/* Copyright (C) 2019 Alessandro Languasco */ /**************** A. LANGUASCO ******************** ************* COMPUTATION OF THE EULER KRONECKER CONSTANTS MOD q(PRIME) *******/ /************************* Building the T approach ****************/ \\ Global variables: global(Dilcher_matrix_T); global(psi_matrix); global(EULER_GEN_gamma0); global(EULER_GEN_gamma1); global(tab); \\global variable used to initialise sumnum global(phir); global(pir); global(defaultprecision); /************* COMPUTATION OF THE EULER KRONECKER CONSTANTS MOD q(PRIME) ******* ************* FOR r1<=q<=r2 ************* ************* Using the T-function ********************/ {global_eulerkroneckerT(r1,r2,defaultprecision,flag=0)=local(minutes, millisec, seconds, rows, columns, elaptimefinalcomp, elaptimeprecomp, oddresult, evenresult, phiq, EK,qminusonehalfminusone, qminusone, qminustwo, correctionderlog, twoPi,twoPiI, u,v,a,g1,g, e, chi, denom, numer, i, logtwoPi, EulerpluslogtwoPi, q1, last, minuslogq, gamma1, qminusonehalf ); \\ flag=1 computes \gamma_0(a,q) and \gamma_1(a,q) \\ minutes,millisec,seconds: used just to compute the elapsed computation time; local variables \\ defaultprecision: used to fix the precision used in the computations; global variable print("************ A. LANGUASCO *************"); print("********* COMPUTATION OF THE EULER-KRONECKER **********"); print("******* CONSTANTS IN ONE INTERVAL ********"); if(flag!=0, print("******* AND EULER GENERALISED CONSTANTS ********")); print("********* with the T-function **********"); \\ precision setting if(defaultprecision >90 , print("Internal constant are defined with 100 decimal digits; you cannot set the default precision larger than 90 decimal digits"); return); default(realprecision,defaultprecision); r1=nextprime(r1); r2=precprime(r2); if (r1>r2, print("error: no odd primes in this interval. END PROGRAM");return); if (r1 < 3, r1=3); print("Interval=[",r1,",",r2,"]"); phir=r2-1; pir=primepi(r2)-primepi(r1)+1; tab = sumnuminit(); \\ needed for the sumnum functions gettime(); print("Performing precomputations of T(a/q), psi(a/q) for this interval"); precompT(r1,r2,flag); elaptimeprecomp=gettime(); twoPi=2*Pi; logtwoPi = log(twoPi); EulerpluslogtwoPi = Euler + logtwoPi; twoPiI=twoPi*I; i=0; gettime(); print("Starting computation of EK_q"); forprime(q=r1,r2, i+=1; phiq=q-1; evenresult=0; oddresult=0; EK=0; qminusone=phiq; qminustwo=q-2; minuslogq=-log(q); qminusonehalf=qminusone/2; qminusonehalfminusone=qminusonehalf-1; correctionderlog= minuslogq * qminustwo ; u=twoPiI/qminusone; \\ even characters for (m=1, qminusonehalfminusone, \\\ even characters numer=0; denom=0; v=exp(u*2*m); \\ j=2m+1; j-1 even (j odd) means an even character chi=1; for (k=0,qminustwo, \\chi=v^(k) numer += chi*Dilcher_matrix_T[i,k+1]; \\Dilcher_T(g^k%q/q) denom += chi*psi_matrix[i,k+1]; \\psi(g^k%q/q); chi=chi*v; \\print(numer); print(denom); ); evenresult += numer/denom; ); print("EK(",q")^+ = ", Euler + minuslogq * qminusonehalfminusone + real(evenresult)); \\ odd characters for(m=1, qminusonehalf, \\\ odd characters numer=0; denom=0; v=exp(u*(2*m-1)); \\ j=2m; j-1 odd (j even) means an odd character chi=1; for (k=0,qminustwo, \\chi=v^(k) numer += chi*Dilcher_matrix_T[i,k+1]; \\Dilcher_T(g^k%q/q) denom += chi*psi_matrix[i,k+1]; \\psi(g^k%q/q); chi=chi*v; \\print(numer); print(denom); ); oddresult += numer/denom; ); EK = Euler + oddresult + evenresult + correctionderlog; print("EK(",q") = ", real(EK)); ); elaptimefinalcomp=gettime(); seconds=floor(elaptimeprecomp/1000)%60; minutes=floor(elaptimeprecomp/60000); millisec=elaptimeprecomp- minutes*60000 - seconds*1000; \\print(elaptimeprecomp); print("Precomputation time: ", minutes, " min, ", seconds, " sec, ", millisec, " millisec"); \\print(elaptimefinalcomp); seconds=floor(elaptimefinalcomp/1000)%60; minutes=floor(elaptimefinalcomp/60000); millisec=elaptimefinalcomp- minutes*60000 - seconds*1000; print("Final step EK computation time (output time included): ", minutes, " min, ", seconds, " sec, ", millisec, " millisec"); seconds=floor((elaptimefinalcomp+elaptimeprecomp)/1000)%60; minutes=floor((elaptimefinalcomp+elaptimeprecomp)/60000); millisec=(elaptimefinalcomp+elaptimeprecomp)- minutes*60000 - seconds*1000; print("Total elapsed time: ", minutes, " min, ", seconds, " sec, ", millisec, " millisec"); if(flag!=0, gamma1=-0.072815845483676724860586375874901319137736338334337952599006559741401433571511484878086928244844014604; print("********* Euler Generalised constants *********"); for(i=1,pir, q1=EULER_GEN_gamma0[i,phir+1]; print("modulo ",q1); last=q1-1; for(a=1,last, print("gamma0(", a,",", q1,") = ",EULER_GEN_gamma0[i,a])); print("gamma0(", q1,",",q1,") = ", (Euler -log(q1))/q1); for(a=1,last, print("gamma1(", a,",", q1 ,") = ",EULER_GEN_gamma1[i,a])); print("gamma1(", q1,",",q1,") = ", (gamma1+Euler*log(q1)-(log(q1))^2/2)/q1); ); ); print("****** END PROGRAM ********"); } /***************** T-function ****************/ {DilcherT(x)= local(T,m,gamma1,ord,eps); \\ computes -T(x) \\tab is a global variable gamma1=-0.072815845483676724860586375874901319137736338334337952599006559741401433571511484878086928244844014604; eps=1/100.; ord=x; \\rate of decay for the integral formula of S-DIF if (ord < eps, T=sumnum(m=0, (log(x+m)/(x+m))-(log(1+m)/(1+m)),tab), T = - gamma1 +intnum(t=0,[+oo,ord], (1-exp(-t)-t*exp((1-x)*t))*(Euler+log(t))/(t*(exp(t)-1))) ); return(T); } {DilcherTtab(x,tabstandalone)= local(T,m,gamma1,ord,eps); \\ for the standalone precomputations \\ computes -T(x) gamma1=-0.072815845483676724860586375874901319137736338334337952599006559741401433571511484878086928244844014604; eps=1/100.; ord=x; \\rate of decay for the integral formula of S-DIF if (ord < eps, T=sumnum(m=0, (log(x+m)/(x+m))-(log(1+m)/(1+m)),tabstandalone), T = - gamma1 +intnum(t=0,[+oo,ord], (1-exp(-t)-t*exp((1-x)*t))*(Euler+log(t))/(t*(exp(t)-1))) ); return(T); } /***************** Precomputations ****************/ {precompT(r1,r2,flag)= local(rows, columns, i, aoverq, m, logq, logqsquared, oneoverq, oneovertwiceq, minusoneoverq, g1, g, a, C1, minuslogqoverq); C1=-0.145631690967353449721172751749802638275472676668675905198013119482802867143022969756173856489688029208; \\-0.072815845483676724860586375874901319137736338334337952599006559741401433571511484878086928244844014604*2 Dilcher_matrix_T=matrix(pir,phir+1,rows,columns,0); psi_matrix=matrix(pir,phir+1,rows,columns,0); if(flag!=0,EULER_GEN_gamma0=matrix(pir,phir+1,rows,columns,0); EULER_GEN_gamma1=matrix(pir,phir+1,rows,columns,0); ); i=0; forprime(q=r1,r2, print("Precomputation for q = ",q); g1=znprimroot(q); \\ needed here to sort the sequences T(a,q) psi(a/q) using a=a=g^k%q g=lift(g1); i+=1; Dilcher_matrix_T[i,phir+1]=q; psi_matrix[i,phir+1]=q; if(flag!=0, EULER_GEN_gamma0[i,phir+1]=q; EULER_GEN_gamma1[i,phir+1]=q; logq=log(q); logqsquared=(logq)^2; oneoverq = 1/q; oneovertwiceq = oneoverq/2; minusoneoverq=-oneoverq; minuslogqoverq=logq*minusoneoverq ); a=1; for(k=0, q-2, aoverq = a/q; Dilcher_matrix_T[i,k+1]=DilcherT(aoverq); \\ already sorted for the final summation psi_matrix[i,k+1] = psi(aoverq); if(flag!=0, EULER_GEN_gamma0[i,k+1] = minuslogqoverq+psi_matrix[i,k+1]; \\ unsorted EULER_GEN_gamma1[i,k+1] = (C1-logqsquared)*oneovertwiceq+minuslogqoverq*psi_matrix[i,k+1]+oneoverq*Dilcher_matrix_T[i,k+1]); a=(a*g)%q \\a=g^k%q; ); ); } /************************************ **** 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 EK-T-final.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 PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER. *************** with the T-function ************ ? init_EK_T_final();global_eulerkroneckerT(3,300,30) ************ A. LANGUASCO ************* ********* COMPUTATION OF THE EULER-KRONECKER ********** ******* CONSTANTS IN ONE INTERVAL ******** ********* with the T-function ********** Interval=[3,293] Performing precomputations of T(a/q), psi(a/q) for this interval Precomputation for q = 3 Precomputation for q = 5 Precomputation for q = 7 Precomputation for q = 11 Precomputation for q = 13 Precomputation for q = 17 Precomputation for q = 19 Precomputation for q = 23 Precomputation for q = 29 Precomputation for q = 31 Precomputation for q = 37 Precomputation for q = 41 Precomputation for q = 43 Precomputation for q = 47 Precomputation for q = 53 Precomputation for q = 59 Precomputation for q = 61 Precomputation for q = 67 Precomputation for q = 71 Precomputation for q = 73 Precomputation for q = 79 Precomputation for q = 83 Precomputation for q = 89 Precomputation for q = 97 Precomputation for q = 101 Precomputation for q = 103 Precomputation for q = 107 Precomputation for q = 109 Precomputation for q = 113 Precomputation for q = 127 Precomputation for q = 131 Precomputation for q = 137 Precomputation for q = 139 Precomputation for q = 149 Precomputation for q = 151 Precomputation for q = 157 Precomputation for q = 163 Precomputation for q = 167 Precomputation for q = 173 Precomputation for q = 179 Precomputation for q = 181 Precomputation for q = 191 Precomputation for q = 193 Precomputation for q = 197 Precomputation for q = 199 Precomputation for q = 211 Precomputation for q = 223 Precomputation for q = 227 Precomputation for q = 229 Precomputation for q = 233 Precomputation for q = 239 Precomputation for q = 241 Precomputation for q = 251 Precomputation for q = 257 Precomputation for q = 263 Precomputation for q = 269 Precomputation for q = 271 Precomputation for q = 277 Precomputation for q = 281 Precomputation for q = 283 Precomputation for q = 293 Starting computation of EK_q EK(3)^+ = 0.577215664901532860606512090082 EK(3) = 0.945497280871680703239749994158 EK(5)^+ = 1.40489514161703774859755907976 EK(5) = 1.72062421251340476169572878865 EK(7)^+ = 1.95715645444971475271382186143 EK(7) = 2.08759407471733013281542471957 EK(11)^+ = 2.66207409890433174906654072453 EK(11) = 2.41542590428326783034287963583 EK(13)^+ = 2.89959572414790509559591203013 EK(13) = 2.61075773741765019699776108857 EK(17)^+ = 3.23179164885108167689200470642 EK(17) = 3.58197604409757765927178812919 EK(19)^+ = 3.36702810226943360422911738361 EK(19) = 4.79040941571428332590703936458 EK(23)^+ = 3.56605274186303485506490005633 EK(23) = 2.61128917618820092550739164964 EK(29)^+ = 3.77451272291818155837540505527 EK(29) = 3.09373170599426872316275179819 EK(31)^+ = 3.74063417131631765163927862231 EK(31) = 4.31444292526747509770757441042 EK(37)^+ = 3.88346103237113739135523493388 EK(37) = 4.30493818995760201798557926417 EK(41)^+ = 3.90067243331576039538420460289 EK(41) = 3.97152162792133216028257040014 EK(43)^+ = 4.37462848511375110150884874389 EK(43) = 4.37862750574695049413775062336 EK(47)^+ = 4.78330592374031492736088514964 EK(47) = 4.79939425890741613452758429988 EK(53)^+ = 4.06734814093911422415451881781 EK(53) = 4.33773685859709231869696082307 EK(59)^+ = 5.74977495098717868985714511291 EK(59) = 5.43351634538500398077634438193 EK(61)^+ = 4.71919160448137601223479232791 EK(61) = 5.07108519057651619595805098113 EK(67)^+ = 5.49478574409231087894450914285 EK(67) = 5.29213930662896260873428461831 EK(71)^+ = 5.02459221437013823603453457463 EK(71) = 5.25525819281894616772013128637 EK(73)^+ = 5.56638018904420607773144876527 EK(73) = 4.06694909044749529201648815625 EK(79)^+ = 4.31392816983842153234814442952 EK(79) = 4.99827631817068010789431392945 EK(83)^+ = 4.06119890648015486954960478374 EK(83) = 3.03313611343607418716403819105 EK(89)^+ = 5.44834851555434719261902953243 EK(89) = 4.16409079888983276880841110372 EK(97)^+ = 4.44563411256346738186380452664 EK(97) = 4.89124074040389666830751468857 EK(101)^+ = 5.93364557387726998305789899164 EK(101) = 5.29701289150966971887860032739 EK(103)^+ = 5.53312508630999898815400644939 EK(103) = 5.14433955125208822113330503220 EK(107)^+ = 5.35744691959596839332603590620 EK(107) = 5.45827420997024503421680245453 EK(109)^+ = 6.28639312060842026587282318484 EK(109) = 6.90663814626423653219469837704 EK(113)^+ = 4.71308052553071355344451609738 EK(113) = 4.02173038257803067578318006617 EK(127)^+ = 5.28427526641642291108714895825 EK(127) = 5.08859912415333449423215636240 EK(131)^+ = 4.29182422162389365669036230041 EK(131) = 2.83682634158837909860285797321 EK(137)^+ = 5.17281966401368126952267004684 EK(137) = 4.93700022614368468691962999711 EK(139)^+ = 5.15673467267785693456200640445 EK(139) = 5.88916863399867186726383730369 EK(149)^+ = 6.35744273145487616682151978517 EK(149) = 5.98342477769515981450242785739 EK(151)^+ = 5.66732269410388218441768644382 EK(151) = 5.04201611352872179914519461022 EK(157)^+ = 5.67766459100970078752076942990 EK(157) = 7.40802206572222729350845201390 EK(163)^+ = 5.54289611872522541669860167904 EK(163) = 5.92966482288720678755499913844 EK(167)^+ = 6.80394798958259907108839110755 EK(167) = 8.03300175268872470467583357802 EK(173)^+ = 4.74313680866654143318864467269 EK(173) = 3.38434753653206190344297798897 EK(179)^+ = 5.59074764196693719810304550344 EK(179) = 3.86236132549903008112126130282 EK(181)^+ = 5.52401113238735460988935254057 EK(181) = 5.14111848776848135810136664257 EK(191)^+ = 6.21621633683078754687889560801 EK(191) = 4.69286990201422664003552434812 EK(193)^+ = 6.33516880970302226248749231989 EK(193) = 5.16342219673915483320078262720 EK(197)^+ = 6.72431280547758930911931614898 EK(197) = 7.55148715896640647886485129372 EK(199)^+ = 4.97867314026834059118807347477 EK(199) = 6.47366513609320738699497459778 EK(211)^+ = 5.43928767077706865027592727891 EK(211) = 7.73613578424586162532810587585 EK(223)^+ = 6.97640718267880419790301145060 EK(223) = 7.81777971785991367471336734851 EK(227)^+ = 6.16478105833535800088839052312 EK(227) = 8.08053156951296218697071193757 EK(229)^+ = 5.19368182825228459062582716349 EK(229) = 7.16298632058099546745778115058 EK(233)^+ = 5.48268694035180653761326391137 EK(233) = 3.11948354485127541303115295258 EK(239)^+ = 4.89826038220509731091188200357 EK(239) = 3.99911017207833249512632297919 EK(241)^+ = 6.91099570349028181262249488655 EK(241) = 6.03752521401034215065709250935 EK(251)^+ = 5.85522475367262429906377535883 EK(251) = 5.04313708502347351042811119022 EK(257)^+ = 7.41413126491779482941571986652 EK(257) = 8.16991391232741391670225155227 EK(263)^+ = 6.88761891078185993452639437420 EK(263) = 7.30343624736815435414348077406 EK(269)^+ = 6.33572466741282346876839833227 EK(269) = 6.26034831666577102735252755712 EK(271)^+ = 4.91607375378349595312704873315 EK(271) = 5.97717804854803304223773905976 EK(277)^+ = 6.07306330239530923314413596279 EK(277) = 4.59280817714077895164777081661 EK(281)^+ = 4.99043740542558229612252801406 EK(281) = 4.66496432366211457505220852623 EK(283)^+ = 7.04969230270522888347459792033 EK(283) = 7.15028579741068251409225231188 EK(293)^+ = 5.12676122531917231941583293241 EK(293) = 3.38438152121953978658468259238 Precomputation time: 0 min, 31 sec, 788 millisec Final step EK computation time (output time included): 0 min, 0 sec, 818 millisec Total elapsed time: 0 min, 32 sec, 606 millisec ****** END PROGRAM ******** ? for(n=1,10,m=nextprime(n*10^3); init_EK_T_final();global_eulerkroneckerT(m,m,30)) ************ A. LANGUASCO ************* ********* COMPUTATION OF THE EULER-KRONECKER ********** ******* CONSTANTS IN ONE INTERVAL ******** ********* with the T-function ********** Interval=[1009,1009] Performing precomputations of T(a/q), psi(a/q) for this interval Precomputation for q = 1009 Starting computation of EK_q EK(1009)^+ = 6.27335408443221031721862501118 EK(1009) = 8.44213515184929927586069467274 Precomputation time: 0 min, 3 sec, 901 millisec Final step EK computation time (output time included): 0 min, 0 sec, 499 millisec Total elapsed time: 0 min, 4 sec, 400 millisec ****** END PROGRAM ******** ************ A. LANGUASCO ************* ********* COMPUTATION OF THE EULER-KRONECKER ********** ******* CONSTANTS IN ONE INTERVAL ******** ********* with the T-function ********** Interval=[2003,2003] Performing precomputations of T(a/q), psi(a/q) for this interval Precomputation for q = 2003 Starting computation of EK_q EK(2003)^+ = 6.99352586114139787466168421420 EK(2003) = 5.79342136907936332803849821625 Precomputation time: 0 min, 7 sec, 749 millisec Final step EK computation time (output time included): 0 min, 1 sec, 961 millisec Total elapsed time: 0 min, 9 sec, 710 millisec ****** END PROGRAM ******** ************ A. LANGUASCO ************* ********* COMPUTATION OF THE EULER-KRONECKER ********** ******* CONSTANTS IN ONE INTERVAL ******** ********* with the T-function ********** Interval=[3001,3001] Performing precomputations of T(a/q), psi(a/q) for this interval Precomputation for q = 3001 Starting computation of EK_q EK(3001)^+ = 8.64597006729841389989349765775 EK(3001) = 8.64746513696838693880234535092 Precomputation time: 0 min, 11 sec, 610 millisec Final step EK computation time (output time included): 0 min, 4 sec, 396 millisec Total elapsed time: 0 min, 16 sec, 6 millisec ****** END PROGRAM ******** ************ A. LANGUASCO ************* ********* COMPUTATION OF THE EULER-KRONECKER ********** ******* CONSTANTS IN ONE INTERVAL ******** ********* with the T-function ********** Interval=[4001,4001] Performing precomputations of T(a/q), psi(a/q) for this interval Precomputation for q = 4001 Starting computation of EK_q EK(4001)^+ = 8.78053800942307358728679938495 EK(4001) = 7.00343554620314399435685176843 Precomputation time: 0 min, 15 sec, 476 millisec Final step EK computation time (output time included): 0 min, 7 sec, 811 millisec Total elapsed time: 0 min, 23 sec, 287 millisec ****** END PROGRAM ******** ************ A. LANGUASCO ************* ********* COMPUTATION OF THE EULER-KRONECKER ********** ******* CONSTANTS IN ONE INTERVAL ******** ********* with the T-function ********** Interval=[5003,5003] Performing precomputations of T(a/q), psi(a/q) for this interval Precomputation for q = 5003 Starting computation of EK_q EK(5003)^+ = 7.24402247427910626344123306179 EK(5003) = 5.54929300458161422773687954041 Precomputation time: 0 min, 19 sec, 368 millisec Final step EK computation time (output time included): 0 min, 12 sec, 225 millisec Total elapsed time: 0 min, 31 sec, 593 millisec ****** END PROGRAM ******** ************ A. LANGUASCO ************* ********* COMPUTATION OF THE EULER-KRONECKER ********** ******* CONSTANTS IN ONE INTERVAL ******** ********* with the T-function ********** Interval=[6007,6007] Performing precomputations of T(a/q), psi(a/q) for this interval Precomputation for q = 6007 Starting computation of EK_q EK(6007)^+ = 9.87426664724257694868961234209 EK(6007) = 8.31161012199848381656290344038 Precomputation time: 0 min, 23 sec, 250 millisec Final step EK computation time (output time included): 0 min, 17 sec, 610 millisec Total elapsed time: 0 min, 40 sec, 860 millisec ****** END PROGRAM ******** ************ A. LANGUASCO ************* ********* COMPUTATION OF THE EULER-KRONECKER ********** ******* CONSTANTS IN ONE INTERVAL ******** ********* with the T-function ********** Interval=[7001,7001] Performing precomputations of T(a/q), psi(a/q) for this interval Precomputation for q = 7001 Starting computation of EK_q EK(7001)^+ = 9.68333277349107864470848805445 EK(7001) = 8.50527787610087713931687803847 Precomputation time: 0 min, 27 sec, 79 millisec Final step EK computation time (output time included): 0 min, 23 sec, 934 millisec Total elapsed time: 0 min, 51 sec, 13 millisec ****** END PROGRAM ******** ************ A. LANGUASCO ************* ********* COMPUTATION OF THE EULER-KRONECKER ********** ******* CONSTANTS IN ONE INTERVAL ******** ********* with the T-function ********** Interval=[8009,8009] Performing precomputations of T(a/q), psi(a/q) for this interval Precomputation for q = 8009 Starting computation of EK_q EK(8009)^+ = 11.4431421556247084876087109206 EK(8009) = 11.6868463915493575353450869960 Precomputation time: 0 min, 30 sec, 969 millisec Final step EK computation time (output time included): 0 min, 31 sec, 336 millisec Total elapsed time: 1 min, 2 sec, 305 millisec ****** END PROGRAM ******** ************ A. LANGUASCO ************* ********* COMPUTATION OF THE EULER-KRONECKER ********** ******* CONSTANTS IN ONE INTERVAL ******** ********* with the T-function ********** Interval=[9001,9001] Performing precomputations of T(a/q), psi(a/q) for this interval Precomputation for q = 9001 Starting computation of EK_q EK(9001)^+ = 9.48683888314549627674927600069 EK(9001) = 10.1094784318383409358225035802 Precomputation time: 0 min, 34 sec, 839 millisec Final step EK computation time (output time included): 0 min, 39 sec, 603 millisec Total elapsed time: 1 min, 14 sec, 442 millisec ****** END PROGRAM ******** ************ A. LANGUASCO ************* ********* COMPUTATION OF THE EULER-KRONECKER ********** ******* CONSTANTS IN ONE INTERVAL ******** ********* with the T-function ********** Interval=[10007,10007] Performing precomputations of T(a/q), psi(a/q) for this interval Precomputation for q = 10007 Starting computation of EK_q EK(10007)^+ = 11.0601624759024741933308283063 EK(10007) = 12.6646120045606923275389356783 Precomputation time: 0 min, 38 sec, 732 millisec Final step EK computation time (output time included): 0 min, 47 sec, 813 millisec Total elapsed time: 1 min, 26 sec, 545 millisec ****** END PROGRAM ******** ****************** larger q's ********************** ? init_EK_T_final();global_eulerkroneckerT(20011,20011,30) ************ A. LANGUASCO ************* ********* COMPUTATION OF THE EULER-KRONECKER ********** ******* CONSTANTS IN ONE INTERVAL ******** ********* with the T-function ********** Interval=[20011,20011] Performing precomputations of T(a/q), psi(a/q) for this interval Precomputation for q = 20011 Starting computation of EK_q EK(20011)^+ = 10.5489807692170969459672226221 EK(20011) = 10.7996803112999205186430402899 Precomputation time: 1 min, 15 sec, 608 millisec Final step EK computation time (output time included): 3 min, 14 sec, 338 millisec Total elapsed time: 4 min, 29 sec, 946 millisec ****** END PROGRAM ******** ? init_EK_T_final();global_eulerkroneckerT(30011,30011,30) ************ A. LANGUASCO ************* ********* COMPUTATION OF THE EULER-KRONECKER ********** ******* CONSTANTS IN ONE INTERVAL ******** ********* with the T-function ********** Interval=[30011,30011] Performing precomputations of T(a/q), psi(a/q) for this interval Precomputation for q = 30011 Starting computation of EK_q EK(30011)^+ = 11.0127039500540893278498877674 EK(30011) = 10.3330799721240242255136062255 Precomputation time: 1 min, 58 sec, 998 millisec Final step EK computation time (output time included): 7 min, 19 sec, 891 millisec Total elapsed time: 9 min, 18 sec, 889 millisec ****** END PROGRAM ******** *********************************************************************** GENERALIZED EULER CONSTANTS gamma0(a,q) and gamma1(a,q) ? init_EK_T_final();global_eulerkroneckerT(1,100,30,1) ************ A. LANGUASCO ************* ********* COMPUTATION OF THE EULER-KRONECKER ********** ******* CONSTANTS IN ONE INTERVAL ******** ******* AND EULER GENERALISED CONSTANTS ******** ********* with the T-function ********** Interval=[3,97] Performing precomputations of T(a/q), psi(a/q) for this interval Precomputation for q = 3 Precomputation for q = 5 Precomputation for q = 7 Precomputation for q = 11 Precomputation for q = 13 Precomputation for q = 17 Precomputation for q = 19 Precomputation for q = 23 Precomputation for q = 29 Precomputation for q = 31 Precomputation for q = 37 Precomputation for q = 41 Precomputation for q = 43 Precomputation for q = 47 Precomputation for q = 53 Precomputation for q = 59 Precomputation for q = 61 Precomputation for q = 67 Precomputation for q = 71 Precomputation for q = 73 Precomputation for q = 79 Precomputation for q = 83 Precomputation for q = 89 Precomputation for q = 97 Starting computation of EK_q EK(3)^+ = 0.577215664901532860606512090082 EK(3) = 0.945497280871680703239749994158 EK(5)^+ = 1.40489514161703774859755907976 EK(5) = 1.72062421251340476169572878865 EK(7)^+ = 1.95715645444971475271382186143 EK(7) = 2.08759407471733013281542471957 EK(11)^+ = 2.66207409890433174906654072453 EK(11) = 2.41542590428326783034287963583 EK(13)^+ = 2.89959572414790509559591203013 EK(13) = 2.61075773741765019699776108857 EK(17)^+ = 3.23179164885108167689200470642 EK(17) = 3.58197604409757765927178812919 EK(19)^+ = 3.36702810226943360422911738361 EK(19) = 4.79040941571428332590703936458 EK(23)^+ = 3.56605274186303485506490005633 EK(23) = 2.61128917618820092550739164964 EK(29)^+ = 3.77451272291818155837540505527 EK(29) = 3.09373170599426872316275179819 EK(31)^+ = 3.74063417131631765163927862231 EK(31) = 4.31444292526747509770757441042 EK(37)^+ = 3.88346103237113739135523493388 EK(37) = 4.30493818995760201798557926417 EK(41)^+ = 3.90067243331576039538420460289 EK(41) = 3.97152162792133216028257040014 EK(43)^+ = 4.37462848511375110150884874389 EK(43) = 4.37862750574695049413775062336 EK(47)^+ = 4.78330592374031492736088514964 EK(47) = 4.79939425890741613452758429988 EK(53)^+ = 4.06734814093911422415451881781 EK(53) = 4.33773685859709231869696082307 EK(59)^+ = 5.74977495098717868985714511291 EK(59) = 5.43351634538500398077634438193 EK(61)^+ = 4.71919160448137601223479232791 EK(61) = 5.07108519057651619595805098113 EK(67)^+ = 5.49478574409231087894450914285 EK(67) = 5.29213930662896260873428461831 EK(71)^+ = 5.02459221437013823603453457463 EK(71) = 5.25525819281894616772013128637 EK(73)^+ = 5.56638018904420607773144876527 EK(73) = 4.06694909044749529201648815625 EK(79)^+ = 4.31392816983842153234814442952 EK(79) = 4.99827631817068010789431392945 EK(83)^+ = 4.06119890648015486954960478374 EK(83) = 3.03313611343607418716403819105 EK(89)^+ = 5.44834851555434719261902953243 EK(89) = 4.16409079888983276880841110372 EK(97)^+ = 4.44563411256346738186380452664 EK(97) = 4.89124074040389666830751468857 Precomputation time: 0 min, 3 sec, 997 millisec Final step EK computation time (output time included): 0 min, 0 sec, 35 millisec Total elapsed time: 0 min, 4 sec, 32 millisec ********* Euler Generalised constants ********* modulo 3 gamma0(1,3) = -3.49823787624350955346150081993 gamma0(2,3) = -1.68443851200929170286742256229 gamma0(3,3) = -0.173798874588858943596244382280 gamma1(1,3) = -0.140713732356570779950538950043 gamma1(2,3) = 0.0819492546120307295361213127214 gamma1(3,3) = -0.0140513677391366744461687385530 modulo 5 gamma0(1,5) = -5.61092747907900837046735982910 gamma0(2,5) = -2.88327212707193622065082734869 gamma0(3,5) = -1.28689614919295853431144949980 gamma0(4,5) = -1.86250679638001048968081581545 gamma0(5,5) = -0.206444449506513502798849448629 gamma1(1,5) = -0.162593875614818542786521844475 gamma1(2,5) = 0.114887169778078735145202952100 gamma1(3,5) = -0.00803754386935957624435781459147 gamma1(4,5) = 0.0707220577685046446886019752049 gamma1(5,5) = -0.0877936535460819856635116441139 modulo 7 gamma0(1,7) = -7.64196740637510224213599426637 gamma0(2,7) = -2.64380592144574164079995237562 gamma0(3,7) = -3.96350514443657437720951040251 gamma0(4,7) = -1.11838304188143202047041016011 gamma0(5,7) = -1.92675789907183648184839163629 gamma0(6,7) = -1.45816860449025779843115668380 gamma0(7,7) = -0.195527783450540063499834379052 gamma1(1,7) = -0.169244255281333222740235566875 gamma1(2,7) = 0.110095723713805356657136984434 gamma1(3,7) = 0.132263831829445646090646744027 gamma1(4,7) = -0.0673153661042553192013996993996 gamma1(5,7) = 0.0514958800961286829082161197561 gamma1(6,7) = -0.00969891987228087402554326254559 gamma1(7,7) = -0.120412739865186994549407695272 modulo 11 gamma0(1,11) = -11.6548529013390113988125583747 gamma0(2,11) = -6.03032119922538683269627499882 gamma0(3,11) = -3.06732963684198682844033759144 gamma0(4,11) = -1.36303067890668347781239918554 gamma0(5,11) = -2.42487040148494967220850612547 gamma0(6,11) = -0.955570891220036383891379601431 gamma0(7,11) = -1.14190761072315341061054988850 gamma0(8,11) = -1.63261234490130350008781482855 gamma0(9,11) = -4.08523620928328920114698887548 gamma0(10,11) = -1.97317756932466801600509404122 gamma0(11,11) = -0.165516327990621607586857407989 gamma1(1,11) = -0.167987835995947788974326652262 gamma1(2,11) = 0.154418657376452806756260806673 gamma1(3,11) = 0.110286431454837348906428820525 gamma1(4,11) = -0.0518123335416601637612146183496 gamma1(5,11) = 0.0653143771907921453130898753916 gamma1(6,11) = -0.114390778849209902605281595586 gamma1(7,11) = -0.0843993826993273174923849604191 gamma1(8,11) = -0.0162171144623599232002460419793 gamma1(9,11) = 0.151341000099815968391238892362 gamma1(10,11) = 0.0227824067507036194113020637970 gamma1(11,11) = -0.142151272807773517605452966028 modulo 13 gamma0(1,13) = -13.6546399574960171611730024962 gamma0(2,13) = -7.04646744390117998452461949648 gamma0(3,13) = -3.60780493550283707900131206738 gamma0(4,13) = -1.68313229423808221620033144344 gamma0(5,13) = -4.78136508434962104177404801443 gamma0(6,13) = -2.36406112213561169020921561467 gamma0(7,13) = -0.908697522973166239502005224755 gamma0(8,13) = -1.06066274852664043904163428023 gamma0(9,13) = -1.43932009752115290589888367973 gamma0(10,13) = -2.87458123084728351734409544224 gamma0(11,13) = -1.23524003740025096272428021339 gamma0(12,13) = -1.98260271166025487647558071758 gamma0(13,13) = -0.152902591735384913495921180883 gamma1(1,13) = -0.164887226813867908252040887339 gamma1(2,13) = 0.162733684762101203157326581391 gamma1(3,13) = 0.127848108553689380312426653076 gamma1(4,13) = -0.0191665144351815756546779201134 gamma1(5,13) = 0.164456672134200265010571117820 gamma1(6,13) = 0.0483566775950485603493942173269 gamma1(7,13) = -0.123267221211638681839995356296 gamma1(8,13) = -0.100234533343432884033943639563 gamma1(9,13) = -0.0485046435142311687945631863533 gamma1(10,13) = 0.0870157020384866139424665412628 gamma1(11,13) = -0.0754112569639231254054991551783 gamma1(12,13) = 0.0129962057034519340967736537520 gamma1(13,13) = -0.144751499988379337748824995661 modulo 17 gamma0(1,17) = -17.6510652526586962689719944780 gamma0(2,17) = -6.15260313501130407787896119846 gamma0(3,17) = -1.99191694821799827249735156170 gamma0(4,17) = -1.75076034806024455468614401223 gamma0(5,17) = -1.21570300767269339383974877767 gamma0(6,17) = -3.74254339281406318818815871715 gamma0(7,17) = -0.956021376338846639104102732270 gamma0(8,17) = -1.54643016273804147505926034767 gamma0(9,17) = -0.845028941172649241775072261699 gamma0(10,17) = -1.07875678610083722653691000187 gamma0(11,17) = -2.28302837850680248469115810621 gamma0(12,17) = -2.64462052456148175541355943423 gamma0(13,17) = -4.66186598523202547203172033841 gamma0(14,17) = -1.37012274608160581492164870446 gamma0(15,17) = -9.06540680934569469606942189699 gamma0(16,17) = -3.11075742844953558898651372238 gamma0(17,17) = -0.132705745832628424684883678105 gamma1(1,17) = -0.157500996319789925913952509084 gamma1(2,17) = 0.183960411470963788013978856980 gamma1(3,17) = -0.000801225090435774448945379598336 gamma1(4,17) = -0.0238333926168230463425178156366 gamma1(5,17) = -0.0825415849792540803348988255341 gamma1(6,17) = 0.117053240609120986045793448604 gamma1(7,17) = -0.115232765740245411635948712182 gamma1(8,17) = -0.0449576804783963935145265818772 gamma1(9,17) = -0.130116544702621523528790801022 gamma1(10,17) = -0.0994172503799424108610973173588 gamma1(11,17) = 0.0244687072808063280615530162459 gamma1(12,17) = 0.0523482686568474434812892249414 gamma1(13,17) = 0.152790821747410608637240455748 gamma1(14,17) = -0.0644509666430911671621457283108 gamma1(15,17) = 0.176405103346677818309013223765 gamma1(16,17) = 0.0831858699877710888456201148061 gamma1(17,17) = -0.144175861632675052512251046362 modulo 19 gamma0(1,19) = -19.6487902279550844576553836338 gamma0(2,19) = -10.0712074060543172132350963627 gamma0(3,19) = -5.18075081652823747904206262994 gamma0(4,19) = -2.56998496842623833657988690726 gamma0(5,19) = -1.02690411630930927038517639632 gamma0(6,19) = -1.42056167872252881092253351931 gamma0(7,19) = -2.96352336642902869546773707078 gamma0(8,19) = -1.27474379439667465776690195051 gamma0(9,19) = -2.25448299762432471806405575353 gamma0(10,19) = -0.822257598480446693184843049717 gamma0(11,19) = -0.920060638111228545047320116890 gamma0(12,19) = -1.14443249268003538627494433037 gamma0(13,19) = -1.77442566226372845871911002148 gamma0(14,19) = -6.83205887970591424227458438843 gamma0(15,19) = -3.47306659867352053966357233784 gamma0(16,19) = -1.58549306314444474903695509279 gamma0(17,19) = -4.16678356497372996639911968586 gamma0(18,19) = -1.99416320848990107874642893636 gamma0(19,19) = -0.124590700750784610494869228516 gamma1(1,19) = -0.153716075050352351913639065013 gamma1(2,19) = 0.182183339124252479290477622063 gamma1(3,19) = 0.162183886208471704865963941959 gamma1(4,19) = 0.0399565487866036353231050035182 gamma1(5,19) = -0.105324384696254570666907924943 gamma1(6,19) = -0.0608992690638886476165818235074 gamma1(7,19) = 0.0664297421993335148096850442945 