/* Copyright (C) 2019 Alessandro Languasco */ /**************** A. LANGUASCO ******************** ************* COMPUTATION OF THE GEN. EULER CONSTANTS in ARITH. PROGR. *******/ /***************** psi_n FUNCTION ****************/ {T(n,x,defaultprecision)= local(T=0,T1=0,m=0,tab); default(realprecision,defaultprecision); if (x==1, T=0; return(T)); if (n==0, T=psi(x)+Euler;return(T)); if (n==1, tab = sumnuminit(); T1=sumnum(m=0, log(x+m)/(x+m)-log(1+m)/(1+m)); T=-T1; return(T)); tab = sumnuminit(); \\ precomputations for sumnum T1=sumnum(m=0, -(log(x+m))^n/(x+m)+(log(1+m))^n/(1+m),tab); T=T1; return(T) } /***************** function to evaluate the generalised euler constants gamma_n ****************/ {gamman(n, defaultprecision) = local(T,m,tab); default(realprecision,defaultprecision); tab = sumnuminit(); \\ precomputations for sumnum T= sumnum(m=1, log(m)^n/m-(1/(n+1))*sum(j=0,n,binomial(n+1,j)*log(m)^j*log(1+1/m)^(n+1-j)),tab); return(T) } /***************** computations for gamma_k(a,q) ****************/ {gk(k,r1,r2,defaultprecision)= local(columns, aoverq, gamma_kaq, n, S, gamma1, Gn_vector, minusoneoverq, logq, logqkpow, oneoverq, minuslogqpowoverq, minuslogqoverq, oneoverkplusone); if ( defaultprecision >28, error("USE A PRECISION LESS THAN 28 DIGITS")); if ( k >30, error("USE k LESS OR EQUAL THAN 30")); if (k<1, error("USE k GREATER OF EQUAl 1")); default(realprecision,defaultprecision); \\print(defaultprecision); Gn_vector=vector(k+1,columns,0); Gn_vector[1]=Euler; gamma1=-0.072815845483676724860586375874901319137736338334337952599006559741401433571511484878086928244844014604; Gn_vector[2]=gamma1; for(n=2,k,Gn_vector[n+1]=gamman(n,defaultprecision)); \\print(Gn_vector); oneoverkplusone=1/(k+1); for(q=r1,r2, if(q==1, print("gamma_",k,"(", 1,",", 1,") = ", Gn_vector[k+1]), logq=log(q); logqkpow=(logq)^k; oneoverq = 1/q; minusoneoverq=-oneoverq; minuslogqpowoverq=logqkpow*minusoneoverq; for(a=1, q, aoverq = a/q; S=0; for(n=0,k, S += (-Gn_vector[n+1]+T(n,aoverq,defaultprecision))*binomial(k,n)/(logq)^n ); gamma_kaq=minuslogqpowoverq*(logq*oneoverkplusone+S); print("gamma_",k,"(", a,",", q,") = ",gamma_kaq) ); ); ); } /*** *** *** *** *** *** *** *** *** *** *** *** *************************************************** Computation of Generalised Euler constants gamma_n **** RESULTS **** gp2.11.2 and gp2c0.0.11 compiled by myself, see below ******************* gp 2.11.2 on Dell Optiplex languasc@languasco1:~/Desktop/EK$ gp2c-run -pmy_ -g -W Gen-Euler-constants.gp GP/PARI CALCULATOR Version 2.11.2 (released) amd64 running linux (x86-64/GMP-6.1.2 kernel) 64-bit version compiled: May 21 2019, gcc version 7.4.0 (Ubuntu 7.4.0-1ubuntu1~18.04) threading engine: single (readline v7.0 enabled, extended help enabled) Copyright (C) 2000-2018 The PARI Group PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER. Type ? for help, \q to quit. Type ?17 for how to get moral (and possibly technical) support. parisize = 8000000, primelimit = 500000 g(n)=sumnum(m=1, log(m)^n/m-(1/(n+1))*sum(j=0,n,binomial(n+1,j)*log(m)^j*log(1+1/m)^(n+1-j))); g1(n)=sumnum(m=1, log(m)^n*(1/m-log(1+1/m))-(1/(n+1))*sum(j=0,n-1,binomial(n+1,j)*log(m)^j*log(1+1/m)^(n+1-j))); \p90 ? for(n=0,30,print(g1(n))) 0.577215664901532860606512090082402431042159335939923598805767234884867726777664670936947063 -0.0728158454836767248605863758749013191377363383343379525990065597414014335715114848780869282 -0.00969036319287231848453038603521252935906580610134074988070136545185075538228041417197819738 0.00205383442030334586616004654275338428571580444541061824548148333691383449211297005357055717 0.00232537006546730005746817017752606800090446941378485099075804090712484100531552190030167806 0.000793323817301062701753334877444444830731539404584887075734256269823148211801715202379720064 -0.000238769345430199609872421841908004277783715156358078631476425307391067559992963871436861114 -0.000527289567057751046074097505478858281996253472969895331013404226885682732465141182144041381 -0.000352123353803039509602052165001208741729180533792350356657331507364281776506065301080140918 -3.43947744180880481779146237982273906207895385944416297592919048431501033444615283709575363 E-5 0.000205332814909064794683722289237065302959853774166764303840208714353009024071069175198497147 0.000270184439543903526672902082067955673827842058688402503973735803136799990964292980238119578 0.000167272912105140193353501543341183446607806632805565828047790937651219597032740762617713151 -2.74638066037601588600076036933551815267853376703955360928330891675705186070088565481664925 E-5 -0.000209209262059299945837139697344584957831544211506069562434208325718757761841343820754051691 -0.000283468655320241446642934474997126977068702980717675253969943292967625690532103533666326739 -0.000199696858308969774707784563203240391915764974034061279859667162554380594472529864770525277 2.62770371099183366994665976305101228160786929291140607971175183522832514737065865790206896 E-5 0.000307368408149252826592754751948625645523811290731461691081103652314826170819857054323176210 0.000503605453047355629055596437717160035321269807649497837323790927014979580187482028137550064 0.000466343561511559449400594824433550525113143473925688997670726629281075086983024852678869287 0.000104437769756000115810795674367720491044428250705546747834371793349358562197804516732358661 -0.000541599582203997701655196173174105584543860928700748801839111386723948928884588034948912704 -0.00124396209040824577929974159953716580914702811396463771651212439638098213132689945712399828 -0.00158851127890356156190619661152111585731872282214412906201424713250235282613667076009138681 -0.00107459195273848882472429198735317308927397933145316892661142644490279155918506660024968125 0.000656803518637154431504773003356215248886065060477913247551122271742623889654355904362234583 0.00347783691361853820900735957425881154766291566398462229956247725986760452974440843226836724 0.00640006853170062945810722822194586366663719817058936925178986479176189717807511330877531905 0.00737115177047223913441240242355940215784133435827234290744534711979488404691274719392034520 0.00355772885557316094791353774890840261081146546635300348146425729309205402222378551311798580 ? ## *** last