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
110 1.001320593420021188006867  0.1452652762
120 1.0012008541292640590332  0.1441024955
130 1.001101446010855235095184  0.1431879814
140 1.001017923958398526405105  0.1425093542
150 1.000946765212617891142817  0.1420147819
153 1.000927440104010047883651  0.1418983359
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
K=125: six largest Gauss nodes and weights
     node 2.585826606048204448631515236116841507809   weight 0.251331654638419314530505674329
     node 2.011485694644863753488492667048333918867   weight 0.00312850458208539547555401293637
     node 2.001683898372487107903677086170258775829   weight 0.00023888960363510593999809464182
     node 1.999150165939081444015016564051693191562   weight 0.000304744486551484727606526770749
     node 1.99521930618712817200889496714538140628   weight 0.000456069550526440907674119790244
     node 1.989809976684550926372751578211514847953   weight 0.00059536246373835449795326058349
     total Gauss weight of nodes in [-2,2]: 0.49060190235172 ; number of nodes outside [-2,2]: 6
     measure nu (compression QbQ): three largest nodes/weights: 2.101990760466021919875 / 0.0998095879805, 2.004589950145754760351 / 0.00210946434084, 2.00082100600337631713 / 0.000515959306412
K=153: six largest Gauss nodes and weights
     node 2.585826606048204448631515236116841507809   weight 0.251331654638419314530505674329
     node 2.01148569465811608550203192390666465279   weight 0.00312850453464497157858772442006
     node 2.001744366889160399459766770897760426881   weight 0.000211536661040700201938251765727
     node 1.999983890987236058170834221861094358634   weight 0.000189441280538487938136838896933
     node 1.997491231828199030695747142065274331168   weight 0.000292191632154334900196117869668
     node 1.993988754851232940555077809080740500866   weight 0.0003878709726245849797912866246
     total Gauss weight of nodes in [-2,2]: 0.49065660833179 ; number of nodes outside [-2,2]: 6
     measure nu (compression QbQ): three largest nodes/weights: 2.101990760466021919875 / 0.0998095879805, 2.004590149049584836173 / 0.00210872213191, 2.001057714009696368263 / 0.000365634495873
rough density -Im G(x+i0)/pi with the continued fraction terminated after K levels (tail beta=1):
   x     K=100        K=125        K=153      
   0.0   0.132093013  0.131921372  0.131935871
  0.25   0.131370058  0.1312051    0.131220721
   0.5   0.12983526   0.129658819  0.129726775
  0.75   0.127829248  0.127704605  0.127803825
   1.0   0.125285722  0.125462613  0.125437985
  1.25   0.12268645   0.122767585  0.122745312
  1.41   0.120481154  0.120564284  0.120596007
   1.5   0.11907187   0.119310204  0.119071107
  1.75   0.109925649  0.110019665  0.110331398
   1.9   0.101570739  0.100595454  0.101081658
  1.97   0.0952719045  0.0988576187  0.0958073224