gamma1(8,19) = -0.0766868110456766685508589081427 gamma1(9,19) = 0.0160272147083417658079457419044 gamma1(10,19) = -0.130782282457501740598156844659 gamma1(11,19) = -0.118404707604285750897321923420 gamma1(12,19) = -0.0914533271659809186275260803801 gamma1(13,19) = -0.0256221351734294659087042346626 gamma1(14,19) = 0.191602932593152556840266416006 gamma1(15,19) = 0.0957883042828593803291922274596 gamma1(16,19) = -0.0439390868140008902766747329196 gamma1(17,19) = 0.128095973912714068012639275115 gamma1(18,19) = -0.00572412962911460765728520985399 gamma1(19,19) = -0.142531578598920217426204900693 modulo 23 gamma0(1,23) = -23.6442095454399850838742861254 gamma0(2,23) = -5.00354510443072023497448911751 gamma0(3,23) = -12.0789360173809763354663068792 gamma0(4,23) = -2.46263166362739684372082544160 gamma0(5,23) = -6.20894047225464422563714153585 gamma0(6,23) = -0.951295048601004709945620404170 gamma0(7,23) = -3.12759814473134498344411106462 gamma0(8,23) = -1.25013337886450227920484007397 gamma0(9,23) = -1.36873252093436098905204975380 gamma0(10,23) = -2.21126502533901894264629760846 gamma0(11,23) = -2.76221967668383390603155361898 gamma0(12,23) = -0.787425518372509136152747550568 gamma0(13,23) = -1.14200898399962369136016588714 gamma0(14,23) = -0.866444989510872605726558855111 gamma0(15,23) = -1.80980120302020464428190527351 gamma0(16,23) = -1.04281144878353895987874410325 gamma0(17,23) = -8.18396674563664564928243419318 gamma0(18,23) = -1.49975603997102538154235068966 gamma0(19,23) = -4.18417609874947727804837131710 gamma0(20,23) = -3.58631076821832326116628229066 gamma0(21,23) = -1.99637420073835116708644986461 gamma0(22,23) = -1.64569737936977478284237826067 gamma0(23,23) = -0.111229502218592036095662640945 gamma1(1,23) = -0.146440838992775571891454414995 gamma1(2,23) = 0.145502550457010923750494506993 gamma1(3,23) = 0.192219148774578744887531000648 gamma1(4,23) = 0.0217325887909741952802497545269 gamma1(5,23) = 0.177268970486439629046266936821 gamma1(6,23) = -0.111203848871670934411072555345 gamma1(7,23) = 0.0636665756937162021915875178991 gamma1(8,23) = -0.0798971806727971427670453840815 gamma1(9,23) = -0.0682359379812548430534249179782 gamma1(10,23) = 0.00359387942901331489543585101106 gamma1(11,23) = 0.0416508020072809259497881921565 gamma1(12,23) = -0.129604948448479083636497311742 gamma1(13,23) = -0.0908995633148543244042216285346 gamma1(14,23) = -0.120618911624857827067242183151 gamma1(15,23) = -0.0283634583927233635493754884578 gamma1(16,23) = -0.101314796257042509115123274431 gamma1(17,23) = 0.204236130440891327507533781070 gamma1(18,23) = -0.0558308902182658001595578515544 gamma1(19,23) = 0.115398963934424923990287074612 gamma1(20,23) = 0.0881383002861070051505191792561 gamma1(21,23) = -0.0130317718813139520942843446695 gamma1(22,23) = -0.0425806762626960117718649647568 gamma1(23,23) = -0.138200932865382553589115851172 modulo 29 gamma0(1,29) = -29.6379938089901014989242304203 gamma0(2,29) = -15.0852698111041793927364343446 gamma0(3,29) = -7.73680142339272245517305021620 gamma0(4,29) = -3.93803793293175458339219466956 gamma0(5,29) = -1.84484901718703282913925154530 gamma0(6,29) = -10.2016038817034456108648441279 gamma0(7,29) = -5.22978131983078240403978721988 gamma0(8,29) = -2.58011531288242067784432607405 gamma0(9,29) = -1.01932206579565155419139722037 gamma0(10,29) = -1.47006092453856801911007382903 gamma0(11,29) = -3.49585679144998189849282768294 gamma0(12,29) = -1.58356561370281009599997659013 gamma0(13,29) = -4.49679576395991896128574192035 gamma0(14,29) = -2.16729392885801892436966088869 gamma0(15,29) = -0.751526392085511640476692317801 gamma0(16,29) = -0.812870498195065140532520553451 gamma0(17,29) = -0.946360184451136984375122812022 gamma0(18,29) = -1.26954508075902016048959140395 gamma0(19,29) = -2.35988699016760538401625416476 gamma0(20,29) = -0.877689149847643866595379324038 gamma0(21,29) = -1.09708685928795386905056017372 gamma0(22,29) = -1.70785640626038989127680452615 gamma0(23,29) = -6.24068967336937989619449290374 gamma0(24,29) = -3.13562793681919511171027963780 gamma0(25,29) = -1.36580411978466344480652321593 gamma0(26,29) = -2.83529053298655636708800369497 gamma0(27,29) = -1.18025672266463804118337519881 gamma0(28,29) = -1.99696172452111379439064516048 gamma0(29,29) = -0.0962096608649979712612675842165 gamma1(1,29) = -0.136630059133565291064658199927 gamma1(2,29) = 0.204482769323075055272848657454 gamma1(3,29) = 0.194071872545697939792662278415 gamma1(4,29) = 0.0883668564888908537547492013610 gamma1(5,29) = -0.0309930352730472542156454955768 gamma1(6,29) = 0.218826496650152638616914766477 gamma1(7,29) = 0.136324509419614821410789274992 gamma1(8,29) = 0.0183778476101290190016829884905 gamma1(9,29) = -0.0993996844622397439661445831685 gamma1(10,29) = -0.0601453083839200903665362941054 gamma1(11,29) = 0.0681252288159559776710788931431 gamma1(12,29) = -0.0510013615976897267138714698336 gamma1(13,29) = 0.110991047754085603298096629435 gamma1(14,29) = -0.00815964459004982687511094013499 gamma1(15,29) = -0.125135049717184991612919294102 gamma1(16,29) = -0.119071351700391558520703232157 gamma1(17,29) = -0.106224427207335050883577501249 gamma1(18,29) = -0.0770091199791105875597313634116 gamma1(19,29) = 0.00457717270914954491665650137843 gamma1(20,29) = -0.112774314211302021027565181073 gamma1(21,29) = -0.0922751539406440609175464743651 gamma1(22,29) = -0.0413070816130618884980138433278 gamma1(23,29) = 0.164414148767518069020366971424 gamma1(24,29) = 0.0499133706654014367981152678757 gamma1(25,29) = -0.0687978037032746086201881234471 gamma1(26,29) = 0.0334182291979688346851572168789 gamma1(27,29) = -0.0848224552424831412646674261897 gamma1(28,29) = -0.0199767671801537920182468192843 gamma1(29,29) = -0.130982777495862884974578781845 modulo 31 gamma0(1,31) = -31.6361426539076168833945497479 gamma0(2,31) = -10.8724953105019863950063062466 gamma0(3,31) = -3.73544224494830621416483244147 gamma0(4,31) = -0.922906756368099206200047307328 gamma0(5,31) = -1.60528691006254638069177651437 gamma0(6,31) = -0.989947648451529941184826945336 gamma0(7,31) = -1.99681318019406251945077465989 gamma0(8,31) = -1.85352525335259441043364371712 gamma0(9,31) = -1.49665929774599143736632890634 gamma0(10,31) = -0.799427406753077946252726821615 gamma0(11,31) = -1.06103854592371774496205829938 gamma0(12,31) = -2.53711119549016107113037564598 gamma0(13,31) = -4.20361436788123998076676714147 gamma0(14,31) = -1.13664423846511856173896346020 gamma0(15,31) = -3.35465350106534243764526788205 gamma0(16,31) = -0.742340164645277939805171177982 gamma0(17,31) = -0.859515593308202814803607413231 gamma0(18,31) = -1.30366852179776557708061393204 gamma0(19,31) = -8.24368334054101497690129499871 gamma0(20,31) = -2.76880506532631096822696287549 gamma0(21,31) = -6.65001317063658282632992065798 gamma0(22,31) = -2.15613672755871641734236416748 gamma0(23,31) = -2.33479954575965814781113239373 gamma0(24,31) = -3.03768406453862949128892366226 gamma0(25,31) = -16.0865942774022860561757759283 gamma0(26,31) = -5.57468787753233590969814093263 gamma0(27,31) = -1.72369650093574252539262109057 gamma0(28,31) = -1.21730786804800132530571668331 gamma0(29,31) = -4.79616165335687958382840974323 gamma0(30,31) = -1.39648382728202657026068213493 gamma0(31,31) = -0.0921539206317294640426662011116 gamma1(1,31) = -0.133665453250794553972767983839 gamma1(2,31) = 0.222885459054448443729433667246 gamma1(3,31) = 0.0749551098816396009179188883276 gamma1(4,31) = -0.106544973188243215229383975886 gamma1(5,31) = -0.0498110176307491222990758742820 gamma1(6,31) = -0.100500276370699550062083175303 gamma1(7,31) = -0.0216019918506977280658128640199 gamma1(8,31) = -0.0315929093154993741326392498482 gamma1(9,31) = -0.0581655925912735511080599664836 gamma1(10,31) = -0.117967560587381477505943158351 gamma1(11,31) = -0.0942083374496611366214872682810 gamma1(12,31) = 0.0129400863637224213852851647155 gamma1(13,31) = 0.0947789902542701557528865028695 gamma1(14,31) = -0.0876474164734900289770635437932 gamma1(15,31) = 0.0571462522710190831886073988770 gamma1(16,31) = -0.123377893527713760780710183194 gamma1(17,31) = -0.112361689124524730977685693480 gamma1(18,31) = -0.0736166141643853079919274742787 gamma1(19,31) = 0.198641563876147712559090300798 gamma1(20,31) = 0.0263763836421381298412043844026 gamma1(21,31) = 0.169472906253513306950693076925 gamma1(22,31) = -0.0109182529815276611013637779804 gamma1(23,31) = 0.000556367733494724904837701290774 gamma1(24,31) = 0.0410403613892998414737252242188 gamma1(25,31) = 0.208007423877389408133029070441 gamma1(26,31) = 0.141852374821356051302618706238 gamma1(27,31) = -0.0409729349097271635732237076701 gamma1(28,31) = -0.0807928667618029561890886926154 gamma1(29,31) = 0.116969584363825632062220880346 gamma1(30,31) = -0.0660865194662447004950822424616 gamma1(31,31) = -0.128606409621525217978738510802 modulo 37 gamma0(1,37) = -37.6312075897314362150258246648 gamma0(2,37) = -19.0892423723667450783770076031 gamma0(3,37) = -9.75978676125315878256201562171 gamma0(4,37) = -4.99127226896343664688312237480 gamma0(5,37) = -2.43873219478535985810777261448 gamma0(6,37) = -0.922117461945645347984019567557 gamma0(7,37) = -1.23609540335469490665269884585 gamma0(8,37) = -2.27616750446379849229133239855 gamma0(9,37) = -0.816709177809864281043766877044 gamma0(10,37) = -0.978632430819478687238992445527 gamma0(11,37) = -1.38852022731797451923238342469 gamma0(12,37) = -3.05621955889744945761692387654 gamma0(13,37) = -1.30997975509928031329396469276 gamma0(14,37) = -2.62011552185101708248955085757 gamma0(15,37) = -1.03799744981511587932757542319 gamma0(16,37) = -1.56184249562870923752899933504 gamma0(17,37) = -4.44427753428751731827043965995 gamma0(18,37) = -2.12936667955510741150552161857 gamma0(19,37) = -0.720165708872007453792653804413 gamma0(20,37) = -0.767415902455449411012844627219 gamma0(21,37) = -0.868213605936883875515546968005 gamma0(22,37) = -1.10048334069135403704257069958 gamma0(23,37) = -1.76166718555404601960356316812 gamma0(24,37) = -7.87210545870291295277573405787 gamma0(25,37) = -4.00104469333280135743386895743 gamma0(26,37) = -1.87387082708847146960590801546 gamma0(27,37) = -12.8821354296468507901310018829 gamma0(28,37) = -6.60234200414542716524510557774 gamma0(29,37) = -3.32287553855441792750635370686 gamma0(30,37) = -1.47226187144865994608056630052 gamma0(31,37) = -3.63348956340633384398180329035 gamma0(32,37) = -1.65801358541721908460639388511 gamma0(33,37) = -5.68613499444582807340480445755 gamma0(34,37) = -2.82423825307274181230155966340 gamma0(35,37) = -1.16639842867606852488054803986 gamma0(36,37) = -1.99591346152503713599992374687 gamma0(37,37) = -0.0819919526416943671286914481338 gamma1(1,37) = -0.125604224673702524970696000903 gamma1(2,37) = 0.217302260480197543435179872095 gamma1(3,37) = 0.210251860657434115584513455457 gamma1(4,37) = 0.110511451271240911810533641834 gamma1(5,37) = 0.000887488816928996663901533200781 gamma1(6,37) = -0.101225629782770478794173216409 gamma1(7,37) = -0.0768492143257922141703054239108 gamma1(8,37) = -0.00836467205543268526392120404429 gamma1(9,37) = -0.109852350567981810409058432219 gamma1(10,37) = -0.0966942582440075287751526635839 gamma1(11,37) = -0.0656906830403209689455485956880 gamma1(12,37) = 0.0330860435741922943947421860492 gamma1(13,37) = -0.0713873208837917467773938227205 gamma1(14,37) = 0.0108120571912349562887963152628 gamma1(15,37) = -0.0920035561853108533686062569696 gamma1(16,37) = -0.0535056139435400921337799381898 gamma1(17,37) = 0.0916287304749165235864036279694 gamma1(18,37) = -0.0170252762389265918789798340471 gamma1(19,37) = -0.117958070565339666365002944872 gamma1(20,37) = -0.113966229787859365728105478899 gamma1(21,37) = -0.105608421092015497040835351818 gamma1(22,37) = -0.0871415946611084845336606557831 gamma1(23,37) = -0.0400869848002144840885076620235 gamma1(24,37) = 0.182172623165880288829325526693 gamma1(25,37) = 0.0747299270161405306099297950970 gamma1(26,37) = -0.0328331771729033886518367715525 gamma1(27,37) = 0.233361987623290702085304962544 gamma1(28,37) = 0.155600376119281677526505156760 gamma1(29,37) = 0.0456945152725274504817307623655 gamma1(30,37) = -0.0597381277865618557362922278016 gamma1(31,37) = 0.0595049438952468908049195940161 gamma1(32,37) = -0.0469657148863119712705589430888 gamma1(33,37) = 0.131727628656020448201141704942 gamma1(34,37) = 0.0215059256447894347160645141877 gamma1(35,37) = -0.0820950930804661817436683667505 gamma1(36,37) = -0.0251622746075776662885574351355 gamma1(37,37) = -0.121835176961063432944937797940 modulo 41 gamma0(1,41) = -41.6283699892374722132963881624 gamma0(2,41) = -7.28316881819263569461135137054 gamma0(3,41) = -0.888492960557555384223418404499 gamma0(4,41) = -4.02361817239792638496770000504 gamma0(5,41) = -1.59618584294622151112164844989 gamma0(6,41) = -1.43396580282941548454193011591 gamma0(7,41) = -0.751023414356604180948147061446 gamma0(8,41) = -1.29003212784891949390578085695 gamma0(9,41) = -4.42535403781873888444813135830 gamma0(10,41) = -2.24674620530772268650553492027 gamma0(11,41) = -1.10131410630135831653292653636 gamma0(12,41) = -1.35994455600400550138042500011 gamma0(13,41) = -10.7678312681468385756144356457 gamma0(14,41) = -1.68549914996500937426965509636 gamma0(15,41) = -1.99512708699444324395376545247 gamma0(16,41) = -14.2201357210591189084371251974 gamma0(17,41) = -2.39045893440492349374825781848 gamma0(18,41) = -1.51254118819816496395979480691 gamma0(19,41) = -1.04441896063823095385258863495 gamma0(20,41) = -0.990117278607588283403471673826 gamma0(21,41) = -0.708642100645090448462128676965 gamma0(22,41) = -0.938203166706046258531815166312 gamma0(23,41) = -8.68330787422753572459742675353 gamma0(24,41) = -1.22384145002106740799611979563 gamma0(25,41) = -2.72451030887158169030491619650 gamma0(26,41) = -3.14230973401099163859971136538 gamma0(27,41) = -21.0902902174894882209446398482 gamma0(28,41) = -3.68476413954509905296079632282 gamma0(29,41) = -1.16103437783321355181029940460 gamma0(30,41) = -1.88406465829457987226556898169 gamma0(31,41) = -4.91071847547519658630722327123 gamma0(32,41) = -3.39441937310850475650412060533 gamma0(33,41) = -0.840822256550273209693352632891 gamma0(34,41) = -2.54882393391822922613732321357 gamma0(35,41) = -2.11554704021099544524986988959 gamma0(36,41) = -0.795043409714388280842565235341 gamma0(37,41) = -1.78118294307742744673354414839 gamma0(38,41) = -2.92089399047387612267805352059 gamma0(39,41) = -5.51081480109935859062861082677 gamma0(40,41) = -6.27449859610020249233137886298 gamma0(41,41) = -0.0764964976049457303234207629989 gamma1(1,41) = -0.120845323753897317572419146320 gamma1(2,41) = 0.163024697243610310408319948192 gamma1(3,41) = -0.100467099053420386174772381405 gamma1(4,41) = 0.0691787350053743420165949697392 gamma1(5,41) = -0.0511299315884660090184519270044 gamma1(6,41) = -0.0617092718398054239587131483734 gamma1(7,41) = -0.111074690097794602599918488804 gamma1(8,41) = -0.0714449780789228886207273974993 gamma1(9,41) = 0.0839811770884700975954948590797 gamma1(10,41) = -0.0124949743465396702875523782991 gamma1(11,41) = -0.0847324944767301980696054176881 gamma1(12,41) = -0.0666741116227633677593467246020 gamma1(13,41) = 0.216667824307453531977049466541 gamma1(14,41) = -0.0454760142301599986271217981170 gamma1(15,41) = -0.0267602038215393221065586265707 gamma1(16,41) = 0.239246215559154756580744901503 gamma1(17,41) = -0.00469952941106020815144226351628 gamma1(18,41) = -0.0565340432074998421145207309109 gamma1(19,41) = -0.0888592847714967296143599224338 gamma1(20,41) = -0.0928516789301277250766309341991 gamma1(21,41) = -0.114417664612858612938708379294 gamma1(22,41) = -0.0967183299043921930840676023885 gamma1(23,41) = 0.189101543641107961952320270991 gamma1(24,41) = -0.0760364989249926456816833291152 gamma1(25,41) = 0.0125045270878248743658911580366 gamma1(26,41) = 0.0323771377576840773823069217769 gamma1(27,41) = 0.222634628650890282928888112516 gamma1(28,41) = 0.0557787119663712775402807740934 gamma1(29,41) = -0.0804617570320848866990720103148 gamma1(30,41) = -0.0333202938908317038065459485960 gamma1(31,41) = 0.100444582485530655376950327245 gamma1(32,41) = 0.0435691757440766208513091373817 gamma1(33,41) = -0.104105147615086595126465692234 gamma1(34,41) = 0.00361112854129182468036129590480 gamma1(35,41) = -0.0198323216567736640641123680574 gamma1(36,41) = -0.107639015600788476587295598623 gamma1(37,41) = -0.0395485160915322207990399537887 gamma1(38,41) = 