result computed in 6,949 ms. ? for(n=0,30,print(g1(n)-g(n))) 0.E-96 -3.452736311585496266 E-96 -4.945020649643634483 E-96 -4.073972818495238365 E-95 -1.0597779091969253635 E-94 -1.8250582591056248842 E-94 -1.4286045100339331896 E-93 -6.814572207527182742 E-93 -2.2301251725423067671 E-92 -7.099977310690163522 E-92 1.2880902875364232570 E-91 4.485554482247713890 E-89 1.0817041040512819544 E-86 4.949871923923476638 E-84 -4.694708175891877512 E-82 5.7084465891509178851785320943021620726 E-79 1.99031904492976279030771655412038284797 E-76 5.8361651798190450405010861436846776250 E-74 1.21865293455447619272386596789994874456 E-71 4.05453593757363008166181783276853662922 E-70 3.38718626396226385266726544424354633362 E-67 1.88039628699423012680670867361251903547 E-64 -5.9306362744943507676717295087957195611 E-63 2.379831668270986001477595270338555604212539081945771039550 E-59 1.918323344944347773373624495342081319851408238399987701139 E-58 1.713907058591812919596789013565455438639848228729055064520 E-54 -1.456411247185863668412690090342215972712166584918727907148 E-53 6.733677015739319673267798295315554988875054266101605005312 E-50 -4.733256877455923481428268467581659890824110330000677357501 E-48 1.615513920250886389895896689003266153850611521334408260989 E-45 2.077864777217072905542034210092846728515158373362786380493 E-42 truncated at 40 digits are 0.57721566490153286060651209008240243104 -0.0728158454836767248605863758749013191 -0.0096903631928723184845303860352125293 0.00205383442030334586616004654275338428 0.00232537006546730005746817017752606800 0.00079332381730106270175333487744444483 -0.0002387693454301996098724218419080042 -0.0005272895670577510460740975054788582 -0.0003521233538030395096020521650012087 -3.4394774418088048177914623798227390620 E-5 0.00020533281490906479468372228923706530 0.00027018443954390352667290208206795567 0.00016727291210514019335350154334118344 -2.7463806603760158860007603693355181526 E-5 -0.0002092092620592999458371396973445849 -0.0002834686553202414466429344749971269 -0.0001996968583089697747077845632032403 2.62770371099183366994665976305101228160 E-5 0.00030736840814925282659275475194862564 0.00050360545304735562905559643771716003 0.00046634356151155944940059482443355052 0.00010443776975600011581079567436772049 -0.0005415995822039977016551961731741055 -0.0012439620904082457792997415995371658 -0.0015885112789035615619061966115211158 -0.0010745919527384888247242919873531730 0.00065680351863715443150477300335621524 0.00347783691361853820900735957425881154 0.00640006853170062945810722822194586366 0.00737115177047223913441240242355940215 0.00355772885557316094791353774890840261 *** in the paper I used ? for(n=0,30,print("\\diff{",n,"}&=",g1(n)-g(n),"\\dotsc\\\\")) \diff{0}&=0.E-96\dotsc\\ \diff{1}&=-3.452736311585496266 E-96\dotsc\\ \diff{2}&=-4.945020649643634483 E-96\dotsc\\ \diff{3}&=-4.073972818495238365 E-95\dotsc\\ \diff{4}&=-1.0597779091969253635 E-94\dotsc\\ \diff{5}&=-1.8250582591056248842 E-94\dotsc\\ \diff{6}&=-1.4286045100339331896 E-93\dotsc\\ \diff{7}&=-6.814572207527182742 E-93\dotsc\\ \diff{8}&=-2.2301251725423067671 E-92\dotsc\\ \diff{9}&=-7.099977310690163522 E-92\dotsc\\ \diff{10}&=1.2880902875364232570 E-91\dotsc\\ \diff{11}&=4.485554482247713890 E-89\dotsc\\ \diff{12}&=1.0817041040512819544 E-86\dotsc\\ \diff{13}&=4.949871923923476638 E-84\dotsc\\ \diff{14}&=-4.694708175891877512 E-82\dotsc\\ \diff{15}&=5.7084465891509178851785320943021620726 E-79\dotsc\\ \diff{16}&=1.99031904492976279030771655412038284797 E-76\dotsc\\ \diff{17}&=5.8361651798190450405010861436846776250 E-74\dotsc\\ \diff{18}&=1.21865293455447619272386596789994874456 E-71\dotsc\\ \diff{19}&=4.05453593757363008166181783276853662922 E-70\dotsc\\ \diff{20}&=3.38718626396226385266726544424354633362 E-67\dotsc\\ \diff{21}&=1.88039628699423012680670867361251903547 E-64\dotsc\\ \diff{22}&=-5.9306362744943507676717295087957195611 E-63\dotsc\\ \diff{23}&=2.379831668270986001477595270338555604212539081945771039550 E-59\dotsc\\ \v{24}&=1.918323344944347773373624495342081319851408238399987701139 E-58\dotsc\\ \diff{25}&=1.713907058591812919596789013565455438639848228729055064520 E-54\dotsc\\ \diff{26}&=-1.456411247185863668412690090342215972712166584918727907148 E-53\dotsc\\ \diff{27}&=6.733677015739319673267798295315554988875054266101605005312 E-50\dotsc\\ \diff{28}&=-4.733256877455923481428268467581659890824110330000677357501 E-48\dotsc\\ \diff{29}&=1.615513920250886389895896689003266153850611521334408260989 E-45\dotsc\\ \diff{30}&=2.077864777217072905542034210092846728515158373362786380493 E-42\dotsc\\ ? for(n=0,30,print("\\gamma_{",n,"}&=",g1(n),"\\dotsc\\\\")) \gamma_{0}&=0.577215664901532860606512090082402431042159335939923598805767234884867726777664670936947063\dotsc\\ \gamma_{1}&=-0.0728158454836767248605863758749013191377363383343379525990065597414014335715114848780869282\dotsc\\ \gamma_{2}&=-0.00969036319287231848453038603521252935906580610134074988070136545185075538228041417197819738\dotsc\\ \gamma_{3}&=0.00205383442030334586616004654275338428571580444541061824548148333691383449211297005357055717\dotsc\\ \gamma_{4}&=0.00232537006546730005746817017752606800090446941378485099075804090712484100531552190030167806\dotsc\\ \gamma_{5}&=0.000793323817301062701753334877444444830731539404584887075734256269823148211801715202379720064\dotsc\\ \gamma_{6}&=-0.000238769345430199609872421841908004277783715156358078631476425307391067559992963871436861114\dotsc\\ \gamma_{7}&=-0.000527289567057751046074097505478858281996253472969895331013404226885682732465141182144041381\dotsc\\ \gamma_{8}&=-0.000352123353803039509602052165001208741729180533792350356657331507364281776506065301080140918\dotsc\\ \gamma_{9}&=-3.43947744180880481779146237982273906207895385944416297592919048431501033444615283709575363 E-5\dotsc\\ \gamma_{10}&=0.000205332814909064794683722289237065302959853774166764303840208714353009024071069175198497147\dotsc\\ \gamma_{11}&=0.000270184439543903526672902082067955673827842058688402503973735803136799990964292980238119578\dotsc\\ \gamma_{12}&=0.000167272912105140193353501543341183446607806632805565828047790937651219597032740762617713151\dotsc\\ \gamma_{13}&=-2.74638066037601588600076036933551815267853376703955360928330891675705186070088565481664925 