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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance portfol_classical050_1

Formats ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)
-0.09476012 p1 ( gdx sol )
(infeas: 8e-11)
Other points (infeas > 1e-08)  
Dual Bounds
-0.09808658 (ALPHAECP)
-0.09476634 (ANTIGONE)
-0.09476012 (BARON)
-0.09476120 (COUENNE)
-0.09476012 (CPLEX)
-0.09476231 (GUROBI)
-0.09476012 (LINDO)
-0.09476044 (SCIP)
-0.09476012 (SHOT)
References Vielma, Juan Pablo, Ahmed, S, and Nemhauser, G L, A Lifted Linear Programming Branch-and-Bound Algorithm for Mixed Integer Conic Quadratic Programs, INFORMS Journal on Computing, 20:3, 2008, 438-450.
Source Juan Pablo Vielma Portfolio Optimization Instances Testset
Application Portfolio Optimization
Added to library 01 Mar 2014
Problem type MBQCP
#Variables 150
#Binary Variables 50
#Integer Variables 0
#Nonlinear Variables 50
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 50
#Nonlinear Nonzeros in Objective 0
#Constraints 103
#Linear Constraints 102
#Quadratic Constraints 1
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature convex
#Nonzeros in Jacobian 2800
#Nonlinear Nonzeros in Jacobian 50
#Nonzeros in (Upper-Left) Hessian of Lagrangian 50
#Nonzeros in Diagonal of Hessian of Lagrangian 50
#Blocks in Hessian of Lagrangian 50
Minimal blocksize in Hessian of Lagrangian 1
Maximal blocksize in Hessian of Lagrangian 1
Average blocksize in Hessian of Lagrangian 1.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 6.6824e-05
Maximal coefficient 1.2522e+00
Infeasibility of initial point 1
Sparsity Jacobian Sparsity of Objective Gradient and Jacobian
Sparsity Hessian of Lagrangian Sparsity of Hessian of Lagrangian

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*        104       52        0       52        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*        151      101       50        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*       2851     2801       50        0
*
*  Solve m using MINLP minimizing objvar;


Variables  objvar,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18
          ,x19,x20,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34,x35
          ,x36,x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49,x50,x51,x52
          ,x53,x54,x55,x56,x57,x58,x59,x60,x61,x62,x63,x64,x65,x66,x67,x68,x69
          ,x70,x71,x72,x73,x74,x75,x76,x77,x78,x79,x80,x81,x82,x83,x84,x85,x86
          ,x87,x88,x89,x90,x91,x92,x93,x94,x95,x96,x97,x98,x99,x100,x101,b102
          ,b103,b104,b105,b106,b107,b108,b109,b110,b111,b112,b113,b114,b115
          ,b116,b117,b118,b119,b120,b121,b122,b123,b124,b125,b126,b127,b128
          ,b129,b130,b131,b132,b133,b134,b135,b136,b137,b138,b139,b140,b141
          ,b142,b143,b144,b145,b146,b147,b148,b149,b150,b151;

Positive Variables  x52,x53,x54,x55,x56,x57,x58,x59,x60,x61,x62,x63,x64,x65
          ,x66,x67,x68,x69,x70,x71,x72,x73,x74,x75,x76,x77,x78,x79,x80,x81,x82
          ,x83,x84,x85,x86,x87,x88,x89,x90,x91,x92,x93,x94,x95,x96,x97,x98,x99
          ,x100,x101;

Binary Variables  b102,b103,b104,b105,b106,b107,b108,b109,b110,b111,b112,b113
          ,b114,b115,b116,b117,b118,b119,b120,b121,b122,b123,b124,b125,b126
          ,b127,b128,b129,b130,b131,b132,b133,b134,b135,b136,b137,b138,b139
          ,b140,b141,b142,b143,b144,b145,b146,b147,b148,b149,b150,b151;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16,e17,e18,e19
          ,e20,e21,e22,e23,e24,e25,e26,e27,e28,e29,e30,e31,e32,e33,e34,e35,e36
          ,e37,e38,e39,e40,e41,e42,e43,e44,e45,e46,e47,e48,e49,e50,e51,e52,e53
          ,e54,e55,e56,e57,e58,e59,e60,e61,e62,e63,e64,e65,e66,e67,e68,e69,e70
          ,e71,e72,e73,e74,e75,e76,e77,e78,e79,e80,e81,e82,e83,e84,e85,e86,e87
          ,e88,e89,e90,e91,e92,e93,e94,e95,e96,e97,e98,e99,e100,e101,e102,e103
          ,e104;


e1..  - objvar - 0.0399775*x52 - 0.0629738*x53 - 0.027838*x54 - 0.00361039*x55
      - 0.0761837*x56 - 0.135299*x57 - 0.0122123*x58 - 0.0399709*x59
      - 0.0256571*x60 - 0.0991766*x61 - 0.0210495*x62 - 0.044223*x63
      - 0.0128715*x64 - 0.00399952*x65 - 0.0501755*x66 - 0.149247*x67
      - 0.0613428*x68 - 0.041802*x69 - 0.0754226*x70 - 0.0434943*x71
      - 0.10135*x72 - 0.15397*x73 - 0.0576577*x74 - 0.0340755*x75
      - 0.0426673*x76 - 0.0298566*x77 - 0.0952893*x78 - 0.169485*x79
      - 0.0440279*x80 - 0.0470473*x81 - 0.00699576*x82 - 0.127417*x83
      - 0.126305*x84 - 0.0486665*x85 - 0.153319*x86 - 0.0202574*x87
      - 0.0272516*x88 - 0.0695536*x89 - 0.030744*x90 - 0.0325349*x91
      - 0.0163484*x92 - 0.0753619*x93 - 0.0271795*x94 - 0.0113752*x95
      - 0.0394797*x96 - 0.123927*x97 - 0.00514876*x98 - 0.0380825*x99
      - 0.142836*x100 - 0.0540865*x101 =E= 0;

e2.. x2*x2 + x3*x3 + x4*x4 + x5*x5 + x6*x6 + x7*x7 + x8*x8 + x9*x9 + x10*x10 + 
     x11*x11 + x12*x12 + x13*x13 + x14*x14 + x15*x15 + x16*x16 + x17*x17 + x18*
     x18 + x19*x19 + x20*x20 + x21*x21 + x22*x22 + x23*x23 + x24*x24 + x25*x25
      + x26*x26 + x27*x27 + x28*x28 + x29*x29 + x30*x30 + x31*x31 + x32*x32 + 
     x33*x33 + x34*x34 + x35*x35 + x36*x36 + x37*x37 + x38*x38 + x39*x39 + x40*
     x40 + x41*x41 + x42*x42 + x43*x43 + x44*x44 + x45*x45 + x46*x46 + x47*x47
      + x48*x48 + x49*x49 + x50*x50 + x51*x51 =L= 0.04;

e3..    x52 - b102 =L= 0;

e4..    x53 - b103 =L= 0;

e5..    x54 - b104 =L= 0;

e6..    x55 - b105 =L= 0;

e7..    x56 - b106 =L= 0;

e8..    x57 - b107 =L= 0;

e9..    x58 - b108 =L= 0;

e10..    x59 - b109 =L= 0;

e11..    x60 - b110 =L= 0;

e12..    x61 - b111 =L= 0;

e13..    x62 - b112 =L= 0;

e14..    x63 - b113 =L= 0;

e15..    x64 - b114 =L= 0;

e16..    x65 - b115 =L= 0;

e17..    x66 - b116 =L= 0;

e18..    x67 - b117 =L= 0;

e19..    x68 - b118 =L= 0;

e20..    x69 - b119 =L= 0;

e21..    x70 - b120 =L= 0;

e22..    x71 - b121 =L= 0;

e23..    x72 - b122 =L= 0;

e24..    x73 - b123 =L= 0;

e25..    x74 - b124 =L= 0;

e26..    x75 - b125 =L= 0;

e27..    x76 - b126 =L= 0;

e28..    x77 - b127 =L= 0;

e29..    x78 - b128 =L= 0;

e30..    x79 - b129 =L= 0;

e31..    x80 - b130 =L= 0;

e32..    x81 - b131 =L= 0;

e33..    x82 - b132 =L= 0;

e34..    x83 - b133 =L= 0;

e35..    x84 - b134 =L= 0;

e36..    x85 - b135 =L= 0;

e37..    x86 - b136 =L= 0;

e38..    x87 - b137 =L= 0;

e39..    x88 - b138 =L= 0;

e40..    x89 - b139 =L= 0;

e41..    x90 - b140 =L= 0;

e42..    x91 - b141 =L= 0;

e43..    x92 - b142 =L= 0;

e44..    x93 - b143 =L= 0;

e45..    x94 - b144 =L= 0;

e46..    x95 - b145 =L= 0;

e47..    x96 - b146 =L= 0;

e48..    x97 - b147 =L= 0;

e49..    x98 - b148 =L= 0;

e50..    x99 - b149 =L= 0;

e51..    x100 - b150 =L= 0;

e52..    x101 - b151 =L= 0;

e53..    x52 + x53 + x54 + x55 + x56 + x57 + x58 + x59 + x60 + x61 + x62 + x63
       + x64 + x65 + x66 + x67 + x68 + x69 + x70 + x71 + x72 + x73 + x74 + x75
       + x76 + x77 + x78 + x79 + x80 + x81 + x82 + x83 + x84 + x85 + x86 + x87
       + x88 + x89 + x90 + x91 + x92 + x93 + x94 + x95 + x96 + x97 + x98 + x99
       + x100 + x101 =E= 1;