0.0220610623458261414649833489713 gamma1(39,41) = 0.118878264233221606753354444369 gamma1(40,41) = 0.139630908226400629130045198198 gamma1(41,41) = -0.117672990808401027326349342259 modulo 43 gamma0(1,43) = -43.6270679499166767353013755574 gamma0(2,43) = -14.8887623790093840752995277789 gamma0(3,43) = -5.14256140655931629371250955748 gamma0(4,43) = -1.53032868182109888454389566453 gamma0(5,43) = -0.874125260249255471204069076980 gamma0(6,43) = -1.45411359201124954106678014516 gamma0(7,43) = -0.743908432303462097861263868881 gamma0(8,43) = -0.921011074903547390613237816300 gamma0(9,43) = -1.69751611310238241306710590596 gamma0(10,43) = -1.18819929217181775033383072447 gamma0(11,43) = -4.63601140622284427789114420745 gamma0(12,43) = -1.31410159152753800365138036047 gamma0(13,43) = -11.2712700322155345919774937416 gamma0(14,43) = -3.86400041394134563125317481339 gamma0(15,43) = -0.969857053202086255776136886638 gamma0(16,43) = -1.99471112113019298229753762792 gamma0(17,43) = -1.88843014556945519861847834451 gamma0(18,43) = -1.61128335644830009606071338347 gamma0(19,43) = -1.02081707879965110926926205976 gamma0(20,43) = -2.36993527874902009450246999760 gamma0(21,43) = -3.29945900862438912714799902425 gamma0(22,43) = -0.703603750873636850423301853605 gamma0(23,43) = -0.785693207151461594410482675031 gamma0(24,43) = -1.07406255584898659093640796800 gamma0(25,43) = -2.86536080192097381960219346997 gamma0(26,43) = -9.08813538451985164195665499574 gamma0(27,43) = -3.06931773544371992620470854865 gamma0(28,43) = -22.0906730590771813491488801471 gamma0(29,43) = -7.62263585464706722375153886295 gamma0(30,43) = -2.51883605718631636033495989339 gamma0(31,43) = -4.21707534602510411467110678472 gamma0(32,43) = -1.12978502902773423285316826456 gamma0(33,43) = -3.56171840382043553280869027543 gamma0(34,43) = -0.829061027141416188685505526480 gamma0(35,43) = -1.24954709559813834829670685424 gamma0(36,43) = -6.56757692885607669592625461354 gamma0(37,43) = -2.10952503875463336375262841488 gamma0(38,43) = -2.23410363414045552211187369041 gamma0(39,43) = -2.68304590953064446455708685957 gamma0(40,43) = -5.76933937213684261772430274959 gamma0(41,43) = -1.78965369062405726796749850545 gamma0(42,43) = -1.38217269544543662225238407159 gamma0(43,43) = -0.0740461500184192921596821028666 gamma1(1,43) = -0.118627580560271076271263976400 gamma1(2,43) = 0.241927429575339771535323626260 gamma1(3,43) = 0.104342607757002580954592756006 gamma1(4,43) = -0.0551494155280745675721186172349 gamma1(5,43) = -0.0998784150713154019928091160440 gamma1(6,43) = -0.0599950666060808351031103413904 gamma1(7,43) = -0.109621134435836387554769768579 gamma1(8,43) = -0.0964446971797257094860104029004 gamma1(9,43) = -0.0448155113063061361535795762143 gamma1(10,43) = -0.0775982070325057581585533528549 gamma1(11,43) = 0.0880609803351033746743137046404 gamma1(12,43) = -0.0691256912253470251146112033057 gamma1(13,43) = 0.219568764408415263970751102384 gamma1(14,43) = 0.0602069635895270635813708923101 gamma1(15,43) = -0.0929084165278022412567457740022 gamma1(16,43) = -0.0273931703110674622285087052025 gamma1(17,43) = -0.0334895981301465246517795650046 gamma1(18,43) = -0.0500956971636123535034135268304 gamma1(19,43) = -0.0892630882048075184022742666386 gamma1(20,43) = -0.00698086298326094920503608634954 gamma1(21,43) = 0.0371354199567232102584583366551 gamma1(22,43) = -0.112699287870622325257227221371 gamma1(23,43) = -0.106461409947532007959072263440 gamma1(24,43) = -0.0855016088818600756005135893456 gamma1(25,43) = 0.0175762390486911666999748112684 gamma1(26,43) = 0.192214876000358557915620017641 gamma1(27,43) = 0.0269780310656556994104901683569 gamma1(28,43) = 0.225088290284637536898906622964 gamma1(29,43) = 0.166343538306991806659468921698 gamma1(30,43) = 0.000670583233059347992364879007678 gamma1(31,43) = 0.0734351891143397504674306535912 gamma1(32,43) = -0.0816161781058640889469903580123 gamma1(33,43) = 0.0481646250313322914222014563072 gamma1(34,43) = -0.103215504823083586680284419004 gamma1(35,43) = -0.0734382121785140498619563745092 gamma1(36,43) = 0.143148786963032363593061641467 gamma1(37,43) = -0.0209677267796237082173141331357 gamma1(38,43) = -0.0141774702625432958009542050622 gamma1(39,43) = 0.00883382965511094449446750896124 gamma1(40,43) = 0.122589088287317967068706030309 gamma1(41,43) = -0.0392880347645326814678329279451 gamma1(42,43) = -0.0646489772154557385666679391526 gamma1(43,43) = -0.115700125000523917444691795771 modulo 47 gamma0(1,47) = -47.6246690486506378553331148237 gamma0(2,47) = -9.89656198211472705063209299435 gamma0(3,47) = -1.89600854995340315695476075160 gamma0(4,47) = -1.42206967114025616674325494947 gamma0(5,47) = -3.61066780181082601810854772404 gamma0(6,47) = -2.09889820870838040594435179530 gamma0(7,47) = -2.33445583454802819263864865675 gamma0(8,47) = -4.60137611147419696907720687675 gamma0(9,47) = -6.28437994481552908973582413341 gamma0(10,47) = -0.934961242089371147897937869832 gamma0(11,47) = -4.21968817562013673393826259465 gamma0(12,47) = -3.89337334799486266664169466998 gamma0(13,47) = -2.77201136821704731229286215417 gamma0(14,47) = -0.808561243000471588618458628627 gamma0(15,47) = -1.71876118098239711388808035640 gamma0(16,47) = -0.891281790363280774163480476778 gamma0(17,47) = -2.94802031480709717597553485101 gamma0(18,47) = -1.02751548387103879723429860379 gamma0(19,47) = -24.0912330243723281463429237225 gamma0(20,47) = -5.05489797072949159340743964200 gamma0(21,47) = -16.2254367763866784582858994861 gamma0(22,47) = -3.36293946524942213470908185292 gamma0(23,47) = -1.63810129590160449989273019167 gamma0(24,47) = -0.694687101252699472151217124562 gamma0(25,47) = -0.849182165185546642386354397692 gamma0(26,47) = -2.21205568657653007686314954258 gamma0(27,47) = -3.14370971349847882420031135504 gamma0(28,47) = -1.29592621993169480761048142915 gamma0(29,47) = -1.99386330712256346381642399585 gamma0(30,47) = -1.80453509480327446851935767717 gamma0(31,47) = -1.12787902375809412237205649322 gamma0(32,47) = -0.980331657080939318948751556732 gamma0(33,47) = -7.15196280915268551088820219511 gamma0(34,47) = -1.18137506407719722007492158448 gamma0(35,47) = -1.23732164725916150837742902727 gamma0(36,47) = -1.56204964652085785872182106664 gamma0(37,47) = -12.2772289544878036337268897522 gamma0(38,47) = -2.46744069231745176531165409090 gamma0(39,47) = -8.30005837445270725369256916978 gamma0(40,47) = -1.49016693179689727062757003908 gamma0(41,47) = -5.60402020530143120603541630495 gamma0(42,47) = -0.731394492583008835672609675199 gamma0(43,47) = -1.07664799077446040634034407223 gamma0(44,47) = -0.769326790850462829459316509865 gamma0(45,47) = -1.35742153010102135650696977304 gamma0(46,47) = -2.61263250178820543780401236348 gamma0(47,47) = -0.0696368497193303346003072038232 gamma1(1,47) = -0.114481284623612949847127671498 gamma1(2,47) = 0.197865401274214747990959408410 gamma1(3,47) = -0.0337121946052568960255804473798 gamma1(4,47) = -0.0611146912566912725281790262344 gamma1(5,47) = 0.0455749824888028542072706058448 gamma1(6,47) = -0.0228250452745731812110318726534 gamma1(7,47) = -0.0107601765562094249536564616602 gamma1(8,47) = 0.0810206343390779538940990316111 gamma1(9,47) = 0.129249013294786435783579545400 gamma1(10,47) = -0.0925282165359140610637413585822 gamma1(11,47) = 0.0680845098375974545818713561123 gamma1(12,47) = 0.0563267543387909309665771144956 gamma1(13,47) = 0.0101549082830318865602529493035 gamma1(14,47) = -0.101278346771562758529648022762 gamma1(15,47) = -0.0436241651555323617277436151234 gamma1(16,47) = -0.0955226884066548274842110646948 gamma1(17,47) = 0.0180661104728971899739528794164 gamma1(18,47) = -0.0862832773839771370807886296761 gamma1(19,47) = 0.229629759967526560330148638716 gamma1(20,47) = 0.0953464109857627209683243978244 gamma1(21,47) = 0.246850799521508064156276709364 gamma1(22,47) = 0.0356882200334655972502499735550 gamma1(23,47) = -0.0482647627374107269937273354394 gamma1(24,47) = -0.109386786819374059021395489767 gamma1(25,47) = -0.0984380042776787448933556218480 gamma1(26,47) = -0.0169547442982544922322506931879 gamma1(27,47) = 0.0265505677579545568805818677721 gamma1(28,47) = -0.0689141854849887202468775364115 gamma1(29,47) = -0.0284019120103453238955761008536 gamma1(30,47) = -0.0387793916880472209532304787462 gamma1(31,47) = -0.0796619473464202472814867265063 gamma1(32,47) = -0.0894500545331829854701673776866 gamma1(33,47) = 0.149482266991345255763961488198 gamma1(34,47) = -0.0761951525509941177447736083640 gamma1(35,47) = -0.0726151320080192820970343447193 gamma1(36,47) = -0.0527173669823070230673641146943 gamma1(37,47) = 0.224861571766885241137933445969 gamma1(38,47) = -0.00420574866126573116335939634347 gamma1(39,47) = 0.172340744943490161709950523721 gamma1(40,47) = -0.0569963851374963316832711364321 gamma1(41,47) = 0.111319684589240554704126388875 gamma1(42,47) = -0.106749288279052544380763805148 gamma1(43,47) = -0.0830225242960431322568977701461 gamma1(44,47) = -0.104047581633175512564469163820 gamma1(45,47) = -0.0650838294680905348629027964428 gamma1(46,47) = 0.00274986043485162669805968219762 gamma1(47,47) = -0.111963162022774917158150715839 modulo 53 gamma0(1,53) = -53.6215111309115617398349054012 gamma0(2,53) = -27.0917094398853121037293091508 gamma0(3,53) = -13.7843938043881020049477299690 gamma0(4,53) = -7.05296918602214502476751261895 gamma0(5,53) = -3.55446408679674700520590713237 gamma0(6,53) = -1.60187934926064161498023858105 gamma0(7,53) = -5.17260963514643032557508296030 gamma0(8,53) = -2.53002118935401820958327954514 gamma0(9,53) = -0.972452364604690129211813745494 gamma0(10,53) = -1.41256260691482350184970581701 gamma0(11,53) = -3.33846260576150919259651401799 gamma0(12,53) = -1.47264742943775633457078000549 gamma0(13,53) = -3.79687107520189116496283178754 gamma0(14,53) = -1.74509783160942555919190002472 gamma0(15,53) = -8.02505434891242236771956425151 gamma0(16,53) = -4.07126728948268133049125024875 gamma0(17,53) = -1.90514837001034864584055449081 gamma0(18,53) = -18.2293491963232699387275807161 gamma0(19,53) = -9.31322971812285219555427902980 gamma0(20,53) = -4.74764573274274391924111852405 gamma0(21,53) = -2.29179639041394622905575927527 gamma0(22,53) = -0.819006816454762687464447218274 gamma0(23,53) = -1.01416816645216264516329823334 gamma0(24,53) = -1.53566634542709791663455026452 gamma0(25,53) = -4.38495037739683706109851214711 gamma0(26,53) = -2.08573870098765300709723391558 gamma0(27,53) = -0.683598659264636526164545104826 gamma0(28,53) = -0.715971881756927017179586747360 gamma0(29,53) = -0.783621298543533181822822406673 gamma0(30,53) = -0.932160546532155642134662508501 gamma0(31,53) = -1.30029346772759423284892426748 gamma0(32,53) = -2.66398156563857953914422920147 gamma0(33,53) = -1.05740153734888080177636582355 gamma0(34,53) = -1.67157939015672872064372182096 gamma0(35,53) = -6.29178914842629237799882189064 gamma0(36,53) = -3.14452094753623428025586657863 gamma0(37,53) = -1.35518028703771649471880389989 gamma0(38,53) = -2.96920583397866216560976032144 gamma0(39,53) = -1.24771652174898364189985603450 gamma0(40,53) = -2.40637893344238058301827476324 gamma0(41,53) = -0.893207030651518763848274423077 gamma0(42,53) = -1.19728247597351067260829033873 gamma0(43,53) = -2.18521521052409713285150004262 gamma0(44,53) = -0.749295242107728669631211632160 gamma0(45,53) = -0.855513208332294153690549795248 gamma0(46,53) = -1.10225491788665366423394796424 gamma0(47,53) = -1.82281103800492417939170660588 gamma0(48,53) = -11.1068090801587984564908392480 gamma0(49,53) = -5.67839423515148481310955597014 gamma0(50,53) = -2.80976844122874589298894393748 gamma0(51,53) = -1.14884069759336522519750905739 gamma0(52,53) = -1.99260195373980039713395029887 gamma0(53,53) = -0.0640203065783129995007161707348 gamma1(1,53) = -0.108895759120520370904479860176 gamma1(2,53) = 0.235666464536770855708426694365 gamma1(3,53) = 0.231759640492401558374701313291 gamma1(4,53) = 0.137725719375336759480440374373 gamma1(5,53) = 0.0377297165134020606364208028332 gamma1(6,53) = -0.0497122354204296089922210855185 gamma1(7,53) = 0.0905737866110740485017549808311 gamma1(8,53) = -0.00404922917018387934681542279083 gamma1(9,53) = -0.0862052120485741502391130470432 gamma1(10,53) = -0.0601628982675739571893585968683 gamma1(11,53) = 0.0295485506644356044949656869867 gamma1(12,53) = -0.0567995732476835199877756331680 gamma1(13,53) = 0.0465572098164148295004332212645 gamma1(14,53) = -0.0420836565521884508220982010975 gamma1(15,53) = 0.157580745140388805379034346793 gamma1(16,53) = 0.0561266352262541651223825652961 gamma1(17,53) = -0.0338268497331846847337223700148 gamma1(18,53) = 0.253324758322402572666632210576 gamma1(19,53) = 0.180050430727509811043243060805 gamma1(20,53) = 0.0779786087242643852590315055650 gamma1(21,53) = -0.0149662471847665070596787846228 gamma1(22,53) = -0.0959049555434445126176597962085 gamma1(23,53) = -0.0836257305361696333144282659229 gamma1(24,53) = -0.0533188081229879619854672997928 gamma1(25,53) = 0.0665535610865237246970643527641 gamma1(26,53) = -0.0248334044910542355195124070930 gamma1(27,53) = -0.104748852217801759576578011146 gamma1(28,53) = -0.102609684976202031988911103428 gamma1(29,53) = -0.0981899395484402145376962625024 gamma1(30,53) = -0.0887197405408768502625469652790 gamma1(31,53) = -0.0665668989628177733082406290385 gamma1(32,53) = 0.00187233666847702407333831739330 gamma1(33,53) = -0.0809777908335034077643906314376 gamma1(34,53) = -0.0459706041911405949300547162462 gamma1(35,53) = 0.120164587248580198690903988181 gamma1(36,53) = 0.0219340641386231511338758960052 gamma1(37,53) = -0.0634163727444537930634713716246 gamma1(38,53) = 0.0148194305949248754924391315911 gamma1(39,53) = -0.0696207700487851825687330475985 gamma1(40,53) = -0.00965188125621817184855156458233 gamma1(41,53) = -0.0911725649000188248655419842400 gamma1(42,53) = -0.0725837375529169972783198879216 gamma1(43,53) = -0.0200189832197439868053619977113 gamma1(44,53) = -0.100424090548185849538875438996 gamma1(45,53) = -0.0935667015364778652768388274292 gamma1(46,53) = -0.0782576046340312362365495283220 gamma1(47,53) = -0.0380399826809944639837294983854 gamma1(48,53) = 0.205175156630799146205262868738 gamma1(49,53) = 0.104549974953200503587414167438 gamma1(50,53) = 0.00814819279731973224975627955267 gamma1(51,53) = -0.0754610701258883171080182724002 gamma1(52,53) = -0.0294299990378199674045869922303 gamma1(53,53) = -0.106843586757701776098780639682 modulo 59 gamma0(1,59) = -59.6187863643265411245194058014 gamma0(2,59) = -30.0919064359376742892880852908 gamma0(3,59) = -15.2900138950294110604927959657 gamma0(4,59) = -7.81799622692892979102999212500 gamma0(5,59) = -3.95899084211982022488675476475 gamma0(6,59) = -1.83748719082133516794358508104 gamma0(7,59) = -12.3149489082521574148457273795 gamma0(8,59) = -6.29752003523437999401374439336 gamma0(9,59) = -3.14497261319467224549684133112 gamma0(10,59) = -1.35318918616816318701205668398 gamma0(11,59) = -2.98619154034990313329868298986 gamma0(12,59) = -1.25595586805697791071534630074 gamma0(13,59) = -2.46643933065910798556851044617 gamma0(14,59) = -0.929721689523782350116568905984 gamma0(15,59) = -1.30362853557346681983206200823 gamma0(16,59) = -2.70619156354734585331729052831 gamma0(17,59) = -1.08182674944253070479184517254 gamma0(18,59) = -1.76645626103055046748639834884 gamma0(19,59) = -8.89503337190445617603053295108 gamma0(20,59) = -4.52617857508396039468949037549 gamma0(21,59) = -2.16380161867260885822061712193 gamma0(22,59) = -0.733224641536363529592401779053 gamma0(23,59) = -0.827300903264490240983538162429 gamma0(24,59) = -1.04193975174737344087132406353 gamma0(25,59) = -1.63461374165893990001865768462 gamma0(26,59) = -5.73910907516545705078141100180 gamma0(27,59) = -2.84048968546815432877768193748 gamma0(28,59) = -1.16579021573494391509740641469 gamma0(29,59) = -2.07505554645214329189503123075 gamma0(30,59) = -0.674557383781025298146273814888 gamma0(31,59) = -0.703511798921007076169989543188 gamma0(32,59) = -0.763733274983026197568958082702 gamma0(33,59) = -0.894571383625732588054877048600 gamma0(34,59) = -1.21004736246344705778855716165 gamma0(35,59) = -2.25817866080986899137367921635 gamma0(36,59) = -0.795077720428426500606341624210 gamma0(37,59) = -0.965957477798882837838063182211 gamma0(38,59) = -1.40477405950047451925060494979 gamma0(39,59) = -3.31885953461398598935176315126 gamma0(40,59) = -1.45853343453405792396521414970 gamma0(41,59) = -3.72243219680331631565487713321 