E-5\dotsc\\ \gamma_{14}&=-0.000209209262059299945837139697344584957831544211506069562434208325718757761841343820754051691\dotsc\\ \gamma_{15}&=-0.000283468655320241446642934474997126977068702980717675253969943292967625690532103533666326739\dotsc\\ \gamma_{16}&=-0.000199696858308969774707784563203240391915764974034061279859667162554380594472529864770525277\dotsc\\ \gamma_{17}&=2.62770371099183366994665976305101228160786929291140607971175183522832514737065865790206896 E-5\dotsc\\ \gamma_{18}&=0.000307368408149252826592754751948625645523811290731461691081103652314826170819857054323176210\dotsc\\ \gamma_{19}&=0.000503605453047355629055596437717160035321269807649497837323790927014979580187482028137550064\dotsc\\ \gamma_{20}&=0.000466343561511559449400594824433550525113143473925688997670726629281075086983024852678869287\dotsc\\ \gamma_{21}&=0.000104437769756000115810795674367720491044428250705546747834371793349358562197804516732358661\dotsc\\ \gamma_{22}&=-0.000541599582203997701655196173174105584543860928700748801839111386723948928884588034948912704\dotsc\\ \gamma_{23}&=-0.00124396209040824577929974159953716580914702811396463771651212439638098213132689945712399828\dotsc\\ \gamma_{24}&=-0.00158851127890356156190619661152111585731872282214412906201424713250235282613667076009138681\dotsc\\ \gamma_{25}&=-0.00107459195273848882472429198735317308927397933145316892661142644490279155918506660024968125\dotsc\\ \gamma_{26}&=0.000656803518637154431504773003356215248886065060477913247551122271742623889654355904362234583\dotsc\\ \gamma_{27}&=0.00347783691361853820900735957425881154766291566398462229956247725986760452974440843226836724\dotsc\\ \gamma_{28}&=0.00640006853170062945810722822194586366663719817058936925178986479176189717807511330877531905\dotsc\\ \gamma_{29}&=0.00737115177047223913441240242355940215784133435827234290744534711979488404691274719392034520\dotsc\\ \gamma_{30}&=0.00355772885557316094791353774890840261081146546635300348146425729309205402222378551311798580\dotsc\\ *************************************************** Repeating Dilcher's computation for gamma_k(a,q) with 20 digits ? init_Gen_Euler_constants();for(k=1, 20,gk(k,1,9,20)) gamma_1(1,1) = -0.072815845483676724861 gamma_1(1,2) = -0.11634237461305384831 gamma_1(2,2) = 0.043526529129377123448 gamma_1(1,3) = -0.14071373235657077995 gamma_1(2,3) = 0.081949254612030729536 gamma_1(3,3) = -0.014051367739136674446 gamma_1(1,4) = -0.15462184570498313884 gamma_1(2,4) = 0.10190929210863117495 gamma_1(3,4) = 0.038279471091929290527 gamma_1(4,4) = -0.058382762979254051503 gamma_1(1,5) = -0.16259387561481854279 gamma_1(2,5) = 0.11488716977807873515 gamma_1(3,5) = 0.070722057768504644689 gamma_1(4,5) = -0.0080375438693595762444 gamma_1(5,5) = -0.087793653546081985664 gamma_1(1,6) = -0.16702235153619460481 gamma_1(2,6) = 0.12451544493205130493 gamma_1(3,6) = 0.093246167243161331889 gamma_1(4,6) = 0.026308619179623824857 gamma_1(5,6) = -0.042566190320020575390 gamma_1(6,6) = -0.10729753498229800634 gamma_1(1,7) = -0.16924425528133322274 gamma_1(2,7) = 0.13226383182944564609 gamma_1(3,7) = 0.11009572371380535666 gamma_1(4,7) = 0.051495880096128682908 gamma_1(5,7) = -0.0096989198722808740255 gamma_1(6,7) = -0.067315366104255319201 gamma_1(7,7) = -0.12041273986518699455 gamma_1(1,8) = -0.17004727626341209903 gamma_1(2,8) = 0.13882844749906261329 gamma_1(3,8) = 0.12337838288825318004 gamma_1(4,8) = 0.070938259022119458945 gamma_1(5,8) = 0.015425430558428960194 gamma_1(6,8) = -0.036919155390431438340 gamma_1(7,8) = -0.085098911796323889508 gamma_1(8,8) = -0.12932102200137351045 gamma_1(1,9) = -0.16991658085621328664 gamma_1(2,9) = 0.14457914179691708848 gamma_1(3,9) = 0.13425846232954483752 gamma_1(4,9) = 0.086529530967153328240 gamma_1(5,9) = 0.035370528882691477484 gamma_1(6,9) = -0.012927460983823145340 gamma_1(7,9) = -0.057326682467510821547 gamma_1(8,9) = -0.098000416067577836431 gamma_1(9,9) = -0.13538236908485836663 gamma_2(1,1) = -0.0096903631928723184845 gamma_2(1,2) = -0.037531477875885458815 gamma_2(2,2) = 0.027841114683013140331 gamma_2(1,3) = -0.068200237650717016475 gamma_2(2,3) = 0.030177519448770423109 gamma_2(3,3) = 0.028332355009074274881 gamma_2(1,4) = -0.095836601152610671110 gamma_2(2,4) = 0.025427232254876631713 gamma_2(3,4) = 0.058305123276725212294 gamma_2(4,4) = 0.0024138824281365086174 gamma_2(1,5) = -0.11940008959921739654 gamma_2(2,5) = 0.019061176323282698922 gamma_2(3,5) = 0.074481944199489701291 gamma_2(4,5) = 0.043877910670268765345 gamma_2(5,5) = -0.027711304786696087505 gamma_2(1,6) = -0.13917687475301314441 gamma_2(2,6) = 0.012690432118418355554 gamma_2(3,6) = 0.084158309546775618043 gamma_2(4,6) = 0.070976637102296127938 gamma_2(5,6) = 0.017487087330352067555 gamma_2(6,6) = -0.055825954537701343162 gamma_2(1,7) = -0.15573486952405715155 gamma_2(2,7) = 0.0068404335720321178358 gamma_2(3,7) = 0.090396586899079670632 gamma_2(4,7) = 0.090020360304354064535 gamma_2(5,7) = 0.049673576979426219516 gamma_2(6,7) = -0.010384009168311344041 gamma_2(7,7) = -0.080502442255395895409 gamma_2(1,8) = -0.16963136127667906426 gamma_2(2,8) = 0.0016604117705950270426 gamma_2(3,8) = 0.094678160158348268982 gamma_2(4,8) = 0.10414135319453301068 gamma_2(5,8) = 0.073794760124068393146 gamma_2(6,8) = 0.023766820484281604671 gamma_2(7,8) = -0.036373036881623056688 gamma_2(8,8) = -0.10172747076639650206 gamma_2(1,9) = -0.18134195196033126024 gamma_2(2,9) = -0.0028425303262196788401 gamma_2(3,9) = 0.097789619582327774571 gamma_2(4,9) = 0.11506152640354530253 gamma_2(5,9) = 0.092589263350561707858 gamma_2(6,9) = 0.050422039116213101327 gamma_2(7,9) = -0.0019198120939310587664 gamma_2(8,9) = -0.059569213575571605909 gamma_2(9,9) = -0.11987930368946660102 gamma_3(1,1) = 0.0020538344203033458662 gamma_3(1,2) = -0.0036800579060948719345 gamma_3(2,2) = 0.0057338923263982178007 gamma_3(1,3) = -0.022593835248791132896 gamma_3(2,3) = -0.011235516170652372195 gamma_3(3,3) = 0.035883185839746850957 gamma_3(1,4) = -0.049281458555849286038 gamma_3(2,4) = -0.033369510388861612542 gamma_3(3,4) = 0.045601400649754414104 gamma_3(4,4) = 0.039103402715259830342 gamma_3(1,5) = -0.079268389317194284973 gamma_3(2,5) = -0.056912306260650291154 