e54..    b102 + b103 + b104 + b105 + b106 + b107 + b108 + b109 + b110 + b111
       + b112 + b113 + b114 + b115 + b116 + b117 + b118 + b119 + b120 + b121
       + b122 + b123 + b124 + b125 + b126 + b127 + b128 + b129 + b130 + b131
       + b132 + b133 + b134 + b135 + b136 + b137 + b138 + b139 + b140 + b141
       + b142 + b143 + b144 + b145 + b146 + b147 + b148 + b149 + b150 + b151
       =L= 10;

e55..  - x2 + 0.437623*x52 + 0.00776152*x53 + 0.00831088*x54 - 0.00522971*x55
       + 0.015015*x56 - 0.0107741*x57 - 0.00662896*x58 - 0.00824877*x59
       + 0.00953726*x60 - 0.0162102*x61 + 0.06876*x62 + 0.0307553*x63
       + 0.00493869*x64 + 0.00905031*x65 + 0.00428006*x66 + 0.0159505*x67
       + 0.0372772*x68 + 0.00356282*x69 + 0.0102555*x70 - 0.0161653*x71
       - 0.00678775*x72 - 0.000991393*x73 + 0.0104307*x74 - 0.00554627*x75
       + 0.000275614*x76 + 0.00146767*x77 - 0.0219202*x78 - 0.0152471*x79
       - 0.0133041*x80 + 0.00532027*x81 + 0.0190296*x82 + 9.52152E-5*x83
       - 0.0180784*x84 + 0.00127079*x85 - 0.00331643*x86 - 0.0107273*x87
       - 6.72321E-5*x88 + 0.0019753*x89 - 0.00561942*x90 - 0.0137411*x91
       + 0.0266953*x92 + 0.0039322*x93 + 0.0312023*x94 + 0.00475029*x95
       + 0.00458043*x96 - 0.0111713*x97 + 0.00233202*x98 + 0.00279105*x99
       + 0.00588268*x100 + 0.0171354*x101 =E= 0;

e56..  - x3 + 0.00776152*x52 + 0.305432*x53 + 0.0022503*x54 + 0.0131826*x55
       + 0.013322*x56 + 0.0622902*x57 + 0.00612167*x58 + 0.00797614*x59
       + 0.00886071*x60 - 0.0285042*x61 + 0.003025*x62 + 0.0159085*x63
       - 0.00357187*x64 + 0.0016128*x65 + 0.012642*x66 + 0.119815*x67
       + 0.00505566*x68 + 0.0131274*x69 + 0.00269972*x70 + 0.00899326*x71
       + 0.0193615*x72 + 0.114117*x73 + 0.0118212*x74 + 0.00695719*x75
       - 0.00146012*x76 - 0.00455327*x77 - 0.00233478*x78 - 0.00354018*x79
       - 0.0108257*x80 + 0.00548427*x81 + 0.00843954*x82 + 0.0957415*x83
       + 0.0724208*x84 + 0.00920314*x85 - 0.00921773*x86 + 0.0112775*x87
       + 0.010577*x88 - 0.00268772*x89 + 0.0104329*x90 - 0.00184253*x91
       + 0.0230614*x92 + 0.0797692*x93 - 0.00718849*x94 + 0.00668562*x95
       - 0.00479877*x96 + 0.037467*x97 - 0.000833339*x98 - 0.00287641*x99
       - 0.00540049*x100 + 0.0133618*x101 =E= 0;

e57..  - x4 + 0.00831088*x52 + 0.0022503*x53 + 0.179315*x54 + 0.0238256*x55
       - 0.00566425*x56 - 0.0137602*x57 + 0.00878864*x58 + 0.0166554*x59
       + 0.0152274*x60 - 0.0193213*x61 + 0.0171146*x62 + 0.0117301*x63
       + 0.0108599*x64 + 0.011655*x65 - 0.00502711*x66 + 0.011192*x67
       + 0.0247138*x68 + 0.00188025*x69 + 0.00635281*x70 + 0.0217042*x71
       + 0.0189843*x72 - 0.00893642*x73 + 0.020493*x74 + 0.0060982*x75
       + 0.00709161*x76 + 0.0192029*x77 + 0.00489188*x78 + 0.0141398*x79
       + 0.0183881*x80 + 0.0132555*x81 + 0.0089825*x82 - 0.00433095*x83
       + 0.000368443*x84 + 0.00845006*x85 + 0.0106863*x86 + 0.0165343*x87
       + 0.0182906*x88 + 0.000474699*x89 + 0.0125524*x90 + 0.00998269*x91
       + 0.00663781*x92 - 0.00941355*x93 + 0.0166904*x94 + 0.00602889*x95
       + 0.00224387*x96 - 0.00806098*x97 + 0.0151626*x98 - 0.000965771*x99
       + 0.0157379*x100 + 0.0187837*x101 =E= 0;

e58..  - x5 - 0.00522971*x52 + 0.0131826*x53 + 0.0238256*x54 + 0.220297*x55
       + 0.0243861*x56 - 0.00430317*x57 + 0.0174604*x58 + 0.00681665*x59
       + 0.0242063*x60 + 0.00144938*x61 + 0.015222*x62 + 0.014716*x63
       + 0.00177302*x64 + 0.0176392*x65 + 0.021276*x66 + 0.00889693*x67
       + 0.00407666*x68 + 0.00949954*x69 + 0.00937267*x70 + 0.0242093*x71
       + 0.00460206*x72 - 0.00745268*x73 + 0.0160821*x74 + 0.00240536*x75
       + 0.0042418*x76 + 0.00264811*x77 + 0.00832847*x78 + 0.0040175*x79
       + 0.0153818*x80 + 0.0182359*x81 + 0.00961571*x82 + 0.0122098*x83
       - 0.000558226*x84 + 0.0179991*x85 + 0.0126379*x86 + 0.0175827*x87
       + 0.00566779*x88 - 0.000955585*x89 + 0.0234718*x90 - 0.00128625*x91
       + 0.00397589*x92 + 0.00253364*x93 + 0.0161477*x94 + 0.0163612*x95
       + 0.012804*x96 + 0.0254602*x97 + 0.0164285*x98 + 0.0113336*x99
       + 0.00992279*x100 + 0.00909239*x101 =E= 0;

e59..  - x6 + 0.015015*x52 + 0.013322*x53 - 0.00566425*x54 + 0.0243861*x55
       + 0.404084*x56 + 0.058688*x57 + 0.0144003*x58 + 0.0371145*x59
       + 0.0227472*x60 + 0.0120821*x61 + 0.00730434*x62 + 0.0238735*x63
       + 0.00933373*x64 + 0.0051169*x65 + 0.0488881*x66 + 0.0227134*x67
       + 0.00590284*x68 + 0.0335068*x69 + 0.0167733*x70 + 0.044455*x71
       + 0.069787*x72 + 0.040347*x73 + 0.039664*x74 + 0.0102778*x75
       + 0.0172657*x76 + 0.00473961*x77 + 0.0132399*x78 - 0.0118559*x79
       + 0.0329745*x80 + 0.00776731*x81 + 0.00146596*x82 + 0.0398038*x83
       + 0.0268424*x84 + 0.0120171*x85 + 0.0145295*x86 + 0.0354297*x87
       - 0.00170776*x88 + 0.0255113*x89 + 0.0115797*x90 + 0.0340249*x91
       + 0.00175196*x92 + 0.0214384*x93 + 0.0113414*x94 + 0.039091*x95
       + 0.00619763*x96 + 0.0133319*x97 + 0.0121082*x98 + 0.0357203*x99
       + 0.0381607*x100 + 0.0203578*x101 =E= 0;

e60..  - x7 - 0.0107741*x52 + 0.0622902*x53 - 0.0137602*x54 - 0.00430317*x55
       + 0.058688*x56 + 0.452644*x57 + 0.0193845*x58 + 0.0341649*x59
       + 0.00602161*x60 + 0.0583255*x61 - 0.00423459*x62 + 0.016241*x63
       + 0.0157118*x64 - 0.00370551*x65 + 0.0511023*x66 + 0.148921*x67
       + 0.0156037*x68 + 0.0155171*x69 + 0.0112086*x70 + 0.030702*x71
       + 0.0216234*x72 + 0.105953*x73 + 0.0128583*x74 + 0.00399753*x75
       + 0.0184167*x76 + 0.010492*x77 + 0.0244629*x78 + 0.047228*x79
       + 0.00547127*x80 + 0.0133769*x81 + 0.0119332*x82 + 0.161483*x83
       + 0.187982*x84 + 0.00916881*x85 + 0.0209491*x86 + 0.0327261*x87
       + 0.028455*x88 + 0.0105724*x89 + 0.0238296*x90 - 0.00223337*x91
       + 0.0230382*x92 + 0.112083*x93 + 0.00257709*x94 - 0.0088657*x95
       + 0.0101284*x96 + 0.0087194*x97 + 0.016345*x98 + 0.0145296*x99
       + 0.00606395*x100 + 0.00747571*x101 =E= 0;

