996600274220275
15   80  -1.9996512677781950
15   81  -1.9996425420338435
15   82  -1.9996335609792559
15   83  -1.9996244996659620
15   84  -1.9996153277916449
15   85  -1.9996060563028366
15   86  -1.9995966639155185
15   87  -1.9995871635205751
15   88  -1.9995775408275684
15   89  -1.9995678544996665
15   90  -1.9995580088199141
15   91  -1.9995480624984270
15   92  -1.9995379993959470
15   93  -1.9995278348030421
15   94  -1.9995175366372091
15   95  -1.9995071042025663
15   96  -1.9994963463813391
15   97  -1.9994865135378130
15   98  -1.9994755333469738
15   99  -1.9994646565315561
15  100  -1.9994536905621596
15  101  -1.9994426394523803
15  102  -1.9994314633312207
15  103  -1.9994201825204885
15  104  -1.9994087726203318
15  105  -1.9993973304753971
15  106  -1.9993856978239339
15  107  -1.9993739721043520
15  108  -1.9993621277176106
15  109  -1.9993501916511771
15  110  -1.9993381180411074
15  111  -1.9993259289375995
15  112  -1.9993135421056480
15  113  -1.9993014418926853
15  114  -1.9992888263381332
15  115  -1.9992761799683356
15  116  -1.9992634179298763
15  117  -1.9992505676559584
15  118  -1.9992375707987191
15  119  -1.9992244586597296
15  120  -1.9992111901144027
15  121  -1.9991979093208223
15  122  -1.9991843603249924
15  123  -1.9991706752840324
15  124  -1.9991567774601673
15  125  -1.9991426261048184
15  126  -1.9991279139250164
15  127  -1.9991115428082833
15  128  -1.9990799039306182
15  129  -1.9990630884392688
15  130  -1.9990477075456823
15  131  -1.9990326715712876
15  132  -1.9990176594334144
15  133  -1.9990026394312168
15  134  -1.9989875202094840
15  135  -1.9989725020462807
15  136  -1.9989572177166881
15  137  -1.9989418807116559
15  138  -1.9989264300391680
15  139  -1.9989109223706669
15  140  -1.9988952561351536
15  141  -1.9988794789922171
15  142  -1.9988634129837215
15  143  -1.9988480983911792
15  144  -1.9988318154605247
15  145  -1.9988156056018052
15  146  -1.9987992883823460
15  147  -1.9987829231520429
15  148  -1.9987663926437467
15  149  -1.9987329719742666
15  150  -1.9987497674257284
15  151  -1.9987163112870190
15  152  -1.9986992885320627
15  153  -1.9986822085050158
15  154  -1.9986649891770591
15  155  -1.9986477061734904
15  156  -1.9986302031994263
15  157  -1.9986124793248481
15  158  -1.9985935086616697
15  159  -1.9985796736595127
15  160  -1.9985423090609098
15  161  -1.9985604792993228
15  162  -1.9985241331670551
15  163  -1.9985059639455618
15  164  -1.9984876234515410
15  165  -1.9984692015386676
15  166  -1.9984505931486862
15  167  -1.9984322104264638
15  168  -1.9984133813204019
15  169  -1.9983945200921376
15  170  -1.9983755199738984
15  171  -1.9983564914329648
15  172  -1.9983372493977927
15  173  -1.9983178850329066
15  174  -1.9982596810325288
15  175  -1.9982980681509988
15  176  -1.9982797277888644
15  177  -1.9982398579390519
15  178  -1.9982199230421867
15  179  -1.9981999829128927
15  180  -1.9981798246217048
15  181  -1.9981595741086480
15  182  -1.9981390931783047
15  183  -1.9981189239850428
15  184  -1.9980773658026778
15  185  -1.9980981703131264
15  186  -1.9980563405250715
15  187  -1.9980351779288745
15  188  -1.9980134573885964
15  189  -1.9979905641694815
15  190  -1.9979352003259239
15  191  -1.9979118535953653
15  192  -1.9978894478503868
15  193  -1.9978673875949067
15  194  -1.9978452206749744
15  195  -1.9978230511597299
15  196  -1.9978006753924251
15  197  -1.9977787836005303
15  198  -1.9977562237993092
15  199  -1.9977336974718296
15  200  -1.9977110206632660
15  201  -1.9976883771480654
15  202  -1.9976654551454918
15  203  -1.9976424071489600
15  204  -1.9976186725292189
15  205  -1.9975975005275615
15  206  -1.9975735367592977
15  207  -1.9975500323741311
15  208  -1.9975264203534997