gamma_3(3,5) = 0.043950453132711814156 gamma_3(4,5) = 0.070607447935991916167 gamma_3(5,5) = 0.023676628929444191670 gamma_3(1,6) = -0.10998322179798232339 gamma_3(2,6) = -0.080370508191859863911 gamma_3(3,6) = 0.037168171870679959736 gamma_3(4,6) = 0.087389386549191190491 gamma_3(5,6) = 0.069134992021207491717 gamma_3(6,6) = -0.0012849860309331087794 gamma_3(1,7) = -0.14007362183717028709 gamma_3(2,7) = -0.10305798177232669610 gamma_3(3,7) = 0.027939678028022357041 gamma_3(4,7) = 0.096087108183439931335 gamma_3(5,7) = 0.099104662582774892522 gamma_3(6,7) = 0.052496076896037853835 gamma_3(7,7) = -0.030442087660474705673 gamma_3(1,8) = -0.16886989340983576519 gamma_3(2,8) = -0.12465842304031825422 gamma_3(3,8) = 0.017590007665992412728 gamma_3(4,8) = 0.10001119004580607524 gamma_3(5,8) = 0.11958843485398647915 gamma_3(6,8) = 0.091288912651456641681 gamma_3(7,8) = 0.028011392983762001376 gamma_3(8,8) = -0.060907787330546244893 gamma_3(1,9) = -0.19607411969635750439 gamma_3(2,9) = -0.14504380018044038939 gamma_3(3,9) = 0.0068279573620352439830 gamma_3(4,9) = 0.10098611095126557778 gamma_3(5,9) = 0.13391374123244415754 gamma_3(6,9) = 0.12020908656866095034 gamma_3(7,9) = 0.072494173496300793710 gamma_3(8,9) = -0.00010545722265614034731 gamma_3(9,9) = -0.091153858090949343367 gamma_4(1,1) = 0.0023253700654673000575 gamma_4(1,2) = 0.010161154086179353926 gamma_4(2,2) = -0.0078357840207120538689 gamma_4(1,3) = 0.010432667873043640623 gamma_4(2,3) = -0.033353821366267623332 gamma_4(3,3) = 0.025246523558691282766 gamma_4(1,4) = -0.0020757303108142850664 gamma_4(2,4) = -0.066296210822460940887 gamma_4(3,4) = 0.012236884396993638993 gamma_4(4,4) = 0.058460426801748887018 gamma_4(1,5) = -0.025999192928266681721 gamma_4(2,5) = -0.10414208976322050628 gamma_4(3,5) = -0.012506429526192940310 gamma_4(4,5) = 0.072204793735644585857 gamma_4(5,5) = 0.072768288547502842510 gamma_4(1,6) = -0.058509565878732615760 gamma_4(2,6) = -0.14523126667118827058 gamma_4(3,6) = -0.043206725340008677561 gamma_4(4,6) = 0.068942233751776256383 gamma_4(5,6) = 0.11187744530492064725 gamma_4(6,6) = 0.068453248898699960328 gamma_4(1,7) = -0.096995439181350949762 gamma_4(2,7) = -0.18832466952524228434 gamma_4(3,7) = -0.077162572801905322612 gamma_4(4,7) = 0.056188335837610082797 gamma_4(5,7) = 0.13079386981058120961 gamma_4(6,7) = 0.12810107031944544883 gamma_4(7,7) = 0.049724775606329115531 gamma_4(1,8) = -0.13940702060569066847 gamma_4(2,8) = -0.23249735781474016307 gamma_4(3,8) = -0.11288325560775348901 gamma_4(4,8) = 0.037773451618527065972 gamma_4(5,8) = 0.13733129029487638341 gamma_4(6,8) = 0.16620114699227922219 gamma_4(7,8) = 0.12512014000474712800 gamma_4(8,8) = 0.020686975183221821046 gamma_4(1,9) = -0.18422404401228283800 gamma_4(2,9) = -0.27706872543425159125 gamma_4(3,9) = -0.14946026843301578734 gamma_4(4,9) = 0.015868820894500179823 gamma_4(5,9) = 0.13585691304049837656 gamma_4(6,9) = 0.19013619405059947675 gamma_4(7,9) = 0.17878789099082629880 gamma_4(8,9) = 0.10785799102748559136 gamma_4(9,9) = -0.015429402058892406649 gamma_5(1,1) = 0.00079332381730106270175 gamma_5(1,2) = 0.012654115736855422805 gamma_5(2,2) = -0.011860791919554360103 gamma_5(1,3) = 0.032776359832860882890 gamma_5(2,3) = -0.035393355978847464736 gamma_5(3,3) = 0.0034103199632876445479 gamma_5(1,4) = 0.047452120746084259183 gamma_5(2,4) = -0.068345462519446590301 gamma_5(3,4) = -0.034798005009228836378 gamma_5(4,4) = 0.056484670599892230198 gamma_5(1,5) = 0.048930547181809829581 gamma_5(2,5) = -0.11114268506138344019 gamma_5(3,5) = -0.087718356592657856059 gamma_5(4,5) = 0.038237272264625769837 gamma_5(5,5) = 0.11248654602490675953 gamma_5(1,6) = 0.034944311004986732396 gamma_5(2,6) = -0.16343095692868590172 gamma_5(3,6) = -0.15032779621796974658 gamma_5(4,6) = -0.0021679511721258495065 gamma_5(5,6) = 0.12803760094983843699 gamma_5(6,6) = 0.15373811618125739113 gamma_5(1,7) = 0.0060028780131753492432 gamma_5(2,7) = -0.22428794186323056134 gamma_5(3,7) = -0.22008414437303763128 gamma_5(4,7) = -0.056040537268296060359 gamma_5(5,7) = 0.11493507784891180743 gamma_5(6,7) = 0.20555868597933874041 gamma_5(7,7) = 0.17470930548043941860 gamma_5(1,8) = -0.036260631276443974268 gamma_5(2,8) = -0.29255454686900004989 gamma_5(3,8) = -0.29535111345830814896 gamma_5(4,8) = -0.11883366151256725395 gamma_5(5,8) = 0.083712752022528233450 gamma_5(6,8) = 0.22420908434955345959 gamma_5(7,8) = 0.26055310844907931258 gamma_5(8,8) = 0.17531833211245948415 gamma_5(1,9) = -0.089897835618788201270 gamma_5(2,9) = -0.36704124726593288269 gamma_5(3,9) = -0.37492118037466377345 gamma_5(4,9) = -0.18784945340681352093 gamma_5(5,9) = 0.040327486400090723023 gamma_5(6,9) = 0.22076652570800470661 gamma_5(7,9) = 0.31052364885846260509 gamma_5(8,9) = 0.29132040488699469493 gamma_5(9,9) = 0.15756497462994671139 gamma_6(1,1) = -0.00023876934543019960987 gamma_6(1,2) = 0.0082235133274978313145 gamma_6(2,2) = -0.0084622826729280309243 gamma_6(1,3) = 0.041822252694592059892 gamma_6(2,3) = -0.018572400631810130279 gamma_6(3,3) = -0.023488621408212129224 gamma_6(1,4) = 0.093066361189123740970 gamma_6(2,4) = -0.033560681736671227539 gamma_6(3,4) = -0.084842847861625909655 gamma_6(4,4) = 0.025098399063743196614 gamma_6(1,5) = 0.14612977537987821588 gamma_6(2,5) = -0.058829800552121406372 gamma_6(3,5) = -0.16466707645128905268 gamma_6(4,5) = -0.045229227978187533328 gamma_6(5,5) = 0.12235756025628957689 gamma_6(1,6) = 0.18850023156306800682 gamma_6(2,6) = -0.098442719308099482320 gamma_6(3,6) = -0.26014703691185952754 gamma_6(4,6) = -0.14667797886847594692 gamma_6(5,6) = 0.079870318676289352042 gamma_6(6,6) = 0.23665841550364739832 gamma_6(1,7) = 0.21258192971753177444 gamma_6(2,7) = -0.15470523339071916107 gamma_6(3,7) = -0.37024805474019402259 gamma_6(4,7) = -0.26969037201726943849 gamma_6(5,7) = -0.0061522597609519967560 gamma_6(6,7) = 0.24286817439981794246 gamma_6(7,7) = 0.34510704644635470239 gamma_6(1,8) = 0.21457457237740348793 gamma_6(2,8) = -0.22851537020849346216 gamma_6(3,8) = -0.49424366248290576941 gamma_6(4,8) = -0.40935322335179809659 gamma_6(5,8) = -0.12150821118827974696 gamma_6(6,8) = 0.19495468847182223462 gamma_6(7,8) = 0.40940081462127985975 gamma_6(8,8) = 