Lemma/Modules/FDEM1D/src/FHT.cpp

/* This file is part of Lemma, a geophysical modelling and inversion API.
 * More information is available at http://lemmasoftware.org
 */

/* This Source Code Form is subject to the terms of the Mozilla Public
 * License, v. 2.0. If a copy of the MPL was not distributed with this
 * file, You can obtain one at http://mozilla.org/MPL/2.0/.
 */

/**
 * @file
 * @date      05/02/2018 10:04:58 PM
 * @version   $Id$
 * @author    Trevor Irons (ti)
 * @email     tirons@egi.utah.edu
 * @copyright Copyright (c) 2018, University of Utah
 * @copyright Copyright (c) 2018, Trevor Irons & Lemma Software, LLC
 */

#include "FHT.h"

namespace Lemma {

    template<>
    const Eigen::Matrix<Real, Eigen::Dynamic, 3>  FHT<FHTKEY201>::WT =
        ( Eigen::Matrix<Real, 201, 3>()   <<
        // Base                   J0                      J1
        4.1185887075357082e-06, 1.5020099209519960e-03, 4.7827871332506182e-10,
        4.6623077830484039e-06,-1.0381698214761684e-02,-2.9784175503440788e-09,
        5.2778064058937756e-06, 3.6840860097595164e-02, 9.7723832770897220e-09,
        5.9745606155328603e-06,-8.9903380392274704e-02,-2.2382340996085809e-08,
        6.7632974390298035e-06, 1.7082286536833860e-01, 4.0446774329470848e-08,
        7.6561600412698171e-06,-2.7115749656836280e-01,-6.1734815854553919e-08,
        8.6668946776271221e-06, 3.7649328091859574e-01, 8.3293912185608189e-08,
        9.8110623273521872e-06,-4.7220778569122657e-01,-1.0249453502284080e-07,
        1.1106278265924788e-05, 5.4778211089647089e-01, 1.1780779749909977e-07,
        1.2572483264760042e-05,-5.9823516853035097e-01,-1.2870061460834850e-07,
        1.4232250593579901e-05, 6.2345791612185331e-01, 1.3559243438349901e-07,
        1.6111133551969887e-05,-6.2650436648257724e-01,-1.3921010821521872e-07,
        1.8238058880617237e-05, 6.1197225351173345e-01, 1.4065745722769670e-07,
        2.0645772109076137e-05,-5.8470173866140451e-01,-1.4074881908375281e-07,
        2.3371341696506312e-05, 5.4911055789616858e-01, 1.4051720878600928e-07,
        2.6456729726989950e-05,-5.0878861684860843e-01,-1.4040746687777830e-07,
        2.9949437945688260e-05, 4.6652106345430200e-01, 1.4127886061686993e-07,
        3.3903239082024059e-05,-4.2426478870289325e-01,-1.4315595655055356e-07,
        3.8379004719130766e-05, 3.8339538911933357e-01, 1.4689283208027915e-07,
        4.3445642455208216e-05,-3.4472344791723936e-01,-1.5210916706348747e-07,
        4.9181156785051293e-05, 3.0876891466890510e-01, 1.5989801550138741e-07,
        5.5673850034776868e-05,-2.7570439368364807e-01,-1.6940918407911260e-07,
        6.3023681838995322e-05, 2.4562331000974616e-01, 1.8227089415749844e-07,
        7.1343808090545215e-05,-2.1839207265400126e-01,-1.9695856878603369e-07,
        8.0762323056016586e-05, 1.9393194321380827e-01, 2.1603952427106760e-07,
        9.1424231478173270e-05,-1.7198162962644575e-01,-2.3691320619292838e-07,
        1.0349368102719458e-04, 1.5242270280410272e-01, 2.6369843208466607e-07,
        1.1715648947091054e-04,-1.3494945901825492e-01,-2.9202021404039016e-07,
        1.3262300547161834e-04, 1.1946763189654602e-01, 3.2852445086324662e-07,
        1.5013134705348249e-04,-1.0565870880444576e-01,-3.6589094553627693e-07,
        1.6995106759902750e-04, 9.3482355548033913e-02, 4.1487501036863030e-07,
        1.9238730581535294e-04,-8.2612525279836244e-02,-4.6327136995173986e-07,
        2.1778548356175115e-04, 7.3077763526174969e-02, 5.2852697369750518e-07,
        2.4653662386513240e-04,-6.4536481281701225e-02,-5.9034983719954077e-07,
        2.7908337099788406e-04, 5.7096310621587334e-02, 6.7710211611560898e-07,
        3.1592680530155527e-04,-5.0384859605213800e-02,-7.5512942807901028e-07,
        3.5763415767542709e-04, 4.4599557396733047e-02, 8.7062473466409799e-07,
        4.0484754250000483e-04,-3.9316995063444334e-02,-9.6788530918130449e-07,
        4.5829384344501882e-04, 3.4838544754296139e-02, 1.1222658353725904e-06,
        5.1879590436097246e-04,-3.0664946477420088e-02,-1.2417228058919743e-06,
        5.8728519754599128e-04, 2.7221072240291456e-02, 1.4493467036899140e-06,
        6.6481616442494776e-04,-2.3901586108434601e-02,-1.5932456559208080e-06,
        7.5258244942583781e-04, 2.1281566646364738e-02, 1.8747045814274419e-06,
        8.5193527698548301e-04,-1.8612484595521447e-02,-2.0433320340041385e-06,
        9.6440425461164468e-04, 1.6655386303461400e-02, 2.4285695351967146e-06,
        1.0917209222795108e-03,-1.4472420076504743e-02,-2.6179926456520528e-06,
        1.2358454107222641e-03, 1.3057747649606617e-02, 3.1511729661391781e-06,
        1.3989966190390965e-03,-1.1226286001060300e-02,-3.3492412032881268e-06,
        1.5836863762264436e-03, 1.0266818557930830e-02, 4.0964186613549959e-06,
        1.7927581125735061e-03,-8.6738022421653585e-03,-4.2758275751239154e-06,
        2.0294306362957340e-03, 8.1103368670848164e-03, 5.3371197552207799e-06,
        2.2973476893787268e-03,-6.6573628142085938e-03,-5.4435423773626499e-06,
        2.6006340455800008e-03, 6.4551189810889585e-03, 6.9725766921672099e-06,
        2.9439590142573526e-03,-5.0524015117839084e-03,-6.9045562968161745e-06,
        3.3326083277104117e-03, 5.1989014270506263e-03, 9.1397025436977438e-06,
        3.7725655187922052e-03,-3.7597430078747883e-03,-8.7148373033635960e-06,
        4.2706040416570154e-03, 4.2640545165292636e-03, 1.2029590806160379e-05,
        4.8343915539089625e-03,-2.6994965688974474e-03,-1.0927976968519436e-05,
        5.4726079656493079e-03, 3.5928000560587229e-03, 1.5912526719455299e-05,
        6.1950790728715292e-03,-1.8061291289989019e-03,-1.3582559661331659e-05,
        7.0129278325854246e-03, 3.1436470898586703e-03, 2.1176226828087565e-05,
        7.9387456086585442e-03,-1.0244200001620755e-03,-1.6678205993448338e-05,
        8.9867860248264830e-03, 2.8888297674091743e-03, 2.8384979250408712e-05,
        1.0173184409377162e-02,-3.0605070741955765e-04,-2.0132088397797457e-05,
        1.1516206210016314e-02, 2.8125907445050334e-03, 3.8372045311188108e-05,
        1.3036528203437736e-02, 3.9337862066047565e-04,-2.3702184335455945e-05,
        1.4757556829019875e-02, 2.9102041487017727e-03, 5.2385308850007940e-05,
        1.6705788547622769e-02, 1.1170884769911178e-03,-2.6854373943701261e-05,
        1.8911217773465227e-02, 3.1876763415953362e-03, 7.2318581557902158e-05,
        2.1407798659484324e-02, 1.9097806429850762e-03,-2.8535361884516687e-05,
        2.4233967845691123e-02, 3.6621020321465411e-03, 1.0108123118106823e-04,
        2.7433236218606032e-02, 2.8203783587849949e-03,-2.6788477540644352e-05,
        3.1054858792331431e-02, 4.3626885599390430e-03, 1.4319185407094621e-04,
        3.5154593024557458e-02, 3.9050024915686802e-03,-1.8108424211338017e-05,
        3.9795557242315927e-02, 5.3324923486866077e-03, 2.0573561552327273e-04,
        4.5049202393557801e-02, 5.2303399394270488e-03, 3.6361648565843316e-06,
        5.0996412085361466e-02, 6.6309348458396984e-03, 2.9991264692859609e-04,
        5.7728747844643331e-02, 6.8775540687037451e-03, 4.8993332079278846e-05,
        6.5349858773045680e-02, 8.3371689988226087e-03, 4.4354733854670903e-04,
        7.3977077298642363e-02, 8.9468564745410102e-03, 1.3589101811995494e-04,
        8.3743225592195963e-02, 1.0554326601376745e-02, 6.6515823521273764e-04,
        9.4798660459030126e-02, 1.1562765604509096e-02, 2.9451991608624389e-04,
        1.0731358818908403e-01, 1.3414536265660639e-02, 1.0105553806271136e-03,
        1.2148068500391276e-01, 1.4879837399735491e-02, 5.7533964792254050e-04,
        1.3751806344428075e-01, 1.7084241336519569e-02, 1.5535077418254303e-03,
        1.5567263036799733e-01, 1.9088092654441269e-02, 1.0621193133794828e-03,
        1.7622388825676111e-01, 2.1768513715084332e-02, 2.4128970258747457e-03,
        1.9948823835583873e-01, 2.4416120601223806e-02, 1.8929698186109245e-03,
        2.2582385189647586e-01, 2.7711234465350204e-02, 3.7800177772191607e-03,
        2.5563618439697788e-01, 3.1127164234404547e-02, 3.2937343278959356e-03,
        2.8938421793905067e-01, 3.5184140220277452e-02, 5.9612179800391544e-03,
        3.2758752752368947e-01, 3.9497913113638941e-02, 5.6295935320552241e-03,
