exact Jacobi parameters beta_1..beta_280 from m_0..m_560; algorithms (i) and (ii) agree on beta_1..beta_279: True
beta_1..beta_8 = 4, 2, 4/3, 7/6, 11/10, 414/385, 16868/15939, 102259729/97766928
all beta_k > 0: True
k:                   10         20         50        100        120        140        150        153        160        200        240        280
beta_k:        1.030482   1.010177  1.0031056  1.0014666  1.0012009  1.0010179  1.0009468  1.0009274  1.0008852  1.0007018   1.000579  1.0004931
k(beta_k-1):     0.3048     0.2035     0.1553     0.1467     0.1441     0.1425      0.142     0.1419     0.1416     0.1404     0.1389     0.1381
k^2(beta_k-1-0.14/k) and other fits are not attempted here.
K = 153: Gauss nodes of mu above 1.99 (node / weight):
    2.5858266060482044486315152361168 / 0.2513316546384193145305057
    2.0114856946581160855020319239067 / 0.003128504534644971578587724
    2.0017443668891603994597667708978 / 0.0002115366610407002019382518
    1.9999838909872360581708342218611 / 0.0001894412805384879381368389
    1.9974912318281990306957471420653 / 0.0002921916321543349001961179
    1.9939887548512329405550778090807 / 0.0003878709726245849797912866
    total Gauss weight of the nodes in [-2,2]: 0.49065661   (2 * sum of weights above 2 = 0.50934339)
    compression nu (K-1 = 152 levels): node above 2.05: 2.101990760466021919875227 / weight 0.0998095879805496
    density estimate at x = 0, 0.5, 1.0, 1.41, 1.5, 1.75, 1.9, 1.97: 0.13206, 0.12978, 0.12545, 0.12052, 0.11913, 0.11042, 0.10137, 0.095593
K = 200: Gauss nodes of mu above 1.99 (node / weight):
    2.5858266060482044486315152361168 / 0.2513316546384193145305057
    2.0114856946581595807934205563861 / 0.00312850453445193504396644
    2.0017588861642014683683988907856 / 0.0002023613229284432240182036
    2.0004804141346317328405544334239 / 0.0001019238936839838362553957
    1.9991362066723456919947902030951 / 0.0001602084085576816185730527
    1.9971834511175097078918642033397 / 0.000217731144458864812895479
    1.9946609346638205773459118940787 / 0.0002723814606444545166884224
    1.9915914551710891789513245654915 / 0.0003249356186022542437322563
    total Gauss weight of the nodes in [-2,2]: 0.49047111   (2 * sum of weights above 2 = 0.50952889)
    compression nu (K-1 = 199 levels): node above 2.05: 2.101990760466021919875227 / weight 0.0998095879805496
    density estimate at x = 0, 0.5, 1.0, 1.41, 1.5, 1.75, 1.9, 1.97: 0.13195, 0.12969, 0.12535, 0.12062, 0.11925, 0.11004, 0.1014, 0.097587
K = 240: Gauss nodes of mu above 1.99 (node / weight):
    2.5858266060482044486315152361168 / 0.2513316546384193145305057
    2.011485694658159583434307187688 / 0.003128504534451919572083461
    2.0017596631799712244273333510124 / 0.0002016467118581913632776718
    2.0006083476268079100536421247293 / 0.00007163861416535166041677255
    1.9997251048839501224264210204678 / 0.0001054342315782705061477195
    1.998422666900562086467017384085 / 0.0001461562137076664883373898
    1.9967162351079074118341015368777 / 0.0001847061533145644902332449
    1.9946247320052991929227046253257 / 0.0002219001464709235900984094
    1.9921589245394938778851345812206 / 0.0002580275414240465894267725
    total Gauss weight of the nodes in [-2,2]: 0.49053311   (2 * sum of weights above 2 = 0.50946689)
    compression nu (K-1 = 239 levels): node above 2.05: 2.101990760466021919875227 / weight 0.0998095879805496
    density estimate at x = 0, 0.5, 1.0, 1.41, 1.5, 1.75, 1.9, 1.97: 0.13196, 0.12971, 0.12544, 0.1206, 0.11914, 0.11034, 0.10138, 0.096278
K = 280: Gauss nodes of mu above 1.99 (node / weight):
    2.5858266060482044486315152361168 / 0.2513316546384193145305057
    2.0114856946581595834349453749259 / 0.003128504534451919567578973
    2.0017597172696961221300525290149 / 0.0002015837569434227598197296
    2.0006521394534946135201884970778 / 0.00005834607314054663973887558
    2.0000198347326467581637787494707 / 0.00007335258063234615358544425
    1.9991015079369669439912817672411 / 0.0001039246545381763577054608
    1.9978793894312675382676795963616 / 0.0001326116172459029086270229
    1.9963704514991034809073331334924 / 0.0001602656507897270696713837
    1.9945837945294892453488801019963 / 0.000187195151564518802502981
    1.9925251579570424664515313998352 / 0.0002135217972551228456455521
    1.9901985669362474552085283732421 / 0.0002393445990617586797114994
    total Gauss weight of the nodes in [-2,2]: 0.49041312   (2 * sum of weights above 2 = 0.50958688)
    compression nu (K-1 = 279 levels): node above 2.05: 2.101990760466021919875227 / weight 0.0998095879805496
    density estimate at x = 0, 0.5, 1.0, 1.41, 1.5, 1.75, 1.9, 1.97: 0.13196, 0.12976, 0.12542, 0.12059, 0.11913, 0.11009, 0.10134, 0.096474