e61..  - x8 - 0.00662896*x52 + 0.00612167*x53 + 0.00878864*x54 + 0.0174604*x55
       + 0.0144003*x56 + 0.0193845*x57 + 0.28381*x58 + 0.0129912*x59
       + 0.00711013*x60 + 0.023726*x61 + 0.0135222*x62 + 0.00245137*x63
       + 0.0139941*x64 + 0.0146659*x65 - 0.000316803*x66 + 0.0195659*x67
       + 0.0130298*x68 + 0.0143949*x69 - 0.0152357*x70 + 0.0229109*x71
       + 0.0178969*x72 + 0.00747729*x73 + 0.0262*x74 + 0.0176229*x75
       + 0.0184672*x76 + 0.00333289*x77 + 0.0125282*x78 + 0.0160426*x79
       - 0.00910903*x80 + 0.0168617*x81 + 0.00649361*x82 + 0.000720061*x83
       + 0.0015496*x84 + 0.0120757*x85 + 0.0231367*x86 + 0.0160891*x87
       + 0.000127307*x88 + 0.00590674*x89 + 0.0251974*x90 + 0.0109883*x91
       + 0.0197048*x92 + 0.00281047*x93 + 0.0113665*x94 + 0.0128475*x95
       + 0.00622782*x96 + 0.0245605*x97 + 0.00706149*x98 + 0.00272192*x99
       + 0.00300911*x100 + 0.0133916*x101 =E= 0;

e62..  - x9 - 0.00824877*x52 + 0.00797614*x53 + 0.0166554*x54 + 0.00681665*x55
       + 0.0371145*x56 + 0.0341649*x57 + 0.0129912*x58 + 0.189607*x59
       + 0.0210316*x60 + 0.00633527*x61 + 0.00869335*x62 + 0.031581*x63
       - 0.00230763*x64 + 0.00682721*x65 + 0.0158862*x66 + 0.016982*x67
       + 0.0111502*x68 + 0.0375819*x69 + 0.0223572*x70 + 0.0434772*x71
       + 0.0304477*x72 + 0.00554913*x73 + 0.0268377*x74 + 0.00229807*x75
       + 0.01809*x76 + 0.0114054*x77 + 0.0148192*x78 + 0.0286969*x79
       + 0.0156643*x80 + 0.0214673*x81 + 0.00423722*x82 + 0.0101393*x83
       + 0.00438509*x84 + 0.0186319*x85 + 0.046181*x86 + 0.0332107*x87
       + 0.0160758*x88 + 0.00541803*x89 + 0.0243196*x90 + 0.0145438*x91
       + 0.00473001*x92 + 0.00681241*x93 + 0.00988793*x94 + 0.0149668*x95
       + 0.023562*x96 + 0.0173729*x97 + 0.016267*x98 + 0.0121424*x99
       - 0.00299957*x100 + 0.00907044*x101 =E= 0;

e63..  - x10 + 0.00953726*x52 + 0.00886071*x53 + 0.0152274*x54 + 0.0242063*x55
       + 0.0227472*x56 + 0.00602161*x57 + 0.00711013*x58 + 0.0210316*x59
       + 0.186866*x60 + 0.00832283*x61 + 0.0180258*x62 + 0.0154265*x63
       + 0.0114402*x64 + 0.0209618*x65 + 0.0173064*x66 - 0.000705565*x67
       + 0.0143527*x68 + 0.0248206*x69 + 0.0181781*x70 + 0.0279005*x71
       + 0.0285813*x72 + 0.00289351*x73 + 0.0153119*x74 + 0.00890117*x75
       + 0.0222796*x76 + 0.0442301*x77 + 0.0119004*x78 + 0.00720201*x79
       + 0.0201433*x80 + 0.0169933*x81 + 0.019457*x82 + 0.0111733*x83
       + 0.00689119*x84 + 0.00669496*x85 + 0.0331297*x86 + 0.0197397*x87
       + 0.0120744*x88 + 0.0127905*x89 + 0.0406861*x90 + 0.0323148*x91
       + 0.0200869*x92 + 0.00172542*x93 + 0.0311244*x94 + 0.00519737*x95
       + 0.0142684*x96 + 0.0178041*x97 + 0.00992985*x98 + 0.0146222*x99
       + 0.00920343*x100 + 0.0199828*x101 =E= 0;

e64..  - x11 - 0.0162102*x52 - 0.0285042*x53 - 0.0193213*x54 + 0.00144938*x55
       + 0.0120821*x56 + 0.0583255*x57 + 0.023726*x58 + 0.00633527*x59
       + 0.00832283*x60 + 0.63428*x61 - 0.00280448*x62 - 0.00545788*x63
       - 0.00396523*x64 - 0.0183861*x65 + 0.0180971*x66 + 0.00513145*x67
       + 0.00613144*x68 - 0.0110514*x69 + 0.0194917*x70 + 0.00495793*x71
       + 0.0244718*x72 + 0.00915034*x73 - 0.000197643*x74 - 0.00657968*x75
       - 0.00738206*x76 + 0.0105229*x77 - 0.0124412*x78 - 0.00440667*x79
       + 0.0123441*x80 + 0.00670955*x81 + 0.000975768*x82 + 0.0409171*x83
       - 0.0110323*x84 - 0.00482281*x85 - 0.00546107*x86 - 0.0142879*x87
       + 0.018699*x88 + 0.0440906*x89 - 0.00363253*x90 + 0.00273765*x91
       + 0.00673168*x92 + 0.0033605*x93 + 0.0241296*x94 - 0.00441557*x95
       - 0.00703875*x96 + 0.016325*x97 + 0.00222896*x98 - 0.0077883*x99
       - 0.00313691*x100 + 0.0264584*x101 =E= 0;

e65..  - x12 + 0.06876*x52 + 0.003025*x53 + 0.0171146*x54 + 0.015222*x55
       + 0.00730434*x56 - 0.00423459*x57 + 0.0135222*x58 + 0.00869335*x59
       + 0.0180258*x60 - 0.00280448*x61 + 0.316413*x62 + 0.0323352*x63
       - 0.00236891*x64 + 0.00787061*x65 + 0.0149546*x66 + 0.0036316*x67
       - 0.0116267*x68 + 0.032345*x69 - 0.000144027*x70 - 0.00218381*x71
       + 0.00530167*x72 + 0.000497945*x73 + 0.0156557*x74 + 0.0127479*x75
       + 0.0111445*x76 + 0.0085222*x77 - 0.00157042*x78 + 0.00905753*x79
       - 0.00402737*x80 + 0.00937755*x81 + 0.00827346*x82 + 0.00543371*x83
       + 0.0230998*x84 + 0.0238731*x85 + 0.0199311*x86 + 0.0174054*x87
       + 0.00185204*x88 + 0.0156839*x89 + 0.00443354*x90 + 0.0202129*x91
       + 0.0114171*x92 + 0.00122747*x93 + 0.0118384*x94 + 0.0228483*x95
       + 0.0131884*x96 - 0.0151598*x97 + 0.00844519*x98 + 0.0198609*x99
       + 0.0242712*x100 + 0.0138048*x101 =E= 0;

e66..  - x13 + 0.0307553*x52 + 0.0159085*x53 + 0.0117301*x54 + 0.014716*x55
       + 0.0238735*x56 + 0.016241*x57 + 0.00245137*x58 + 0.031581*x59
       + 0.0154265*x60 - 0.00545788*x61 + 0.0323352*x62 + 0.187022*x63
       + 0.00222855*x64 + 0.00747903*x65 + 0.0223879*x66 + 0.0408618*x67
       + 0.00998685*x68 + 0.0255*x69 + 0.0234902*x70 + 0.0410056*x71
       + 0.0457515*x72 + 0.0404933*x73 + 0.0173727*x74 + 0.0186957*x75
       + 0.0206278*x76 + 0.0197312*x77 + 0.0258626*x78 + 0.0281149*x79
       + 0.020796*x80 + 0.0154147*x81 + 0.00821687*x82 + 0.0277493*x83
       + 0.0231334*x84 + 0.0242186*x85 + 0.0562299*x86 + 0.0315629*x87
       + 0.0122553*x88 + 0.0146058*x89 + 0.0225422*x90 + 0.0126094*x91
       + 0.0195556*x92 + 0.0148528*x93 + 0.016949*x94 + 0.0309886*x95
       + 0.0111695*x96 + 0.023004*x97 + 0.00865625*x98 + 0.0218181*x99
       + 0.0268327*x100 + 0.0203605*x101 =E= 0;

e67..  - x14 + 0.00493869*x52 - 0.00357187*x53 + 0.0108599*x54 + 0.00177302*x55
       + 0.00933373*x56 + 0.0157118*x57 + 0.0139941*x58 - 0.00230763*x59
       + 0.0114402*x60 - 0.00396523*x61 - 0.00236891*x62 + 0.00222855*x63
       + 0.221194*x64 + 0.0104987*x65 + 0.0399316*x66 - 0.000811365*x67
       + 0.00762929*x68 - 0.0044099*x69 + 0.0198057*x70 + 0.00234582*x71
       - 0.0069834*x72 + 0.00152018*x73 - 0.00484524*x74 + 0.0034154*x75
       - 0.0060451*x76 + 0.0102102*x77 + 0.019147*x78 + 0.00861968*x79
       - 0.0013634*x80 + 0.00686903*x81 + 0.0133687*x82 + 0.00136495*x83
       + 0.00888952*x84 + 0.00809492*x85 + 0.00573295*x86 + 0.00828577*x87
       + 0.0152408*x88 + 0.0110413*x89 + 0.0069969*x90 + 0.0053944*x91
       + 0.0104813*x92 - 0.00694263*x93 + 0.0141714*x94 - 0.00184581*x95
       + 0.0147295*x96 - 0.00369236*x97 + 0.00526228*x98 + 0.00828497*x99
       - 0.0189632*x100 + 0.0101028*x101 =E= 0;