        3.7083428029819565e-01, 4.4449762157204989e-02, 9.4422526803168080e-03,
        4.1979029080811425e-01, 4.9758433269983887e-02, 9.4810228247137925e-03,
        4.7520927168614446e-01, 5.5667457114992429e-02, 1.4979159139973408e-02,
        5.3794443759467447e-01, 6.1949790434151823e-02, 1.5745093424331037e-02,
        6.0896164107289685e-01, 6.8682064905571841e-02, 2.3708966370000140e-02,
        6.8935424252422239e-01, 7.5616743950118387e-02, 2.5740590762136872e-02,
        7.8035994327803426e-01, 8.2584983563572259e-02, 3.7232782843117498e-02,
        8.8337984088275090e-01, 8.9193635262987042e-02, 4.1225008900614292e-02,
        1.0000000000000000e+00, 9.4874686942005279e-02, 5.7507103212277359e-02,
        1.1320158709991752e+00, 9.8891681869094042e-02, 6.4044642846235691e-02,
        1.2814599321940212e+00, 1.0004294654495730e-01, 8.6091796551857253e-02,
        1.4506329812931589e+00, 9.7016844329802857e-02, 9.4717139804457451e-02,
        1.6421395578187052e+00, 8.7789596149914384e-02, 1.2172497389177185e-01,
        1.8589280418463421e+00, 7.0509767592855419e-02, 1.2853597000398900e-01,
        2.1043360464154781e+00, 4.2778853484849347e-02, 1.5450777327408322e-01,
        2.3821418024579781e+00, 3.5584532926218175e-03, 1.4755964090969320e-01,
        2.6966223273530128e+00,-4.7210453264879347e-02, 1.5621399202016978e-01,
        3.0526192726543444e+00,-1.0489787743225988e-01, 1.1147620703185755e-01,
        3.4556134647626755e+00,-1.6020950407348281e-01, 7.7489831356083380e-02,
        3.9118092861497971e+00,-1.9459781573132096e-01,-2.7628266850147711e-02,
        4.4282301962435247e+00,-1.8490774599542381e-01,-1.0198730178317840e-01,
        5.0128268625854631e+00,-1.0754165020025190e-01,-2.2039889971111640e-01,
        5.6745995670177445e+00, 3.6037727487476613e-02,-2.1185762869925318e-01,
        6.4237367714291338e+00, 1.9759013047489976e-01,-1.6052415083152241e-01,
        7.2717719763787807e+00, 2.6132313321851336e-01, 9.1649025798681089e-02,
        8.2317612875478190e+00, 1.1713996822458939e-01, 2.3792823877700942e-01,
        9.3184844237807365e+00,-1.8758779281301441e-01, 2.6075777853738125e-01,
        1.0548672261378394e+01,-3.0238114997462151e-01,-1.5662188259001042e-01,
        1.1941264417849103e+01, 4.8163135684567732e-02,-2.8932081756330175e-01,
        1.3517700840802913e+01, 3.6399529664885466e-01, 1.3148519116247689e-02,
        1.5302251891207787e+01,-1.4910233461562913e-01, 4.2691302759079564e-01,
        1.7322392002874359e+01,-2.6373490348543854e-01,-4.0005050006489040e-01,
        1.9609222670922968e+01, 4.0362661807718703e-01, 1.1513789407450359e-01,
        2.2197951281441636e+01,-3.1409794650104578e-01, 9.3748244358717620e-02,
        2.5128433154258410e+01, 1.8179369405131079e-01,-1.6037231301955096e-01,
        2.8445785143962375e+01,-9.0738718042631769e-02, 1.5071857939129532e-01,
        3.2201080245997971e+01, 4.2946487545160242e-02,-1.2120369075996129e-01,
        3.6452133901787732e+01,-2.0586135807067835e-02, 9.4110656079982341e-02,
        4.1264394108610787e+01, 1.0392667161913182e-02,-7.3742238434584328e-02,
        4.6711949038112273e+01,-5.6117848068723023e-03, 5.9038567576124905e-02,
        5.2878667676447755e+01, 3.2402025511569896e-03,-4.8288117528475852e-02,
        5.9859491047029913e+01,-1.9858724388273777e-03, 4.0197054299576880e-02,
        6.7761893895170928e+01, 1.2807317326135252e-03,-3.3919787720641081e-02,
        7.6707539338295589e+01,-8.6253791756068252e-04, 2.8918247156763971e-02,
        8.6834151956244213e+01, 6.0296590782143555e-04,-2.4845271759013743e-02,
        9.8297638159222487e+01,-4.3548936996943465e-04, 2.1470449751150148e-02,
        1.1127448647797397e+02, 3.2375891570874245e-04,-1.8635828020057092e-02,
        1.2596448473034971e+02,-2.4698212240059978e-04, 1.6229579362363859e-02,
        1.4259379589698909e+02, 1.9279062274925971e-04,-1.4170085406786529e-02,
        1.6141844006140866e+02,-1.5357911509105972e-04, 1.2396084121011890e-02,
        1.8272823602144376e+02, 1.2453787849367440e-04,-1.0860414401084047e-02,
        2.0685126325595743e+02,-1.0255126402954421e-04, 9.5259444245356633e-03,
        2.3415891294197226e+02, 8.5558482209476271e-05,-8.3628577447233381e-03,
        2.6507160578622688e+02,-7.2170928476334345e-05, 7.3468029551253195e-03,
        3.0006526470124555e+02, 6.1436863283080017e-05,-6.4576043210966359e-03,
        3.3967864197737873e+02,-5.2693349406473615e-05, 5.6783439955994880e-03,
        3.8452161375783919e+02, 4.5471255142623729e-05,-4.9946949167265437e-03,
        4.3528456951608860e+02,-3.9433284158653591e-05, 4.3944258108608806e-03,
        4.9274904109325632e+02, 3.4332971164795619e-05,-3.8670264019660858e-03,
        5.5779973493719069e+02,-2.9987212220165472e-05, 3.4034180355556670e-03,
        6.3143815278803334e+02, 2.6257657435614391e-05,-2.9957260668529964e-03,
        7.1479801051045558e+02,-2.3037978256349448e-05, 2.6370977166248776e-03,
        8.0916269245647072e+02, 2.0245071331016652e-05,-2.3215540117372982e-03,
        9.1598501008114988e+02,-1.7812925644382519e-05, 2.0438677474690805e-03,
        1.0369095690092008e+03, 1.5688305607849465e-05,-1.7994616759226389e-03,
        1.1737980889093292e+03,-1.3827679492110470e-05, 1.5843226896713463e-03,
        1.3287580659938624e+03, 1.2195005442258958e-05,-1.3949288614414647e-03,
        1.5041752194232211e+03,-1.0760110818279243e-05, 1.2281869708886250e-03,
        1.7027502211507524e+03, 9.4974857670959145e-06,-1.0813786997088304e-03,
        1.9275402746900081e+03,-8.3853711343938338e-06, 9.5211407460757294e-04,
        2.1820061829391980e+03, 7.4050612540713192e-06,-8.3829103020448140e-04,
        2.4700656297055034e+03,-6.5403682860228500e-06, 7.3806018220987763e-04,
        2.7961534952362003e+03, 5.7772102413267325e-06,-6.4979406671247244e-04,
        3.1652901343571971e+03,-5.1032933218796731e-06, 5.7206022901230412e-04,
        3.5831586684094545e+03, 4.5078641320869195e-06,-5.0359764543483573e-04,
        4.0561924809477755e+03,-3.9815111951817114e-06, 4.4329604122300101e-04,
        4.5916742642604040e+03, 3.5159993210292339e-06,-3.9017773206623073e-04,
        5.1978481416012310e+03,-3.1041249680128287e-06, 3.4338166974098888e-04,
        5.8840465913361650e+03, 2.7395854235553632e-06,-3.0214941633163506e-04,
        6.6608341270911405e+03,-2.4168587823583312e-06, 2.6581280850704716e-04,
        7.5401699459601114e+03, 2.1310948134441218e-06,-2.3378310479588391e-04,
        8.5355920488578286e+03,-1.8780185742021288e-06, 2.0554143583887405e-04,
        9.6624256676814348e+03, 1.6538488252707735e-06,-1.8063040107732216e-04,
        1.0938019208165191e+04,-1.4552318768651144e-06, 1.5864667598176302e-04,
        1.2382011340936813e+04, 1.2791890865306748e-06,-1.3923451235168759e-04,
        1.4016633352832258e+04,-1.1230741959148155e-06, 1.2208003098625932e-04,
        1.5867051413382505e+04, 9.8453630538596172e-07,-1.0690622166177854e-04,
        1.7961754025908867e+04,-8.6148574493190796e-07, 9.3468580362568137e-05,
        2.0332990628312182e+04, 7.5206242699701732e-07,-8.1551328581234316e-05,
        2.3017268096126892e+04,-6.5460810334682633e-07, 7.0964174631531072e-05,
        2.6055912791858576e+04, 5.6764451596029765e-07,-6.1539592468666665e-05,
        2.9495706813754354e+04,-4.8985884555184997e-07, 5.3130609116145443e-05,
        3.3389608239508460e+04, 4.2009674106879252e-07,-4.5609105983126460e-05,
        3.7797566453568354e+04,-3.5736212641225517e-07, 3.8864648584181207e-05,
        4.2787445110585410e+04, 3.0082215969939671e-07,-3.2803856352344075e-05,
        4.8436066944688770e+04,-2.4981510481639669e-07, 2.7350296775876261e-05,
        5.4830396510166145e+04, 2.0385823466866512e-07,-2.2444816150805301e-05,
        6.2068879062685897e+04,-1.6265189071584773e-07, 1.8046076281584239e-05,
        7.0262956194088882e+04, 1.2607416700611311e-07,-1.4130826937491561e-05,
        7.9538781555028458e+04,-9.4158417913450858e-08, 1.0693106849359383e-05,
        9.0039163080228551e+04, 6.7043911217063425e-08,-7.7412053314530284e-06,
        1.0192576161830177e+05,-4.4891090827293947e-08, 5.2910576443698300e-06,
