exact Jacobi parameters beta_1..beta_8: 4, 2, 4/3, 7/6, 11/10, 414/385, 16868/15939, 102259729/97766928
k   beta_k (25 digits)            k*(beta_k-1)
  1 4.0  3.0
  2 2.0  2.0
  3 1.333333333333333333333333  1.0
  4 1.166666666666666666666667  0.6666666667
  5 1.1  0.5
  6 1.075324675324675324675325  0.4519480519
  7 1.058284710458623502101763  0.4079929732
  8 1.045954200381544155708769  0.3676336031
  9 1.036218303888865256854383  0.325964735
 10 1.030481959926422399134777  0.3048195993
 11 1.026263905996549002503541  0.288902966
 12 1.022849787982362533370587  0.2741974558
 20 1.010176986736879681567648  0.2035397347
 30 1.005733506410382899330555  0.1720051923
 40 1.004013678693640969461557  0.1605471477
 50 1.003105643433860820127306  0.1552821717
 60 1.002548833849975974126126  0.152930031
 70 1.002160337044147421407215  0.1512235931
 80 1.00187187579477910661862  0.1497500636
 90 1.001646409516857120178806  0.1481768565
100 1.001466637276361823816302  0.1466637276
K=60: six largest Gauss nodes and weights
     node 2.58582660604820444863151523611684150777   weight 0.251331654638419314530505674329
     node 2.011480579778937676165753618851152367341   weight 0.00313633071337904212258669332202
     node 1.998877974696413943750132834039782096266   weight 0.000916469003129682137620796786834
     node 1.98591202999985687764756940823601191118   weight 0.0015830377341190535420938086948
     node 1.966513219562446824878339934713363073269   weight 0.00217953517400194533947224881257
     node 1.941112248441318550947694976200342810477   weight 0.0027844673408271027155649039439
     total Gauss weight of nodes in [-2,2]: 0.491064029296403 ; number of nodes outside [-2,2]: 4
     measure nu (compression QbQ): three largest nodes/weights: 2.101990760466021669769 / 0.0998095879806, 2.004337981701766862674 / 0.00247046323148, 1.994784985499978712388 / 0.00271718529192
K=80: six largest Gauss nodes and weights
     node 2.585826606048204448631515236116841507809   weight 0.251331654638419314530505674329
     node 2.011485586268943186979428904648144321719   weight 0.00312874054595339386568215877646
     node 2.00087122703031784997102136149937921293   weight 0.000473853164685829026523009696788
     node 1.994132778885809738116232893072831962643   weight 0.000843232304772143355145664628623
     node 1.983665911342927042047379974333570382427   weight 0.00118694313208958470868620091493
     node 1.96974636563304263566134551454449171346   weight 0.00151316002293572654335394502022
     total Gauss weight of nodes in [-2,2]: 0.490131503301883 ; number of nodes outside [-2,2]: 6
     measure nu (compression QbQ): three largest nodes/weights: 2.101990760466021919874 / 0.0998095879805, 2.004558287312270421687 / 0.00217600321229, 1.998780577768699835946 / 0.00141035645508
K=100: six largest Gauss nodes and weights
     node 2.585826606048204448631515236116841507809   weight 0.251331654638419314530505674329
     node 2.011485692596787944326656783167098998221   weight 0.00312851032374297731700915224165
     node 2.001462983470675967575653264500780553546   weight 0.000313649732097475144922795020347
     node 1.997393652366621527365743113521927833599   weight 0.000509775277109946669619845670641
     node 1.990954108428920306843362417569901770991   weight 0.000738947850304699931156922310805
     node 1.982257675887911585107993821079382043856   weight 0.000949724282436441560740954066687
     total Gauss weight of nodes in [-2,2]: 0.49045237061148 ; number of nodes outside [-2,2]: 6
     measure nu (compression QbQ): three largest nodes/weights: 2.101990760466021919875 / 0.0998095879805, 2.004586539357214549045 / 0.00211900003162, 2.000182989942715252172 / 0.000838660794072
rough density -Im G(x+i0)/pi with the continued fraction terminated after K levels (tail beta=1):
   x     K=60         K=80         K=100      
   0.0   0.132163178  0.132119374  0.132093013
  0.25   0.131172253  0.131347382  0.131370058
   0.5   0.1297374    0.129656553  0.12983526 
  0.75   0.127778817  0.12767716   0.127829248
   1.0   0.125506868  0.125492281  0.125285722
  1.25   0.122537316  0.122856238  0.12268645 
  1.41   0.120445518  0.120464282  0.120481154
   1.5   0.1194167    0.119178919  0.11907187 
  1.75   0.11056125   0.109891656  0.109925649
   1.9   0.101326628  0.101511483  0.101570739
  1.97   0.0950186975  0.0941687324  0.0952719045