e68..  - x15 + 0.00905031*x52 + 0.0016128*x53 + 0.011655*x54 + 0.0176392*x55
       + 0.0051169*x56 - 0.00370551*x57 + 0.0146659*x58 + 0.00682721*x59
       + 0.0209618*x60 - 0.0183861*x61 + 0.00787061*x62 + 0.00747903*x63
       + 0.0104987*x64 + 0.172607*x65 + 0.010781*x66 + 0.0114342*x67
       + 0.00907137*x68 + 0.0104462*x69 + 0.0151955*x70 + 0.00458498*x71
       + 0.0183508*x72 - 0.0158535*x73 + 0.0070277*x74 + 0.00809957*x75
       + 0.0120566*x76 + 0.0156797*x77 + 0.019146*x78 + 0.0230557*x79
       + 0.00625971*x80 + 0.0154784*x81 + 0.0113709*x82 - 0.00207874*x83
       - 0.00747722*x84 + 0.00726553*x85 + 0.037832*x86 + 0.0123555*x87
       - 0.000156492*x88 + 0.0119264*x89 + 0.0124128*x90 + 0.0206051*x91
       + 0.0182519*x92 - 0.0063393*x93 + 0.0162264*x94 + 0.0114734*x95
       + 0.0298746*x96 + 0.00393739*x97 + 0.0153743*x98 + 0.00989917*x99
       + 0.0228823*x100 + 0.017772*x101 =E= 0;

e69..  - x16 + 0.00428006*x52 + 0.012642*x53 - 0.00502711*x54 + 0.021276*x55
       + 0.0488881*x56 + 0.0511023*x57 - 0.000316803*x58 + 0.0158862*x59
       + 0.0173064*x60 + 0.0180971*x61 + 0.0149546*x62 + 0.0223879*x63
       + 0.0399316*x64 + 0.010781*x65 + 0.30953*x66 + 0.0123346*x67
       - 0.00454343*x68 + 0.00554417*x69 + 0.0322368*x70 + 0.0122026*x71
       + 0.0154661*x72 + 0.0109601*x73 + 0.0128077*x74 + 0.00710322*x75
       + 0.0100525*x76 + 0.0141544*x77 - 0.00302889*x78 + 0.0202446*x79
       + 0.0273331*x80 + 0.0142628*x81 + 0.0130754*x82 + 0.00886564*x83
       + 0.0125267*x84 + 0.00167144*x85 + 0.0368131*x86 + 0.0135909*x87
       - 0.000550234*x88 + 0.0369853*x89 + 0.00970355*x90 + 0.0253109*x91
       + 0.01371*x92 + 0.0151066*x93 + 0.0201164*x94 + 0.0193544*x95
       + 0.0166079*x96 + 0.0113423*x97 + 0.0488179*x98 + 0.016393*x99
       - 0.00100315*x100 + 0.0101386*x101 =E= 0;

e70..  - x17 + 0.0159505*x52 + 0.119815*x53 + 0.011192*x54 + 0.00889693*x55
       + 0.0227134*x56 + 0.148921*x57 + 0.0195659*x58 + 0.016982*x59
       - 0.000705565*x60 + 0.00513145*x61 + 0.0036316*x62 + 0.0408618*x63
       - 0.000811365*x64 + 0.0114342*x65 + 0.0123346*x66 + 0.506241*x67
       + 0.025301*x68 + 0.0356088*x69 + 0.0108864*x70 + 0.0190276*x71
       + 0.0288312*x72 + 0.12559*x73 + 0.0213959*x74 + 0.0275661*x75
       + 0.0260354*x76 + 0.00490195*x77 - 8.95127E-5*x78 + 0.0278101*x79
       + 0.0154943*x80 + 0.0110009*x81 + 0.0209885*x82 + 0.129895*x83
       + 0.104593*x84 + 0.0164835*x85 + 0.0238469*x86 + 0.0319592*x87
       + 0.016159*x88 - 0.00048612*x89 + 0.0206697*x90 - 0.0044719*x91
       + 0.0412523*x92 + 0.150222*x93 + 0.0060731*x94 + 0.00469106*x95
       + 0.032667*x96 + 0.00513266*x97 + 0.00884207*x98 + 0.0125003*x99
       - 0.00578404*x100 + 0.0225237*x101 =E= 0;

e71..  - x18 + 0.0372772*x52 + 0.00505566*x53 + 0.0247138*x54 + 0.00407666*x55
       + 0.00590284*x56 + 0.0156037*x57 + 0.0130298*x58 + 0.0111502*x59
       + 0.0143527*x60 + 0.00613144*x61 - 0.0116267*x62 + 0.00998685*x63
       + 0.00762929*x64 + 0.00907137*x65 - 0.00454343*x66 + 0.025301*x67
       + 0.272867*x68 + 0.013367*x69 + 0.0153675*x70 + 0.0202051*x71
       + 0.0334085*x72 + 0.0195246*x73 + 0.0119803*x74 + 0.0131243*x75
       + 0.009587*x76 + 0.00326145*x77 + 0.0055836*x78 + 0.0160137*x79
       - 0.00700837*x80 + 0.00816694*x81 + 0.0133907*x82 + 0.00598212*x83
       - 0.00201041*x84 + 0.0153712*x85 + 0.00839091*x86 + 0.00597115*x87
       - 0.000508298*x88 - 0.00265155*x89 + 0.0148232*x90 - 0.000660928*x91
       + 0.0219128*x92 + 0.0200429*x93 + 0.00803816*x94 + 0.0174527*x95
       + 0.00328568*x96 + 0.00580133*x97 - 0.000537323*x98 + 0.0127107*x99
       + 0.0134156*x100 + 0.00882735*x101 =E= 0;

e72..  - x19 + 0.00356282*x52 + 0.0131274*x53 + 0.00188025*x54 + 0.00949954*x55
       + 0.0335068*x56 + 0.0155171*x57 + 0.0143949*x58 + 0.0375819*x59
       + 0.0248206*x60 - 0.0110514*x61 + 0.032345*x62 + 0.0255*x63
       - 0.0044099*x64 + 0.0104462*x65 + 0.00554417*x66 + 0.0356088*x67
       + 0.013367*x68 + 0.243112*x69 + 0.00434594*x70 + 0.057792*x71
       + 0.0294945*x72 + 0.030868*x73 + 0.0219596*x74 + 0.00928365*x75
       + 0.0279232*x76 + 0.0138525*x77 + 0.0582128*x78 + 0.0225874*x79
       + 0.0216165*x80 + 0.0188341*x81 + 0.0113276*x82 + 0.0272881*x83
       + 0.0118425*x84 + 0.0244022*x85 + 0.0305204*x86 + 0.0378227*x87
       + 0.00150342*x88 + 0.000336096*x89 + 0.0330899*x90 + 0.0189859*x91
       + 0.0161305*x92 + 0.00657093*x93 + 0.0118269*x94 + 0.0262376*x95
       + 0.0229703*x96 + 0.0245122*x97 + 0.00497315*x98 + 0.0222552*x99
       + 0.00180371*x100 + 0.00323067*x101 =E= 0;

e73..  - x20 + 0.0102555*x52 + 0.00269972*x53 + 0.00635281*x54 + 0.00937267*x55
       + 0.0167733*x56 + 0.0112086*x57 - 0.0152357*x58 + 0.0223572*x59
       + 0.0181781*x60 + 0.0194917*x61 - 0.000144027*x62 + 0.0234902*x63
       + 0.0198057*x64 + 0.0151955*x65 + 0.0322368*x66 + 0.0108864*x67
       + 0.0153675*x68 + 0.00434594*x69 + 0.486402*x70 + 0.0205735*x71
       + 0.0176842*x72 + 0.016224*x73 + 0.029091*x74 + 0.0174387*x75
       + 0.0237535*x76 + 0.0139083*x77 + 0.0112918*x78 + 0.0315031*x79
       + 0.0104372*x80 + 0.0253639*x81 + 0.00237959*x82 - 0.00567431*x83
       + 0.0125939*x84 + 0.0195843*x85 + 0.0768331*x86 + 0.0267106*x87
       + 0.00312045*x88 + 0.00720686*x89 + 0.0261195*x90 + 0.0295481*x91
       - 0.00121588*x92 + 0.00174197*x93 + 0.000971523*x94 + 0.016521*x95
       + 0.0242338*x96 + 0.0387835*x97 + 0.0249114*x98 + 0.0106646*x99
       - 0.0157855*x100 + 0.0165385*x101 =E= 0;

e74..  - x21 - 0.0161653*x52 + 0.00899326*x53 + 0.0217042*x54 + 0.0242093*x55
       + 0.044455*x56 + 0.030702*x57 + 0.0229109*x58 + 0.0434772*x59
       + 0.0279005*x60 + 0.00495793*x61 - 0.00218381*x62 + 0.0410056*x63
       + 0.00234582*x64 + 0.00458498*x65 + 0.0122026*x66 + 0.0190276*x67
       + 0.0202051*x68 + 0.057792*x69 + 0.0205735*x70 + 0.30309*x71
       + 0.0477266*x72 + 0.0307124*x73 + 0.0320937*x74 + 0.00895684*x75
       + 0.0261585*x76 + 0.0224334*x77 + 0.0281506*x78 + 0.0324489*x79
       + 0.0266137*x80 + 0.0183526*x81 - 0.0016676*x82 + 0.0194921*x83
       + 0.0366494*x84 + 0.0166731*x85 + 0.0415684*x86 + 0.0425512*x87
       + 0.0185632*x88 + 0.0150068*x89 + 0.0206301*x90 + 0.00808519*x91
       - 0.00805047*x92 + 0.0108192*x93 + 0.01367*x94 + 0.0348135*x95
       + 0.0320515*x96 + 0.0132639*x97 - 0.00327629*x98 + 0.0267494*x99
       + 0.0178498*x100 + 0.0295494*x101 =E= 0;