15  209  -1.9975028764977714
15  210  -1.9974551582096476
15  211  -1.9974790526140316
15  212  -1.9974309714916130
15  213  -1.9974073825532728
15  214  -1.9973829425895107
15  215  -1.9973585403588388
15  216  -1.9973339379449067
15  217  -1.9973093507184132
15  218  -1.9972843333798853
15  219  -1.9972588788330274
15  220  -1.9972290962355614
15  221  -1.9972169890659670
15  222  -1.9971869531541082
15  223  -1.9971609937769839
15  224  -1.9971352113028886
15  225  -1.9971096251826812
15  226  -1.9970837435411264
15  227  -1.9970578094500391
15  228  -1.9970315338617406
15  229  -1.9970060291228557
15  230  -1.9969794728935097
15  231  -1.9969529812845492
15  232  -1.9969262604772577
15  233  -1.9968995972103527
15  234  -1.9968724904434729
15  235  -1.9968451713966431
15  236  -1.9968167119526470
15  237  -1.9967923608808882
15  238  -1.9967634295882575
15  239  -1.9966778983256723
15  240  -1.9967351564341054
15  241  -1.9967065709271139
15  242  -1.9966484841747338
15  243  -1.9966185343906167
15  244  -1.9965874512244088
15  245  -1.9965564269188973
15  246  -1.9965221635184702
15  247  -1.9964844704440430
15  248  -1.9964361139242781
15  249  -1.9962306867277446
15  250  -1.9963192499981817
15  251  -1.9962697467778170
15  252  -1.9961947751843645
15  253  -1.9961621041886750
15  254  -1.9961289149813546
15  255  -1.9960966873542014
15  256  -1.9960647412627148
15  257  -1.9960333861695261
15  258  -1.9960017912366730
15  259  -1.9959702636962797
15  260  -1.9959373945642056
15  261  -1.9959109270897939
15  262  -1.9958780718626261
15  263  -1.9958465878131961
15  264  -1.9958150877591345
15  265  -1.9957839539111648
15  266  -1.9957523950051546
15  267  -1.9957208749335140
15  268  -1.9956888934839687
15  269  -1.9956584230360432
15  270  -1.9956262470247541
15  271  -1.9955943356109793
15  272  -1.9955621619334476
15  273  -1.9955301938659809
15  274  -1.9954974622363724
15  275  -1.9954639341290332
15  276  -1.9953740047769364
15  277  -1.9953400702245090
15  278  -1.9953067188239504
15  279  -1.9952739613428478
15  280  -1.9952407602072875
15  281  -1.9952076308657083
15  282  -1.9951739727211311
15  283  -1.9951421106775769
15  284  -1.9951082583238897
15  285  -1.9950747503208470
15  286  -1.9950409896101942
15  287  -1.9950075740765261
15  288  -1.9949392729268347
15  289  -1.9949735040284511
15  290  -1.9949029380200975
15  291  -1.9948754607429702
15  292  -1.9948388790796878
15  293  -1.9947349544624033
15  294  -1.9948041573330606
15  295  -1.9947693355814147
15  296  -1.9946999252420357
15  297  -1.9946648915802752
15  298  -1.9946291500831599
15  299  -1.9945954455330717
15  300  -1.9945592517132296
15  301  -1.9945232689940346
15  302  -1.9944866392768730
15  303  -1.9944497594955581
15  304  -1.9944103860904618
15  305  -1.9943628595384433
15  306  -1.9943033459775006
15  307  -1.9942553584744442
15  308  -1.9942152796354440
15  309  -1.9941775048697741
15  310  -1.9941397009027100
15  311  -1.9941023235859405
15  312  -1.9940644160269785
15  313  -1.9940291357888580
15  314  -1.9939912122656107
15  315  -1.9939538552952485
15  316  -1.9939162284956358
15  317  -1.9938791410170467
15  318  -1.9938412222627113
15  319  -1.9938031431320253
15  320  -1.9937335922415560
15  321  -1.9937621450912735
15  322  -1.9936923732285663
15  323  -1.9936538576977068
15  324  -1.9936152714519713
15  325  -1.9935773485174044
15  326  -1.9935386255605452
15  327  -1.9934999836047422
15  328  -1.9934604909518239
15  329  -1.9934238694288695
15  330  -1.9933840771926048
15  331  -1.9933448288329021
15  332  -1.9933051382052729
15  333  -1.9932658815141582
15  334  -1.9932252498647323
15  335  -1.9931831231579160
15  336  -1.9930772655310729
15  337  -1.9930346281856357
15  338  -1.9929932121600740