0.43445162241554129321 gamma_6(1,9) = 0.19316252879302586971 gamma_6(2,9) = -0.31980586455914025243 gamma_6(3,9) = -0.63136492817904882186 gamma_6(4,9) = -0.56270759804804272238 gamma_6(5,9) = -0.25816313651042797948 gamma_6(6,9) = 0.10978620288989387643 gamma_6(7,9) = 0.41136732194960891256 gamma_6(8,9) = 0.55939660043775810163 gamma_6(9,9) = 0.49809010388094281621 gamma_7(1,1) = -0.00052728956705775104607 gamma_7(1,2) = 0.00015355590107907185981 gamma_7(2,2) = -0.00068084546813682290588 gamma_7(1,3) = 0.032971198360333230175 gamma_7(2,3) = 0.013764130707448508870 gamma_7(3,3) = -0.047262618634839490091 gamma_7(1,4) = 0.11857105667355265528 gamma_7(2,4) = 0.042751376389793534661 gamma_7(3,4) = -0.11841750077247358342 gamma_7(4,4) = -0.043432221857930357567 gamma_7(1,5) = 0.24918404551729145833 gamma_7(2,5) = 0.077917086438610207231 gamma_7(3,5) = -0.20559565878925150804 gamma_7(4,5) = -0.18678036567489116517 gamma_7(5,5) = 0.064747602941183256594 gamma_7(1,6) = 0.40525485209444347612 gamma_7(2,6) = 0.10856993353665920225 gamma_7(3,6) = -0.31029549336415371088 gamma_7(4,6) = -0.37228365373411024594 gamma_7(5,6) = -0.094805802829210693376 gamma_7(6,6) = 0.26303287472931422079 gamma_7(1,7) = 0.56667358765707304481 gamma_7(2,7) = 0.12481501339278725159 gamma_7(3,7) = -0.43587676068200031450 gamma_7(4,7) = -0.59089994834673357932 gamma_7(5,7) = -0.32197246971546781675 gamma_7(6,7) = 0.13922867437101554618 gamma_7(7,7) = 0.51750461375626811694 gamma_7(1,8) = 0.71685467526103443427 gamma_7(2,8) = 0.11871618326400207236 gamma_7(3,8) = -0.58555873864394012261 gamma_7(4,8) = -0.83900846511853058293 gamma_7(5,8) = -0.59828361858748177900 gamma_7(6,8) = -0.075964806874208537701 gamma_7(7,8) = 0.46714123787146653920 gamma_7(8,8) = 0.79557624326060022536 gamma_7(1,9) = 0.84346229164453489644 gamma_7(2,9) = 0.084461139666322603549 gamma_7(3,9) = -0.76183658761349212141 gamma_7(4,9) = -1.1150064182339284464 gamma_7(5,9) = -0.91374961468306140400 gamma_7(6,9) = -0.35704452277001682496 gamma_7(7,9) = 0.30451532494972678014 gamma_7(8,9) = 0.84305260572418730932 gamma_7(9,9) = 1.0716184917486694563 gamma_8(1,1) = -0.00035212335380303950960 gamma_8(1,2) = -0.0083840995653484156921 gamma_8(2,2) = 0.0080319762115453761825 gamma_8(1,3) = 0.0019131801713059697327 gamma_8(2,3) = 0.054187729501011500613 gamma_8(3,3) = -0.056453033026120509856 gamma_8(1,4) = 0.094815923224013043284 gamma_8(2,4) = 0.15699880827883410654 gamma_8(3,4) = -0.10320002278936145898 gamma_8(4,4) = -0.14896683206728873036 gamma_8(1,5) = 0.30687665640624737241 gamma_8(2,5) = 0.31922856081447378534 gamma_8(3,5) = -0.13948231750319540706 gamma_8(4,5) = -0.37096697409035454090 gamma_8(5,5) = -0.11600804898097424930 gamma_8(1,6) = 0.63810119335622975007 gamma_8(2,6) = 0.53059097614451958139 gamma_8(3,6) = -0.17008204627807008498 gamma_8(4,6) = -0.63618801318492378034 gamma_8(5,6) = -0.47640324664350808078 gamma_8(6,6) = 0.11362901325194957512 gamma_8(1,7) = 1.0670311927380386268 gamma_8(2,7) = 0.77376548580594169658 gamma_8(3,7) = -0.20499005606469956019 gamma_8(4,7) = -0.93788616826484904784 gamma_8(5,7) = -0.93495724145999685971 gamma_8(6,7) = -0.30303706292474153816 gamma_8(7,7) = 0.53972172681650364300 gamma_8(1,8) = 1.5637576330276492496 gamma_8(2,8) = 1.0291365249226445102 gamma_8(3,8) = -0.25582374703237686843 gamma_8(4,8) = -1.2769811803130827718 gamma_8(5,8) = -1.4689417098036362063 gamma_8(6,8) = -0.87213771664381040370 gamma_8(7,8) = 0.15262372424301540945 gamma_8(8,8) = 1.1280143482457940414 gamma_8(1,9) = 2.0974084430444101676 gamma_8(2,9) = 1.2776300618131010966 gamma_8(3,9) = -0.33402239269524221734 gamma_8(4,9) = -1.6572332288521339628 gamma_8(5,9) = -2.0679884592869837947 gamma_8(6,9) = -1.5558984419727195993 gamma_8(7,9) = -0.43826203402097023509 gamma_8(8,9) = 0.84454612697489419864 gamma_8(9,9) = 1.8334678016418413068 gamma_9(1,1) = -3.4394774418088048178 E-5 gamma_9(1,2) = -0.014073779843997689542 gamma_9(2,2) = 0.014039385069579601494 gamma_9(1,3) = -0.051769595631643856178 gamma_9(2,3) = 0.088446310048463940901 gamma_9(3,3) = -0.036711109191238172772 gamma_9(1,4) = -0.020644330571280697168 gamma_9(2,4) = 0.28373033314815678587 gamma_9(3,4) = 0.0065705507272830076261 gamma_9(4,4) = -0.26969094807857718438 gamma_9(1,5) = 0.20654013932076545581 gamma_9(2,5) = 0.64976146887107050713 gamma_9(3,5) = 0.14666455047596452265 gamma_9(4,5) = -0.52206935450649331984 gamma_9(5,5) = -0.48093119893572525380 gamma_9(1,6) = 0.71665210651685533877 gamma_9(2,6) = 1.2107455689840584319 gamma_9(3,6) = 0.39157337257474146272 gamma_9(4,6) = -0.76842170214849919494 gamma_9(5,6) = -1.1222992589355944910 gamma_9(6,6) = -0.42828448176597963549 gamma_9(1,7) = 1.5431665267207099261 gamma_9(2,7) = 1.9657356825026900048 gamma_9(3,7) = 0.73401614260990587998 gamma_9(4,7) = -1.0003150244213578630 gamma_9(5,7) = -1.8712877090216244917 gamma_9(6,7) = -1.4046678218413838766 gamma_9(7,7) = 0.033317808676642332358 gamma_9(1,8) = 2.6783583238471695028 gamma_9(2,8) = 2.8952767016919198389 gamma_9(3,8) = 1.1564707581377820161 gamma_9(4,8) = -1.2237934422111050275 gamma_9(5,8) = -2.6990026544184502000 gamma_9(6,8) = -2.6115463685437630530 gamma_9(7,8) = -1.1499002074104990084 gamma_9(8,8) = 0.95410249413252784316 gamma_9(1,9) = 4.0886997963930043717 gamma_9(2,9) = 3.9685026248561024556 gamma_9(3,9) = 1.6352805842493187544 gamma_9(4,9) = -1.4521915799959227341 gamma_9(5,9) = -3.5968252184244939103 gamma_9(6,9) = -3.9929746426993074172 gamma_9(7,9) = -2.6882778120287254938 gamma_9(8,9) = -0.28323109638314460441 gamma_9(9,9) = 2.3209829492587504900 gamma_10(1,1) = 0.00020533281490906479468 gamma_10(1,2) = -0.013711459556974466294 gamma_10(2,2) = 0.013916792371883531089 gamma_10(1,3) = -0.11880194819415265755 gamma_10(2,3) = 0.093011704921097974083 gamma_10(3,3) = 0.025995576087963748259 gamma_10(1,4) = -0.27438930406414194294 gamma_10(2,4) = 0.35383174020688652472 gamma_10(3,4) = 0.26067784450716747665 gamma_10(4,4) = -0.33991494783500299363 gamma_10(1,5) = -0.25419330185993479626 gamma_10(2,5) = 0.95221716118219606791 gamma_10(3,5) = 0.79487542302182170513 gamma_10(4,5) = -0.44403598332780639596 gamma_10(5,5) = -1.0486579662013675160 gamma_10(1,6) = 0.21929580321422344820 gamma_10(2,6) = 