        1.1538157981559623e+05, 2.7761325666544702e-08,-3.3552268362550323e-06,
        1.3061377957221285e+05,-1.5480404355710375e-08, 1.9282956206367452e-06,
        1.4785687144693290e+05, 7.5327300141098751e-09,-9.7253712572058755e-07,
        1.6737632511421290e+05,-3.0524770418657847e-09, 4.1100807632959352e-07,
        1.8947265645880660e+05, 9.5877856096830783e-10,-1.3553176263207053e-07,
        2.1448605423174356e+05,-2.0575286298055636e-10, 3.0748587523233524e-08,
        2.4280161749832361e+05, 2.2414416956474645e-11,-3.5668195345476294e-09).finished();

    template<>
    const Eigen::Matrix<Real, Eigen::Dynamic, 3>  FHT<FHTKEY101>::WT =
        ( Eigen::Matrix<Real, 101, 3>()   <<
       // Base                   J0                        J1
       5.5308437014783363e-04,   5.1818808036862153e-02,   4.1746363961646286e-06,
       6.4259236035555788e-04,  -2.9258492652779172e-01,  -2.5993370843637242e-05,
       7.4658580837667996e-04,   8.7289913080159265e-01,   9.2506838353721647e-05,
       8.6740895730700251e-04,  -1.8525183961240297e+00,  -2.4318740269846489e-04,
       1.0077854290485113e-03,   3.2096055660873608e+00,   5.2276050788732404e-04,
       1.1708796207911744e-03,  -4.9248158048315069e+00,  -9.5803859755432658e-04,
       1.3603680375478939e-03,   7.0219167445719828e+00,   1.5308357107396591e-03,
       1.5805221687362171e-03,  -9.4781099645811544e+00,  -2.1584605764249656e-03,
       1.8363047770289071e-03,   1.2098564895534539e+01,   2.7161344302423967e-03,
       2.1334817700377098e-03,  -1.4476661837664896e+01,  -3.0845361397036195e-03,
       2.4787521766663585e-03,   1.6146079632847474e+01,   3.2133980102756368e-03,
       2.8798991580882430e-03,  -1.6810370923047440e+01,  -3.1305779240645847e-03,
       3.3459654574712720e-03,   1.6506202923977266e+01,   2.9239120736637542e-03,
       3.8874572434761303e-03,  -1.5534747212675301e+01,  -2.6680602560576316e-03,
       4.5165809426126703e-03,   1.4267433361428399e+01,   2.4131379039476304e-03,
       5.2475183991813838e-03,  -1.2939053370802849e+01,  -2.1549566068119440e-03,
       6.0967465655156379e-03,   1.1628520257389562e+01,   1.9058200916563901e-03,
       7.0834089290521185e-03,  -1.0325503688577493e+01,  -1.6533122444456158e-03,
       8.2297470490200302e-03,   9.0574401975545840e+00,   1.4391633836110848e-03,
       9.5616019305435132e-03,  -7.8759096646654951e+00,  -1.2363666069459527e-03,
       1.1108996538242306e-02,   6.8446506699312666e+00,   1.0907227256323094e-03,
       1.2906812580479873e-02,  -5.9542991234257840e+00,  -9.2712769282234358e-04,
       1.4995576820477703e-02,   5.1830565431894602e+00,   8.2888526218099687e-04,
       1.7422374639493515e-02,  -4.4805481279340267e+00,  -6.7675613963809832e-04,
       2.0241911445804391e-02,   3.8608298760715378e+00,   6.3558641899842260e-04,
       2.3517745856009110e-02,  -3.3125736597743227e+00,  -4.8591507683128695e-04,
       2.7323722447292573e-02,   2.8648088091590589e+00,   5.1892328126100203e-04,
       3.1745636378067953e-02,  -2.4710577422247479e+00,  -3.3190335155472070e-04,
       3.6883167401240015e-02,   2.1450315408533416e+00,   4.6189809360776176e-04,
       4.2852126867040180e-02,  -1.8334353019592327e+00,  -1.8326476919948130e-04,
       4.9787068367863944e-02,   1.5850020809005190e+00,   4.7669939315323097e-04,
       5.7844320874838456e-02,  -1.3468969891769780e+00,  -1.7380345519175726e-05,
       6.7205512739749784e-02,   1.1802299801807625e+00,   5.9009214750893949e-04,
       7.8081666001153169e-02,  -9.9988174688478793e-01,   2.1645139320505843e-04,
       9.0717953289412512e-02,   8.8503813256539254e-01,   8.5203135609860704e-04,
       1.0539922456186433e-01,  -7.3165077099639619e-01,   5.9560990889710838e-04,
       1.2245642825298191e-01,   6.5909386165012596e-01,   1.3651107378683781e-03,
       1.4227407158651359e-01,  -5.3038429622108840e-01,   1.2606987195022564e-03,
       1.6529888822158656e-01,   5.0119791866928076e-01,   2.3131990435032663e-03,
       1.9204990862075413e-01,  -3.8269840749371159e-01,   2.4572002938857678e-03,
       2.2313016014842982e-01,   3.8622329595139565e-01,   4.0408430887840449e-03,
       2.5924026064589156e-01,  -2.6413330193320073e-01,   4.6278078809669602e-03,
       3.0119421191220208e-01,   3.0353632730294311e-01,   7.1437051276295131e-03,
       3.4993774911115533e-01,  -1.7255655176111537e-01,   8.5723466849983495e-03,
       4.0656965974059917e-01,   2.5119774955173280e-01,   1.2684763573137947e-02,
       4.7236655274101469e-01,  -9.8536724013140092e-02,   1.5643387012124067e-02,
       5.4881163609402650e-01,   2.1755876398162183e-01,   2.2480928663078600e-02,
       6.3762815162177333e-01,  -3.4268716744688760e-02,   2.8124131719595692e-02,
       7.4081822068171788e-01,   1.9925218957836366e-01,   3.9373999883133115e-02,
       8.6070797642505781e-01,   1.8319735495994052e-02,   4.9445586323210833e-02,
       1.0000000000000000e+00,   1.8963099219918259e-01,   6.7326587032714463e-02,
       1.1618342427282831e+00,   5.7228135568732394e-02,   8.3541701874077570e-02,
       1.3498588075760032e+00,   1.7266316834158107e-01,   1.0961776964853986e-01,
       1.5683121854901687e+00,   6.8141322181604499e-02,   1.3118216481048459e-01,
       1.8221188003905089e+00,   1.2468074033081850e-01,   1.6144181878027153e-01,
       2.1170000166126748e+00,   2.1678852838804014e-02,   1.7704476632134886e-01,
       2.4596031111569494e+00,   1.1114005126278175e-02,   1.9032654055463888e-01,
       2.8576511180631639e+00,  -1.0424806190544497e-01,   1.6333927603825021e-01,
       3.3201169227365472e+00,  -1.6473681128667569e-01,   1.1034442879456068e-01,
       3.8574255306969740e+00,  -2.3603153458714107e-01,  -1.1282682226217962e-02,
       4.4816890703380645e+00,  -2.2093965064386309e-01,  -1.4579378661401318e-01,
       5.2069798271798486e+00,  -7.5633542915308175e-02,  -2.7560051939484942e-01,
       6.0496474644129448e+00,   1.3358180223826097e-01,  -2.3333751023296440e-01,
       7.0286875805892928e+00,   3.3949946683489907e-01,  -5.9615109981928909e-03,
       8.1661699125676499e+00,   1.2815187347111337e-01,   3.2380356528743487e-01,
       9.4877358363585262e+00,  -2.2988301163130145e-01,   2.1970582679149839e-01,
       1.1023176380641601e+01,  -3.3425750283830036e-01,  -2.8302631898505476e-01,
       1.2807103782663029e+01,   4.4350537603751145e-01,  -2.2706962776315812e-01,
       1.4879731724872830e+01,  -8.8943820418669634e-02,   4.7351258711649669e-01,
       1.7287781840567639e+01,  -1.8646079800862164e-01,  -3.5417866045339608e-01,
       2.0085536923187668e+01,   2.4494657419883456e-01,   1.6582378621661517e-01,
       2.3336064580942711e+01,  -2.0169045144304532e-01,  -5.1221107687420810e-02,
       2.7112638920657883e+01,   1.4661206655803793e-01,   3.5484710794282063e-03,
       3.1500392308747923e+01,  -1.0564640256629308e-01,   1.1614894738175324e-02,
       3.6598234443677974e+01,   7.8487036158411266e-02,  -1.4776256489774963e-02,
       4.2521082000062783e+01,  -6.0533748554794195e-02,   1.4194293010344678e-02,
       4.9402449105530167e+01,   4.8243702864613026e-02,  -1.2609914713728791e-02,
       5.7397457045446188e+01,  -3.9347085461672239e-02,   1.0854082569077052e-02,
       6.6686331040925154e+01,   3.2489421068688185e-02,  -9.2082270347668624e-03,
       7.7478462925260828e+01,  -2.6982535264609676e-02,   7.7880648968821110e-03,
       9.0017131300521811e+01,   2.2530196869950080e-02,  -6.6089268276601255e-03,
       1.0458498557711414e+02,  -1.8947601435977172e-02,   5.6159700146012417e-03,
       1.2151041751873485e+02,   1.6017457455233256e-02,  -4.7432063636330263e-03,
       1.4117496392147686e+02,  -1.3519422964231352e-02,   3.9609893136500528e-03,
       1.6402190729990167e+02,   1.1318328695851308e-02,  -3.2753768787828126e-03,
       1.9056626845862999e+02,  -9.3839154851987506e-03,   2.6945716306237466e-03,
       2.2140641620418697e+02,   7.7256174599644543e-03,  -2.2042319512562145e-03,
       2.5723755590577474e+02,  -6.3199190181430056e-03,   1.7733135127602079e-03,
       2.9886740096706029e+02,   5.0986473606509210e-03,  -1.3773733375919272e-03,
       3.4723438047873447e+02,  -3.9929354358609528e-03,   1.0137885881408651e-03,