15  339  -1.9929529663632677
15  340  -1.9929119668590589
15  341  -1.9928711632970961
15  342  -1.9928294406914475
15  343  -1.9927910988874362
15  344  -1.9927491374151542
15  345  -1.9927078723246159
15  346  -1.9926661965077570
15  347  -1.9926251985113212
15  348  -1.9925406309079774
15  349  -1.9925830458872513
15  350  -1.9924940391879589
15  351  -1.9924647295623426
15  352  -1.9924177024503458
15  353  -1.9923744139938862
15  354  -1.9923308990962982
15  355  -1.9922881130677508
15  356  -1.9922440021754082
15  357  -1.9921996723984909
15  358  -1.9921536704623404
15  359  -1.9921110524684482
15  360  -1.9920627977785699
15  361  -1.9920133534895312
15  362  -1.9919591127677336
15  363  -1.9918934504509580
15  364  -1.9914692032673007
15  365  -1.9917365317209792
15  366  -1.9916699296208318
15  367  -1.9916144311003128
15  368  -1.9915634990027564
15  369  -1.9915133755380954
15  370  -1.9914208308147068
15  371  -1.9913740214607416
15  372  -1.9912814791695237
15  373  -1.9913271196678746
15  374  -1.9912346236960425
15  375  -1.9911877020624293
15  376  -1.9911352885605702
15  377  -1.9911064967525058
15  378  -1.9910540149073330
15  379  -1.9910069718145398
15  380  -1.9909599431533263
15  381  -1.9909141800192534
15  382  -1.9908671546600363
15  383  -1.9908203795860400
15  384  -1.9907722360080324
15  385  -1.9907291557740749
15  386  -1.9906332953413937
15  387  -1.9906807024219135
15  388  -1.9905852298333186
15  389  -1.9905379984800218
15  390  -1.9904885029131345
15  391  -1.9904363936696825
15  392  -1.9903163202975327
15  393  -1.9902637073134355
15  394  -1.9902134310920960
15  395  -1.9901652421285889
15  396  -1.9901158802002210
15  397  -1.9900669454037636
15  398  -1.9900165490360511
15  399  -1.9899719627393992
15  400  -1.9899213699088885
15  401  -1.9898720695741494
15  402  -1.9898221986512343
15  403  -1.9897735727109571
15  404  -1.9897231576445074
15  405  -1.9896724433456234
15  406  -1.9895872416407583
15  407  -1.9896139622988231
15  408  -1.9895284035408434
15  409  -1.9893236973150650
15  410  -1.9894769813890023
15  411  -1.9894254640102749
15  412  -1.9893754550618914
15  413  -1.9892721135041456
15  414  -1.9892185544580205
15  415  -1.9891713885109925
15  416  -1.9891168387794358
15  417  -1.9890631313702882
15  418  -1.9890075988687557
15  419  -1.9889513160158416
15  420  -1.9888861603229397
15  421  -1.9887005651662997
15  422  -1.9886343019265640
15  423  -1.9885766531290283
15  424  -1.9885192727524930
15  425  -1.9884633790414477
15  426  -1.9883566736311742
15  427  -1.9884060455362389
15  428  -1.9882995702753619
15  429  -1.9882442977382040
15  430  -1.9881883588845846
15  431  -1.9881340871549553
15  432  -1.9880775086049134
15  433  -1.9880205413849239
15  434  -1.9879522187993948
15  435  -1.9879289726508309
15  436  -1.9878601440678554
15  437  -1.9878021789927851
15  438  -1.9877440603039946
15  439  -1.9876878860139704
15  440  -1.9876293997084902
15  441  -1.9875711358434245
15  442  -1.9875102870958510
15  443  -1.9874579716237297
15  444  -1.9873961133921751
15  445  -1.9872740375108588
15  446  -1.9873358058243495
15  447  -1.9872133737610671
15  448  -1.9871482760007877
15  449  -1.9870775636432527
15  450  -1.9869302868702519
15  451  -1.9868562934545355
15  452  -1.9867860839867919
15  453  -1.9867188063019068
15  454  -1.9866480609850419
15  455  -1.9865766677368353
15  456  -1.9865004164709410
15  457  -1.9864343024163555
15  458  -1.9863526673192500
15  459  -1.9862702041414781
15  460  -1.9861814092677257
15  461  -1.9860888028872383
15  462  -1.9859802961773181
15  463  -1.9858497759994294
15  464  -1.9855261058118514
15  465  -1.9850516805356759
15  466  -1.9849163902322764
15  467  -1.9848028755513747
15  468  -1.9847056668853693