2.0330640319779654074 gamma_10(3,6) = 1.7070450642856695188 gamma_10(4,6) = -0.33809775140837610575 gamma_10(5,6) = -1.9400523270568674333 gamma_10(6,6) = -1.6810494881977057706 gamma_10(1,7) = 1.3756190253022800113 gamma_10(2,7) = 3.7007708908693764991 gamma_10(3,7) = 3.0455930681387480626 gamma_10(4,7) = 0.020843660443078429716 gamma_10(5,7) = -2.8212427386086914379 gamma_10(6,7) = -3.5449469006480309857 gamma_10(7,7) = -1.7764316726818515144 gamma_10(1,8) = 3.3636943836134191299 gamma_10(2,8) = 6.0117827862294784148 gamma_10(3,8) = 4.8289076963628965803 gamma_10(4,8) = 0.64538417687954691822 gamma_10(5,8) = -3.6380836876775610729 gamma_10(6,8) = -5.6579510460225918901 gamma_10(7,8) = -4.5682298518557291036 gamma_10(8,8) = -0.98529912471454991185 gamma_10(1,9) = 6.2545404067507728799 gamma_10(2,9) = 8.9791038935668119672 gamma_10(3,9) = 7.0492439131430455830 gamma_10(4,9) = 1.5266830637369889991 gamma_10(5,9) = -4.3741386511954700770 gamma_10(6,9) = -7.9274534412811063539 gamma_10(7,9) = -7.9000254186819145365 gamma_10(8,9) = -4.5119535374502439162 gamma_10(9,9) = 0.90420510422602451914 gamma_11(1,1) = 0.00027018443954390352667 gamma_11(1,2) = -0.0049724689414046962223 gamma_11(2,2) = 0.0052426533809485997490 gamma_11(1,3) = -0.17211776250568296412 gamma_11(2,3) = 0.035138322839505051954 gamma_11(3,3) = 0.13724962410572181569 gamma_11(1,4) = -0.68562900178419861391 gamma_11(2,4) = 0.22651127518922829167 gamma_11(3,4) = 0.68065653284279391769 gamma_11(4,4) = -0.22126862180827969192 gamma_11(1,5) = -1.3680923175976116603 gamma_11(2,5) = 0.88516419921040549919 gamma_11(3,5) = 1.8994916317167701893 gamma_11(4,5) = 0.25780888178854573978 gamma_11(5,5) = -1.6741022106785658645 gamma_11(1,6) = -1.7029137817140094624 gamma_11(2,6) = 2.4206374141690701688 gamma_11(3,6) = 4.0834404041021698831 gamma_11(4,6) = 1.5307960192083264983 gamma_11(5,6) = -2.3854990913295651169 gamma_11(6,6) = -3.9461907799964480674 gamma_11(1,7) = -1.0399973765522120067 gamma_11(2,7) = 5.2550408527222457530 gamma_11(3,7) = 7.5019989737662774264 gamma_11(4,7) = 3.7998201499423618995 gamma_11(5,7) = -2.5281396164846710886 gamma_11(6,7) = -6.7928451109160938801 gamma_11(7,7) = -6.1956076880383642001 gamma_11(1,8) = 1.2435543161014790010 gamma_11(2,8) = 9.7590648059961767931 gamma_11(3,8) = 12.377791687461684043 gamma_11(4,8) = 7.2150676655435411391 gamma_11(5,8) = -1.9291833178856776149 gamma_11(6,8) = -9.5325535308069485015 gamma_11(7,8) = -11.697135154618890126 gamma_11(8,8) = -7.4363362873518208310 gamma_11(1,9) = 5.6613339213387206389 gamma_11(2,9) = 16.220627949042197013 gamma_11(3,9) = 18.873780292273909611 gamma_11(4,9) = 11.877172637458804642 gamma_11(5,9) = -0.48737779160733412830 gamma_11(6,9) = -11.958308243553605864 gamma_11(7,9) = -17.710624321303208245 gamma_11(8,9) = -15.698111834595357833 gamma_11(9,9) = -6.7782224246145819320 gamma_12(1,1) = 0.00016727291210514019335 gamma_12(1,2) = 0.012281471346872474192 gamma_12(2,2) = -0.012114198434767333999 gamma_12(1,3) = -0.15822854404001778570 gamma_12(2,3) = -0.12023934209029008955 gamma_12(3,3) = 0.27863515904241301544 gamma_12(1,4) = -1.1717613750228595083 gamma_12(2,4) = -0.33148528267396911095 gamma_12(3,4) = 1.1840428463697319825 gamma_12(4,4) = 0.31937108423920177695 gamma_12(1,5) = -3.4122460117816556559 gamma_12(2,5) = -0.30032526911047726921 gamma_12(3,5) = 3.2827640771522114869 gamma_12(4,5) = 2.2275812138880398327 gamma_12(5,5) = -1.7976067372360132543 gamma_12(1,6) = -6.4468956569129477034 gamma_12(2,6) = 0.74133415425459553201 gamma_12(3,6) = 7.3207506246047057991 gamma_12(4,6) = 6.2886671128729299177 gamma_12(5,6) = -0.86157349634488562156 gamma_12(6,6) = -7.0421154655622927837 gamma_12(1,7) = -9.1182263646592226878 gamma_12(2,7) = 3.8653439889223738590 gamma_12(3,7) = 14.162723354064518316 gamma_12(4,7) = 13.213403737391070960 gamma_12(5,7) = 2.4249446993019322558 gamma_12(6,7) = -9.7449219089779629534 gamma_12(7,7) = -14.803100233130604609 gamma_12(1,8) = -9.8610335413715992458 gamma_12(2,8) = 10.278129548930892504 gamma_12(3,8) = 24.702217592594941860 gamma_12(4,8) = 23.681551361150423035 gamma_12(5,8) = 8.6892721663487397375 gamma_12(6,8) = -10.609614831604861615 gamma_12(7,8) = -23.518174746225209878 gamma_12(8,8) = -23.362180276911221258 gamma_12(1,9) = -6.9925313535930250686 gamma_12(2,9) = 21.178030654050857361 gamma_12(3,9) = 39.787107477406706823 gamma_12(4,9) = 38.310819489841637746 gamma_12(5,9) = 18.447441572549335535 gamma_12(6,9) = -9.0116000357312868356 gamma_12(7,9) = -31.476516680288630463 gamma_12(8,9) = -39.745711568690482986 gamma_12(9,9) = -30.496872282633006972 gamma_13(1,1) = -2.7463806603760158860 E-5 gamma_13(1,2) = 0.034262249391928002830 gamma_13(2,2) = -0.034289713198531762989 gamma_13(1,3) = 0.0061371606556255278005 gamma_13(2,3) = -0.38959504061819781425 gamma_13(3,3) = 0.38343041615596852629 gamma_13(1,4) = -1.4057388663688731148 gamma_13(2,4) = -1.6194095349516940274 gamma_13(3,4) = 1.4400011157608011176 gamma_13(4,4) = 1.5851198217531622644 gamma_13(1,5) = -6.2589663363272671700 gamma_13(2,5) = -3.9428951832514675790 gamma_13(3,5) = 3.9837074415585308616 gamma_13(4,5) = 6.2338327087949470902 gamma_13(5,5) = -0.015706094581346962959 gamma_13(1,6) = -15.640665885242502854 gamma_13(2,6) = -6.6485780903677184023 gamma_13(3,6) = 9.4159450848849102685 gamma_13(4,6) = 15.646803045898128382 gamma_13(5,6) = 6.2589830497495205881 gamma_13(6,6) = -9.0325146687289417422 gamma_13(1,7) = -28.823788400599659590 gamma_13(2,7) = -7.9324482308592087709 gamma_13(3,7) = 19.761839127488763300 gamma_13(4,7) = 31.803993793334770604 gamma_13(5,7) = 19.558301297889251152 gamma_13(6,7) = -6.6195673921177862495 gamma_13(7,7) = -27.748357658942734207 gamma_13(1,8) = -43.347731400839835047 gamma_13(2,8) = -5.0727884675878476235 gamma_13(3,8) = 37.529613990980617910 gamma_13(4,8) = 56.910546846923358641 gamma_13(5,8) = 41.941992534470961933 gamma_13(6,8) = 3.4533789326361535961 gamma_13(7,8) = -36.089612875219816792 gamma_13(8,8) = -55.325427025170196377 gamma_13(1,9) = -55.499253815026020594 gamma_13(2,9) = 5.2613809286301807409 gamma_13(3,9) = 65.517843972697921334 gamma_13(4,9) = 93.287381070732480692 gamma_13(5,9) = 75.420290798695739489 