       4.0342879349273511e+02,   2.9783618569305080e-03,  -6.9751488719640639e-04,
       4.6871738678241655e+02,  -2.0802747552777045e-03,   4.4545125438205673e-04,
       5.4457191012592898e+02,   1.3429398653973710e-03,  -2.6373575275283686e-04,
       6.3270229281225352e+02,  -7.9345560431147465e-04,   1.4519595835116970e-04,
       7.3509518924197266e+02,   4.2530878973518046e-04,  -7.4640168948626184e-05,
       8.5405876252615155e+02,  -2.0457624610548748e-04,   3.5826939350044606e-05,
       9.9227471560502534e+02,   8.6750842046621606e-05,  -1.5854604622793124e-05,
       1.1528587427833875e+03,  -3.1406113278782205e-05,   6.2412989356183992e-06,
       1.3394307643944169e+03,   9.1385289919391839e-06,  -2.0349222128793154e-06,
       1.5561965278371533e+03,  -1.8949818224609619e-06,   4.8072849734177625e-07,
       1.8080424144560632e+03,   2.0794387557779629e-07,  -6.0462736574031818e-08 ).finished();

    template<>
    const Eigen::Matrix<Real, Eigen::Dynamic, 3>  FHT<FHTKEY51>::WT =
        ( Eigen::Matrix<Real, 51, 3>()   <<
           // Base                   J0                        J1
           4.9915939069102170e-03,   6.5314496156480717e-02,   3.8409924166118657e-05,
           6.1703482511978082e-03,  -2.2265895125268051e-01,  -9.4382633059055269e-05,
           7.6274629409160176e-03,   4.2794928430042073e-01,   1.6377612356675232e-04,
           9.4286721829279947e-03,  -5.8890658905204007e-01,  -1.7853487610334151e-04,
           1.1655233178024955e-02,   6.7897324897038758e-01,   1.9759569268356316e-04,
           1.4407591843112350e-02,  -6.8296549495756353e-01,  -1.2796247718553291e-04,
           1.7809914185937643e-02,   6.4702210424566342e-01,   1.3163370416771999e-04,
           2.2015687754376449e-02,  -5.6843090153083187e-01,   1.7066927559149181e-05,
           2.7214645856121149e-02,   4.9960500362966542e-01,   4.1368007808198310e-05,
           3.3641326918204623e-02,  -4.0923517268678855e-01,   2.3582259002758631e-04,
           4.1585655121173182e-02,   3.5487831784012780e-01,  -1.9929745662753875e-05,
           5.1406019627642255e-02,  -2.7408257835871558e-01,   5.8196110748926486e-04,
           6.3545442443014022e-02,   2.4668368971888163e-01,   1.1164151202379049e-05,
           7.8551564282309541e-02,  -1.7348161774657314e-01,   1.2053942009238238e-03,
           9.7101350057185065e-02,   1.7509173908347012e-01,   2.8328713800714110e-04,
           1.2003162851145673e-01,  -1.0007796678766585e-01,   2.4375075610646724e-03,
           1.4837684372696586e-01,   1.3297302593795621e-01,   1.1709289200267103e-03,
           1.8341572156771246e-01,  -4.3822390117083297e-02,   5.0080095645252103e-03,
           2.2672895630607542e-01,   1.1415804492335258e-01,   3.5856849047131551e-03,
           2.8027051982381157e-01,   4.2584271963990363e-03,   1.0536604059335859e-02,
           3.4645581033005746e-01,   1.1496183925974515e-01,   9.6674718436839564e-03,
           4.2827061721265969e-01,   5.1313336759457658e-02,   2.2583365267100426e-02,
           5.2940581770869455e-01,   1.3312389010285514e-01,   2.4201911801947001e-02,
           6.5442388190885858e-01,   1.0111673764393908e-01,   4.8602551164692191e-02,
           8.0896469756649991e-01,   1.6331446488042209e-01,   5.6856974938076565e-02,
           1.0000000000000000e+00,   1.4704406144951229e-01,   1.0202078096072606e-01,
           1.2361478850785035e+00,   1.8341391219815678e-01,   1.2202639829343022e-01,
           1.5280615937840571e+00,   1.5073655145087875e-01,   1.9561985197118459e-01,
           1.8889101074258496e+00,   1.2356364992866918e-01,   2.1570853920674185e-01,
           2.3349722343978727e+00,   1.1529465836107913e-02,   2.8552388758852060e-01,
           2.8863709892679585e+00,  -1.2852626053530605e-01,   2.0559964796530625e-01,
           3.5679813939355345e+00,  -2.9874216118407571e-01,   1.1666011451374350e-01,
           4.4105526541128617e+00,  -3.1330553036684633e-01,  -2.3636714743601936e-01,
           5.4520953354089947e+00,  -3.2332453606385231e-02,  -3.4036030266164258e-01,
           6.7395961181122024e+00,   4.2056051544727674e-01,  -1.9475364255836261e-01,
           8.3311374876876929e+00,   1.3883637369942961e-01,   5.7608115965662166e-01,
           1.0298517985703377e+01,  -5.0223684329542873e-01,  -2.1471464584834585e-01,
           1.2730491227470161e+01,   3.7996073748731690e-01,  -1.2611070492338947e-01,
           1.5736769806847677e+01,  -1.7984404170109178e-01,   2.0019703515125831e-01,
           1.9452974714702009e+01,   7.0557286965350657e-02,  -1.6147664664730754e-01,
           2.4046753552064487e+01,  -2.7522277139686569e-02,   1.1398023016900673e-01,
           2.9725343546388515e+01,   1.1909130661901874e-02,  -7.9924455203352035e-02,
           3.6744920558100112e+01,  -5.8977428045126450e-03,   5.7024556382799692e-02,
           4.5422155835273074e+01,   3.2648420034561555e-03,  -4.1006636508593382e-02,
           5.6148501871478999e+01,  -1.9304039780209286e-03,   2.9192063091319696e-02,
           6.9407851838755207e+01,   1.1594138315987755e-03,  -2.0089573135329029e-02,
           8.5798369258319340e+01,  -6.7050941490060716e-04,   1.2965400526524978e-02,
           1.0605947270185592e+02,   3.5089803807606258e-04,  -7.5154910983038946e-03,
           1.3110519287294045e+02,  -1.5287051174029577e-04,   3.6269079130258285e-03,
           1.6206540689269471e+02,   4.8238483411813232e-05,  -1.2668720233377250e-03,
           2.0033680997479166e+02,  -8.0433917146487977e-06,   2.3403502580547994e-04).finished();

    template<>
    const Eigen::Matrix<Real, Eigen::Dynamic, 3>  FHT<FHTKONG61>::WT =
        ( Eigen::Matrix<Real, 61, 3>()   <<
        // Base                   J0                        J1
        0.23517745856009100e-01,   0.14463210615326699e+03,   0.46440396425864918e+02,
        0.26649097336355482e-01,   -.11066222143752420e+04,   -.45034239857914162e+03,
        0.30197383422318501e-01,   0.37030010025325978e+04,   0.17723440076223640e+04,
        0.34218118311666032e-01,   -.68968188464424520e+04,   -.37559735516994660e+04,
        0.38774207831722009e-01,   0.71663544112656937e+04,   0.44736494009764137e+04,
        0.43936933623407420e-01,   -.24507884783377681e+04,   -.22476603569606068e+04,
        0.49787068367863938e-01,   -.40166567754046082e+04,   -.15219842155931799e+04,
        0.56416139503777350e-01,   0.68623845298546094e+04,   0.34904608559273802e+04,
        0.63927861206707570e-01,   -.50013321011775661e+04,   -.24814243247472318e+04,
        0.72439757034251456e-01,   0.21291291365196648e+04,   0.57328164634108396e+03,
        0.82084998623898800e-01,   -.13845222435542289e+04,   0.53132044837659631e+00,
        0.93014489210663506e-01,   0.21661554291595580e+04,   0.68895205008006235e+03,
        0.10539922456186430e+00,   -.22260393789657141e+04,   -.12012013872160269e+04,
        0.11943296826671961e+00,   0.80317156013986391e+03,   0.79679138423597340e+03,
        0.13533528323661270e+00,   0.10142221718890841e+04,   0.49874460187939818e+02,
        0.15335496684492850e+00,   -.19350455051432630e+04,   -.56367338332457007e+03,
        0.17377394345044520e+00,   0.16601169447226580e+04,   0.47971936503711203e+03,
        0.19691167520419400e+00,   -.75159684285420133e+03,   -.58979702298044558e+02,
        0.22313016014842979e+00,   -.90315984178183285e+02,   -.31935800954986922e+03,
        0.25283959580474641e+00,   0.50705574889546148e+03,   0.45762551999442371e+03,
        0.28650479686019009e+00,   -.51207646422722519e+03,   -.37239927283248380e+03,
        0.32465246735834979e+00,   0.29722959494490038e+03,   0.18255852885279569e+03,
        0.36787944117144239e+00,   -.50248319908072993e+02,   -.23504740340815669e+00,
        0.41686201967850839e+00,   -.12290725861955920e+03,   -.11588151583545380e+03,
        0.47236655274101469e+00,   0.19695244755899429e+03,   0.15740956677133170e+03,
        0.53526142851899028e+00,   -.19175679966946601e+03,   -.14334746114883359e+03,
        0.60653065971263342e+00,   0.14211755630338590e+03,   0.99857411013284818e+02,
        0.68728927879097224e+00,   -.77463216543224149e+02,   -.48246322019171487e+02,