e75..  - x22 - 0.00678775*x52 + 0.0193615*x53 + 0.0189843*x54 + 0.00460206*x55
       + 0.069787*x56 + 0.0216234*x57 + 0.0178969*x58 + 0.0304477*x59
       + 0.0285813*x60 + 0.0244718*x61 + 0.00530167*x62 + 0.0457515*x63
       - 0.0069834*x64 + 0.0183508*x65 + 0.0154661*x66 + 0.0288312*x67
       + 0.0334085*x68 + 0.0294945*x69 + 0.0176842*x70 + 0.0477266*x71
       + 0.574196*x72 + 0.0396485*x73 + 0.0302363*x74 + 0.0130538*x75
       + 0.02932*x76 + 0.0266188*x77 + 0.0279647*x78 + 0.0180419*x79
       + 0.0293269*x80 + 0.02223*x81 + 0.00413185*x82 + 0.0241439*x83
       + 0.0263683*x84 - 0.0132754*x85 + 0.0388595*x86 + 0.0578838*x87
       + 0.00722557*x88 + 0.0210916*x89 + 0.0335768*x90 - 0.00914657*x91
       + 0.0153621*x92 + 0.0170669*x93 + 0.00771841*x94 + 0.0161467*x95
       + 0.0470226*x96 + 0.0696792*x97 + 0.00688465*x98 + 0.0406248*x99
       - 0.00265226*x100 + 0.0216914*x101 =E= 0;

e76..  - x23 - 0.000991393*x52 + 0.114117*x53 - 0.00893642*x54 - 0.00745268*x55
       + 0.040347*x56 + 0.105953*x57 + 0.00747729*x58 + 0.00554913*x59
       + 0.00289351*x60 + 0.00915034*x61 + 0.000497945*x62 + 0.0404933*x63
       + 0.00152018*x64 - 0.0158535*x65 + 0.0109601*x66 + 0.12559*x67
       + 0.0195246*x68 + 0.030868*x69 + 0.016224*x70 + 0.0307124*x71
       + 0.0396485*x72 + 0.567664*x73 + 0.0167088*x74 + 0.00851376*x75
       + 0.0194063*x76 - 0.00258911*x77 + 0.000352563*x78 + 0.0170447*x79
       + 0.00326757*x80 + 0.0111415*x81 + 0.0158008*x82 + 0.10889*x83
       + 0.116075*x84 + 0.0169971*x85 + 0.0341233*x86 + 0.0267429*x87
       - 0.0114268*x88 - 0.00234199*x89 + 0.0350183*x90 - 0.00327782*x91
       + 0.0234788*x92 + 0.0976326*x93 + 0.000202835*x94 + 0.00567421*x95
       + 0.0334415*x96 + 0.0182382*x97 - 0.00355687*x98 + 0.0188454*x99
       + 0.0261119*x100 + 0.0236217*x101 =E= 0;

e77..  - x24 + 0.0104307*x52 + 0.0118212*x53 + 0.020493*x54 + 0.0160821*x55
       + 0.039664*x56 + 0.0128583*x57 + 0.0262*x58 + 0.0268377*x59
       + 0.0153119*x60 - 0.000197643*x61 + 0.0156557*x62 + 0.0173727*x63
       - 0.00484524*x64 + 0.0070277*x65 + 0.0128077*x66 + 0.0213959*x67
       + 0.0119803*x68 + 0.0219596*x69 + 0.029091*x70 + 0.0320937*x71
       + 0.0302363*x72 + 0.0167088*x73 + 0.227104*x74 + 0.0110539*x75
       + 0.0685123*x76 + 0.0166982*x77 + 0.00939654*x78 + 0.00636519*x79
       + 0.0242445*x80 + 0.0724648*x81 + 0.0194513*x82 + 0.00366476*x83
       + 0.0134866*x84 + 0.00878361*x85 + 0.0269894*x86 + 0.0281086*x87
       + 0.00493919*x88 + 0.0265072*x89 + 0.0495917*x90 + 0.00899853*x91
       + 0.0191737*x92 + 0.0112022*x93 + 0.0106917*x94 + 0.0282436*x95
       + 0.0119814*x96 + 0.00852934*x97 + 0.0132486*x98 - 0.00483593*x99
       + 0.00268557*x100 + 0.0264927*x101 =E= 0;

e78..  - x25 - 0.00554627*x52 + 0.00695719*x53 + 0.0060982*x54 + 0.00240536*x55
       + 0.0102778*x56 + 0.00399753*x57 + 0.0176229*x58 + 0.00229807*x59
       + 0.00890117*x60 - 0.00657968*x61 + 0.0127479*x62 + 0.0186957*x63
       + 0.0034154*x64 + 0.00809957*x65 + 0.00710322*x66 + 0.0275661*x67
       + 0.0131243*x68 + 0.00928365*x69 + 0.0174387*x70 + 0.00895684*x71
       + 0.0130538*x72 + 0.00851376*x73 + 0.0110539*x74 + 0.183511*x75
       + 0.00968069*x76 + 0.00777885*x77 + 0.00484151*x78 + 0.0120339*x79
       + 0.0182045*x80 + 0.0142639*x81 + 0.014134*x82 + 0.0123093*x83
       + 0.00543117*x84 + 0.0065975*x85 + 0.016776*x86 + 0.00170557*x87
       + 0.0026933*x88 + 0.00792354*x89 + 0.00735961*x90 - 0.000614984*x91
       + 0.0118767*x92 + 0.00947244*x93 + 0.00574257*x94 + 0.0110814*x95
       + 0.00174348*x96 + 0.00448876*x97 + 0.0220952*x98 + 0.0063483*x99
       + 0.000150809*x100 + 6.68242E-5*x101 =E= 0;

e79..  - x26 + 0.000275614*x52 - 0.00146012*x53 + 0.00709161*x54
       + 0.0042418*x55 + 0.0172657*x56 + 0.0184167*x57 + 0.0184672*x58
       + 0.01809*x59 + 0.0222796*x60 - 0.00738206*x61 + 0.0111445*x62
       + 0.0206278*x63 - 0.0060451*x64 + 0.0120566*x65 + 0.0100525*x66
       + 0.0260354*x67 + 0.009587*x68 + 0.0279232*x69 + 0.0237535*x70
       + 0.0261585*x71 + 0.02932*x72 + 0.0194063*x73 + 0.0685123*x74
       + 0.00968069*x75 + 0.190498*x76 + 0.0273631*x77 + 0.0144043*x78
       + 0.00276303*x79 + 0.00422846*x80 + 0.0638216*x81 + 0.017823*x82
       + 0.0135183*x83 + 0.00365697*x84 - 0.000986928*x85 + 0.0169049*x86
       + 0.0266562*x87 + 0.00523559*x88 + 0.014168*x89 + 0.0413952*x90
       + 0.00776725*x91 + 0.0326211*x92 + 0.0119027*x93 + 0.011424*x94
       + 0.015665*x95 + 0.0129933*x96 + 0.0057329*x97 + 0.00863731*x98
       + 0.00782909*x99 + 0.0385547*x100 + 0.0147477*x101 =E= 0;

e80..  - x27 + 0.00146767*x52 - 0.00455327*x53 + 0.0192029*x54 + 0.00264811*x55
       + 0.00473961*x56 + 0.010492*x57 + 0.00333289*x58 + 0.0114054*x59
       + 0.0442301*x60 + 0.0105229*x61 + 0.0085222*x62 + 0.0197312*x63
       + 0.0102102*x64 + 0.0156797*x65 + 0.0141544*x66 + 0.00490195*x67
       + 0.00326145*x68 + 0.0138525*x69 + 0.0139083*x70 + 0.0224334*x71
       + 0.0266188*x72 - 0.00258911*x73 + 0.0166982*x74 + 0.00777885*x75
       + 0.0273631*x76 + 0.14242*x77 + 0.0237243*x78 + 0.00294961*x79
       + 0.0200953*x80 + 0.0206276*x81 + 0.0230949*x82 + 0.00859757*x83
       + 0.0169*x84 + 0.0129568*x85 + 0.0262844*x86 + 0.0202602*x87
       + 0.0135266*x88 + 0.0134485*x89 + 0.0259415*x90 + 0.0189386*x91
       + 0.0167553*x92 + 0.012156*x93 + 0.0312321*x94 + 0.0133677*x95
       + 0.0168904*x96 + 0.021903*x97 + 0.00904192*x98 + 0.00640522*x99
       + 0.000393756*x100 + 0.0123718*x101 =E= 0;

e81..  - x28 - 0.0219202*x52 - 0.00233478*x53 + 0.00489188*x54 + 0.00832847*x55
       + 0.0132399*x56 + 0.0244629*x57 + 0.0125282*x58 + 0.0148192*x59
       + 0.0119004*x60 - 0.0124412*x61 - 0.00157042*x62 + 0.0258626*x63
       + 0.019147*x64 + 0.019146*x65 - 0.00302889*x66 - 8.95127E-5*x67
       + 0.0055836*x68 + 0.0582128*x69 + 0.0112918*x70 + 0.0281506*x71
       + 0.0279647*x72 + 0.000352563*x73 + 0.00939654*x74 + 0.00484151*x75
       + 0.0144043*x76 + 0.0237243*x77 + 0.507964*x78 + 0.0151067*x79
       + 0.0166188*x80 + 0.010503*x81 + 0.006312*x82 + 0.00351795*x83
       + 0.0068205*x84 + 0.00479431*x85 + 0.0145654*x86 + 0.033506*x87
       + 0.00559812*x88 + 0.0126415*x89 + 0.0123446*x90 + 0.028821*x91
       + 0.00981253*x92 + 0.0284364*x93 + 0.0179957*x94 + 0.0240785*x95
       + 0.0203486*x96 + 0.0246958*x97 + 0.0301721*x98 + 0.00697773*x99
       + 0.00248209*x100 - 0.00975878*x101 =E= 0;