gamma0(42,59) = -1.69892762241827866406478961045 gamma0(43,59) = -6.97557745899079614925244765911 gamma0(44,59) = -3.51032752092326942545266675829 gamma0(45,59) = -1.57325861203449950846337976357 gamma0(46,59) = -4.87113630964221548598985143675 gamma0(47,59) = -2.35881516845309418866061780325 gamma0(48,59) = -0.860448927733514995492137933022 gamma0(49,59) = -1.12308142865356721567761833934 gamma0(50,59) = -1.91234453218471177337202808559 gamma0(51,59) = -20.2323246106604565367285987775 gamma0(52,59) = -10.3237724273663767209360694896 gamma0(53,59) = -5.27052964448567423702330313923 gamma0(54,59) = -2.58189974989030890993593811973 gamma0(55,59) = -1.00334102742975283334033090206 gamma0(56,59) = -1.51463351237397737444588220843 gamma0(57,59) = -4.22483612658474739646843929056 gamma0(58,59) = -1.99139506352394414452794326443 gamma0(59,59) = -0.0593274877797319761018565810786 gamma1(1,59) = -0.103951038804534173246734508684 gamma1(2,59) = 0.240945690913024999029056805388 gamma1(3,59) = 0.237680193723205179798633734916 gamma1(4,59) = 0.144830458078542573913851915104 gamma1(5,59) = 0.0468857469348194708932330965014 gamma1(6,59) = -0.0373241558581228431171640488691 gamma1(7,59) = 0.211403452788212726624454307390 gamma1(8,59) = 0.112203580614524847461556137194 gamma1(9,59) = 0.0182043914844001536474479193253 gamma1(10,59) = -0.0617523533966527580118150348261 gamma1(11,59) = 0.0121426640763242069926261885493 gamma1(12,59) = -0.0669620222539098232056571075879 gamma1(13,59) = -0.00893111364490858603973799631257 gamma1(14,59) = -0.0852581615412186034538216009652 gamma1(15,59) = -0.0643943048004877349680880481760 gamma1(16,59) = 0.00103472816961641343611866431601 gamma1(17,59) = -0.0765669347684817070634582371495 gamma1(18,59) = -0.0407568121273001203061367925079 gamma1(19,59) = 0.164400760149750898192222441843 gamma1(20,59) = 0.0648038499769421252178332234467 gamma1(21,59) = -0.0221630162930285895611961989279 gamma1(22,59) = -0.0969221664968433465226374468578 gamma1(23,59) = -0.0912750762146328156369364211753 gamma1(24,59) = -0.0788183458766567617297968900699 gamma1(25,59) = -0.0472610280673386261556772159388 gamma1(26,59) = 0.0984921484684793795662916031481 gamma1(27,59) = 0.00643118601512050019227584443538 gamma1(28,59) = -0.0718906185358516457201311105784 gamma1(29,59) = -0.0261906122522768830343062508003 gamma1(30,59) = -0.100503401826206816155474165925 gamma1(31,59) = -0.0987301491202143978700108957362 gamma1(32,59) = -0.0950780226804495352596229079277 gamma1(33,59) = -0.0873079516797205870894855658410 gamma1(34,59) = -0.0694595493616733964211300523156 gamma1(35,59) = -0.0179548547378585155201530214187 gamma1(36,59) = -0.0931961978210473823847074124008 gamma1(37,59) = -0.0831614795553387704511218257825 gamma1(38,59) = -0.0590317789312046532278761757899 gamma1(39,59) = 0.0246573041146615303875147534158 gamma1(40,59) = -0.0562278077541526874740812232810 gamma1(41,59) = 0.0389365185118871144533118312108 gamma1(42,59) = -0.0440663410413625719180949044350 gamma1(43,59) = 0.127547084050016987131633460167 gamma1(44,59) = 0.0315492518691998381728029145323 gamma1(45,59) = -0.0503483843497683640276928433518 gamma1(46,59) = 0.0749834738036586096950406806277 gamma1(47,59) = -0.0135502101134703138698375734038 gamma1(48,59) = -0.0893129382770881248389933067892 gamma1(49,59) = -0.0742586812472929331622413402106 gamma1(50,59) = -0.0337592070937765287172844913407 gamma1(51,59) = 0.258929103137406901078270693627 gamma1(52,59) = 0.186578418614332445844533926369 gamma1(53,59) = 0.0861556524415921864199987273019 gamma1(54,59) = -0.00407719721603006445666343614491 gamma1(55,59) = -0.0810156719155502400607461913477 gamma1(56,59) = -0.0533352371450690681415048240258 gamma1(57,59) = 0.0554763911026230295349195484029 gamma1(58,59) = -0.0300517977925779547345106457951 gamma1(59,59) = -0.102243273929920918989687080397 modulo 61 gamma0(1,61) = -61.6179592595790018527121259168 gamma0(2,61) = -31.0919299763593100288744522308 gamma0(3,61) = -15.7916240984640512233167199804 gamma0(4,61) = -8.07238340256787335472540042646 gamma0(5,61) = -4.09272315075597413752729823935 gamma0(6,61) = -1.91441159840042487721259975698 gamma0(7,61) = -20.8998264387549980849165870677 gamma0(8,61) = -10.6601651572441143193009889734 gamma0(9,61) = -5.44392790325401890929696946122 gamma0(10,61) = -2.67718758763021410821467908417 gamma0(11,61) = -1.06294383447263151491631027171 gamma0(12,61) = -1.70696272738448451237007223406 gamma0(13,61) = -7.20280959312909819585501671071 gamma0(14,61) = -3.63106398956523781282373356053 gamma0(15,61) = -1.64426617072445657541207047308 gamma0(16,61) = -5.92710800419630509289107778109 gamma0(17,61) = -2.94262963558316187268876043897 gamma0(18,61) = -1.22843793782470716001626146779 gamma0(19,61) = -2.34520709320347065877438057118 gamma0(20,61) = -0.851037454495609301958834497997 gamma0(21,61) = -1.10225027404692753286843302642 gamma0(22,61) = -1.84175496175194783191514613082 gamma0(23,61) = -12.7172998294375356710464415199 gamma0(24,61) = -6.50312733006560464953331511995 gamma0(25,61) = -3.25542883759617112358136918716 gamma0(26,61) = -1.41955872628495257971577865738 gamma0(27,61) = -3.43417086648854881489635743297 gamma0(28,61) = -1.52708845534067969684369696466 gamma0(29,61) = -4.36642984431452455442804412239 gamma0(30,61) = -2.07192501915130286878642927946 gamma0(31,61) = -0.671901063161278087535758806717 gamma0(32,61) = -0.699870875990845578394759362295 gamma0(33,61) = -0.757965981694307561256542275195 gamma0(34,61) = -0.883804605178361433837255635230 gamma0(35,61) = -1.18491189184828183282311380703 gamma0(36,61) = -2.15759073860883598666389424089 gamma0(37,61) = -0.728547976200562899395556247624 gamma0(38,61) = -0.819170915113496884138008377968 gamma0(39,61) = -1.02488440355332075374871032357 gamma0(40,61) = -1.58437858362156436966869565672 gamma0(41,61) = -5.03224352454835254614795218901 gamma0(42,61) = -2.44837003951837583871192369686 gamma0(43,61) = -0.917519816461326615522763570576 gamma0(44,61) = -1.27355429402129035897934035071 gamma0(45,61) = -2.55873800612252766342233388466 gamma0(46,61) = -0.988002548083044025848604059363 gamma0(47,61) = -1.47220564539074205272268379362 gamma0(48,61) = -3.84926626406391740662832190969 gamma0(49,61) = -1.77270425976194113631581967854 gamma0(50,61) = -9.18448521180291026625266579145 gamma0(51,61) = -4.67680601962294174621472456440 gamma0(52,61) = -2.24849702763523675168346397700 gamma0(53,61) = -0.788160816170491052697916326314 gamma0(54,61) = -0.952234132766428872487207251050 gamma0(55,61) = -1.36899271440407183094637653410 gamma0(56,61) = -3.09227986341159365647370508432 gamma0(57,61) = -1.32036712432787129543625565712 gamma0(58,61) = -2.80474683794805910315734921333 gamma0(59,61) = -1.14287902252426875086918818303 gamma0(60,61) = -1.99100873639117048441674994573 gamma0(61,61) = -0.0579288229388816129204078198909 gamma1(1,61) = -0.102425725082112277151115809848 gamma1(2,61) = 0.242563541519947015321817932823 gamma1(3,61) = 0.239475903713802975821252716823 gamma1(4,61) = 0.146956046048936049231524190437 gamma1(5,61) = 0.0495868746293367339836271962171 gamma1(6,61) = -0.0337073846795759187292548918801 gamma1(7,61) = 0.260637046903841159205209691275 gamma1(8,61) = 0.188543110050884408968218959961 gamma1(9,61) = 0.0885814884029847471357407824832 gamma1(10,61) = -0.000886284943606653971481035176421 gamma1(11,61) = -0.0766846716376974036481461648152 gamma1(12,61) = -0.0434978849798385942216706763899 gamma1(13,61) = 0.129750309813118732779970052642 gamma1(14,61) = 0.0343798539657622979396191341792 gamma1(15,61) = -0.0465378755310369992212002233640 gamma1(16,61) = 0.100845425779189873519342033233 gamma1(17,61) = 0.00950634743739398191595627597036 gamma1(18,61) = -0.0677240731781629616438148526263 gamma1(19,61) = -0.0145976627061187129346940513761 gamma1(20,61) = -0.0886330219162893430474043877038 gamma1(21,61) = -0.0745276912647663579846254183440 gamma1(22,61) = -0.0370905164130223929819650866924 gamma1(23,61) = 0.213284711264529813910964222193 gamma1(24,61) = 0.114482677951204645782202012151 gamma1(25,61) = 0.0211595547628145316081875697385 gamma1(26,61) = -0.0577589746839692650806557827324 gamma1(27,61) = 0.0275507782073999139423336695260 gamma1(28,61) = -0.0523245827832188839942900394726 gamma1(29,61) = 0.0581108190977155438357199660735 gamma1(30,61) = -0.0265363918658046965655745993671 gamma1(31,61) = -0.0991710022808757792931170618030 gamma1(32,61) = -0.0974984048389205254381297056873 gamma1(33,61) = -0.0940567596080306278522940668516 gamma1(34,61) = -0.0867494741011656650164755741978 gamma1(35,61) = -0.0700502408513978152443707116559 gamma1(36,61) = -0.0227270959711277346080796045526 gamma1(37,61) = -0.0957940788929525340178512521097 gamma1(38,61) = -0.0904776974010507434086319036896 gamma1(39,61) = -0.0787906243846843496135416773355 gamma1(40,61) = -0.0494780407928208161825030230771 gamma1(41,61) = 0.0774803133392667618735277437058 gamma1(42,61) = -0.0102475087833730851341522970313 gamma1(43,61) = -0.0848253444787637550993789708950 gamma1(44,61) = -0.0653354428398515972598801449561 gamma1(45,61) = -0.00568382838399836434551228810952 gamma1(46,61) = -0.0808479301789886753249083075429 gamma1(47,61) = -0.0550831657581859859614978100953 gamma1(48,61) = 0.0417030209204169769395134088895 gamma1(49,61) = -0.0403512619936596022749506679427 gamma1(50,61) = 0.166446864801547139079468730433 gamma1(51,61) = 0.0673702005151452941037127959435 gamma1(52,61) = -0.0187522288443305130500160773650 gamma1(53,61) = -0.0922851064943000216283404956873 gamma1(54,61) = -0.0828588111853601657905345402267 gamma1(55,61) = -0.0603567661623432081555293195490 gamma1(56,61) = 0.0151583763176127382880679611321 gamma1(57,61) = -0.0628809129265071464505999780853 gamma1(58,61) = 0.00416827742083069535229783247859 gamma1(59,61) = -0.0723171291186103342210846405942 gamma1(60,61) = -0.0301927245383777551168753430291 gamma1(61,61) = -0.100813065872461493734712772326 modulo 67 gamma0(1,67) = -67.6156852468808631605200420947 gamma0(2,67) = -34.0919128861727883099415079544 gamma0(3,67) = -17.2958338402174827441977397918 gamma0(4,67) = -8.83404625786133208873768600928 gamma0(5,67) = -4.49119692096319563274619591597 gamma0(6,67) = -2.14115541888430921497111429471 gamma0(7,67) = -0.716137561927161167110743893935 gamma0(8,67) = -0.797770234433714495966204760702 gamma0(9,67) = -0.980660810325956691835015289168 gamma0(10,67) = -1.45957511867168282957593174844 gamma0(11,67) = -3.77704866952279195369052808188 gamma0(12,67) = -1.72844033683961908774761372718 gamma0(13,67) = -7.88282043802093779620858143209 gamma0(14,67) = -3.99032223713529210647761258103 gamma0(15,67) = -1.85306210126025533544219379028 gamma0(16,67) = -13.9234906000587879251522944388 gamma0(17,67) = -7.11808789383220680922923290898 gamma0(18,67) = -3.58364174692101593193672936205 gamma0(19,67) = -1.61427477633210274710589253449 gamma0(20,67) = -5.51323554398886073595146192391 gamma0(21,67) = -2.71337832251277383890331062078 gamma0(22,67) = -1.08397712945220593957609339098 gamma0(23,67) = -1.78934290548467313208887341790 gamma0(24,67) = -10.0515409536341195144891213926 gamma0(25,67) = -5.12622002257355601615890214883 gamma0(26,67) = -2.49879062392652643883097387272 gamma0(27,67) = -0.948125330139925432126177349734 gamma0(28,67) = -1.36583861666457950967395536206 gamma0(29,67) = -3.09698759376601696835253467660 gamma0(30,67) = -1.32144070010492998267241220894 gamma0(31,67) = -2.83205099293569762845362477924 gamma0(32,67) = -1.15813919762898591628788418520 gamma0(33,67) = -2.06356897500864305396607714470 gamma0(34,67) = -0.664794955029774157089833994542 gamma0(35,67) = -0.690175530823784020934811716490 gamma0(36,67) = -0.742706046439081671448833228221 gamma0(37,67) = -0.855601378841337894815651250785 gamma0(38,67) = -1.12049128207949168443042931817 gamma0(39,67) = -1.91982904649197362985630301063 gamma0(40,67) = -22.9019686759988854091843820422 gamma0(41,67) = -11.6682554405320045398426570225 gamma0(42,67) = -5.96194003391378024928481537640 gamma0(43,67) = -2.95954506931170101839713332486 gamma0(44,67) = -1.23709960420481247813884217831 gamma0(45,67) = -2.40134027671533157778117076718 gamma0(46,67) = -0.885635928133816678441314962342 gamma0(47,67) = -1.19698538792981572901362200290 gamma0(48,67) = -2.22302708571031766565620972422 gamma0(49,67) = -0.769907530788698213905426849028 gamma0(50,67) = -0.916464263984531667851386967838 gamma0(51,67) = -1.27855738904472711451095459872 gamma0(52,67) = -2.60256626523038915337318578632 gamma0(53,67) = -1.01411537855363547259252858715 gamma0(54,67) = -1.56065540330473109799979470281 gamma0(55,67) = -4.78861166490920509942557801127 gamma0(56,67) = -2.30959835893331199171080482322 gamma0(57,67) = -0.826324186930928108071023277178 gamma0(58,67) = -1.04853697760056469580475430763 gamma0(59,67) = -1.67014669309158229066661060696 gamma0(60,67) = -6.48907802119928000212546555255 gamma0(61,67) = -3.24570959598940431385188622149 gamma0(62,67) = -1.41184814221248230746788624896 gamma0(63,67) = -3.40729461071936558118035918207 gamma0(64,67) = -1.50913527084705631504525601363 gamma0(65,67) = -4.22692818311358218601168317998 gamma0(66,67) = -1.98990171313492004795281977760 gamma0(67,67) = -0.0541414470819318387919934314370 gamma1(1,67) = -0.0981706590021312128217412077897 gamma1(2,67) = 0.247053274197583211501193628196 gamma1(3,67) = 0.244417605863104362588131445449 gamma1(4,67) = 0.152739137044248641078194877367 gamma1(5,67) = 0.0568468691586010336833062722735 gamma1(6,67) = -0.0240779257311439227632211498958 gamma1(7,67) = -0.0925424253743413129977565171986 gamma1(8,67) = -0.0880563575653092858351678970928 gamma1(9,67) = -0.0782826169345085971788595332133 gamma1(10,67) = -0.0543847531066458770351589291704 gamma1(11,67) = 0.0353066567529031218829614438035 gamma1(12,67) = -0.0419497502117149051508150894096 gamma1(13,67) = 0.135731988223249593937127954144 gamma1(14,67) = 0.0419735252000472997389230073965 gamma1(15,67) = -0.0364044823810399012877950779357 gamma1(16,67) = 0.218444232291359843469986900408 gamma1(17,67) = 0.120658625929271785790495622633 gamma1(18,67) = 0.0290746978975088340849689571635 gamma1(19,67) = -0.0471492139629138775511486423911 gamma1(20,67) = 0.0842148553499533556205593422084 gamma1(21,67) = -0.00143320158842935231085450765715 gamma1(22,67) = -0.0729251599732727472010344957842 gamma1(23,67) = -0.0392230914442709451244737338235 gamma1(24,67) = 0.172026866146254486351151323629 gamma1(25,67) = 0.0742833874330968721277991340376 gamma1(26,67) = -0.00965765118547010781781799614373 gamma1(27,67) = -0.0799938914685121538257914563059 gamma1(28,67) = -0.0588794517225205755453500590611 gamma1(29,67) = 0.0125445519488454740745508920699 gamma1(30,67) = -0.0610383377144715116651244413924 gamma1(31,67) = 0.00298689457037712132398752219980 gamma1(32,67) = -0.0691500090839223724594297369298 gamma1(33,67) = -0.0273323143961617075141152891891 gamma1(34,67) = -0.0954040546293834848222739716016 gamma1(35,67) = -0.0939855365964593577969743183235 gamma1(36,67) = -0.0910738280793847368561126676438 gamma1(37,67) = -0.0849249461371233318555570482461 gamma1(38,67) = -0.0710591739819307686363799479456 gamma1(39,67) = -0.0334877684765728525050721191850 gamma1(40,67) = 0.265355569534768487437785487839 gamma1(41,67) = 0.193915323942720477857209621155 gamma1(42,67) = 0.0951337083326485171984155614673 gamma1(43,67) = 0.00763845378016523959491293872051 gamma1(44,67) = -0.0651938025636134205366133291796 gamma1(45,67) = -0.0134956894777551601728881744859 gamma1(46,67) = -0.0833136973320316723133270304701 gamma1(47,67) = -0.0671956163009529113923638012540 gamma1(48,67) = -0.0206939397979273649040456131264 gamma1(49,67) = -0.0895788032928204888499281564829 gamma1(50,67) = -0.0816704518675226745977186329565 gamma1(51,67) = -0.0631422173390457391337269545436 gamma1(52,67) = -0.00564209491655007969418873545167 gamma1(53,67) = -0.0765351415711005632410883711038 gamma1(54,67) = -0.0496318745540940439818531664957 gamma1(55,67) = 0.0651991129035372021223603189095 gamma1(56,67) = -0.0171702709317914836247386896117 gamma1(57,67) = -0.0865054416081030766686188569753 gamma1(58,67) = -0.0747498839580020980020881232083 gamma1(59,67) = -0.0445900773374514041662687992222 gamma1(60,67) = 0.107211499482118860748042690511 gamma1(61,67) = 0.0177315939754765309752197842448 gamma1(62,67) = -0.0566626396595218451375816724442 gamma1(63,67) = 0.0232299431491193293860744631070 gamma1(64,67) = -0.0520423913146328611935343233310 