15  469  -1.9846114156257793
15  470  -1.9845234105559246
15  471  -1.9844351712793482
15  472  -1.9843654158920621
15  473  -1.9842819788248338
15  474  -1.9842038873313068
15  475  -1.9841258073664596
15  476  -1.9840515532472409
15  477  -1.9839725183482468
15  478  -1.9838866384120717
15  479  -1.9837348515077777
15  480  -1.9836512605719663
15  481  -1.9835757719461098
15  482  -1.9835062945732014
15  483  -1.9834345895645065
15  484  -1.9833645398791946
15  485  -1.9832914183142751
15  486  -1.9832330458085572
15  487  -1.9831604751887484
15  488  -1.9830915878942108
15  489  -1.9830218168285656
15  490  -1.9829553807563431
15  491  -1.9828851952112487
15  492  -1.9828146995748226
15  493  -1.9826241230003052
15  494  -1.9825534850101545
15  495  -1.9824830337111874
15  496  -1.9824163473012075
15  497  -1.9823460560230268
15  498  -1.9822764996513351
15  499  -1.9822026827811476
15  500  -1.9821439942544148
15  501  -1.9820686025005156
15  502  -1.9819955479553002
15  503  -1.9819185020062218
15  504  -1.9818394229227838
15  505  -1.9817310252222706
15  506  -1.9815817081806608
15  507  -1.9814728461255717
15  508  -1.9813932927258586
15  509  -1.9813154831040081
15  510  -1.9811648505654287
15  511  -1.9812415621774080
15  512  -1.9811059890015161
15  513  -1.9810305742750236
15  514  -1.9809596206775970
15  515  -1.9808876772228530
15  516  -1.9808196079375586
15  517  -1.9807471642615189
15  518  -1.9806743221850287
15  519  -1.9804800059557013
15  520  -1.9804069701153924
15  521  -1.9803342091360492
15  522  -1.9802658909325273
15  523  -1.9801935282911238
15  524  -1.9801222210894993
15  525  -1.9800462818072144
15  526  -1.9799882710158720
15  527  -1.9799117719022312
15  528  -1.9798392962976459
15  529  -1.9797648621690527
15  530  -1.9796934683171441
15  531  -1.9796144962200213
15  532  -1.9795236536057055
15  533  -1.9793000758606114
15  534  -1.9793915625097478
15  535  -1.9792200713891712
15  536  -1.9791475013956057
15  537  -1.9790713372006210
15  538  -1.9789968369249471
15  539  -1.9789174908040763
15  540  -1.9788581539875052
15  541  -1.9787786010303119
15  542  -1.9787037670802212
15  543  -1.9786272581818714
15  544  -1.9785549355556962
15  545  -1.9784769281920809
15  546  -1.9783979433402947
15  547  -1.9781876593859657
15  548  -1.9781060891969851
15  549  -1.9780238790706333
15  550  -1.9779461189043364
15  551  -1.9778615104126831
15  552  -1.9776800181094703
15  553  -1.9777759238322172
15  554  -1.9776054154926164
15  555  -1.9774919763846377
15  556  -1.9773541804053278
15  557  -1.9770102453366980
15  558  -1.9768708359758749
15  559  -1.9767550323818723
15  560  -1.9766797345052034
15  561  -1.9765809108030590
15  562  -1.9764926395102249
15  563  -1.9764048828924556
15  564  -1.9763242785558490
15  565  -1.9762382186544856
15  566  -1.9761523630793094
15  567  -1.9759327573161996
15  568  -1.9758484195458139
15  569  -1.9757648282083142
15  570  -1.9756877714391408
15  571  -1.9753754602076108
15  572  -1.9756052279364484
15  573  -1.9755243703645018
15  574  -1.9754369934066489
15  575  -1.9752876104469255
15  576  -1.9752057393597249
15  577  -1.9751212586344267
15  578  -1.9750411523975364
15  579  -1.9749504043406603
15  580  -1.9748395733151640
15  581  -1.9747225157146806
15  582  -1.9746112652557666
15  583  -1.9745198219354474
15  584  -1.9744390162405252
15  585  -1.9743533990933331
15  586  -1.9742702478129188
15  587  -1.9741803892852532
15  588  -1.9741187735955514
15  589  -1.9740290102589491
15  590  -1.9739461588569951
15  591  -1.9738612776994928
15  592  -1.9737823577172886
15  593  -1.9736960535296928
15  594  -1.9736087800800604
15  595  -1.9733856637591940
15  596  -1.9732972800510753
15  597  -1.9732091648560299
15  598  -1.9731281174090638