        0.77880078307140488e+00,   0.17638009334931201e+02,   0.20371404343057380e+01,
        0.88249690258459546e+00,   0.28855056499202671e+02,   0.33003938094974323e+02,
        0.10000000000000000e+01,   -.59225643887809561e+02,   -.55476151884197712e+02,
        0.11331484530668261e+01,   0.75987941373668960e+02,   0.67354852323852583e+02,
        0.12840254166877421e+01,   -.81687962781233580e+02,   -.70735403363284121e+02,
        0.14549914146182010e+01,   0.80599209238447102e+02,   0.68872932663164747e+02,
        0.16487212707001280e+01,   -.74895905328771619e+02,   -.63272750944993042e+02,
        0.18682459574322221e+01,   0.67516291538794434e+02,   0.56501568721817442e+02,
        0.21170000166126748e+01,   -.59325033647358048e+02,   -.48706577819918110e+02,
        0.23988752939670981e+01,   0.51617042242841528e+02,   0.41737211284663481e+02,
        0.27182818284590451e+01,   -.44664967446820263e+02,   -.34776621242200903e+02,
        0.30802168489180310e+01,   0.38366152052928278e+02,   0.29161717578906430e+02,
        0.34903429574618419e+01,   -.33308787868993100e+02,   -.23886749056000909e+02,
        0.39550767229205772e+01,   0.28278671651033459e+02,   0.19554007583544220e+02,
        0.44816890703380636e+01,   -.24505863388620480e+02,   -.15966397353366460e+02,
        0.50784190371800806e+01,   0.20469632532079750e+02,   0.12429310210239199e+02,
        0.57546026760057307e+01,   -.17074034940700429e+02,   -.10139180791868180e+02,
        0.65208191203301116e+01,   0.14206119215530070e+02,   0.74716493393871861e+01,
        0.73890560989306504e+01,   -.10904435643084650e+02,   -.55509479014742613e+01,
        0.83728974881272649e+01,   0.87518389425802283e+01,   0.43380799768234208e+01,
        0.94877358363585262e+01,   -.67721665239085622e+01,   -.25911516181746550e+01,
        0.10751013186076360e+02,   0.45096884588095891e+01,   0.16300524630626780e+01,
        0.12182493960703470e+02,   -.32704247166629590e+01,   -.14041567266387460e+01,
        0.13804574186067100e+02,   0.26827195063720430e+01,   0.75225141726873213e+00,
        0.15642631884188170e+02,   -.18406031821386459e+01,   0.46808777208492733e-01,
        0.17725424121461639e+02,   0.91586697140412443e+00,   -.36630197849601159e+00,
        0.20085536923187671e+02,   -.32436011485890798e+00,   0.28948389902792782e+00,
        0.22759895093526730e+02,   0.80675176189581893e-01,   -.13705521898064801e+00,
        0.25790339917193059e+02,   -.12881307195759690e-01,   0.46292091649913013e-01,
        0.29224283781234941e+02,   0.70489137468452920e-03,   -.11721281347435180e-01,
        0.33115451958692312e+02,   0.23846917590855061e-03,   0.22002397354029149e-02,
        0.37524723159601002e+02,   -.69102205995825531e-04,   -.28146036357227600e-03,
        0.42521082000062783e+02,   0.67792635718095777e-05,   0.18788896009128770e-04 ).finished();

    template<>
    const Eigen::Matrix<Real, Eigen::Dynamic, 3>  FHT<FHTKONG121>::WT =
        ( Eigen::Matrix<Real, 121, 3>()   <<
       // Base                   J0                        J1
        0.10077854290485105e-02,  0.30018305463183890e+03,  0.14159106906236584e+05,
        0.11306077036215634e-02,  -.14997153161927693e+04,  -.63894162353990403e+05,
        0.12683987510072388e-02,  0.32362173919097522e+04,  0.12310811383612661e+06,
        0.14229828670044432e-02,  -.35889806191080561e+04,  -.11486817725824723e+06,
        0.15964066806122474e-02,  0.99319938998747637e+03,  -.14753412401589708e+04,
        0.17909662505412698e-02,  0.38179279963153253e+04,  0.17820074382693824e+06,
        0.20092374640700602e-02,  -.85085234766944122e+04,  -.32884341392696078e+06,
        0.22541101407146007e-02,  0.11207327477259456e+05,  0.40034208858031681e+06,
        0.25288262922292556e-02,  -.11531776512925609e+05,  -.39292610305676475e+06,
        0.28370230454855348e-02,  0.10180936873156406e+05,  0.33649847192558867e+06,
        0.31827807965096669e-02,  -.81063361758784658e+04,  -.26286375592255167e+06,
        0.35706772332182498e-02,  0.60085437844429871e+04,  0.19276161687520225e+06,
        0.40058479420904168e-02,  -.42367917320848228e+04,  -.13532470402888930e+06,
        0.44940544011834518e-02,  0.28856159727039544e+04,  0.92200446462483131e+05,
        0.50417602596909790e-02,  -.19188095349896853e+04,  -.61548829780693632e+05,
        0.56562169139531080e-02,  0.12551171902691910e+04,  0.40522494324288629e+05,
        0.63455595129091099e-02,  -.81182810371631717e+03,  -.26431609499963735e+05,
        0.71189146640646597e-02,  0.52111815723616189e+03,  0.17133134814156092e+05,
        0.79865212659555023e-02,  -.33278260848862072e+03,  -.11059551444776085e+05,
        0.89598660668788899e-02,  0.21176915752357209e+03,  0.71191992278972921e+04,
        0.10051835744633576e-01,  -.13443218355814457e+03,  -.45742755998737493e+04,
        0.11276887520740558e-01,  0.85194650584339684e+02,  0.29354874569128351e+04,
        0.12651240568005305e-01,  -.53917022467612526e+02,  -.18822749389993348e+04,
        0.14193090745577676e-01,  0.34088478048287179e+02,  0.12062795877473545e+04,
        0.15922851504511684e-01,  -.21523595959544657e+02,  -.77277108232453850e+03,
        0.17863424153314034e-01,  0.13577090924007551e+02,  0.49492492631541484e+03,
        0.20040501061684014e-01,  -.85434684440849118e+01,  -.31691334079981812e+03,
        0.22482905816735520e-01,  0.53682354535020123e+01,  0.20289254048774126e+03,
        0.25222974835227209e-01,  -.33525766356269853e+01,  -.12987117322606318e+03,
        0.28296985484186854e-01,  0.20885260837282376e+01,  0.83111905719290576e+02,
        0.31745636378067939e-01,  -.12793232916734436e+01,  -.53171419417674883e+02,
        0.35614586211371861e-01,  0.78058884271469897e+00,  0.34001318850873965e+02,
        0.39955058260653903e-01,  -.45242438742651114e+00,  -.21727145676811332e+02,
        0.44824518559266870e-01,  0.26089203241610426e+00,  0.13868836029693362e+02,
        0.50287436723591865e-01,  -.12338615646032285e+00,  -.88371017147469129e+01,
        0.56416139503777350e-01,  0.56281416318118380e-01,  0.56159478530342604e+01,
        0.63291768359640704e-01,  0.70125081568702717e-02,  -.35528681405641978e+01,
        0.71005353739636984e-01,  -.22285034855420188e-01,  0.22326264948682826e+01,
        0.79659020285898011e-01,  0.58388786672113245e-01,  -.13861956199997831e+01,
        0.89367338921753192e-01,  -.50279850215481377e-01,  0.84533815622227582e+00,
        0.10025884372280371e+00,  0.78597196793220414e-01,  -.49730994319610561e+00,
        0.11247773365428958e+00,  -.57780915798218570e-01,  0.27626521874054144e+00,
        0.12618578170503872e+00,  0.86833839108689789e-01,  -.13207677866949757e+00,
        0.14156447669413402e+00,  -.56713538106749770e-01,  0.42681318795235568e-01,
        0.15881742610692068e+00,  0.90861627775228854e-01,  0.18663686575331840e-01,
        0.17817305177289841e+00,  -.51733726817583675e-01,  -.53208742589031535e-01,
        0.19988761407514449e+00,  0.93892545736654870e-01,  0.81715199974391917e-01,
        0.22424860473053532e+00,  -.44578054953703386e-01,  -.92375366349240665e-01,
        0.25157855305975646e+00,  0.97333941326658679e-01,  0.10918440876205196e+00,
        0.28223929614052329e+00,  -.35809206216951828e-01,  -.10784697385032857e+00,
        0.31663676937905316e+00,  0.10187303599617950e+00,  0.12263194639047151e+00,
        0.35522638092495146e+00,  -.25533080595253506e-01,  -.11291394172961393e+00,
        0.39851904108451419e+00,  0.10787869351568864e+00,  0.13120315240462399e+00,
        0.44708792655935642e+00,  -.13731146379316628e-01,  -.11264897932654486e+00,
        0.50157606906605545e+00,  0.11549428371538972e+00,  0.13910357869782769e+00,
        0.56270486880695569e+00,  -.49007131028919334e-03,  -.10858278920034534e+00,
        0.63128364550692595e+00,  0.12453783048394922e+00,  0.14870786320325752e+00,
        0.70822035346779999e+00,  0.13716079779752552e-01,  -.10058646924687212e+00,
        0.79453360250333405e+00,  0.13420142569679816e+00,  0.16184445590085567e+00,
        0.89136614390683133e+00,  0.27562751092388021e-01,  -.87680656207090757e-01,