gamma1(65,67) = 0.0491314350418505196741413816092 gamma1(66,67) = -0.0304661920282667215970001950254 gamma1(67,67) = -0.0967988270336684193424884877180 modulo 71 gamma0(1,71) = -71.6143207964891478409727469858 gamma0(2,71) = -10.6286704076352058792084540898 gamma0(3,71) = -1.30831956953436393590767757192 gamma0(4,71) = -0.955848285245016617417156947852 gamma0(5,71) = -0.986802588256700718673268725800 gamma0(6,71) = -1.22922311071452028728220761452 gamma0(7,71) = -36.0918475062364982700088020935 gamma0(8,71) = -5.42408216557749027876190562500 gamma0(9,71) = -2.77146486715698517786127196790 gamma0(10,71) = -1.39273848262331002854438263312 gamma0(11,71) = -1.48314560095269880725918655531 gamma0(12,71) = -2.37484526893918695143922672142 gamma0(13,71) = -18.2982127276981136676786678007 gamma0(14,71) = -2.66292898368670610042857585298 gamma0(15,71) = -1.11933980040428718765443150837 gamma0(16,71) = -3.28936511325064757874059138007 gamma0(17,71) = -4.00345691949473575510088905400 gamma0(18,71) = -0.867591420918799391175451707342 gamma0(19,71) = -9.34077214071436039254900914681 gamma0(20,71) = -1.05124081620284467003934187177 gamma0(21,71) = -1.92290012387366929234761505059 gamma0(22,71) = -1.43714747515930675359490917574 gamma0(23,71) = -1.85955700287761746723365649738 gamma0(24,71) = -1.15488192135075191081228306300 gamma0(25,71) = -4.75491330003805204440487271767 gamma0(26,71) = -1.68522334907233059968241495048 gamma0(27,71) = -24.2364834500169621493343359703 gamma0(28,71) = -3.61498436342981650704279053100 gamma0(29,71) = -14.7270202393844519891516039422 gamma0(30,71) = -2.05872294720114190848253560885 gamma0(31,71) = -2.28941560348281421919629870529 gamma0(32,71) = -6.86229685875500612678328319761 gamma0(33,71) = -12.3395583011715158934331251516 gamma0(34,71) = -1.63174607134045491751968160927 gamma0(35,71) = -7.52675272690492717440701360671 gamma0(36,71) = -0.660663016516299175157855490403 gamma0(37,71) = -0.812260063161850617691695172763 gamma0(38,71) = -3.44537644678651844950786157668 gamma0(39,71) = -6.30574119451352720030059707639 gamma0(40,71) = -5.83225031517070271743255285345 gamma0(41,71) = -3.80020003638512135812797759235 gamma0(42,71) = -0.684568268162981529492131478883 gamma0(43,71) = -1.01858643878723042342583399782 gamma0(44,71) = -1.53083520471750306835483265369 gamma0(45,71) = -3.14527353870502616538719070458 gamma0(46,71) = -2.88742855271966988916112006291 gamma0(47,71) = -1.74090685894967222987929112653 gamma0(48,71) = -0.733945641844822182785766159862 gamma0(49,71) = -1.58032797925585887121502412097 gamma0(50,71) = -4.47668433841262862165508385295 gamma0(51,71) = -1.34982465878083662292118596224 gamma0(52,71) = -1.19149022057245883496074982601 gamma0(53,71) = -8.33497811356763243609529950789 gamma0(54,71) = -0.839595507428384758985671869081 gamma0(55,71) = -5.06822372620265259727789291150 gamma0(56,71) = -2.13171961349281919517872534429 gamma0(57,71) = -3.01169241761940376395865997195 gamma0(58,71) = -2.20850275781732660921656785303 gamma0(59,71) = -4.22772798553258460106510595313 gamma0(60,71) = -1.08480959316339708792515281341 gamma0(61,71) = -2.46523006537442534910381251807 gamma0(62,71) = -0.708988866619948869447200715711 gamma0(63,71) = -1.26814356328225884471836294076 gamma0(64,71) = -0.759460635624338361171453441724 gamma0(65,71) = -1.98920734863090738385838413967 gamma0(66,71) = -1.79895850667349545398213954865 gamma0(67,71) = -0.925685205256022871774151153690 gamma0(68,71) = -0.785557193158334269428103328846 gamma0(69,71) = -2.56106830307808976307437112858 gamma0(70,71) = -0.896277463579781133746997173105 gamma0(71,71) = -0.0519079466498560924045484851047 gamma1(1,71) = -0.0955725976549821160294738478371 gamma1(2,71) = 0.175349195541904720859100320359 gamma1(3,71) = -0.0605177961573822200729173208201 gamma1(4,71) = -0.0776938376694882300900736376849 gamma1(5,71) = -0.0761352830779855529639978776240 gamma1(6,71) = -0.0642657644221736445421558987742 gamma1(7,71) = 0.249779131153249217887261464333 gamma1(8,71) = 0.0783407765425275611848681869258 gamma1(9,71) = -0.000448081552554718096287790848433 gamma1(10,71) = -0.0565826851843106282603909180226 gamma1(11,71) = -0.0524410368075382149391668369004 gamma1(12,71) = -0.0151957641574774801537531493801 gamma1(13,71) = 0.247390193710615484138503230636 gamma1(14,71) = -0.00438586975413799156086481216720 gamma1(15,71) = -0.0695731428501570202761965935144 gamma1(16,71) = 0.0174150084539228675476492411950 gamma1(17,71) = 0.0398315914766498446593033084266 gamma1(18,71) = -0.0821928084696303664893563861730 gamma1(19,71) = 0.156173051664215555475035140054 gamma1(20,71) = -0.0729225327673417728474640853313 gamma1(21,71) = -0.0333004001020252250100113536427 gamma1(22,71) = -0.0545390019984972629575686920074 gamma1(23,71) = -0.0359596440071358466815098054145 gamma1(24,71) = -0.0678434614813560469595793677108 gamma1(25,71) = 0.0610964166825536688430365044768 gamma1(26,71) = -0.0434447524900183233131140631931 gamma1(27,71) = 0.268206226377523042419651639521 gamma1(28,71) = 0.0279305636137504149111501756563 gamma1(29,71) = 0.221536001791028339868966199113 gamma1(30,71) = -0.0277026633453477312565060858537 gamma1(31,71) = -0.0185064788286041306674838928251 gamma1(32,71) = 0.110966517591256325402460494352 gamma1(33,71) = 0.197123638482462540015873699206 gamma1(34,71) = -0.0457912663209398277587535905850 gamma1(35,71) = 0.124308797313924671327108926143 gamma1(36,71) = -0.0930711190301859988686486417504 gamma1(37,71) = -0.0850557284254152718260819586004 gamma1(38,71) = 0.0225178399850460638410064263031 gamma1(39,71) = 0.0989914945560332434970580263063 gamma1(40,71) = 0.0881734076733255865811841812868 gamma1(41,71) = 0.0336882309483063896520452931128 gamma1(42,71) = -0.0917902267497253131211321211292 gamma1(43,71) = -0.0745452835524842209102066403087 gamma1(44,71) = -0.0502858877179919035116778132511 gamma1(45,71) = 0.0125917504524605813633014500703 gamma1(46,71) = 0.00368183352643681626731380317935 gamma1(47,71) = -0.0410269149769601015091830758985 gamma1(48,71) = -0.0891647079366587146580886429895 gamma1(49,71) = -0.0480704247637573807528826193741 gamma1(50,71) = 0.0534744322453710429708997766692 gamma1(51,71) = -0.0585747811361007415072978086745 gamma1(52,71) = -0.0660749292062420340053860935784 gamma1(53,71) = 0.139275153514768952761289809426 gamma1(54,71) = -0.0836372335875714360656662473601 gamma1(55,71) = 0.0693534785363726392341304196947 gamma1(56,71) = -0.0247513089104635569751640663565 gamma1(57,71) = 0.00802170382240765457768090605659 gamma1(58,71) = -0.0216886413694111975701298338903 gamma1(59,71) = 0.0464082992785415099286186158776 gamma1(60,71) = -0.0712656438543309893324034815333 gamma1(61,71) = -0.0117464420062953815254193041208 gamma1(62,71) = -0.0904883296556509007165704159264 gamma1(63,71) = -0.0624140647331613861760468324268 gamma1(64,71) = -0.0878186048966986645197208406243 gamma1(65,71) = -0.0305501164502981399550654628816 gamma1(66,71) = -0.0385334429201058281487586253790 gamma1(67,71) = -0.0792221790704255743023202077650 gamma1(68,71) = -0.0864492244533898427624064061745 gamma1(69,71) = -0.00814731431035018825705835626666 gamma1(70,71) = -0.0807214698723135888652648002951 gamma1(71,71) = -0.0943316917332587533058773113909 modulo 73 gamma0(1,73) = -73.6136785612954759052813040558 gamma0(2,73) = -15.1286351985770484573185063208 gamma0(3,73) = -3.10084826148731285252401816147 gamma0(4,73) = -1.24433774744759537113777121246 gamma0(5,73) = -1.74666815191911986024492425537 gamma0(6,73) = -1.00503042588718741871357632090 gamma0(7,73) = -24.9036802292141074823127051449 gamma0(8,73) = -5.20755754760399183214061280868 gamma0(9,73) = -37.0918029822464423513347326295 gamma0(10,73) = -7.73075226945559823827274338166 gamma0(11,73) = -1.32224745907887144215183526200 gamma0(12,73) = -2.45001012336377123654224761265 gamma0(13,73) = -8.56075670616647500007354623239 gamma0(14,73) = -1.54093122211226220414055562253 gamma0(15,73) = -12.6750190082298506421709824621 gamma0(16,73) = -2.54231350994577826532746239543 gamma0(17,73) = -18.7992956215546292527293102048 gamma0(18,73) = -3.90789909579003868002522860057 gamma0(19,73) = -2.85522047869881558149629130349 gamma0(20,73) = -0.915480331763290845237312559286 gamma0(21,73) = -4.34589075296859719854293623695 gamma0(22,73) = -4.60104381873843196671802173655 gamma0(23,73) = -6.47724871632347840077461291151 gamma0(24,73) = -0.974420368620953710987600797079 gamma0(25,73) = -9.59386931546298960856165793968 gamma0(26,73) = -1.80339161323695517337715479103 gamma0(27,73) = -1.17103297756294222291578238764 gamma0(28,73) = -1.28268527863887214634698701833 gamma0(29,73) = -2.05648349209857418413299994136 gamma0(30,73) = -2.20185169482140257508376653433 gamma0(31,73) = -3.23748832333316674104346664238 gamma0(32,73) = -1.44894832990546404372776186868 gamma0(33,73) = -4.88627550118681218684127787658 gamma0(34,73) = -10.9170058276748157505698374446 gamma0(35,73) = -2.12738302321322025959083311792 gamma0(36,73) = -2.64021225553469088309701301359 gamma0(37,73) = -0.658750813440807391914674993879 gamma0(38,73) = -0.754667263884257726389655426488 gamma0(39,73) = -1.40530041330620597942045944630 gamma0(40,73) = -3.71823056739960606859349651222 gamma0(41,73) = -2.36279012238156750969756286934 gamma0(42,73) = -5.57256605336080899199892367170 gamma0(43,73) = -0.705697433887362425903775076580 gamma0(44,73) = -1.03644877205508266240874071225 gamma0(45,73) = -0.681980902408744395882490365778 gamma0(46,73) = -0.887083538581528350573125354115 gamma0(47,73) = -3.38492056592199021672559631458 gamma0(48,73) = -1.69220471517474950947306380115 gamma0(49,73) = -0.859361062476115460422184736042 gamma0(50,73) = -2.74429099899393435538364138023 gamma0(51,73) = -0.779962055940896553690003365625 gamma0(52,73) = -1.63985034949019639101858477003 gamma0(53,73) = -0.729919498277885352367408620042 gamma0(54,73) = -1.20714028128990726505018527606 gamma0(55,73) = -1.49412646027019049392624529035 gamma0(56,73) = -7.04854250310785373142171097520 gamma0(57,73) = -1.13596019316996484271655568134 gamma0(58,73) = -1.10187016749017763090575066371 gamma0(59,73) = -0.944581826831184655622575777321 gamma0(60,73) = -5.99133687108441651643055350707 gamma0(61,73) = -0.832284329817802002533177300378 gamma0(62,73) = -2.28020320654946087396954821238 gamma0(63,73) = -4.11610046207910611382095430649 gamma0(64,73) = -3.54459347566647297698566434701 gamma0(65,73) = -1.98887302677015415254839516935 gamma0(66,73) = -1.86254132083444854774674779887 gamma0(67,73) = -1.36309402820705462798341635880 gamma0(68,73) = -2.97377406540337025867051255005 gamma0(69,73) = -1.06871468489646276202797549710 gamma0(70,73) = -0.805826442767802916149001934269 gamma0(71,73) = -1.92430076465310606934768381146 gamma0(72,73) = -1.58946764185957101008446467090 gamma0(73,73) = -0.0508663530992720310751451611967 gamma1(1,73) = -0.0943376033782583872931156444970 gamma1(2,73) = 0.222991410671848159995762930793 gamma1(3,73) = 0.0103511110095722094342695383552 gamma1(4,73) = -0.0629216866018223142202278207581 gamma1(5,73) = -0.0405930615861208183598743769747 gamma1(6,73) = -0.0743671199024768843020347227107 gamma1(7,73) = 0.269553897633875645329834107900 gamma1(8,73) = 0.0712856696478699080048277392966 gamma1(9,73) = 0.251071107187043757724600865314 gamma1(10,73) = 0.126014373150124115963223166961 gamma1(11,73) = -0.0593128389173178055942286489224 gamma1(12,73) = -0.0126566332668230331409387853334 gamma1(13,73) = 0.140932721757744328699357293396 gamma1(14,73) = -0.0494751448744942088275391891174 gamma1(15,73) = 0.198631186088024899979567099814 gamma1(16,73) = -0.00924098958827802071380388174309 gamma1(17,73) = 0.248792326077507388269793172959 gamma1(18,73) = 0.0358273550296072774064234127764 gamma1(19,73) = 0.00195333426225762752902167235065 gamma1(20,73) = -0.0787954960888712375977615422891 gamma1(21,73) = 0.0484668021033989600114101167041 gamma1(22,73) = 0.0554915725460660875876465659526 gamma1(23,73) = 0.100790304174426023992831132911 gamma1(24,73) = -0.0758716934248979355913581878529 gamma1(25,73) = 0.157781638125335077462714157976 gamma1(26,73) = -0.0382046671893072233352678175265 gamma1(27,73) = -0.0663690130873174380142377604956 gamma1(28,73) = -0.0611383858405961508541230593932 gamma1(29,73) = -0.0278494925516567732581118212085 gamma1(30,73) = -0.0221139523427747201234593641413 gamma1(31,73) = 0.0148843096778703067146049548800 gamma1(32,73) = -0.0535617172261913831721299117988 gamma1(33,73) = 0.0630714614859813334226895012084 gamma1(34,73) = 0.176907788365534720857935437195 gamma1(35,73) = -0.0250334593990115758649731026052 gamma1(36,73) = -0.00567603097914402798060572358637 gamma1(37,73) = -0.0919541734168287076027912893962 gamma1(38,73) = -0.0869558793309810313532283020718 gamma1(39,73) = -0.0555267536962747480913356546381 gamma1(40,73) = 0.0301089913088015007540110981584 gamma1(41,73) = -0.0159341464190795333007797321317 gamma1(42,73) = 0.0802293293084196087673679545660 gamma1(43,73) = -0.0894952906540949389346781677439 gamma1(44,73) = -0.0728325761057050349524376833806 gamma1(45,73) = -0.0907344694739089241370775713320 gamma1(46,73) = -0.0802168528495743935667735532280 gamma1(47,73) = 0.0196701341329732111917068960317 gamma1(48,73) = -0.0429104982765720185315296454095 gamma1(49,73) = -0.0816125032343770909109185618717 gamma1(50,73) = -0.00194926035000986197314332780604 gamma1(51,73) = -0.0856542493230836125647012546534 gamma1(52,73) = -0.0451609365662047423399239311899 gamma1(53,73) = -0.0882359877788889188539118335807 gamma1(54,73) = -0.0646646372107324007499683671300 gamma1(55,73) = -0.0515454100276918684573584567761 gamma1(56,73) = 0.112719162573334877132665984667 gamma1(57,73) = -0.0680364787859167460442142217223 gamma1(58,73) = -0.0696685967800585450101369064497 gamma1(59,73) = -0.0773474542959221893962150900806 gamma1(60,73) = 0.0900175096657986378771143600696 gamma1(61,73) = -0.0829833743018946371650492065055 gamma1(62,73) = -0.0190835712716917983338955146213 gamma1(63,73) = 0.0419307479089130573877106233337 gamma1(64,73) = 0.0247349282047470280256387868640 gamma1(65,73) = -0.0305687724521123511646782819954 gamma1(66,73) = -0.0357410135432406788431522522667 gamma1(67,73) = -0.0574430184487519552501687104904 gamma1(68,73) = 0.00604752063969344971579608154381 gamma1(69,73) = -0.0712668354130045809029436731656 gamma1(70,73) = -0.0843303449921568288857822111318 gamma1(71,73) = -0.0331974180003767363129207535729 gamma1(72,73) = -0.0473480276814602710647815817061 gamma1(73,73) = -0.0931550212944908411608239308505 modulo 79 gamma0(1,79) = -79.6118936187202787895272826792 gamma0(2,79) = -26.9050688805339265476086557871 gamma0(3,79) = -9.23706329731300295636788925389 gamma0(4,79) = -3.10406336484827844862912820832 gamma0(5,79) = -40.0916345107584024157034969654 gamma0(6,79) = -13.6807518753736904429034315391 gamma0(7,79) = -4.69850589417877394393776805374 gamma0(8,79) = -1.32286021021538561794379984175 gamma0(9,79) = -20.3021850333798116374917562414 gamma0(10,79) = -6.99041759536474567953424144444 gamma0(11,79) = -2.25551361289185713236937853374 gamma0(12,79) = -2.87512460437860581718108319023 gamma0(13,79) = -10.3522515939650095974073385647 gamma0(14,79) = -3.51186835001430285581947381892 gamma0(15,79) = -0.788539467074857068122023195981 gamma0(16,79) = -1.18206706856672752154680582734 gamma0(17,79) = -5.27864554097009390257895946515 gamma0(18,79) = -1.56859582250116674572071097420 gamma0(19,79) = -0.969045406475816190281840274833 gamma0(20,79) = -2.18395956248972663031573023198 gamma0(21,79) = -2.58026497198861478082537209254 gamma0(22,79) = -4.97232552945989365470546650309 gamma0(23,79) = -1.43987664983949585362534706710 gamma0(24,79) = -0.741742186016867197610976701201 gamma0(25,79) = -0.997256740151250291629814447934 gamma0(26,79) = -2.40952145908336256782418615113 gamma0(27,79) = -3.66938063860411365161580147752 gamma0(28,79) = -0.862504515891924755090187721627 gamma0(29,79) = -1.52426372839464771618294062590 gamma0(30,79) = -0.888245338369837140719145045290 gamma0(31,79) = -1.66197755527753262227221568235 gamma0(32,79) = -1.14924092542773682446098639618 gamma0(33,79) = -4.45208501971793630851742025066 gamma0(34,79) = -1.21579534296068231289833912166 gamma0(35,79) = -6.46714527083136813375100705986 gamma0(36,79) = -2.05039364738401002890124385653 gamma0(37,79) = -2.11566729498540388203142985510 gamma0(38,79) = -2.33060015016778847143113228899 gamma0(39,79) = -3.23043757387811333464013296107 