15  599  -1.9729531625955967
15  600  -1.9730400047174377
15  601  -1.9728573916911094
15  602  -1.9727923989829150
15  603  -1.9726932363840908
15  604  -1.9725988317168393
15  605  -1.9724955556040971
15  606  -1.9723850084124033
15  607  -1.9720156230159045
15  608  -1.9719037699238726
15  609  -1.9717984907025843
15  610  -1.9717017758474316
15  611  -1.9715991678153346
15  612  -1.9715332865329374
15  613  -1.9714332605515565
15  614  -1.9713425404780771
15  615  -1.9712498625156190
15  616  -1.9711646863482473
15  617  -1.9710709472172938
15  618  -1.9709762615377067
15  619  -1.9707393725990352
15  620  -1.9706440899908528
15  621  -1.9705493914574832
15  622  -1.9704632952920709
15  623  -1.9703692160897468
15  624  -1.9702771024264460
15  625  -1.9701751108357093
15  626  -1.9701101436639503
15  627  -1.9700067907428493
15  628  -1.9699118638400790
15  629  -1.9697196231920178
15  630  -1.9698128202814928
15  631  -1.9696103249079804
15  632  -1.9694591034062081
15  633  -1.9692258242036262
15  634  -1.9693796205462242
15  635  -1.9691124006619340
15  636  -1.9690143399733209
15  637  -1.9689082009734205
15  638  -1.9688047730571934
15  639  -1.9686178342975291
15  640  -1.9686893249409534
15  641  -1.9684996406454738
15  642  -1.9683908511668555
15  643  -1.9682763760057918
15  644  -1.9681690174833262
15  645  -1.9680453567390552
15  646  -1.9679143797065037
15  647  -1.9675506702183791
15  648  -1.9673632108002235
15  649  -1.9671037591822318
15  650  -1.9664765032099913
15  651  -1.9662120348173482
15  652  -1.9660188957417730
15  653  -1.9656448714773682
15  654  -1.9655068617159948
15  655  -1.9653759307780041
15  656  -1.9652628412346902
15  657  -1.9651405600463916
15  658  -1.9650240921739748
15  659  -1.9648231660965867
15  660  -1.9648948830583806
15  661  -1.9646957744599518
15  662  -1.9645828329319357
15  663  -1.9644656625381707
15  664  -1.9643580127804201
15  665  -1.9642292020933649
15  666  -1.9631790095374644
15  667  -1.9638213517979777
15  668  -1.9636943798718569
15  669  -1.9635892688803835
15  670  -1.9634754056733785
15  671  -1.9633666475396587
15  672  -1.9632443268174007
15  673  -1.9630574644614949
15  674  -1.9629504500357209
15  675  -1.9628399153118199
15  676  -1.9627407087754853
15  677  -1.9626279992084334
15  678  -1.9625134867416272
15  679  -1.9622435687213877
15  680  -1.9621278139366409
15  681  -1.9620129946938167
15  682  -1.9619114487061249
15  683  -1.9616850921342237
15  684  -1.9617970133556657
15  685  -1.9615550318581563
15  686  -1.9614872936661905
15  687  -1.9613509910117484
15  688  -1.9612248315733631
15  689  -1.9610791921316892
15  690  -1.9609027693656433
15  691  -1.9606177484046836
15  692  -1.9604401198191319
15  693  -1.9600234414988367
15  694  -1.9602924048666224
15  695  -1.9601639071884702
15  696  -1.9599565426587724
15  697  -1.9598215133970098
15  698  -1.9597057217301224
15  699  -1.9595865916892532
15  700  -1.9594812735166762
15  701  -1.9593606250615216
15  702  -1.9592381923616831
15  703  -1.9588353697219629
15  704  -1.9589580084247267
15  705  -1.9587143609322824
15  706  -1.9586090453923806
15  707  -1.9584897247638062
15  708  -1.9583742245055460
15  709  -1.9582392958227215
15  710  -1.9581768443596290
15  711  -1.9579210889483618
15  712  -1.9580401943812997
15  713  -1.9577950046844861
15  714  -1.9576798242657054
15  715  -1.9575347358000410
15  716  -1.9571147388373309
15  717  -1.9569666876249168
15  718  -1.9568483654947342
15  719  -1.9567173059610679
15  720  -1.9565924371112380
15  721  -1.9563832465098738
15  722  -1.9564463483181740
15  723  -1.9562365779473394
15  724  -1.9561108438835146
15  725  -1.9559791274337568
15  726  -1.9558625102574776
15  727  -1.9557253255498666
15  728  -1.9555836812389245
15  729  -1.9552595498925136