        0.10000000000000000e+01,  0.14247216088490525e+00,  0.18020003971865040e+00,
        0.11218734375719384e+01,  0.38106514837307398e-01,  -.68631869765463246e-01,
        0.12586000099294778e+01,  0.14519350403349998e+00,  0.20499322719217808e+00,
        0.14119899196676591e+01,  0.39680378340821582e-01,  -.43037250192290703e-01,
        0.15840739849944818e+01,  0.13490403422658193e+00,  0.23549230905732943e+00,
        0.17771305269140385e+01,  0.22901601418290750e-01,  -.13817950392389918e-01,
        0.19937155332430825e+01,  0.10048732915054742e+00,  0.26547248491456293e+00,
        0.22366964988199869e+01,  -.24201736611187494e-01,  0.78529706964075002e-02,
        0.25092903899362975e+01,  0.31137736528372380e-01,  0.27711681990519133e+00,
        0.28151062356240644e+01,  -.10740460659967459e+00,  -.39269616914972142e-02,
        0.31581929096897681e+01,  -.67585707297970046e-01,  0.23652124461108126e+00,
        0.35430927361089823e+01,  -.20086348522717648e+00,  -.87535132259551965e-01,
        0.39749016274947486e+01,  -.13938783391528009e+00,  0.11096253210869840e+00,
        0.44593365528478257e+01,  -.21109045469819143e+00,  -.25015308781917761e+00,
        0.50028112278335879e+01,  -.60476076401026799e-01,  -.50607353375473493e-01,
        0.56125210296931574e+01,  -.20240530933718630e-01,  -.35378711425963411e+00,
        0.62965382610266571e+01,  0.20107385437033698e+00,  -.11888933264390817e-01,
        0.70639190237012111e+01,  0.20478593615229865e+00,  -.12848274860566231e+00,
        0.79248231178494901e+01,  0.21005450988434599e+00,  0.34458207638195643e+00,
        0.88906485533713706e+01,  -.10138188698229451e+00,  0.12029950796999150e+00,
        0.99741824548147235e+01,  -.24443221085371702e+00,  0.20091357644979224e+00,
        0.11189770357552707e+02,  -.20919885878257014e+00,  -.40637916861032514e+00,
        0.12553506136668235e+02,  0.25885662664839104e+00,  -.77844503202361123e-01,
        0.14083445083124413e+02,  0.22511239447558806e+00,  0.84393485976334601e-01,
        0.15799842948260402e+02,  -.24749979171782066e+00,  0.38585911280828078e+00,
        0.17725424121461643e+02,  -.15834221813675839e+00,  -.53710156851306179e+00,
        0.19885682491564729e+02,  0.41669469785897478e+00,  0.29613984212416533e+00,
        0.22309218975275826e+02,  -.38746305352335819e+00,  -.25577176944819074e-01,
        0.25028120181337815e+02,  0.24494648145680814e+00,  -.99525029843826690e-01,
        0.28078383223801051e+02,  -.12494432093301468e+00,  0.11347854243597852e+00,
        0.31500392308747937e+02,  0.56623704291934376e-01,  -.87204036114652397e-01,
        0.35339453404279688e+02,  -.24422912005250250e-01,  0.58226255619279292e-01,
        0.39646394072572605e+02,  0.10546622665155797e-01,  -.36883375167178621e-01,
        0.44478236405528754e+02,  -.47164930460653993e-02,  0.23021285157529506e-01,
        0.49898951973407868e+02,  0.22239210348696040e-02,  -.14375628722401815e-01,
        0.55980308781644155e+02,  -.11112568714436552e-02,  0.90237392744176772e-02,
        0.62802821449201709e+02,  0.58623849306147836e-03,  -.56969386329969772e-02,
        0.70456817188432538e+02,  -.32371481890903825e-03,  0.36146490050027961e-02,
        0.79043631699564457e+02,  0.18516534379096563e-03,  -.23030074382742690e-02,
        0.88676950812960627e+02,  -.10858319212643027e-03,  0.14726883339263065e-02,
        0.99484315641933861e+02,  0.64653084189876281e-04,  -.94515928495026650e-03,
        0.11160881117370802e+03,  -.38733129356665885e-04,  0.60913472182886252e-03,
        0.12521096065476522e+03,  0.23124613983496482e-04,  -.39467913721300099e-03,
        0.14047085085144619e+03,  -.13593265028285278e-04,  0.25756984272807789e-03,
        0.15759051632336701e+03,  0.77226585608530268e-05,  -.16970914383967808e-03,
        0.17679661427643231e+03,  -.40941184416352728e-05,  0.11317330787388945e-03,
        0.19834342540938118e+03,  0.18578931549417668e-05,  -.76493433852811981e-04,
        0.22251622048381586e+03,  -.49885201653307130e-06,  0.52337311186417404e-04,
        0.24963503718969392e+03,  -.29669295903973297e-06,  -.36072348136781267e-04,
        0.28005891731040066e+03,  0.72005338190127765e-06,  0.24847205794977743e-04,
        0.31419066028569421e+03,  -.89038493548159272e-06,  -.16954676816358357e-04,
        0.35248215610770893e+03,  0.88868839302693829e-06,  0.11370634951567925e-04,
        0.39544036815532411e+03,  -.77878715022764851e-06,  -.74452601658677115e-05,
        0.44363404517712638e+03,  0.61518900846996585e-06,  0.47280436641109142e-05,
        0.49770125128680706e+03,  -.44159321883066467e-06,  -.28859162979423948e-05,
        0.55835781366498543e+03,  0.28741104780859982e-06,  0.16691593098206021e-05,
        0.62640679981148924e+03,  -.16745354865744502e-06,  -.89400895772153075e-06,
        0.70274914982295252e+03,  0.84959064735970960e-07,  0.42755247064623627e-06,
        0.78839560446263238e+03,  -.35626208459379747e-07,  -.17204733141025195e-06,
        0.88448008694509986e+03,  0.11120656477437054e-07,  0.52194089326250459e-07,
        0.99227471560502624e+03,  -.19689609552964338e-08,  -.90671074377795857e-08 ).finished();

    template<>
    const Eigen::Matrix<Real, Eigen::Dynamic, 3>  FHT<FHTKONG241>::WT =
        ( Eigen::Matrix<Real, 241, 3>()   <<
       // Base                   J0                        J1
        0.40973497897978643e-03,  0.20521734894828349e+02,  -.68036776043707992e+01,
        0.43725238042414673e-03,  -.18902686822627982e+03,  0.12311367914708828e+03,
        0.46661782370309847e-03,  0.73615711333621391e+03,  -.60393880274694629e+03,
        0.49795542150327349e-03,  -.15743636401162100e+04,  0.14366739793969700e+04,
        0.53139762179825294e-03,  0.19044172285355407e+04,  -.18485584122626103e+04,
        0.56708576763830356e-03,  -.93177949828687565e+03,  0.10200389392810666e+04,
        0.60517069453505309e-03,  -.84756674787751410e+03,  0.55616172944428206e+03,
        0.64581336796593124e-03,  0.18896580243120454e+04,  -.13603216652028611e+04,
        0.68918556369279311e-03,  -.14364973619770130e+04,  0.70167261135195611e+03,
        0.73547059377007120e-03,  0.39999475225222255e+03,  0.53402931472384910e+03,
        0.78486408131093165e-03,  -.13542454844021287e+03,  -.11429297666385887e+04,
        0.83757478728596971e-03,  0.92532241451272546e+03,  0.90089651035093164e+03,
        0.89382549284889267e-03,  -.19710056537324476e+04,  -.41234322841018411e+03,
        0.95385394091834482e-03,  0.24446279171484089e+04,  0.20384051761852257e+03,
        0.10179138409954376e-02,  -.21906123203102729e+04,  -.28956552394430940e+03,
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        0.19344630878742183e+03,  0.15239810059902827e-01,  -.42878952176510369e-02,
        0.20643797415630826e+03,  -.13631136080120022e-01,  0.42321726027587606e-02,
        0.22030214709649516e+03,  0.12105408954537602e-01,  -.41811395672186466e-02,
        0.23509742436523857e+03,  -.10658744979296539e-01,  0.41354762911556932e-02,
        0.25088633802084459e+03,  0.92973012802827770e-02,  -.40942937154137878e-02,
        0.26773561971364717e+03,  -.80347421903655229e-02,  0.40554223224550864e-02,
        0.28571648272651305e+03,  0.68891191289946248e-02,  -.40157136359124266e-02,
        0.30490492295690876e+03,  -.58791440085348362e-02,  0.39713297394453244e-02,
        0.32538204011263201e+03,  0.50201744968206546e-02,  -.39180044788809047e-02,
        0.34723438047873475e+03,  -.43205477515280673e-02,  0.38512768724064841e-02,
        0.37055430270433595e+03,  0.37790104974130003e-02,  -.37667091650295829e-02,
        0.39544036815532411e+03,  -.33838316346466528e-02,  0.36601079883520934e-02,
        0.42199775748276141e+03,  0.31138040173687830e-02,  -.35277760443730628e-02,
        0.45033871516762099e+03,  -.29408759849158255e-02,  0.33668346001750932e-02,
        0.48058302392070897e+03,  0.28337622799129800e-02,  -.31756548702066185e-02,
        0.51285851094282907e+03,  -.27617063348841968e-02,  0.29543911277564146e-02,
        0.54730158818487951e+03,  0.26976528553792770e-02,  -.27055140265840505e-02,