e82..  - x29 - 0.0152471*x52 - 0.00354018*x53 + 0.0141398*x54 + 0.0040175*x55
       - 0.0118559*x56 + 0.047228*x57 + 0.0160426*x58 + 0.0286969*x59
       + 0.00720201*x60 - 0.00440667*x61 + 0.00905753*x62 + 0.0281149*x63
       + 0.00861968*x64 + 0.0230557*x65 + 0.0202446*x66 + 0.0278101*x67
       + 0.0160137*x68 + 0.0225874*x69 + 0.0315031*x70 + 0.0324489*x71
       + 0.0180419*x72 + 0.0170447*x73 + 0.00636519*x74 + 0.0120339*x75
       + 0.00276303*x76 + 0.00294961*x77 + 0.0151067*x78 + 0.670433*x79
       + 0.0205952*x80 + 0.00444933*x81 + 0.0225512*x82 + 0.0465233*x83
       + 0.0608492*x84 + 0.0358653*x85 + 0.0417635*x86 - 0.00291679*x87
       - 0.000317393*x88 + 0.0125595*x89 - 0.00116156*x90 - 0.00192373*x91
       + 0.0114605*x92 + 0.0425365*x93 - 0.000808147*x94 + 0.00295518*x95
       + 0.0242798*x96 + 0.0107554*x97 + 0.0120875*x98 + 0.0292966*x99
       - 0.00126318*x100 - 0.0099048*x101 =E= 0;

e83..  - x30 - 0.0133041*x52 - 0.0108257*x53 + 0.0183881*x54 + 0.0153818*x55
       + 0.0329745*x56 + 0.00547127*x57 - 0.00910903*x58 + 0.0156643*x59
       + 0.0201433*x60 + 0.0123441*x61 - 0.00402737*x62 + 0.020796*x63
       - 0.0013634*x64 + 0.00625971*x65 + 0.0273331*x66 + 0.0154943*x67
       - 0.00700837*x68 + 0.0216165*x69 + 0.0104372*x70 + 0.0266137*x71
       + 0.0293269*x72 + 0.00326757*x73 + 0.0242445*x74 + 0.0182045*x75
       + 0.00422846*x76 + 0.0200953*x77 + 0.0166188*x78 + 0.0205952*x79
       + 0.229224*x80 + 0.0223216*x81 + 0.0206237*x82 + 0.0101265*x83
       + 0.0015088*x84 + 0.0223314*x85 + 0.0273206*x86 + 0.00161461*x87
       + 0.00487681*x88 + 0.0183379*x89 + 0.0275921*x90 + 0.0159442*x91
       + 0.0134875*x92 + 0.0270417*x93 + 0.00200928*x94 + 0.0218467*x95
       + 0.00352069*x96 + 0.00446644*x97 + 0.0176237*x98 + 0.0279531*x99
       + 0.0110346*x100 + 0.00696769*x101 =E= 0;

e84..  - x31 + 0.00532027*x52 + 0.00548427*x53 + 0.0132555*x54 + 0.0182359*x55
       + 0.00776731*x56 + 0.0133769*x57 + 0.0168617*x58 + 0.0214673*x59
       + 0.0169933*x60 + 0.00670955*x61 + 0.00937755*x62 + 0.0154147*x63
       + 0.00686903*x64 + 0.0154784*x65 + 0.0142628*x66 + 0.0110009*x67
       + 0.00816694*x68 + 0.0188341*x69 + 0.0253639*x70 + 0.0183526*x71
       + 0.02223*x72 + 0.0111415*x73 + 0.0724648*x74 + 0.0142639*x75
       + 0.0638216*x76 + 0.0206276*x77 + 0.010503*x78 + 0.00444933*x79
       + 0.0223216*x80 + 0.185075*x81 + 0.0205911*x82 + 0.0145088*x83
       + 0.00876387*x84 + 0.0107778*x85 + 0.014933*x86 + 0.0186524*x87
       + 0.0106153*x88 + 0.044217*x89 + 0.0463482*x90 + 0.019405*x91
       + 0.0233399*x92 + 0.0136317*x93 + 0.0110294*x94 + 0.0119847*x95
       + 0.0293732*x96 - 0.00785039*x97 + 0.0195485*x98 + 0.00530393*x99
       - 0.00585743*x100 + 0.0197286*x101 =E= 0;

e85..  - x32 + 0.0190296*x52 + 0.00843954*x53 + 0.0089825*x54 + 0.00961571*x55
       + 0.00146596*x56 + 0.0119332*x57 + 0.00649361*x58 + 0.00423722*x59
       + 0.019457*x60 + 0.000975768*x61 + 0.00827346*x62 + 0.00821687*x63
       + 0.0133687*x64 + 0.0113709*x65 + 0.0130754*x66 + 0.0209885*x67
       + 0.0133907*x68 + 0.0113276*x69 + 0.00237959*x70 - 0.0016676*x71
       + 0.00413185*x72 + 0.0158008*x73 + 0.0194513*x74 + 0.014134*x75
       + 0.017823*x76 + 0.0230949*x77 + 0.006312*x78 + 0.0225512*x79
       + 0.0206237*x80 + 0.0205911*x81 + 0.147147*x82 + 0.0105685*x83
       + 0.00474516*x84 + 0.0149866*x85 - 0.00374475*x86 + 0.0147657*x87
       + 0.00370161*x88 - 0.00382518*x89 + 0.0112733*x90 + 0.00898559*x91
       + 0.047951*x92 + 0.00269973*x93 + 0.00305288*x94 + 0.00998711*x95
       - 0.00599198*x96 + 0.00378519*x97 + 0.00228262*x98 + 0.000223223*x99
       + 0.0131328*x100 + 0.0100911*x101 =E= 0;

e86..  - x33 + 9.52152E-5*x52 + 0.0957415*x53 - 0.00433095*x54 + 0.0122098*x55
       + 0.0398038*x56 + 0.161483*x57 + 0.000720061*x58 + 0.0101393*x59
       + 0.0111733*x60 + 0.0409171*x61 + 0.00543371*x62 + 0.0277493*x63
       + 0.00136495*x64 - 0.00207874*x65 + 0.00886564*x66 + 0.129895*x67
       + 0.00598212*x68 + 0.0272881*x69 - 0.00567431*x70 + 0.0194921*x71
       + 0.0241439*x72 + 0.10889*x73 + 0.00366476*x74 + 0.0123093*x75
       + 0.0135183*x76 + 0.00859757*x77 + 0.00351795*x78 + 0.0465233*x79
       + 0.0101265*x80 + 0.0145088*x81 + 0.0105685*x82 + 0.389649*x83
       + 0.138762*x84 + 0.00825629*x85 + 0.0181004*x86 + 0.0167077*x87
       + 0.00722734*x88 - 0.00583878*x89 + 0.0232216*x90 + 0.0168437*x91
       + 0.0278419*x92 + 0.117531*x93 + 0.00545108*x94 + 0.007432*x95
       + 0.0161894*x96 + 0.0203409*x97 - 0.00640225*x98 + 0.00363753*x99
       + 0.00102053*x100 + 0.0252622*x101 =E= 0;

e87..  - x34 - 0.0180784*x52 + 0.0724208*x53 + 0.000368443*x54
       - 0.000558226*x55 + 0.0268424*x56 + 0.187982*x57 + 0.0015496*x58
       + 0.00438509*x59 + 0.00689119*x60 - 0.0110323*x61 + 0.0230998*x62
       + 0.0231334*x63 + 0.00888952*x64 - 0.00747722*x65 + 0.0125267*x66
       + 0.104593*x67 - 0.00201041*x68 + 0.0118425*x69 + 0.0125939*x70
       + 0.0366494*x71 + 0.0263683*x72 + 0.116075*x73 + 0.0134866*x74
       + 0.00543117*x75 + 0.00365697*x76 + 0.0169*x77 + 0.0068205*x78
       + 0.0608492*x79 + 0.0015088*x80 + 0.00876387*x81 + 0.00474516*x82
       + 0.138762*x83 + 0.397419*x84 + 0.0108491*x85 - 0.00298466*x86
       + 0.0247715*x87 + 0.0157939*x88 + 0.00640654*x89 + 0.0102405*x90
       + 0.0051056*x91 + 0.0145699*x92 + 0.0756527*x93 + 0.00684049*x94
       - 0.000862575*x95 + 0.00996209*x96 + 0.0282548*x97 + 0.0055526*x98
       + 0.00924268*x99 + 0.00369864*x100 - 0.00445725*x101 =E= 0;

e88..  - x35 + 0.00127079*x52 + 0.00920314*x53 + 0.00845006*x54 + 0.0179991*x55
       + 0.0120171*x56 + 0.00916881*x57 + 0.0120757*x58 + 0.0186319*x59
       + 0.00669496*x60 - 0.00482281*x61 + 0.0238731*x62 + 0.0242186*x63
       + 0.00809492*x64 + 0.00726553*x65 + 0.00167144*x66 + 0.0164835*x67
       + 0.0153712*x68 + 0.0244022*x69 + 0.0195843*x70 + 0.0166731*x71
       - 0.0132754*x72 + 0.0169971*x73 + 0.00878361*x74 + 0.0065975*x75
       - 0.000986928*x76 + 0.0129568*x77 + 0.00479431*x78 + 0.0358653*x79
       + 0.0223314*x80 + 0.0107778*x81 + 0.0149866*x82 + 0.00825629*x83
       + 0.0108491*x84 + 0.312298*x85 + 0.0120296*x86 + 0.0106859*x87
       + 0.0204397*x88 + 0.0119026*x89 + 0.0319466*x90 + 0.00664877*x91
       + 0.00548571*x92 + 0.0048078*x93 + 0.0331056*x94 + 0.0274019*x95
       + 0.00104681*x96 + 0.011411*x97 - 0.00331677*x98 - 0.00425863*x99
       + 0.0100274*x100 + 0.00728145*x101 =E= 0;