15  730  -1.9551079505861988
15  731  -1.9549538218422320
15  732  -1.9548162325321936
15  733  -1.9546495337362262
15  734  -1.9544742089654072
15  735  -1.9542256685190311
15  736  -1.9540991808274120
15  737  -1.9533215472726355
15  738  -1.9531956265204860
15  739  -1.9529340662471497
15  740  -1.9527481000685893
15  741  -1.9525686978357355
15  742  -1.9524200819720259
15  743  -1.9522501647850481
15  744  -1.9520805458868864
15  745  -1.9509515530454147
15  746  -1.9517216103044694
15  747  -1.9515571984604270
15  748  -1.9513963859687664
15  749  -1.9512605212272467
15  750  -1.9511030119266286
15  751  -1.9507662185102210
15  752  -1.9507043135764317
15  753  -1.9505159070329168
15  754  -1.9503580904711701
15  755  -1.9501886624567539
15  756  -1.9500360644225874
15  757  -1.9498325057253991
15  758  -1.9489398052039282
15  759  -1.9493149233167137
15  760  -1.9491022161087077
15  761  -1.9487550737501438
15  762  -1.9485795485389343
15  763  -1.9483613597540810
15  764  -1.9482990983296533
15  765  -1.9475319082349489
15  766  -1.9480772807631674
15  767  -1.9478951364964741
15  768  -1.9477009032086274
15  769  -1.9473245238187999
15  770  -1.9471063534157376
15  771  -1.9466331889386836
15  772  -1.9463917699715607
15  773  -1.9461457939670783
15  774  -1.9459330136261312
15  775  -1.9456693075522289
15  776  -1.9454012908873621
15  777  -1.9450264681271525
15  778  -1.9449437514895702
15  779  -1.9444947604799907
15  780  -1.9440550618766046
15  781  -1.9433410533040261
15  782  -1.8451603216609518
15  783  -1.9393377252505004
15  784  -1.9385185062862169
15  785  -1.9380314524965094
15  786  -1.9370372536595524
15  787  -1.9367387508277523
15  788  -1.9364411015678551
15  789  -1.9362077353267291
15  790  -1.9359257868274384
15  791  -1.9356445579700825
15  792  -1.9351444404491527
15  793  -1.9348856368549785
15  794  -1.9346407775130505
15  795  -1.9344503407776255
15  796  -1.9342200983469686
15  797  -1.9340057498388090
15  798  -1.9334183487391177
15  799  -1.9332062809536390
15  800  -1.9329765335507367
15  801  -1.9327812571601619
15  802  -1.9324861348770472
15  803  -1.9317158054817758
15  804  -1.9320055641096103
15  805  -1.9315271805288110
15  806  -1.9313064133585989
15  807  -1.9311049988492053
15  808  -1.9305592863254171
15  809  -1.9303629791125958
15  810  -1.9301530629517485
15  811  -1.9299834999088725
15  812  -1.9297627861372502
15  813  -1.9295290915481909
15  814  -1.9291068165354548
15  815  -1.9288526613558519
15  816  -1.9285937949242726
15  817  -1.9283781507590947
15  818  -1.9280712920166667
15  819  -1.9276904110414483
15  820  -1.9266346110461443
15  821  -1.9262569728558336
15  822  -1.9259532707730331
15  823  -1.9257424882277183
15  824  -1.9254871510896949
15  825  -1.9252357509498721
15  826  -1.9246097468178065
15  827  -1.9248388731645880
15  828  -1.9243950368657841
15  829  -1.9242344540008776
15  830  -1.9240318984742006
15  831  -1.9238441658450833
15  832  -1.9233299622521314
15  833  -1.9231393616119388
15  834  -1.9229284931504451
15  835  -1.9227529792075515
15  836  -1.9224556733703155
15  837  -1.9221180153593391
15  838  -1.9218219892522030
15  839  -1.9216486039213747
15  840  -1.9214400412172339
15  841  -1.9212524593818874
15  842  -1.9207522618658197
15  843  -1.9205709713785091
15  844  -1.9203760003717727
15  845  -1.9202249632751862
15  846  -1.9200214039897696
15  847  -1.9198055669396257
15  848  -1.9192452232270654
15  849  -1.9194649845751761
15  850  -1.9190345037389331
15  851  -1.9188766031846602
15  852  -1.9186678901661325
15  853  -1.9184690613553657
15  854  -1.9178710029003299
15  855  -1.9175880588078551
15  856  -1.9166128306348360
15  857  -1.9163249949654000
15  858  -1.9157106884392543
15  859  -1.9155035248450578