gamma0(40,79) = -0.653541910224475815691966641837 gamma0(41,79) = -0.696785950631993249074056945596 gamma0(42,79) = -0.837320789393557896980699747991 gamma0(43,79) = -1.39966549916817838599839761278 gamma0(44,79) = -0.674957456115175323500625214241 gamma0(45,79) = -0.764902112467591196765547730763 gamma0(46,79) = -1.08612910161379645550077062436 gamma0(47,79) = -3.36599592893309380498661676922 gamma0(48,79) = -0.719042300561716921234162909914 gamma0(49,79) = -0.914566080444440254859186263518 gamma0(50,79) = -1.81540701923348231352104025554 gamma0(51,79) = -1.48138438834352128372558985497 gamma0(52,79) = -0.812672579747460615452051070757 gamma0(53,79) = -1.28614186839662556411189545991 gamma0(54,79) = -11.7812293366778334195904947694 gamma0(55,79) = -4.02588707178326895923454462891 gamma0(56,79) = -1.02615372521541103811209355963 gamma0(57,79) = -2.67289728782370427522383808302 gamma0(58,79) = -6.01647362852709649895831896555 gamma0(59,79) = -1.87059722092469386584250619789 gamma0(60,79) = -1.61446861095394209135041139031 gamma0(61,79) = -1.05576698706523114821399560837 gamma0(62,79) = -2.98590430680414683789031536909 gamma0(63,79) = -16.3329718072544861893451297049 gamma0(64,79) = -5.62392658001654287263471316871 gamma0(65,79) = -1.71122646927186301773843845124 gamma0(66,79) = -1.25047084378381237333832429887 gamma0(67,79) = -8.34160790820523188051487169344 gamma0(68,79) = -2.77099948060099734696869447860 gamma0(69,79) = -7.60602839938401298152657051087 gamma0(70,79) = -2.49261617897004943806178105566 gamma0(71,79) = -4.22898061716465585825243181712 gamma0(72,79) = -1.11727475597747991979265812493 gamma0(73,79) = -3.84009896615900429633304668336 gamma0(74,79) = -0.941490903163984260421358773695 gamma0(75,79) = -1.98791956341158820851860903227 gamma0(76,79) = -1.92804716144057008611736189015 gamma0(77,79) = -1.76232846315878174829713114920 gamma0(78,79) = -1.36068148573582117502835049764 gamma0(79,79) = -0.0480029390831074510578029550810 gamma1(1,79) = -0.0908631236290528640924724858398 gamma1(2,79) = 0.273321724398555329785965077324 gamma1(3,79) = 0.145510363211146046664798695196 gamma1(4,79) = 0.00849076827408791588869684603755 gamma1(5,79) = 0.254693859548025902586605533333 gamma1(6,79) = 0.202816258724913738148810429602 gamma1(7,79) = 0.0540982009244140118963152377183 gamma1(8,79) = -0.0576969461298321894625273233540 gamma1(9,79) = 0.252702153482101969080738494057 gamma1(10,79) = 0.105738423816365940778854704084 gamma1(11,79) = -0.0205183966309445246659810389190 gamma1(12,79) = 0.00104648711693519487879878634455 gamma1(13,79) = 0.162230997417869455716339607013 gamma1(14,79) = 0.0211336886684102802997398954145 gamma1(15,79) = -0.0821747020131226945445227800974 gamma1(16,79) = -0.0638973027926246746213613067136 gamma1(17,79) = 0.0684829882556791612310263885033 gamma1(18,79) = -0.0472710711263831776945283973331 gamma1(19,79) = -0.0736120899317144303742980768895 gamma1(20,79) = -0.0231552894318992280763371783967 gamma1(21,79) = -0.00894367530191905674654737983639 gamma1(22,79) = 0.0610139679769234515200162645091 gamma1(23,79) = -0.0526711097477136742767852322259 gamma1(24,79) = -0.0844461241531961003755655200052 gamma1(25,79) = -0.0723017145688259036715646821531 gamma1(26,79) = -0.0149508954000992084807052343725 gamma1(27,79) = 0.0258205482101482835998536391886 gamma1(28,79) = -0.0786282805657462455662556459441 gamma1(29,79) = -0.0491160207392746999357339115018 gamma1(30,79) = -0.0774064647521829981611513711218 gamma1(31,79) = -0.0434347995858270485627851190818 gamma1(32,79) = -0.0653677073784225309709208399190 gamma1(33,79) = 0.0476693438555787859735786863482 gamma1(34,79) = -0.0623963524844223276281959023167 gamma1(35,79) = 0.0950846065712365296884138387510 gamma1(36,79) = -0.0281658848745068422984191453474 gamma1(37,79) = -0.0257025994842828188045427993462 gamma1(38,79) = -0.0177858294177624323134027203085 gamma1(39,79) = 0.0124903669410701874101650430797 gamma1(40,79) = -0.0887863671071885321501398238472 gamma1(41,79) = -0.0866486304519333458912438738446 gamma1(42,79) = -0.0798298161346950527293333977779 gamma1(43,79) = -0.0543854129943412435539746508525 gamma1(44,79) = -0.0877253502645603735236382457448 gamma1(45,79) = -0.0833193018187316489219120073283 gamma1(46,79) = -0.0682216645847809417821892942582 gamma1(47,79) = 0.0166979528945650889737101878193 gamma1(48,79) = -0.0855557237899711293648417155966 gamma1(49,79) = -0.0761636626014026505004472663385 gamma1(50,79) = -0.0372743272568144803876842783824 gamma1(51,79) = -0.0509153158371834865411889191013 gamma1(52,79) = -0.0810117433480386254732001816376 gamma1(53,79) = -0.0592975848347500720326772262851 gamma1(54,79) = 0.181226323211843647911214668974 gamma1(55,79) = 0.0360567859123326266203598527846 gamma1(56,79) = -0.0709671375534355682930696890122 gamma1(57,79) = -0.00575423702999364010948084585403 gamma1(58,79) = 0.0854132730209379779863792037007 gamma1(59,79) = -0.0351003423317985129943595277787 gamma1(60,79) = -0.0453781575505065141772447572448 gamma1(61,79) = -0.0696074432070983351502052901055 gamma1(62,79) = 0.00468138476004103898429485972994 gamma1(63,79) = 0.227040282803857104539338974619 gamma1(64,79) = 0.0765844007324303652763459723829 gamma1(65,79) = -0.0414383292162715248445426640526 gamma1(66,79) = -0.0608635689774383842550751907110 gamma1(67,79) = 0.130717845217506797674567719464 gamma1(68,79) = -0.00242789963228976454118103016683 gamma1(69,79) = 0.117546099998820039358578167501 gamma1(70,79) = -0.0120062237982359358295161174941 gamma1(71,79) = 0.0416713982500233136650993057756 gamma1(72,79) = -0.0668087796956885442730314119654 gamma1(73,79) = 0.0307848299439414251333631414514 gamma1(74,79) = -0.0748991315210778998782913336292 gamma1(75,79) = -0.0305502283824782386221463413852 gamma1(76,79) = -0.0328602882168500142334528679287 gamma1(77,79) = -0.0393858722194121342610011802159 gamma1(78,79) = -0.0560601052560365379618119397757 gamma1(79,79) = -0.0898321438706795325310704372434 modulo 83 gamma0(1,83) = -83.6108088436682650523348592233 gamma0(2,83) = -42.0915008986587122966818026119 gamma0(3,83) = -21.3038568032771586884582970232 gamma0(4,83) = -10.8571867781705488453532456221 gamma0(5,83) = -5.53897952749621076864387522187 gamma0(6,83) = -2.72330232465203086986977607788 gamma0(7,83) = -1.08665466604513490388604142129 gamma0(8,83) = -1.82249386171679977863662235067 gamma0(9,83) = -12.3568173595993361515007665758 gamma0(10,83) = -6.31129356581240425848070276012 gamma0(11,83) = -3.14516757503704715445740772681 gamma0(12,83) = -1.34709956055099778432065924599 gamma0(13,83) = -3.02988513078776522540136150545 gamma0(14,83) = -1.27668179226171619339106752645 gamma0(15,83) = -2.63224871784527081438890347669 gamma0(16,83) = -1.02938114735353707715564045013 gamma0(17,83) = -1.62937603228754641238329856323 gamma0(18,83) = -5.90032219937560176665864633250 gamma0(19,83) = -2.92157505290920238076663946806 gamma0(20,83) = -1.21002268165642556673712399756 gamma0(21,83) = -2.31193119394959754288791346465 gamma0(22,83) = -0.824495036953909674405297316962 gamma0(23,83) = -1.05767668188179175661763748089 gamma0(24,83) = -1.72251578232073338173025358200 gamma0(25,83) = -7.97678285665052283782444694174 gamma0(26,83) = -4.03553679076636275531220212568 gamma0(27,83) = -1.87532567250649485835314791422 gamma0(28,83) = -17.1355008119615180250815658146 gamma0(29,83) = -8.74802135337342746491370342915 gamma0(30,83) = -4.44156636690441860973237122448 gamma0(31,83) = -2.10877983264455113368284826144 gamma0(32,83) = -0.691533503014592562349655104772 gamma0(33,83) = -0.756086561877754346557779074687 gamma0(34,83) = -0.897201947273598999123978390347 gamma0(35,83) = -1.24290483585442712387479114107 gamma0(36,83) = -2.46404506118527185078680111294 gamma0(37,83) = -0.922479901388763188220503136246 gamma0(38,83) = -1.31139764312615150587656727266 gamma0(39,83) = -2.81957428609150340331784513366 gamma0(40,83) = -1.14678033151337679322683344251 gamma0(41,83) = -2.04678574188730719747314396059 gamma0(42,83) = -0.650449595407807059607908546693 gamma0(43,83) = -0.670805132183645925214543009690 gamma0(44,83) = -0.712647483726882338946893402373 gamma0(45,83) = -0.801237892078374628676457504972 gamma0(46,83) = -1.00173969899950058031113552909 gamma0(47,83) = -1.54230448617560835500230318810 gamma0(48,83) = -4.67465806050374747480062628874 gamma0(49,83) = -2.24113392797159501381291038250 gamma0(50,83) = -0.778440518196739996145590971251 gamma0(51,83) = -0.948313608364655022583426217409 gamma0(52,83) = -1.38383807420038798532465843010 gamma0(53,83) = -3.26818326106167993682222737924 gamma0(54,83) = -1.42166737976552551379904961595 gamma0(55,83) = -3.54106423106916149035858143054 gamma0(56,83) = -1.58512512011782394012393070782 gamma0(57,83) = -5.21854114298913535736986053928 gamma0(58,83) = -2.54596277950476809108180951244 gamma0(59,83) = -0.974725596910642243893055958485 gamma0(60,83) = -1.46064568224954154418958199972 gamma0(61,83) = -3.85740931457098302258055019319 gamma0(62,83) = -1.77159674083554498561917068327 gamma0(63,83) = -9.68719389380958145189702708231 gamma0(64,83) = -4.93222030202839495470966979265 gamma0(65,83) = -2.38614024593366436938934090047 gamma0(66,83) = -0.872458431169776899096762997819 gamma0(67,83) = -1.17799406680457886498325216876 gamma0(68,83) = -2.17349338974361015466635557809 gamma0(69,83) = -0.734160478881547247059260102222 gamma0(70,83) = -0.848229169993857595036704063007 gamma0(71,83) = -1.11634521424999785661290228711 gamma0(72,83) = -1.93022158667298642748880048006 gamma0(73,83) = -28.2391869321694915555100908519 gamma0(74,83) = -14.3507763414986329119524728415 gamma0(75,83) = -7.33155200008950861093000973270 gamma0(76,83) = -3.69313337038088609614854615388 gamma0(77,83) = -1.67514221493937348603665786676 gamma0(78,83) = -6.78330087844488251328304938040 gamma0(79,83) = -3.39980967787727592992212536640 gamma0(80,83) = -1.50083557875293201826576070562 gamma0(81,83) = -4.22947312638291012911312602206 gamma0(82,83) = -1.98732319437706467180716697455 gamma0(83,83) = -0.0462846378662056031670959052194 gamma1(1,83) = -0.0887203238235733505978675588088 gamma1(2,83) = 0.256919867166070988716110252581 gamma1(3,83) = 0.255089552141924417004134058668 gamma1(4,83) = 0.164922718027493898239380073387 gamma1(5,83) = 0.0717204589954754685897483585015 gamma1(6,83) = -0.00480321220890467916946646239290 gamma1(7,83) = -0.0668214148634197498043761347665 gamma1(8,83) = -0.0366952621560336691040850837802 gamma1(9,83) = 0.183844135280681066431936111009 gamma1(10,83) = 0.0885213221820695946643052805758 gamma1(11,83) = 0.00861533914543500634382492603284 gamma1(12,83) = -0.0556763539805987616560282580314 gamma1(13,83) = 0.00503313070972480656939288632120 gamma1(14,83) = -0.0586346592994377258975060671703 gamma1(15,83) = -0.00781584278839658800024678502940 gamma1(16,83) = -0.0693489755877620941687683269501 gamma1(17,83) = -0.0442053387585941365053821920804 gamma1(18,83) = 0.0797577020274096546656230643040 gamma1(19,83) = 0.00161071264633659360937470195704 gamma1(20,83) = -0.0614721835815876647371174111061 gamma1(21,83) = -0.0187715652638139499496391216923 gamma1(22,83) = -0.0786287460561622769733716581031 gamma1(23,83) = -0.0680967010333884255084149568412 gamma1(24,83) = -0.0405503529849397820983015959947 gamma1(25,83) = 0.120451538242980826105734689966 gamma1(26,83) = 0.0343863610114769259214143336893 gamma1(27,83) = -0.0346858978359053996282019497435 gamma1(28,83) = 0.229505986093395766264247323021 gamma1(29,83) = 0.133553333781654453651445730541 gamma1(30,83) = 0.0451553689644798022662703797299 gamma1(31,83) = -0.0260277159818618346644243592873 gamma1(32,83) = -0.0848569841678872617787895898705 gamma1(33,83) = -0.0818124210135565634275598377235 gamma1(34,83) = -0.0752923813094516091431327312922 gamma1(35,83) = -0.0600679067482856008384483486672 gamma1(36,83) = -0.0134975429015836464890112584642 gamma1(37,83) = -0.0741436967016631522115751830308 gamma1(38,83) = -0.0571712350435345133648351563075 gamma1(39,83) = -0.00166435766044695754736734807615 gamma1(40,83) = -0.0641983130580832018554184397543 gamma1(41,83) = -0.0282926227560374161397859999717 gamma1(42,83) = -0.0868153356120599826839315584463 gamma1(43,83) = -0.0858430212915532847916473088575 gamma1(44,83) = -0.0838568216485543577732525795741 gamma1(45,83) = -0.0797062277455156120842047309040 gamma1(46,83) = -0.0705790558256490386718030773248 gamma1(47,83) = -0.0476793305702878257968554193205 gamma1(48,83) = 0.0510931547767531182652347405251 gamma1(49,83) = -0.0212720442943078892619989125536 gamma1(50,83) = -0.0807672855519309728168078267199 gamma1(51,83) = -0.0729756976162011207717970614548 gamma1(52,83) = -0.0541486563723454039414148805718 gamma1(53,83) = 0.0123712932702549626051802116707 gamma1(54,83) = -0.0525866962217098386211088190376 gamma1(55,83) = 0.0204693160362713670520233973498 gamma1(56,83) = -0.0459638675283086741952457554634 gamma1(57,83) = 0.0643145589808104973960465266589 gamma1(58,83) = -0.0107112453551991404009284226651 gamma1(59,83) = -0.0717877175212566947230158177510 gamma1(60,83) = -0.0509889340913177157404587091272 gamma1(61,83) = 0.0294795328409560565891438377894 gamma1(62,83) = -0.0386491260687102422377331006615 gamma1(63,83) = 0.148274627250440121346338942166 gamma1(64,83) = 0.0574608950842320244676260932637 gamma1(65,83) = -0.0161820904687282558190978973404 gamma1(66,83) = -0.0764223860290730511581246391515 gamma1(67,83) = -0.0628486275835389298694591441002 gamma1(68,83) = -0.0236890714960352006589274995284 gamma1(69,83) = -0.0828421135364429657670901839888 gamma1(70,83) = -0.0775343154661715345301045546464 gamma1(71,83) = -0.0655222553301051438360437335383 gamma1(72,83) = -0.0326179429390804007763421927869 gamma1(73,83) = 0.275629244215993541299416118035 gamma1(74,83) = 0.205358748656286821521386185526 gamma1(75,83) = 0.108712578933132458188304740494 gamma1(76,83) = 0.0248492760164040632841334491462 gamma1(77,83) = -0.0424016004525803931857063249374 gamma1(78,83) = 0.0981262858834464866026315820615 gamma1(79,83) = 0.0163167019357652236875728561910 gamma1(80,83) = -0.0493537291806524055839673547299 gamma1(81,83) = 0.0395999876588030799842162284884 gamma1(82,83) = -0.0304880570111449901964475767773 gamma1(83,83) = -0.0877743130664647390401465586316 modulo 89 gamma0(1,89) = -89.6093176129391670739904608141 gamma0(2,89) = -30.2401948769792574212979906957 gamma0(3,89) = -10.3614686712780136729202154870 gamma0(4,89) = -3.51210476878879502970701750278 gamma0(5,89) = -0.786081698229972835425343854428 gamma0(6,89) = -1.18732655410705498422565406737 gamma0(7,89) = -5.58622039209057350735995726074 gamma0(8,89) = -1.69289292761795914579293441531 gamma0(9,89) = -1.21746878238938272630940739181 gamma0(10,89) = -6.75212039749937296730771160545 gamma0(11,89) = -2.15958252493554436124718074814 gamma0(12,89) = -2.50121606980118746072307553693 gamma0(13,89) = -4.32671072799705658172633895053 gamma0(14,89) = -1.15790560337916597615735109469 gamma0(15,89) = -4.75858913983983092303958890664 gamma0(16,89) = -1.34592316412824854244247064176 gamma0(17,89) = -45.0912799702296434647741870665 gamma0(18,89) = -15.3552403592337241086538809736 gamma0(19,89) = -5.28107414470328433437223754123 gamma0(20,89) = -1.56676356234415522563818687956 gamma0(21,89) = -0.969821825256899003990905009576 gamma0(22,89) = -2.22209324847485082476058737202 gamma0(23,89) = -2.74806071982849955257982991975 gamma0(24,89) = -7.25621899445602288112763886755 gamma0(25,89) = -2.35540429469901546057238610472 gamma0(26,89) = -3.38175530315441484051143011083 gamma0(27,89) = -0.724058542033301744194634649629 gamma0(28,89) = -0.945215246132377268235423316784 gamma0(29,89) = -2.04193623390848352810164349383 gamma0(30,89) = -2.09958552572864242136776408264 gamma0(31,89) = -2.28730016424611966928292532878 gamma0(32,89) = -3.03714691107224224716727587129 gamma0(33,89) = -22.8060540461161971943749656495 gamma0(34,89) = -7.84203015300500897392844047793 gamma0(35,89) = -2.57944250157122383848486985091 gamma0(36,89) = -5.00672934563271715486088920828 gamma0(37,89) = -1.45163068806516768685564728208 gamma0(38,89) = -0.765032249557629713613412891318 gamma0(39,89) = -1.10110847723936265349662973202 gamma0(40,89) = -3.65166028767298267138176163481 gamma0(41,89) = -0.851637542715375297986630260509 gamma0(42,89) = -1.48889027702660152416490054854 gamma0(43,89) = -0.829370452896184936006361907033 gamma0(44,89) = -1.38019579202593191187360788749 