        0.58405782889129489e+03,  -.26203758209448719e-02,  0.24341413354852411e-02,
        0.62328258286358414e+03,  0.25154519816519300e-02,  -.21479350621587340e-02,
        0.66514163304436181e+03,  -.23752432671978732e-02,  0.18564376110443456e-02,
        0.70981189619693009e+03,  0.21981931889228849e-02,  -.15699285271508928e-02,
        0.75748217064180938e+03,  -.19877598903184075e-02,  0.12980859369581127e-02,
        0.80835393421053413e+03,  0.17512378319139862e-02,  -.10488156933979571e-02,
        0.86264219578923701e+03,  -.14986007967920582e-02,  0.82752974192331252e-03,
        0.92057640405108020e+03,  0.12413783399553321e-02,  -.63697315746016306e-03,
        0.98240141721825944e+03,  -.99151066433110242e-03,  0.47751718968428873e-03,
        0.10483785379522853e+04,  0.76014790547529541e-03,  -.34772734444372060e-03,
        0.11187866177464875e+04,  -.55645455379022023e-03,  0.24499928240303252e-03,
        0.11939232354884318e+04,  0.38658922048399793e-03,  -.16610663484386119e-03,
        0.12741059551734540e+04,  -.25308541294203246e-03,  0.10758513633705277e-03,
        0.13596736680849924e+04,  0.15481736123335846e-03,  -.65954676827986505e-04,
        0.14509880251144575e+04,  -.87598356988947244e-04,  0.37834534141493396e-04,
        0.15484349652742915e+04,  0.45276882194925013e-04,  -.20025414475625305e-04,
        0.16524263468644833e+04,  -.21044884609057091e-04,  0.96121169858568779e-05,
        0.17634016881866382e+04,  0.86194148443616213e-05,  -.40939692455506115e-05,
        0.18818300251626902e+04,  -.30265483432492266e-05,  0.15034842918522733e-05,
        0.20082118937094979e+04,  0.87586378588036060e-06,  -.45718370169166360e-06,
        0.21430814452477584e+04,  -.19631579670478718e-06,  0.10805490301555136e-06,
        0.22870087042864643e+04,  0.30405955678339503e-07,  -.17684735514194769e-07,
        0.24406019776245007e+04,  -.24535953018971818e-08,  0.15081394131412287e-08).finished();


    template<>
    const Eigen::Matrix<Real, Eigen::Dynamic, 3>  FHT<IRONS>::WT =
        ( Eigen::Matrix<Real, 801, 3>()   <<
5.1090890280633251e-12,-1.1440189709930581e-02,-2.9865298147256597e-01,
5.4522104626800278e-12,1.4089576568198108e-02,1.6825091654945588e+00,
5.8183755980909140e-12,2.2400742043591171e-01,-3.9909636849733179e+00,
6.2091320267595006e-12,-1.1200780381187927e+00,4.9940362909152105e+00,
6.6261312759492981e-12,2.7213598338895371e+00,-3.5227519313240347e+00,
7.0711357878836475e-12,-4.3739317168361938e+00,2.6056656669708347e+00,
7.5460263686860725e-12,5.3351012182835174e+00,-5.3969874367728270e+00,
8.0528101375844027e-12,-5.4120616497647491e+00,9.2866422616630544e+00,
8.5936290099757180e-12,4.7015655598885493e+00,-8.5436765024661732e+00,
9.1707687502053946e-12,-3.2496831747033283e+00,2.1285531019102466e+00,
9.7866686323222072e-12,1.4209329740424859e+00,4.7355533725255139e+00,
1.0443931749640362e-11,-1.4963387858058383e-01,-6.6056705357919920e+00,
1.1145336016681277e-11,2.6558218414368540e-01,2.9876585509408145e+00,
1.1893845909995609e-11,-1.6199971845392389e+00,2.4860597486624316e+00,
1.2692624997486851e-11,3.1194064733684801e+00,-6.0681932841181405e+00,
1.3545049309192453e-11,-3.6130228898198560e+00,6.4546440070305549e+00,
1.4454721606033618e-11,2.6987863548438349e+00,-4.5717873165331087e+00,
1.5425486606839967e-11,-8.2559192716319119e-01,2.0724537708329307e+00,
1.6461447238006732e-11,-1.1629453321896712e+00,-1.6264737070607529e-01,
1.7566981974463148e-11,2.5522158857365116e+00,-7.3201400288193552e-01,
1.8746763345242814e-11,-3.0221273874091255e+00,7.5022476478393596e-01,
2.0005777681870621e-11,2.6302915904655348e+00,-2.5229671131005021e-01,
2.1349346193032131e-11,-1.6511806017788648e+00,-4.1903311849884128e-01,
2.2783147454596494e-11,4.0878534213599976e-01,1.0361419312266800e+00,
2.4313241410048430e-11,8.2974265204149189e-01,-1.4903396588431286e+00,
2.5946094982764667e-11,-1.8935689816158092e+00,1.7574392920188009e+00,
2.7688609408386673e-11,2.7031353831522149e+00,-1.8594960208325853e+00,
2.9548149402808939e-11,-3.2456376483329681e+00,1.8364785912050299e+00,
3.1532574289059990e-11,3.5479588284428769e+00,-1.7296785407909137e+00,
3.3650271214635258e-11,-3.6550311170809886e+00,1.5740339181905207e+00,
3.5910190599673686e-11,3.6155585988395926e+00,-1.3958724576515054e+00,
3.8321883965798226e-11,-3.4740934831732471e+00,1.2133804911533939e+00,
4.0895544305505377e-11,3.2675735955806511e+00,-1.0381241423687504e+00,
4.3642049162723698e-11,-3.0245589411073852e+00,8.7674185354212186e-01,
4.6573006606619252e-11,2.7658773688717910e+00,-7.3242717404068847e-01,
4.9700804292958246e-11,-2.5058651014322049e+00,6.0609218332182901e-01,
5.3038661820383082e-11,2.2537447606959526e+00,-4.9722647403547421e-01,
5.6600686602883008e-11,-2.0149128997135222e+00,4.0450840103947600e-01,
6.0401933494608153e-11,1.7920413357751710e+00,-3.2622722124865133e-01,
6.4458468419025009e-11,-1.5859648396052874e+00,2.6056285491981318e-01,
6.8787436271345855e-11,1.3963618192783833e+00,-2.0575804551718366e-01,
7.3407133381219369e-11,-1.2222554728176813e+00,1.6021051403746242e-01,
7.8337084841942460e-11,1.0623740612824220e+00,-1.2250923828639693e-01,
8.3598127033028842e-11,-9.1540603770286466e-01,9.1436011333782333e-02,
8.9212495684912973e-11,7.8017318339208475e-01,-6.5949026175411415e-02,
9.5203919857990853e-11,-6.5573336780490232e-01,4.5159863942729160e-02,
1.0159772223320414e-10,5.4141878332744220e-01,-2.8310392989868493e-02,
1.0842092613804248e-10,-4.3681584787546263e-01,1.4752641563129120e-02,
1.1570236976030375e-10,3.4170048397819913e-01,-3.9327841039699957e-03,
1.2347282803234503e-10,-2.5595266266700445e-01,-4.6205328480416925e-03,
1.3176514270095466e-10,1.7947617951604222e-01,1.1304045050390869e-02,
1.4061436113259439e-10,-1.1214028602961829e-01,-1.6445439469135886e-02,
1.5005788444066614e-10,5.3747250255077053e-02,2.0308936517406031e-02,
1.6013562556085741e-10,-4.0209064842679221e-03,-2.3102911386081559e-02,
1.7089017794267659e-10,-3.7393876464927547e-02,2.4990320025370463e-02,
1.8236699557014806e-10,7.0930612142167559e-02,-2.6101237213545639e-02,
1.9461458507251581e-10,-9.7102477882718391e-02,2.6545764836599702e-02,
2.0768471073691997e-10,1.1650148514186021e-01,-2.6425125501025087e-02,
2.2163261328952504e-10,-1.2979109071911354e-01,2.5839049048154435e-02,
2.3651724336976888e-10,1.3769051773065349e-01,-2.4888534327397578e-02,
2.5240151068452068e-10,-1.4094971597072878e-01,2.3674269205628515e-02,
2.6935254989518980e-10,1.4031532418620726e-01,-2.2291958810559589e-02,
2.8744200436154466e-10,-1.3649325796206857e-01,2.0826438519948243e-02,
3.0674632894150323e-10,1.3011825401673688e-01,-1.9346645255504447e-02,
3.2734711312664760e-10,-1.2174081727228678e-01,1.7903036958933419e-02,
3.4933142587921442e-10,1.1183870988411707e-01,-1.6527980705191122e-02,
3.7279218362800181e-10,-1.0085281377861434e-01,1.5238586291245136e-02,
3.9782854297851171e-10,8.9234741413878521e-02,-1.4040909578417245e-02,
4.2454631979713245e-10,-7.7483353116465398e-02,1.2934341905312622e-02,
4.5305843644060792e-10,6.6149723508613048e-02,-1.1915213721393574e-02,
4.8348539902098753e-10,-5.5803913386265072e-02,1.0979161725760845e-02,
5.1595580672323794e-10,4.6972406213963855e-02,-1.0122386469767578e-02,
5.5060689532813029e-10,-4.0066468322891777e-02,9.3421605785969294e-03,
5.8758511723757762e-10,3.5326371974312945e-02,-8.6368486182348009e-03,
6.2704676045392328e-10,-3.2800141513530251e-02,8.0056041668918384e-03,
6.6915860912927816e-10,3.2359998267229073e-02,-7.4478744612512951e-03,
7.1409864847668220e-10,-3.3745725206804189e-02,6.9627134741786492e-03,
7.6205681702244763e-10,3.6618871092912661e-02,-6.5478255994165270e-03,
8.1323580937899945e-10,-4.0612368169092070e-02,6.1984798166189381e-03,
8.6785193293118034e-10,4.5364460481880586e-02,-5.9067493200442838e-03,
9.2613602205677541e-10,-5.0534669359687992e-02,5.6615472590875278e-03,
9.8833441374516676e-10,5.5808324213228393e-02,-5.4496414696962384e-03,
1.0547099887376127e-09,-6.0897705942290409e-02,5.2574863183817017e-03,
1.1255432825894951e-09,6.5543911423462359e-02,-5.0733872372297449e-03,
1.2011336713503887e-09,-6.9520954090966480e-02,4.8892869464898271e-03,
1.2818006368732813e-09,7.2642596846878307e-02,-4.7015707472092732e-03,