gamma_13(6,9) = 23.253324480983681285 gamma_13(7,9) = -37.781990095050834570 gamma_13(8,9) = -81.071266767944118044 gamma_13(9,9) = -88.387738037525634093 gamma_14(1,1) = -0.00020920926205929994584 gamma_14(1,2) = 0.051521179298479007681 gamma_14(2,2) = -0.051730388560538307627 gamma_14(1,3) = 0.41892660356304822542 gamma_14(2,3) = -0.72628180214490428963 gamma_14(3,3) = 0.30714598931979676427 gamma_14(1,4) = -0.59350957916667368425 gamma_14(2,4) = -3.8370724253522008025 gamma_14(3,4) = 0.64503075846515269193 gamma_14(4,4) = 3.7853420367916624948 gamma_14(1,5) = -8.3738293159012459025 gamma_14(2,5) = -11.889512749329650711 gamma_14(3,5) = 1.2920127059554705107 gamma_14(4,5) = 12.500337321111528806 gamma_14(5,5) = 6.4707828289018379972 gamma_14(1,6) = -29.343687763729504045 gamma_14(2,6) = -26.427013392313278753 gamma_14(3,6) = 3.6944773528596085890 gamma_14(4,6) = 29.762614367292552270 gamma_14(5,6) = 25.700731590168374463 gamma_14(6,6) = -3.3873313635398118247 gamma_14(1,7) = -67.566574000635076705 gamma_14(2,7) = -46.658397271436200228 gamma_14(3,7) = 11.079214735404546774 gamma_14(4,7) = 59.948893030021951593 gamma_14(5,7) = 62.397531301959337540 gamma_14(6,7) = 18.845898384219415451 gamma_14(7,7) = -38.046775388796033723 gamma_14(1,8) = -122.97500139464066469 gamma_14(2,8) = -68.912327799959300263 gamma_14(3,8) = 28.589698922980482764 gamma_14(4,8) = 108.66404239416035515 gamma_14(5,8) = 122.38149181547399101 gamma_14(6,8) = 65.075255374607099461 gamma_14(7,8) = -27.944668164515330072 gamma_14(8,8) = -104.87870035736869266 gamma_14(1,9) = -191.12855031094531486 gamma_14(2,9) = -86.766713542066587534 gamma_14(3,9) = 63.096682126668237658 gamma_14(4,9) = 182.58641782571852698 gamma_14(5,9) = 212.01917343626671411 gamma_14(6,9) = 141.79786247974164757 gamma_14(7,9) = 8.9610590887898361025 gamma_14(8,9) = -125.97874169634503087 gamma_14(9,9) = -204.58739861709008847 gamma_15(1,1) = -0.00028346865532024144664 gamma_15(1,2) = 0.048245777322780218881 gamma_15(2,2) = -0.048529245978100460328 gamma_15(1,3) = 1.1348027333478164997 gamma_15(2,3) = -0.94428979354736215442 gamma_15(3,3) = -0.19079640845577458672 gamma_15(1,4) = 2.7718117216731029262 gamma_15(2,4) = -6.6057052779797574788 gamma_15(3,4) = -2.7235659443503227074 gamma_15(4,4) = 6.5571760320016570185 gamma_15(1,5) = -4.7111545953941716214 gamma_15(2,5) = -25.411117686828925986 gamma_15(3,5) = -10.703519161347363764 gamma_15(4,5) = 18.728550246246278780 gamma_15(5,5) = 22.096957728668862350 gamma_15(1,6) = -40.376864988237426894 gamma_15(2,6) = -67.834668131010250273 gamma_15(3,6) = -26.465267571902681005 gamma_15(4,6) = 41.511667721585243394 gamma_15(5,6) = 66.890378337462888119 gamma_15(6,6) = 26.274471163446906419 gamma_15(1,7) = -125.72098443615835056 gamma_15(2,7) = -142.28612799553726761 gamma_15(3,7) = -49.220670825619473769 gamma_15(4,7) = 81.666195645919021933 gamma_15(5,7) = 148.34594163733597787 gamma_15(6,7) = 103.79161345276015730 gamma_15(7,7) = -16.576250947355385406 gamma_15(1,8) = -277.40755989650862309 gamma_15(2,8) = -251.60647037823626347 gamma_15(3,8) = -73.337361044037749181 gamma_15(4,8) = 149.77868500780434539 gamma_15(5,8) = 280.17937161818172601 gamma_15(6,8) = 245.00076510025650599 gamma_15(7,8) = 70.613795099687426473 gamma_15(8,8) = -143.22150897580268837 gamma_15(1,9) = -502.72991410036699845 gamma_15(2,9) = -391.12390137057865746 gamma_15(3,9) = -87.508086007059309264 gamma_15(4,9) = 260.61969135935670796 gamma_15(5,9) = 478.98864751323823409 gamma_15(6,9) = 468.18795365205028951 gamma_15(7,9) = 243.24502547435810699 gamma_15(8,9) = -88.809035936206938784 gamma_15(9,9) = -380.87066405344675483 gamma_16(1,1) = -0.00019969685830896977469 gamma_16(1,2) = 0.0044499743995806535345 gamma_16(2,2) = -0.0046496712578896233092 gamma_16(1,3) = 2.0276264696816655859 gamma_16(2,3) = -0.61574937398238520127 gamma_16(3,3) = -1.4120767925575893544 gamma_16(1,4) = 10.924031046382603040 gamma_16(2,4) = -7.9055166350029840226 gamma_16(3,4) = -10.919581071983022386 gamma_16(4,4) = 7.9008669637450943993 gamma_16(1,5) = 16.896265876124851959 gamma_16(2,5) = -41.417964945201075316 gamma_16(3,5) = -42.397486748806088875 gamma_16(4,5) = 15.506320351252565323 gamma_16(5,5) = 51.412665769771437940 gamma_16(1,6) = -20.205273849530672365 gamma_16(2,6) = -135.73402620189278195 gamma_16(3,6) = -114.90855300398014373 gamma_16(4,6) = 22.232900319212337951 gamma_16(5,6) = 135.11827682791039675 gamma_16(6,6) = 113.49647621142255438 gamma_16(1,7) = -166.49531961582304398 gamma_16(2,7) = -333.55829696719700273 gamma_16(3,7) = -247.21818805120735699 gamma_16(4,7) = 29.165173017462092698 gamma_16(5,7) = 279.48391750525250551 gamma_16(6,7) = 317.60632637862387303 gamma_16(7,7) = 121.01618803603062349 gamma_16(1,8) = -497.86021310978931555 gamma_16(2,8) = -675.25165495563988346 gamma_16(3,8) = -451.32795758263059859 gamma_16(4,8) = 45.174649410942085174 gamma_16(5,8) = 508.78424415617191859 gamma_16(6,8) = 667.34613832063689944 gamma_16(7,8) = 440.40837651064757621 gamma_16(8,8) = -37.273782447196990775 gamma_16(1,9) = -1082.9535681828064779 gamma_16(2,9) = -1189.2582034984969803 gamma_16(3,9) = -726.99565682000500528 gamma_16(4,9) = 90.157169366384948289 gamma_16(5,9) = 856.42314409419739622 gamma_16(6,9) = 1206.7708264253423819 gamma_16(7,9) = 994.82402528610319520 gamma_16(8,9) = 332.21931003031719890 gamma_16(9,9) = -481.18724639789496600 gamma_17(1,1) = 2.6277037109918336677 E-5 gamma_17(1,2) = -0.096180724563935442692 gamma_17(2,2) = 0.096207001601045361030 gamma_17(1,3) = 2.5342714196148279361 gamma_17(2,3) = 1.0112043075545932303 gamma_17(3,3) = -3.5454494501323112480 gamma_17(1,4) = 25.895211116468964239 gamma_17(2,4) = -2.1559067378478267311 gamma_17(3,4) = -25.991391841032899682 gamma_17(4,4) = 2.2521137394488720922 gamma_17(1,5) = 80.133973105948012654 gamma_17(2,5) = -42.718396234671785753 gamma_17(3,5) = -107.02881679750953859 gamma_17(4,5) = -22.474035323975575253 gamma_17(5,5) = 92.087301527245996856 gamma_17(1,6) = 110.34245362396105341 gamma_17(2,6) = -204.43530507095460845 gamma_17(3,6) = -315.88514372703419054 gamma_17(4,6) = -107.80818220434622548 gamma_17(5,6) = 205.44650937850920168 gamma_17(6,6) = 312.33969427690187929 