gamma0(45,89) = -0.646285494350096371854606893472 gamma0(46,89) = -0.684505635427333443419572194691 gamma0(47,89) = -0.807523247105311859666772732893 gamma0(48,89) = -1.28004736871635878719540711030 gamma0(49,89) = -11.6137790540726308365174420226 gamma0(50,89) = -3.96293119286543418767359727320 gamma0(51,89) = -0.994950384265426776646848499085 gamma0(52,89) = -2.42662765232218627888641543032 gamma0(53,89) = -3.80151197950274093770530620128 gamma0(54,89) = -0.921111367665187079745629281956 gamma0(55,89) = -1.88162453595617690868205587068 gamma0(56,89) = -1.64951632265252770129399284040 gamma0(57,89) = -1.12917573218611466282551319430 gamma0(58,89) = -4.13740988302076919847505156028 gamma0(59,89) = -1.07367698542761080294697868506 gamma0(60,89) = -3.25967176854096765662042627222 gamma0(61,89) = -0.665234167321676785881516569382 gamma0(62,89) = -0.744361974982096356606215512497 gamma0(63,89) = -1.02062125573199954949897930875 gamma0(64,89) = -2.66161089102679162722657935091 gamma0(65,89) = -5.92791319501133089170809145213 gamma0(66,89) = -1.83197585564597126909381765473 gamma0(67,89) = -1.52724862812410220646324491729 gamma0(68,89) = -0.897491895493895575551605420511 gamma0(69,89) = -1.73770464476520475174436698117 gamma0(70,89) = -1.31255409102692645003058887654 gamma0(71,89) = -18.3388495279091933735641099956 gamma0(72,89) = -6.31342861734064242354203788493 gamma0(73,89) = -1.98648326016293997789839013105 gamma0(74,89) = -1.93308825712829762610708763133 gamma0(75,89) = -1.78403536046992641963800857635 gamma0(76,89) = -1.41541596222001520090021499975 gamma0(77,89) = -0.704110177498885201969932474879 gamma0(78,89) = -0.874339456949333382794847432721 gamma0(79,89) = -1.60749719037050335363954617322 gamma0(80,89) = -1.04685589989894529770517418716 gamma0(81,89) = -2.93537357746584646918705670817 gamma0(82,89) = -13.2195049282010375589037728058 gamma0(83,89) = -4.53293156237088048849933572661 gamma0(84,89) = -1.24836435734640965562144647958 gamma0(85,89) = -8.53178722758057932577210144418 gamma0(86,89) = -2.83917238397406276158873690555 gamma0(87,89) = -9.35661489524820196459088994280 gamma0(88,89) = -3.14503905434442013621513049887 gamma0(89,89) = -0.0439485472452877188506888028156 gamma1(1,89) = -0.0857345063937137367768589825111 gamma1(2,89) = 0.278825744307757481098569162124 gamma1(3,89) = 0.152057583263854265250033174064 gamma1(4,89) = 0.0176000966138177431020038403289 gamma1(5,89) = -0.0777841323177777032807132921850 gamma1(6,89) = -0.0607254009730130696214949672239 gamma1(7,89) = 0.0687901205711210386624506473870 gamma1(8,89) = -0.0409967871246904653846333031005 gamma1(9,89) = -0.0594963333902245564331499123623 gamma1(10,89) = 0.0927477701493552321389464564935 gamma1(11,89) = -0.0243033149363093962307980864107 gamma1(12,89) = -0.0128859994133659197063516026405 gamma1(13,89) = 0.0392522707421766814672336967858 gamma1(14,89) = -0.0619318730768251066148021234126 gamma1(15,89) = 0.0498686524377559909376440825347 gamma1(16,89) = -0.0543362955856116439742538938456 gamma1(17,89) = 0.260012054618438053846471056500 gamma1(18,89) = 0.208856542038277566903856953112 gamma1(19,89) = 0.0620169137379703342467948983233 gamma1(20,89) = -0.0457484987912962111429594946137 gamma1(21,89) = -0.0698076395627283331603435881415 gamma1(22,89) = -0.0221663255611359744596411361683 gamma1(23,89) = -0.00501399861557105266129621136718 gamma1(24,89) = 0.102266982570770052023887923582 gamma1(25,89) = -0.0176817173509783273793878192391 gamma1(26,89) = 0.0139137445281120981775050393009 gamma1(27,89) = -0.0805422191013737854115901437988 gamma1(28,89) = -0.0708593416454943462320660345010 gamma1(29,89) = -0.0283862431448815032038219831638 gamma1(30,89) = -0.0263754199457271387013335950726 gamma1(31,89) = -0.0199605428534624859681381934102 gamma1(32,89) = 0.00383735508967167621779042139786 gamma1(33,89) = 0.258388379135812894238972021801 gamma1(34,89) = 0.112766096998165215547965540497 gamma1(35,89) = -0.0103585281157562784903976892949 gamma1(36,89) = 0.0557284023542142160459662494879 gamma1(37,89) = -0.0501820121626242095594234492735 gamma1(38,89) = -0.0787163986403070509889637445001 gamma1(39,89) = -0.0642802286186953145158385982425 gamma1(40,89) = 0.0214749462720831163969121194729 gamma1(41,89) = -0.0749052858915296877632218813424 gamma1(42,89) = -0.0487369756654404116009748445549 gamma1(43,89) = -0.0758789821157775294945815970891 gamma1(44,89) = -0.0529804382682914212929548004802 gamma1(45,89) = -0.0840487352483060639393821045863 gamma1(46,89) = -0.0823187849471014066602830632078 gamma1(47,89) = -0.0768384592870786560915420097993 gamma1(48,89) = -0.0569669482910948494825560929847 gamma1(49,89) = 0.168612313354219176411504747375 gamma1(50,89) = 0.0298634276855163220253420727846 gamma1(51,89) = -0.0687387997314928326184672259975 gamma1(52,89) = -0.0153252203064248673166004584145 gamma1(53,89) = 0.0255560187066359570291853528991 gamma1(54,89) = -0.0718944498050273809484797348982 gamma1(55,89) = -0.0340830579852201185087922614888 gamma1(56,89) = -0.0426187692574265164420433527793 gamma1(57,89) = -0.0631165594765081083168993623335 gamma1(58,89) = 0.0344200964624634588556436638479 gamma1(59,89) = -0.0654236103075245734538519542931 gamma1(60,89) = 0.0104002059137034101610850087658 gamma1(61,89) = -0.0831894302606340895156336797110 gamma1(62,89) = -0.0796356391525475729010556672199 gamma1(63,89) = -0.0676522519933351174369418392387 gamma1(64,89) = -0.00773674738443472252939414234091 gamma1(65,89) = 0.0761142988040210880539594799557 gamma1(66,89) = -0.0358796322600412354919944496223 gamma1(67,89) = -0.0472596165664528030473215230090 gamma1(68,89) = -0.0729134830885543808236941012199 gamma1(69,89) = -0.0393342871421046146557600438239 gamma1(70,89) = -0.0556647770308455008126901771657 gamma1(71,89) = 0.232905222500590217535413824229 gamma1(72,89) = 0.0840685172122228342553075161312 gamma1(73,89) = -0.0303391107126583983827023680455 gamma1(74,89) = -0.0322370989892189750003504513169 gamma1(75,89) = -0.0376292795079623463723318478063 gamma1(76,89) = -0.0515960761541495303573083564750 gamma1(77,89) = -0.0814364889090957457894286353241 gamma1(78,89) = -0.0739169372097365037775576746016 gamma1(79,89) = -0.0442020931164398665814357638897 gamma1(80,89) = -0.0665473981804701098325014388578 gamma1(81,89) = 0.000764513442768722488505903860055 gamma1(82,89) = 0.187438695236595462983504710871 gamma1(83,89) = 0.0443901477184265571409299118319 gamma1(84,89) = -0.0582438163085262776928755781695 gamma1(85,89) = 0.124416405151525049199624604340 gamma1(86,89) = -0.00218294602432860673939361573348 gamma1(87,89) = 0.137428029788183205711391714270 gamma1(88,89) = 0.00704554930708976299868987471024 gamma1(89,89) = -0.0848969982996471744444181026389 modulo 97 gamma0(1,97) = -97.6075461323757346127919884705 gamma0(2,97) = -19.9426398527263715298638926428 gamma0(3,97) = -4.14539727774349810144708255492 gamma0(4,97) = -3.69357888953103170265961740944 gamma0(5,97) = -2.32086685447957343273190091727 gamma0(6,97) = -4.93454296932334116262554934093 gamma0(7,97) = -12.6213265721453717649160690264 gamma0(8,97) = -2.52093681049926693067770329506 gamma0(9,97) = -16.6936531812208498110073416986 gamma0(10,97) = -3.43921345908749606487525647902 gamma0(11,97) = -1.79836263056705732262972809189 gamma0(12,97) = -1.17976427626960260842340877328 gamma0(13,97) = -1.38663007560448312594868429027 gamma0(14,97) = -3.56235041467146519559855946778 gamma0(15,97) = -2.03633493920663959333994385679 gamma0(16,97) = -2.14373984007292425482105502271 gamma0(17,97) = -2.83300841304056436359645612735 gamma0(18,97) = -0.890609372196110322393981527084 gamma0(19,97) = -3.83378643731724736932088297630 gamma0(20,97) = -2.66966845296798089980296102041 gamma0(21,97) = -0.694333085061885813019134898175 gamma0(22,97) = -1.02647944867098715643069574310 gamma0(23,97) = -0.676434685184610683886926039506 gamma0(24,97) = -0.912195576973631611426802149296 gamma0(25,97) = -4.71184259459719648800560013453 gamma0(26,97) = -7.88474210423517215743544037609 gamma0(27,97) = -1.35491099617654298110392238223 gamma0(28,97) = -3.01347604780461996254029584449 gamma0(29,97) = -1.12648916780133458520196326615 gamma0(30,97) = -1.10070002414457708850069313714 gamma0(31,97) = -0.979436100836114285116596566002 gamma0(32,97) = -14.3686934628165212468530733989 gamma0(33,97) = -2.92092142980205991277917446949 gamma0(34,97) = -1.00272565627909397430610860451 gamma0(35,97) = -49.0909631883499949807864092001 gamma0(36,97) = -10.1664929058066359795420820312 gamma0(37,97) = -1.93631452669208757510940421107 gamma0(38,97) = -1.67291011004797798326223410384 gamma0(39,97) = -0.828146428366523002265100355624 gamma0(40,97) = -2.38477171163225348807727176020 gamma0(41,97) = -6.44405731390089267604640568566 gamma0(42,97) = -0.956594672568273166132184198705 gamma0(43,97) = -8.52077825455344483008767599139 gamma0(44,97) = -1.52197148622764139063311995599 gamma0(45,97) = -11.2590868377194737646948882682 gamma0(46,97) = -2.20050833428660417200574916316 gamma0(47,97) = -3.32339472510159925465857252182 gamma0(48,97) = -1.59529976900178275561595757229 gamma0(49,97) = -0.641464670705113215055150489527 gamma0(50,97) = -0.712517897450955330877542853584 gamma0(51,97) = -1.15283659944389775254104477802 gamma0(52,97) = -1.23545439968295537225544373895 gamma0(53,97) = -1.75525496856817668906174368320 gamma0(54,97) = -1.05071441105269657967284396867 gamma0(55,97) = -0.768878063305086566122640042380 gamma0(56,97) = -1.63354287014468146004661603737 gamma0(57,97) = -0.730997663325472362407711898942 gamma0(58,97) = -1.29376130160853868123449673907 gamma0(59,97) = -2.25950056696688002553583289427 gamma0(60,97) = -3.98399682794225265217901486978 gamma0(61,97) = -3.11108619586162079296316190295 gamma0(62,97) = -1.26426723726232587191794328260 gamma0(63,97) = -1.98545624218937649065892004201 gamma0(64,97) = -1.88881124843276528933402405976 gamma0(65,97) = -1.48678771699156511591617053606 gamma0(66,97) = -7.33771623962875353766553288488 gamma0(67,97) = -1.20729537899680034182855504573 gamma0(68,97) = -1.55812628714536832737557284815 gamma0(69,97) = -24.8085163837188084863609050931 gamma0(70,97) = -5.17839056718031412106356866731 gamma0(71,97) = -32.9079554242343234391833873611 gamma0(72,97) = -6.86193076297721121140847390665 gamma0(73,97) = -1.07544835397932758688069954485 gamma0(74,97) = -0.869414136290188286742525911436 gamma0(75,97) = -3.21421732783801124210663772946 gamma0(76,97) = -1.41915756410782399325605949360 gamma0(77,97) = -4.31937248653695745802603736575 gamma0(78,97) = -4.50754755318223732660080528218 gamma0(79,97) = -5.74353838692886615113528377274 gamma0(80,97) = -0.749781288406665589156702327896 gamma0(81,97) = -1.45253035544437324997315232513 gamma0(82,97) = -5.44670392613895919617456035747 gamma0(83,97) = -0.658814502713967082447617111716 gamma0(84,97) = -0.808050279941310202331582121412 gamma0(85,97) = -2.08905745926043278018219128430 gamma0(86,97) = -2.45139557921456072271197204743 gamma0(87,97) = -9.27005494679984399280668658826 gamma0(88,97) = -1.71345991314350293720244672578 gamma0(89,97) = -0.934186034721604341059438643136 gamma0(90,97) = -6.07390277142810695190923909039 gamma0(91,97) = -0.848597190841544569128789173354 gamma0(92,97) = -2.74936763736038948095659080723 gamma0(93,97) = -0.788297685025090744419881231404 gamma0(94,97) = -1.84285536502191173204742213260 gamma0(95,97) = -1.32396562702492511337729107850 gamma0(96,97) = -2.59361396317543726899608745093 gamma0(97,97) = -0.0412112918928025769227856652744 gamma1(1,97) = -0.0821246019980880587430243357511 gamma1(2,97) = 0.236962931312990474224068989172 gamma1(3,97) = 0.0314633530793441154815345629756 gamma1(4,97) = 0.0200553339705250086332537022875 gamma1(5,97) = -0.0191840874974478099901357196074 gamma1(6,97) = 0.0499701146132209395791734686549 gamma1(7,97) = 0.172985865507316852191437835482 gamma1(8,97) = -0.0129647606573618857304372244300 gamma1(9,97) = 0.213021337076351200103214066356 gamma1(10,97) = 0.0133383355789313546594044407968 gamma1(11,97) = -0.0364022237446012950958165092877 gamma1(12,97) = -0.0588943755953977736366996681116 gamma1(13,97) = -0.0510926909236799440363199082135 gamma1(14,97) = 0.0166178748091454043082365896043 gamma1(15,97) = -0.0283761611783068018435079940537 gamma1(16,97) = -0.0248565030039125332116916511159 gamma1(17,97) = -0.00363399626179674465774065605588 gamma1(18,97) = -0.0703161092720424305242865880479 gamma1(19,97) = 0.0236646205325397030573711458959 gamma1(20,97) = -0.00846350487262932495315963765429 gamma1(21,97) = -0.0784353180246756023525974997629 gamma1(22,97) = -0.0648715409511305700836762135272 gamma1(23,97) = -0.0791911040765044469164803452088 gamma1(24,97) = -0.0694416815866487863094248032341 gamma1(25,97) = 0.0449157741488884422938694820553 gamma1(26,97) = 0.107133311531821587442839358366 gamma1(27,97) = -0.0522698274141177201480707282267 gamma1(28,97) = 0.00157008838868265265180147867568 gamma1(29,97) = -0.0609523538163083454496022468982 gamma1(30,97) = -0.0619559494766472679007228873709 gamma1(31,97) = -0.0667407839536129108585131474804 gamma1(32,97) = 0.191708752574191647958191707351 gamma1(33,97) = -0.00108202089838430004284884881775 gamma1(34,97) = -0.0658133059328433979474394528120 gamma1(35,97) = 0.263736958048712187281561532962 gamma1(36,97) = 0.142003483064229563975384972755 gamma1(37,97) = -0.0317104567700127127983156306935 gamma1(38,97) = -0.0407661899551787468056824279517 gamma1(39,97) = -0.0728668230212458335012057082253 gamma1(40,97) = -0.0171764472909446982544763790237 gamma1(41,97) = 0.0812582189891615532881186036830 gamma1(42,97) = -0.0676544026257116432567402995740 gamma1(43,97) = 0.117537001347799734386542694736 gamma1(44,97) = -0.0461450943509096290044122453679 gamma1(45,97) = 0.156532916800550431751569403595 gamma1(46,97) = -0.0230209285944572444621896628852 gamma1(47,97) = 0.0102043198378850686824215706689 gamma1(48,97) = -0.0435140485995568318576421980340 gamma1(49,97) = -0.0806753438803596946018647545180 gamma1(50,97) = -0.0776701125757001517849428515393 gamma1(51,97) = -0.0599320170141252933335222220063 gamma1(52,97) = -0.0567647839871144609859146954147 gamma1(53,97) = -0.0378911028778503147281872031708 gamma1(54,97) = -0.0639150419563571186726231661932 gamma1(55,97) = -0.0753155090920303233140367689996 gamma1(56,97) = -0.0421553421251362750389557784558 gamma1(57,97) = -0.0768952453315976797045559931830 gamma1(58,97) = -0.0545584808388217050036888992444 gamma1(59,97) = -0.0211311441123754275035100828095 gamma1(60,97) = 0.0274613937480979100723829987036 gamma1(61,97) = 0.00432964780399025353767726806461 gamma1(62,97) = -0.0556715602725977659230968984367 gamma1(63,97) = -0.0300653206917615178680120223785 gamma1(64,97) = -0.0333136890608274601606050301319 gamma1(65,97) = -0.0474197407439970923350643280781 gamma1(66,97) = 0.0977080488332824776152482911021 gamma1(67,97) = -0.0578388382415327619213331413550 gamma1(68,97) = -0.0448435701718523615520077602014 gamma1(69,97) = 0.262337118830309472286248649391 gamma1(70,97) = 0.0553639025337690686341742463502 gamma1(71,97) = 0.282663570359107793563725144799 gamma1(72,97) = 0.0891213128249569610888455517796 gamma1(73,97) = -0.0629433412969404445197671097492 gamma1(74,97) = -0.0711782142233078619610902966183 gamma1(75,97) = 0.00720474016149298403920345102869 gamma1(76,97) = -0.0498925681255878916593420086197 gamma1(77,97) = 0.0356905856184546357240689961464 gamma1(78,97) = 0.0401659869656898139766537116960 gamma1(79,97) = 0.0673390599481148028954655159193 gamma1(80,97) = -0.0761104646327515798186789161466 gamma1(81,97) = -0.0486685659663461009258209877559 gamma1(82,97) = 0.0611377233161903501276988031809 gamma1(83,97) = -0.0799377043063800604096373791383 gamma1(84,97) = -0.0736939762983225639446583937652 gamma1(85,97) = -0.0266407034949962211535094564858 gamma1(86,97) = -0.0151046361152163834552889438796 gamma1(87,97) = 0.129090366163625417198305538623 gamma1(88,97) = -0.0393452521009567162723984983502 gamma1(89,97) = -0.0685545712024652987872503563341 gamma1(90,97) = 0.0740238118343742395632685112744 gamma1(91,97) = -0.0720283416988903337508356022646 gamma1(92,97) = -0.00609247735734575437089920470238 gamma1(93,97) = -0.0745101070998929267259070845320 gamma1(94,97) = -0.0348769954022006935896543834646 gamma1(95,97) = -0.0534248234480008368164432369419 gamma1(96,97) = -0.0107525876041193118722361031812 gamma1(97,97) = -0.0814042399455071522953484845370 ****** END PROGRAM ******** *******/