e89..  - x36 - 0.00331643*x52 - 0.00921773*x53 + 0.0106863*x54 + 0.0126379*x55
       + 0.0145295*x56 + 0.0209491*x57 + 0.0231367*x58 + 0.046181*x59
       + 0.0331297*x60 - 0.00546107*x61 + 0.0199311*x62 + 0.0562299*x63
       + 0.00573295*x64 + 0.037832*x65 + 0.0368131*x66 + 0.0238469*x67
       + 0.00839091*x68 + 0.0305204*x69 + 0.0768331*x70 + 0.0415684*x71
       + 0.0388595*x72 + 0.0341233*x73 + 0.0269894*x74 + 0.016776*x75
       + 0.0169049*x76 + 0.0262844*x77 + 0.0145654*x78 + 0.0417635*x79
       + 0.0273206*x80 + 0.014933*x81 - 0.00374475*x82 + 0.0181004*x83
       - 0.00298466*x84 + 0.0120296*x85 + 0.618581*x86 + 0.0289636*x87
       - 0.00446781*x88 + 0.0224213*x89 + 0.0380495*x90 + 0.0386705*x91
       + 0.0297938*x92 + 0.0058598*x93 + 0.0252835*x94 + 0.0145417*x95
       + 0.0665246*x96 + 0.00798604*x97 + 0.00560573*x98 + 0.0328297*x99
       + 0.0235991*x100 + 0.0470289*x101 =E= 0;

e90..  - x37 - 0.0107273*x52 + 0.0112775*x53 + 0.0165343*x54 + 0.0175827*x55
       + 0.0354297*x56 + 0.0327261*x57 + 0.0160891*x58 + 0.0332107*x59
       + 0.0197397*x60 - 0.0142879*x61 + 0.0174054*x62 + 0.0315629*x63
       + 0.00828577*x64 + 0.0123555*x65 + 0.0135909*x66 + 0.0319592*x67
       + 0.00597115*x68 + 0.0378227*x69 + 0.0267106*x70 + 0.0425512*x71
       + 0.0578838*x72 + 0.0267429*x73 + 0.0281086*x74 + 0.00170557*x75
       + 0.0266562*x76 + 0.0202602*x77 + 0.033506*x78 - 0.00291679*x79
       + 0.00161461*x80 + 0.0186524*x81 + 0.0147657*x82 + 0.0167077*x83
       + 0.0247715*x84 + 0.0106859*x85 + 0.0289636*x86 + 0.270232*x87
       + 0.0400357*x88 + 0.00621348*x89 + 0.0404134*x90 + 0.00592392*x91
       + 0.00614247*x92 + 0.00530712*x93 + 0.00684822*x94 + 0.0187153*x95
       + 0.0225813*x96 + 0.0289411*x97 + 0.00901397*x98 + 0.0166774*x99
       + 0.0332544*x100 + 0.0151416*x101 =E= 0;

e91..  - x38 - 6.72321E-5*x52 + 0.010577*x53 + 0.0182906*x54 + 0.00566779*x55
       - 0.00170776*x56 + 0.028455*x57 + 0.000127307*x58 + 0.0160758*x59
       + 0.0120744*x60 + 0.018699*x61 + 0.00185204*x62 + 0.0122553*x63
       + 0.0152408*x64 - 0.000156492*x65 - 0.000550234*x66 + 0.016159*x67
       - 0.000508298*x68 + 0.00150342*x69 + 0.00312045*x70 + 0.0185632*x71
       + 0.00722557*x72 - 0.0114268*x73 + 0.00493919*x74 + 0.0026933*x75
       + 0.00523559*x76 + 0.0135266*x77 + 0.00559812*x78 - 0.000317393*x79
       + 0.00487681*x80 + 0.0106153*x81 + 0.00370161*x82 + 0.00722734*x83
       + 0.0157939*x84 + 0.0204397*x85 - 0.00446781*x86 + 0.0400357*x87
       + 0.222166*x88 + 0.00907574*x89 + 0.0281441*x90 + 0.0265542*x91
       + 0.00608259*x92 + 0.0066023*x93 + 0.00659999*x94 + 0.0224381*x95
       + 0.00149053*x96 + 0.000405727*x97 - 0.0104234*x98 + 0.000189871*x99
       + 0.00118145*x100 + 0.00362186*x101 =E= 0;

e92..  - x39 + 0.0019753*x52 - 0.00268772*x53 + 0.000474699*x54
       - 0.000955585*x55 + 0.0255113*x56 + 0.0105724*x57 + 0.00590674*x58
       + 0.00541803*x59 + 0.0127905*x60 + 0.0440906*x61 + 0.0156839*x62
       + 0.0146058*x63 + 0.0110413*x64 + 0.0119264*x65 + 0.0369853*x66
       - 0.00048612*x67 - 0.00265155*x68 + 0.000336096*x69 + 0.00720686*x70
       + 0.0150068*x71 + 0.0210916*x72 - 0.00234199*x73 + 0.0265072*x74
       + 0.00792354*x75 + 0.014168*x76 + 0.0134485*x77 + 0.0126415*x78
       + 0.0125595*x79 + 0.0183379*x80 + 0.044217*x81 - 0.00382518*x82
       - 0.00583878*x83 + 0.00640654*x84 + 0.0119026*x85 + 0.0224213*x86
       + 0.00621348*x87 + 0.00907574*x88 + 0.394267*x89 + 0.0165051*x90
       + 0.00980853*x91 - 0.00226117*x92 - 0.00984533*x93 + 0.00565748*x94
       + 0.00895692*x95 + 0.00919195*x96 + 0.00900527*x97 + 0.0181986*x98
       + 0.0249229*x99 - 0.000623048*x100 + 0.0135896*x101 =E= 0;

e93..  - x40 - 0.00561942*x52 + 0.0104329*x53 + 0.0125524*x54 + 0.0234718*x55
       + 0.0115797*x56 + 0.0238296*x57 + 0.0251974*x58 + 0.0243196*x59
       + 0.0406861*x60 - 0.00363253*x61 + 0.00443354*x62 + 0.0225422*x63
       + 0.0069969*x64 + 0.0124128*x65 + 0.00970355*x66 + 0.0206697*x67
       + 0.0148232*x68 + 0.0330899*x69 + 0.0261195*x70 + 0.0206301*x71
       + 0.0335768*x72 + 0.0350183*x73 + 0.0495917*x74 + 0.00735961*x75
       + 0.0413952*x76 + 0.0259415*x77 + 0.0123446*x78 - 0.00116156*x79
       + 0.0275921*x80 + 0.0463482*x81 + 0.0112733*x82 + 0.0232216*x83
       + 0.0102405*x84 + 0.0319466*x85 + 0.0380495*x86 + 0.0404134*x87
       + 0.0281441*x88 + 0.0165051*x89 + 0.226153*x90 + 0.00565646*x91
       + 0.0239442*x92 + 0.00622955*x93 + 0.014515*x94 + 0.0227247*x95
       + 0.026331*x96 + 0.0188097*x97 + 0.00284125*x98 + 0.00673929*x99
       + 0.00450472*x100 + 0.0152845*x101 =E= 0;

e94..  - x41 - 0.0137411*x52 - 0.00184253*x53 + 0.00998269*x54 - 0.00128625*x55
       + 0.0340249*x56 - 0.00223337*x57 + 0.0109883*x58 + 0.0145438*x59
       + 0.0323148*x60 + 0.00273765*x61 + 0.0202129*x62 + 0.0126094*x63
       + 0.0053944*x64 + 0.0206051*x65 + 0.0253109*x66 - 0.0044719*x67
       - 0.000660928*x68 + 0.0189859*x69 + 0.0295481*x70 + 0.00808519*x71
       - 0.00914657*x72 - 0.00327782*x73 + 0.00899853*x74 - 0.000614984*x75
       + 0.00776725*x76 + 0.0189386*x77 + 0.028821*x78 - 0.00192373*x79
       + 0.0159442*x80 + 0.019405*x81 + 0.00898559*x82 + 0.0168437*x83
       + 0.0051056*x84 + 0.00664877*x85 + 0.0386705*x86 + 0.00592392*x87
       + 0.0265542*x88 + 0.00980853*x89 + 0.00565646*x90 + 0.290035*x91
       + 0.0156774*x92 - 0.00869674*x93 + 0.00461003*x94 - 0.000555319*x95
       + 0.016294*x96 + 0.0016488*x97 + 0.0137582*x98 + 0.0245795*x99
       - 0.00658672*x100 + 0.00527527*x101 =E= 0;