15  860  -1.9152838372685435
15  861  -1.9151190403191254
15  862  -1.9146551045648597
15  863  -1.9148938608153478
15  864  -1.9143050671065780
15  865  -1.9140658147465055
15  866  -1.9138397314375719
15  867  -1.9136754221007211
15  868  -1.9134559266385753
15  869  -1.9132511961515897
15  870  -1.9126805296842935
15  871  -1.9124588553009298
15  872  -1.9122046309002663
15  873  -1.9119950548715683
15  874  -1.9115577758862268
15  875  -1.9113332640744432
15  876  -1.9108647303980131
15  877  -1.9106246407191738
15  878  -1.9103135976755996
15  879  -1.9100226138757310
15  880  -1.9087107801891472
15  881  -1.9091339838678589
15  882  -1.9080424035866819
15  883  -1.9066330262158686
15  884  -1.9059521735243385
15  885  -1.9055180916361070
15  886  -1.9046013069377288
15  887  -1.9042956430810907
15  888  -1.9039632865581759
15  889  -1.9037099249117821
15  890  -1.9025534989926425
15  891  -1.9023288798347511
15  892  -1.9020474085470738
15  893  -1.9018049279668232
15  894  -1.9011876507491889
15  895  -1.9009617642037917
15  896  -1.9007153131838075
15  897  -1.9005399248085431
15  898  -1.9002819723170947
15  899  -1.8999992158319816
15  900  -1.8996657107247727
15  901  -1.8993799529151669
15  902  -1.8991158883253692
15  903  -1.8989354903160072
15  904  -1.8986760847928918
15  905  -1.8984326046922568
15  906  -1.8976934613004062
15  907  -1.8972642620759952
15  908  -1.8951643852531403
15  909  -1.8965811490634443
15  910  -1.8961507226900669
15  911  -1.8954096772396758
15  912  -1.8949016052815844
15  913  -1.8947220263210978
15  914  -1.8944531738824579
15  915  -1.8941573327468528
15  916  -1.8938478619202499
15  917  -1.8935553252437374
15  918  -1.8932922460923467
15  919  -1.8931198833876237
15  920  -1.8928697705746671
15  921  -1.8926426749319956
15  922  -1.8920315120004478
15  923  -1.8917893265895203
15  924  -1.8915040277863042
15  925  -1.8912845329246557
15  926  -1.8902622969045946
15  927  -1.8900367362042816
15  928  -1.8897375694423821
15  929  -1.8894800097268707
15  930  -1.8888141787644210
15  931  -1.8885575659759983
15  932  -1.8882667597428060
15  933  -1.8880662498493286
15  934  -1.8877425748490346
15  935  -1.8873564107211911
15  936  -1.8869818436525743
15  937  -1.8860280253294353
15  938  -1.8865202982655511
15  939  -1.8856092794073320
15  940  -1.8836051203895099
15  941  -1.8840322333800070
15  942  -1.8830902173944803
15  943  -1.8825918469562846
15  944  -1.8822312017780682
15  945  -1.8818030308216784
15  946  -1.8814465300976460
15  947  -1.8812317085946466
15  948  -1.8809070805397716
15  949  -1.8806202340996365
15  950  -1.8798722663287519
15  951  -1.8795736636340878
15  952  -1.8792155287290124
15  953  -1.8789511648182073
15  954  -1.8778146668409692
15  955  -1.8775484739371637
15  956  -1.8771831847640765
15  957  -1.8768776376308032
15  958  -1.8761122092149711
15  959  -1.8758168050542547
15  960  -1.8754808599142920
15  961  -1.8752659665851739
15  962  -1.8748999411792138
15  963  -1.8744506671806129
15  964  -1.8741789429912072
15  965  -1.8737090734852349
15  966  -1.8733036896402355
15  967  -1.8730576906415075
15  968  -1.8726484667997150
15  969  -1.8722626475684758
15  970  -1.8709865731791819
15  971  -1.8689730353423564
15  972  -1.8673038869525191
15  973  -1.8666949160959243
15  974  -1.8659586602786078
15  975  -1.8654765200288961
15  976  -1.8644839317656523
15  977  -1.8621409537996811
15  978  -1.8577829881785313
15  979  -1.8566973226273165
15  980  -1.8561902444504323
15  981  -1.8553586978704768
15  982  -1.8546634825742028
15  983  -1.8525995662807293
15  984  -1.8509304007392526
15  985  -1.8492188682454846
15  986  -1.8487231854947337
15  987  -1.8481832115420891
15  988  -1.8479020784914086
15  989  -1.8473548403987554