1.3678851171007296e-09,-7.4770107977191858e-02,4.5107315408425188e-03,
1.4597509470348683e-09,7.5818246348175064e-02,-4.3201261412033447e-03,
1.5577863964816331e-09,-7.5759110731286716e-02,4.1341842163676789e-03,
1.6624058110683089e-09,7.4624545887006830e-02,-3.9565015109325943e-03,
1.7740513634702650e-09,-7.2505602046224513e-02,3.7883426125376496e-03,
1.8931949222483771e-09,6.9547114922562464e-02,-3.6279798647690775e-03,
2.0203400461956881e-09,-6.5938000664829369e-02,3.4709974935156693e-03,
2.1560241126225001e-09,6.1898663588882269e-02,-3.3114719449073757e-03,
2.3008205885750249e-09,-5.7665637323020658e-02,3.1438317774727027e-03,
2.4553414545867905e-09,5.3474628295892453e-02,-2.9649860602611478e-03,
2.6202397912068980e-09,-4.9544963130709753e-02,2.7760698030425868e-03,
2.7962125392369974e-09,4.6066940359917333e-02,-2.5832005813761459e-03,
2.9840034453430037e-09,-4.3191314977865262e-02,2.3969556479924389e-03,
3.1844062054913024e-09,4.1021519366722506e-02,-2.2305992455474576e-03,
3.3982678194950711e-09,-3.9610760399203193e-02,2.0973873143090641e-03,
3.6264921708485495e-09,3.8964240635458142e-02,-2.0076087825038991e-03,
3.8700438469796559e-09,-3.9044770217330035e-02,1.9661607383310168e-03,
4.1299522160668626e-09,3.9780748082079737e-02,-1.9712176636866841e-03,
4.4073157776512375e-09,-4.1075007063210357e-02,2.0142025132661857e-03,
4.7033068054313599e-09,4.2810939250851256e-02,-2.0810710895240794e-03,
5.0191763018636703e-09,-4.4853310986109521e-02,2.1547303137775349e-03,
5.3562592855090820e-09,4.7045390371205476e-02,-2.2180818763506195e-03,
5.7159804334726519e-09,-4.9205730261233455e-02,2.2569640045060260e-03,
6.0998601027838169e-09,5.1127471236897828e-02,-2.2623518676409236e-03,
6.5095207561668245e-09,-5.2583732594827556e-02,2.2313868329772186e-03,
6.9466938193596495e-09,5.3342581222527011e-02,-2.1670062014235610e-03,
7.4132269989635538e-09,-5.3190294372349088e-02,2.0762784417887726e-03,
7.9110920917524833e-09,5.1956785840276395e-02,-1.9679626528135972e-03,
8.4423933184480931e-09,-4.9536696665063260e-02,1.8499705368210503e-03,
9.0093762171826728e-09,4.5901454781179948e-02,-1.7272583022945845e-03,
9.6144371342388217e-09,-4.1098407520732329e-02,1.6005139699207314e-03,
1.0260133352177466e-08,3.5236542896908273e-02,-1.4659170166076304e-03,
1.0949193898161396e-08,-2.8463819059575218e-02,1.3160394057220169e-03,
1.1684531078155286e-08,2.0943412969989878e-02,-1.1416613195150136e-03,
1.2469252785750989e-08,-1.2833710403290413e-02,9.3411475134550100e-04,
1.3306675637641872e-08,4.2752714055172489e-03,-6.8770396335129371e-04,
1.4200338991262822e-08,4.6131279399408455e-03,4.0163150956384875e-04,
1.5154019903840864e-08,-1.3730691028795601e-02,-8.0851954377817283e-05,
1.6171749096081416e-08,2.2988131042884975e-02,-2.6440068048054423e-04,
1.7257827987960214e-08,-3.2302281734781634e-02,6.2022074856397328e-04,
1.8416846878621793e-08,4.1592830617908999e-02,-9.7133699999982248e-04,
1.9653704347223121e-08,-5.0781507869359678e-02,1.3035859089905266e-03,
2.0973627956718020e-08,5.9793746922226498e-02,-1.6059567156440011e-03,
2.2382196348088178e-08,-6.8559866111090995e-02,1.8717304066916095e-03,
2.3885362818401250e-08,7.7012948317981930e-02,-2.0985971118760278e-03,
2.5489480482347579e-08,-8.5084102840099068e-02,2.2879475330694317e-03,
2.7201329123601899e-08,9.2698403461110995e-02,-2.4436166222818381e-03,
2.9028143849496367e-08,-9.9773217325143354e-02,2.5704082845457647e-03,
3.0977645670112584e-08,1.0622060499430758e-01,-2.6728261816559703e-03,
3.3058074131036481e-08,-1.1195536310011608e-01,2.7543457307591876e-03,
3.5278222137697247e-08,1.1690795797802282e-01,-2.8172629960412400e-03,
3.7647473118473871e-08,-1.2103752994485634e-01,2.8629569234492908e-03,
4.0175840683640600e-08,1.2434117193704534e-01,-2.8923970106281074e-03,
4.2874010947768717e-08,-1.2685740960147945e-01,2.9067098933242535e-03,
4.5753387694457955e-08,1.2866246063264691e-01,-2.9075798539915320e-03,
4.8826140574289538e-08,-1.2985804255071667e-01,2.8973881928447817e-03,
5.2105256539704332e-08,1.3055423248037545e-01,-2.8791873792372684e-03,
5.5604594734198818e-08,-1.3085263278124740e-01,2.8565849407209288e-03,
5.9338945067826102e-08,1.3083389014182845e-01,-2.8334690028847106e-03,
6.3324090726568584e-08,-1.3055083523304536e-01,2.8135202400310410e-03,
6.7576874879780872e-08,1.3002919304527422e-01,-2.7995701161917267e-03,
7.2115271867639708e-08,-1.2927468473381507e-01,2.7928906528469589e-03,
7.6958463169471300e-08,1.2828290256097397e-01,-2.7925356720975214e-03,
8.2126918474039618e-08,-1.2704772735804012e-01,2.7950051416928039e-03,
8.7642482194436360e-08,1.2556822206685272e-01,-2.7945315816324534e-03,
9.3528465793223467e-08,-1.2385320727905302e-01,2.7840157013113119e-03,
9.9809746308046822e-08,1.2192335759062189e-01,-2.7563380529638895e-03,
1.0651287149412915e-07,-1.1981109388421521e-01,2.7057053722601607e-03,
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1.0503769188197622e+10,5.0463332707869270e-02,4.5790766329382220e-02,
1.1209192079233732e+10,-5.4539852147009404e-02,-4.8946277114826436e-02,
1.1961990483410105e+10,5.8912588746978516e-02,5.1924250104485731e-02,
1.2765346093968895e+10,-6.3689281962167985e-02,-5.4653737525764287e-02,
1.3622654283566427e+10,6.8960661308154286e-02,5.7056998538953387e-02,
1.4537538454773909e+10,-7.4764171083854122e-02,-5.9049246411556580e-02,
1.5513865354344173e+10,8.1046243604414786e-02,6.0541604919897588e-02,
1.6555761415969675e+10,-8.7631262021416148e-02,-6.1447136972360261e-02,
1.7667630200603680e+10,9.4212087513984424e-02,6.1689262727046612e-02,
1.8854171008056877e+10,-1.0036821202702702e-01,-6.1211359503157640e-02,
2.0120398738530735e+10,1.0560257051803333e-01,5.9985521519878050e-02,
2.1471665088031349e+10,-1.0938857699127119e-01,-5.8018266521490142e-02,
2.2913681167247692e+10,1.1123116970403625e-01,5.5352131383547366e-02,
2.4452541639490528e+10,-1.1074529604274791e-01,-5.2063702955026124e-02,
2.6094750479712498e+10,1.0773889221804786e-01,4.8259218343626974e-02,
2.7847248463478970e+10,-1.0227767596057734e-01,-4.4068356899541840e-02,
2.9717442502070461e+10,9.4715714279097515e-02,3.9636339680207335e-02,
3.1713236947702782e+10,-8.5682323397137439e-02,-3.5114467575017273e-02,
3.3843067001175274e+10,7.6014537431311854e-02,3.0649360257340358e-02,
3.6115934363143112e+10,-6.6632902691332457e-02,-2.6371394138155722e-02,
3.8541445279695259e+10,5.8385498821592823e-02,2.2383759081471374e-02,
4.1129851143036385e+10,-5.1906107962900294e-02,-1.8754831442578744e-02,
4.3892091818869835e+10,4.7522714757700542e-02,1.5516598333022213e-02,
4.6839841883606430e+10,-4.5225454388285354e-02,-1.2669816532921888e-02,
4.9985559966819351e+10,4.4688420081009934e-02,1.0193846488865441e-02,
5.3342541407488373e+10,-4.5339130958555331e-02,-8.0577903400315884e-03,
5.6924974446588760e+10,4.6463596788230858e-02,6.2300512177423523e-03,
6.0748000193516830e+10,-4.7323836618246379e-02,-4.6844334869447796e-03,
6.4827776619804024e+10,4.7267424250363559e-02,3.4017114257330078e-03,
6.9181546850586517e+10,-4.5823651595430309e-02,-2.3668179359128522e-03,
7.3827712042461319e+10,4.2782414978768488e-02,1.5636326056987062e-03,
7.8785909155749954e+10,-3.8234406049544527e-02,-9.7044571300120355e-04,
8.4077093949871857e+10,3.2545369775588688e-02,5.5831629261543264e-04,
8.9723629552603470e+10,-2.6263715487330738e-02,-2.9251502540276694e-04,
9.5749380977564819e+10,1.9994704435918751e-02,1.3593178818465128e-04,
1.0217981598940857e+11,-1.4280566134332921e-02,-5.3283837134423527e-05,
1.0904211274301332e+11,9.5088602008155752e-03,1.5116070508507072e-05,
1.1636527465162538e+11,-5.8610990025049518e-03,-3.4192915218219794e-07,
1.2418025296942732e+11,3.3142061921512035e-03,-3.7142335450441982e-06,
1.3252007760663600e+11,-1.6957774668506845e-03,3.5021759700494138e-06,
1.4141999673001535e+11,7.6714035970995662e-04,-2.0293966192354943e-06,
1.5091762573881909e+11,-2.9501182753750469e-04,7.0288001599310040e-07,
1.6105310624581653e+11,9.0324600119093780e-05,-2.2787356358365474e-08,
1.7186927573532950e+11,-1.9614202213020487e-05,-1.2262798202392089e-07,
1.8341184861533228e+11,2.3423676335839903e-06,6.4149102369353071e-08,
1.9572960942883878e+11,-4.2606808905352592e-08,-1.2257294232480575e-08
        ).finished();

}		// -----  end of Lemma  name  -----