gamma_17(1,7) = -32.851612738800581107 gamma_17(2,7) = -623.39880331876236826 gamma_17(3,7) = -745.67608592471131919 gamma_17(4,7) = -296.99839392200589949 gamma_17(5,7) = 371.62642493037123314 gamma_17(6,7) = 753.37254446492619728 gamma_17(7,7) = 573.92595278601984754 gamma_17(1,8) = -580.18981598421988382 gamma_17(2,8) = -1470.6205995841452136 gamma_17(3,8) = -1498.6868557556459014 gamma_17(4,8) = -629.05560979874095714 gamma_17(5,8) = 606.08502710068884806 gamma_17(6,8) = 1468.4646928462973869 gamma_17(7,8) = 1472.6954639146130017 gamma_17(8,8) = 631.30772353818982923 gamma_17(1,9) = -1806.7696671553834246 gamma_17(2,9) = -2925.4773105725821992 gamma_17(3,9) = -2668.1225832048122880 gamma_17(4,9) = -1126.2271363223793744 gamma_17(5,9) = 943.28215815380596001 gamma_17(6,9) = 2539.1940832923599511 gamma_17(7,9) = 2935.5310748973776269 gamma_17(8,9) = 1983.2063567263308324 gamma_17(9,9) = 125.38305046232002563 gamma_18(1,1) = 0.00030736840814925311688 gamma_18(1,2) = -0.24965829686232071701 gamma_18(2,2) = 0.24996566527046997027 gamma_18(1,3) = 1.2773937328481820441 gamma_18(2,3) = 4.9342917503828611615 gamma_18(3,3) = -6.2113781148228939525 gamma_18(1,4) = 46.061292720776471100 gamma_18(2,4) = 22.438457571215089063 gamma_18(3,4) = -46.310951017638791817 gamma_18(4,4) = -22.188491905944619093 gamma_18(1,5) = 220.51489172840473998 gamma_18(2,5) = 22.546340329544281965 gamma_18(3,5) = -208.19826850143475161 gamma_18(4,5) = -149.38973280739878647 gamma_18(5,5) = 114.52707661929266540 gamma_18(1,6) = 529.42778803670706040 gamma_18(2,6) = -144.68684906381240729 gamma_18(3,6) = -679.29858714776464957 gamma_18(4,6) = -528.15039430385887835 gamma_18(5,6) = 149.62114081419526845 gamma_18(6,6) = 673.08720903294175561 gamma_18(1,7) = 744.44148490711736785 gamma_18(2,7) = -810.28094333419162529 gamma_18(3,7) = -1766.0272776708484627 gamma_18(4,7) = -1375.3507474530374570 gamma_18(5,7) = 53.441206915264380766 gamma_18(6,7) = 1425.5357551255674831 gamma_18(7,7) = 1728.2408288785364625 gamma_18(1,8) = 335.27254058398891455 gamma_18(2,8) = -2494.9937774845983791 gamma_18(3,8) = -3881.8500643575359867 gamma_18(4,8) = -2959.4093586618572408 gamma_18(5,8) = -289.21124786321244345 gamma_18(6,8) = 2517.4322350558134681 gamma_18(7,8) = 3835.5391133398971949 gamma_18(8,8) = 2937.2208667559126217 gamma_18(1,9) = -1506.4336471474753413 gamma_18(2,9) = -5870.5195308499163769 gamma_18(3,9) = -7510.2520312926764700 gamma_18(4,9) = -5569.1295516563018183 gamma_18(5,9) = -984.96988010429097837 gamma_18(6,9) = 4009.0786645918014742 gamma_18(7,9) = 7076.8405925366253416 gamma_18(8,9) = 6860.4237027045902165 gamma_18(9,9) = 3494.9619885860521018 gamma_19(1,1) = 0.00050360545304733374207 gamma_19(1,2) = -0.40460366175068393060 gamma_19(2,2) = 0.40510726720373129353 gamma_19(1,3) = -4.2971859978472607032 gamma_19(2,3) = 11.845686392082575874 gamma_19(3,3) = -7.5479967887822678221 gamma_19(1,4) = 57.258083690440599817 gamma_19(2,4) = 85.600074768400514174 gamma_19(3,4) = -57.662687352191283731 gamma_19(4,4) = -85.194967501196782865 gamma_19(1,5) = 465.26418087143349466 gamma_19(2,5) = 275.87908148194156015 gamma_19(3,5) = -297.92856580322918044 gamma_19(4,5) = -457.56404711942211357 gamma_19(5,5) = 14.349854174729286585 gamma_19(1,6) = 1561.2182391554417099 gamma_19(2,6) = 444.70536864181273382 gamma_19(3,6) = -1128.7631605674622359 gamma_19(4,6) = -1565.5154251532889706 gamma_19(5,6) = -432.85968224973015793 gamma_19(6,6) = 1121.2151637786799681 gamma_19(1,7) = 3311.7600821816394292 gamma_19(2,7) = -0.57504609607996686192 gamma_19(3,7) = -3344.5998919228716689 gamma_19(4,7) = -4149.9876255835273326 gamma_19(5,7) = -1809.0977870541944391 gamma_19(6,7) = 1865.7447159890206466 gamma_19(7,7) = 4126.7560560914663790 gamma_19(1,8) = 4895.1561007873429093 gamma_19(2,8) = -2298.7870720065490370 gamma_19(3,8) = -8211.3355431309715080 gamma_19(4,8) = -9269.6343873280917393 gamma_19(5,8) = -4837.8980170969023095 gamma_19(6,8) = 2384.3871467749495511 gamma_19(7,8) = 8153.6728557787802242 gamma_19(8,8) = 9184.4394198268949564 gamma_19(1,9) = 4490.1930069272258379 gamma_19(2,9) = -8392.9849157359789409 gamma_19(3,9) = -17458.746245286361873 gamma_19(4,9) = -18267.300900363652614 gamma_19(5,9) = -10398.778593125258279 gamma_19(6,9) = 2289.1479640952724890 gamma_19(7,9) = 13772.810707438579515 gamma_19(8,9) = 18803.609195253319795 gamma_19(9,9) = 15162.050284402307116 gamma_20(1,1) = 0.00046634356151013665877 gamma_20(1,2) = -0.42862734357780376619 gamma_20(2,2) = 0.42909368713931897074 gamma_20(1,3) = -17.783979576155927602 gamma_20(2,3) = 20.538975395896467198 gamma_20(3,3) = -2.7545294761790272352 gamma_20(1,4) = 14.411881395165752814 gamma_20(2,4) = 209.83777210639851563 gamma_20(3,4) = -14.840508738743556081 gamma_20(4,4) = -209.40867841925919391 gamma_20(1,5) = 750.17724079411404507 gamma_20(2,5) = 947.63509641546088865 gamma_20(3,5) = -168.89050353531299660 gamma_20(4,5) = -1050.3700792175316968 gamma_20(5,5) = -478.55128811316872350 gamma_20(1,6) = 3609.8542155197335099 gamma_20(2,6) = 2556.0161523622311800 gamma_20(3,6) = -1074.8056658969766031 gamma_20(4,6) = -3627.6381950958894375 gamma_20(5,6) = -2535.4771769663347106 gamma_20(6,6) = 1072.0511364207975778 gamma_20(1,7) = 9978.3160358058415662 gamma_20(2,7) = 4571.2867893082967732 gamma_20(3,7) = -4343.5136905175161745 gamma_20(4,7) = -9982.1060711224117063 gamma_20(5,7) = -8042.4710923606524997 gamma_20(6,7) = -79.541348584806067047 gamma_20(7,7) = 7898.0298438148096278 gamma_20(1,8) = 19853.763647596475682 gamma_20(2,8) = 4890.2449297583686194 gamma_20(3,8) = -13093.227773910830651 gamma_20(4,8) = -23394.401351651965122 gamma_20(5,8) = -19839.351766201309930 gamma_20(6,8) = -4680.4071576519701034 gamma_20(7,8) = 13078.387265172087095 gamma_20(8,8) = 23184.992673232705930 gamma_20(1,9) = 30612.221333116261144 gamma_20(2,9) = -893.74799167762007923 gamma_20(3,9) = -32285.102492680018328 gamma_20(4,9) = -48535.614647035493353 gamma_20(5,9) = -41765.339721839893362 gamma_20(6,9) = -15398.557083187367587 gamma_20(7,9) = 17905.609334343076284 gamma_20(8,9) = 42679.626688913409910 gamma_20(9,9) = 47680.905046391206889 ? ## *** last result computed in 49,407 ms. *** *** *** *** *** *** *** *** *** *** *** ***/