15  990  -1.8459199650334126
15  991  -1.8454092068238626
15  992  -1.8446930769146146
15  993  -1.8442936819344919
15  994  -1.8432843185897296
15  995  -1.8428502767924613
15  996  -1.8422804316521673
15  997  -1.8419061681155497
15  998  -1.8406714141624445
15  999  -1.8402910015951777
15 1000  -1.8396949357078771
15 1001  -1.8392332883457423
15 1002  -1.8381316112422361
15 1003  -1.8376744476691240
15 1004  -1.8371145575739043
15 1005  -1.8368230526566431
15 1006  -1.8361524836934831
15 1007  -1.8337830785044953
15 1008  -1.8309227944935833
15 1009  -1.8284751631616003
15 1010  -1.8277381107004416
15 1011  -1.8274384201293108
15 1012  -1.8268136421653109
15 1013  -1.8263049131117444
15 1014  -1.8250793129078500
15 1015  -1.8245437291874629
15 1016  -1.8238085217963282
15 1017  -1.8233605914912567
15 1018  -1.8221596183948499
15 1019  -1.8217156559923888
15 1020  -1.8209742371818853
15 1021  -1.8204356470164331
15 1022  -1.8192201812779218
15 1023  -1.8187179592138660
15 1024  -1.8181017465584159
15 1025  -1.8178347343825012
15 1026  -1.8171365975375944
15 1027  -1.8154242737263449
15 1028  -1.8146378019269382
15 1029  -1.8143298517923077
15 1030  -1.8135434574557248
15 1031  -1.8128260799813463
15 1032  -1.8070096609703707
15 1033  -1.8061459751300246
15 1034  -1.8051347949833341
15 1035  -1.8047625828965466
15 1036  -1.8036562006736931
15 1037  -1.8011829582679961
15 1038  -1.7999551725926761
15 1039  -1.7995531653823935
15 1040  -1.7983599833939554
15 1041  -1.7973410933142164
15 1042  -1.7945889808858713
15 1043  -1.7930505962953744
15 1044  -1.7900227173230201
15 1045  -1.7877434691472893
15 1046  -1.7836177616336404
15 1047  -1.7372709340695165
15 1048  -1.7343530217756646
15 1049  -1.7300197852838890
15 1050  -1.7283004018034105
15 1051  -1.7234098634226422
15 1052  -1.7204594686002439
15 1053  -1.7156536725254856
15 1054  -1.7135590993153869
15 1055  -1.7088191039072487
15 1056  -1.7068814158545038
15 1057  -1.7027200389410262
15 1058  -1.7007226944384994
15 1059  -1.6973305015008437
15 1060  -1.6962870993381349
15 1061  -1.6941299590818057
15 1062  -1.6928286889969686
15 1063  -1.6873541411985149
15 1064  -1.6858580190765295
15 1065  -1.6831561916298239
15 1066  -1.6816142419440332
15 1067  -1.6646907334837786
15 1068  -1.6664847856572718
15 1069  -1.6615091413654233
15 1070  -1.6595205625849374
15 1071  -1.6526893214701635
15 1072  -1.6504972057019640
15 1073  -1.6469364429838058
15 1074  -1.6448290052337982
15 1075  -1.6324071504889990
15 1076  -1.6088542835452027
15 1077  -1.6063191377934081
15 1078  -1.6022550082846885
15 1079  -1.5992072842960157
15 1080  -1.5922173062740226
15 1081  -1.5890049741389880
15 1082  -1.5845353317028372
15 1083  -1.5809434433997984
15 1084  -1.5694774688662991
15 1085  -1.5658309180921859
15 1086  -1.5615070900363253
15 1087  -1.5580236785479356
15 1088  -1.5527157930206532
15 1089  -1.5495791959281349
15 1090  -1.5463628057066650
15 1091  -1.5442285601195278

References edit

[1] ractalforums.org : primary-separators-misiurewicz-points-of-the-mandelbrot-sets-real-slice

[2] [ Pastor96 ] = G. Pastor, M. Romera and F. Montoya, "An approach to the ordering of one-dimensional quadratic maps", Chaos, Solitons and Fractals, 7/4 (1996), 565-584. Preprint

[3] A scaling constant equal to unity in 1D- quadratic maps by M. ROMERA, G. PASTOR and F. MONTOYA

[4] G. Pastor, M. Romera, G. Álvarez and F. Montoya, "Operating with external arguments in the Mandelbrot set antenna", Physica D, 171 (2002), 52-71

[5] G. Pastor, M. Romera, G. Álvarez and F. Montoya, "Operating with external arguments in the Mandelbrot set antenna", Physica D, 171 (2002), 52-71

[1]

[2]

[3]

[4]

[5]

Fractals/Iterations in the complex plane/Mandelbrot set/chaotic part

Contents