e95..  - x42 + 0.0266953*x52 + 0.0230614*x53 + 0.00663781*x54 + 0.00397589*x55
       + 0.00175196*x56 + 0.0230382*x57 + 0.0197048*x58 + 0.00473001*x59
       + 0.0200869*x60 + 0.00673168*x61 + 0.0114171*x62 + 0.0195556*x63
       + 0.0104813*x64 + 0.0182519*x65 + 0.01371*x66 + 0.0412523*x67
       + 0.0219128*x68 + 0.0161305*x69 - 0.00121588*x70 - 0.00805047*x71
       + 0.0153621*x72 + 0.0234788*x73 + 0.0191737*x74 + 0.0118767*x75
       + 0.0326211*x76 + 0.0167553*x77 + 0.00981253*x78 + 0.0114605*x79
       + 0.0134875*x80 + 0.0233399*x81 + 0.047951*x82 + 0.0278419*x83
       + 0.0145699*x84 + 0.00548571*x85 + 0.0297938*x86 + 0.00614247*x87
       + 0.00608259*x88 - 0.00226117*x89 + 0.0239442*x90 + 0.0156774*x91
       + 0.195197*x92 + 0.0167141*x93 - 0.00108078*x94 + 0.0154638*x95
       + 0.00879495*x96 + 0.0251912*x97 + 0.00951858*x98 + 0.0145509*x99
       + 0.0109233*x100 + 0.00930651*x101 =E= 0;

e96..  - x43 + 0.0039322*x52 + 0.0797692*x53 - 0.00941355*x54 + 0.00253364*x55
       + 0.0214384*x56 + 0.112083*x57 + 0.00281047*x58 + 0.00681241*x59
       + 0.00172542*x60 + 0.0033605*x61 + 0.00122747*x62 + 0.0148528*x63
       - 0.00694263*x64 - 0.0063393*x65 + 0.0151066*x66 + 0.150222*x67
       + 0.0200429*x68 + 0.00657093*x69 + 0.00174197*x70 + 0.0108192*x71
       + 0.0170669*x72 + 0.0976326*x73 + 0.0112022*x74 + 0.00947244*x75
       + 0.0119027*x76 + 0.012156*x77 + 0.0284364*x78 + 0.0425365*x79
       + 0.0270417*x80 + 0.0136317*x81 + 0.00269973*x82 + 0.117531*x83
       + 0.0756527*x84 + 0.0048078*x85 + 0.0058598*x86 + 0.00530712*x87
       + 0.0066023*x88 - 0.00984533*x89 + 0.00622955*x90 - 0.00869674*x91
       + 0.0167141*x92 + 0.306057*x93 + 0.018202*x94 + 0.0064207*x95
       + 0.007465*x96 + 0.0209936*x97 + 0.00813794*x98 + 0.0137895*x99
       + 0.00376129*x100 + 0.00807619*x101 =E= 0;

e97..  - x44 + 0.0312023*x52 - 0.00718849*x53 + 0.0166904*x54 + 0.0161477*x55
       + 0.0113414*x56 + 0.00257709*x57 + 0.0113665*x58 + 0.00988793*x59
       + 0.0311244*x60 + 0.0241296*x61 + 0.0118384*x62 + 0.016949*x63
       + 0.0141714*x64 + 0.0162264*x65 + 0.0201164*x66 + 0.0060731*x67
       + 0.00803816*x68 + 0.0118269*x69 + 0.000971523*x70 + 0.01367*x71
       + 0.00771841*x72 + 0.000202835*x73 + 0.0106917*x74 + 0.00574257*x75
       + 0.011424*x76 + 0.0312321*x77 + 0.0179957*x78 - 0.000808147*x79
       + 0.00200928*x80 + 0.0110294*x81 + 0.00305288*x82 + 0.00545108*x83
       + 0.00684049*x84 + 0.0331056*x85 + 0.0252835*x86 + 0.00684822*x87
       + 0.00659999*x88 + 0.00565748*x89 + 0.014515*x90 + 0.00461003*x91
       - 0.00108078*x92 + 0.018202*x93 + 0.2295*x94 + 0.0263474*x95
       + 0.0158978*x96 - 0.00338835*x97 + 0.0116215*x98 + 0.0102735*x99
       - 0.0164264*x100 + 0.0105885*x101 =E= 0;

e98..  - x45 + 0.00475029*x52 + 0.00668562*x53 + 0.00602889*x54 + 0.0163612*x55
       + 0.039091*x56 - 0.0088657*x57 + 0.0128475*x58 + 0.0149668*x59
       + 0.00519737*x60 - 0.00441557*x61 + 0.0228483*x62 + 0.0309886*x63
       - 0.00184581*x64 + 0.0114734*x65 + 0.0193544*x66 + 0.00469106*x67
       + 0.0174527*x68 + 0.0262376*x69 + 0.016521*x70 + 0.0348135*x71
       + 0.0161467*x72 + 0.00567421*x73 + 0.0282436*x74 + 0.0110814*x75
       + 0.015665*x76 + 0.0133677*x77 + 0.0240785*x78 + 0.00295518*x79
       + 0.0218467*x80 + 0.0119847*x81 + 0.00998711*x82 + 0.007432*x83
       - 0.000862575*x84 + 0.0274019*x85 + 0.0145417*x86 + 0.0187153*x87
       + 0.0224381*x88 + 0.00895692*x89 + 0.0227247*x90 - 0.000555319*x91
       + 0.0154638*x92 + 0.0064207*x93 + 0.0263474*x94 + 0.219232*x95
       + 0.0233015*x96 - 0.00971973*x97 + 0.0161499*x98 + 0.0121398*x99
       - 0.000692501*x100 + 0.00371111*x101 =E= 0;

e99..  - x46 + 0.00458043*x52 - 0.00479877*x53 + 0.00224387*x54 + 0.012804*x55
       + 0.00619763*x56 + 0.0101284*x57 + 0.00622782*x58 + 0.023562*x59
       + 0.0142684*x60 - 0.00703875*x61 + 0.0131884*x62 + 0.0111695*x63
       + 0.0147295*x64 + 0.0298746*x65 + 0.0166079*x66 + 0.032667*x67
       + 0.00328568*x68 + 0.0229703*x69 + 0.0242338*x70 + 0.0320515*x71
       + 0.0470226*x72 + 0.0334415*x73 + 0.0119814*x74 + 0.00174348*x75
       + 0.0129933*x76 + 0.0168904*x77 + 0.0203486*x78 + 0.0242798*x79
       + 0.00352069*x80 + 0.0293732*x81 - 0.00599198*x82 + 0.0161894*x83
       + 0.00996209*x84 + 0.00104681*x85 + 0.0665246*x86 + 0.0225813*x87
       + 0.00149053*x88 + 0.00919195*x89 + 0.026331*x90 + 0.016294*x91
       + 0.00879495*x92 + 0.007465*x93 + 0.0158978*x94 + 0.0233015*x95
       + 0.325248*x96 + 0.0152129*x97 + 0.0136663*x98 + 0.0127301*x99
       - 0.00399355*x100 + 0.00993756*x101 =E= 0;

e100..  - x47 - 0.0111713*x52 + 0.037467*x53 - 0.00806098*x54 + 0.0254602*x55
        + 0.0133319*x56 + 0.0087194*x57 + 0.0245605*x58 + 0.0173729*x59
        + 0.0178041*x60 + 0.016325*x61 - 0.0151598*x62 + 0.023004*x63
        - 0.00369236*x64 + 0.00393739*x65 + 0.0113423*x66 + 0.00513266*x67
        + 0.00580133*x68 + 0.0245122*x69 + 0.0387835*x70 + 0.0132639*x71
        + 0.0696792*x72 + 0.0182382*x73 + 0.00852934*x74 + 0.00448876*x75
        + 0.0057329*x76 + 0.021903*x77 + 0.0246958*x78 + 0.0107554*x79
        + 0.00446644*x80 - 0.00785039*x81 + 0.00378519*x82 + 0.0203409*x83
        + 0.0282548*x84 + 0.011411*x85 + 0.00798604*x86 + 0.0289411*x87
        + 0.000405727*x88 + 0.00900527*x89 + 0.0188097*x90 + 0.0016488*x91
        + 0.0251912*x92 + 0.0209936*x93 - 0.00338835*x94 - 0.00971973*x95
        + 0.0152129*x96 + 0.903924*x97 - 0.0108291*x98 + 0.0425572*x99
        - 0.0154741*x100 + 0.0155463*x101 =E= 0;

e101..  - x48 + 0.00233202*x52 - 0.000833339*x53 + 0.0151626*x54
        + 0.0164285*x55 + 0.0121082*x56 + 0.016345*x57 + 0.00706149*x58
        + 0.016267*x59 + 0.00992985*x60 + 0.00222896*x61 + 0.00844519*x62
        + 0.00865625*x63 + 0.00526228*x64 + 0.0153743*x65 + 0.0488179*x66
        + 0.00884207*x67 - 0.000537323*x68 + 0.00497315*x69 + 0.0249114*x70
        - 0.00327629*x71 + 0.00688465*x72 - 0.00355687*x73 + 0.0132486*x74
        + 0.0220952*x75 + 0.00863731*x76 + 0.00904192*x77 + 0.0301721*x78
        + 0.0120875*x79 + 0.0176237*x80 + 0.0195485*x81 + 0.00228262*x82
        - 0.00640225*x83 + 0.0055526*x84 - 0.00331677*x85 + 0.00560573*x86
        + 0.00901397*x87 - 0.0104234*x88 + 0.0181986*x89 + 0.00284125*x90
        + 0.0137582*x91 + 0.00951858*x92 + 0.00813794*x93 + 0.0116215*x94
        + 0.0161499*x95 + 0.0136663*x96 - 0.0108291*x97 + 0.224056*x98
        + 0.00641426*x99 + 0.0200771*x100 - 0.0157458*x101 =E= 0;

e102..  - x49 + 0.00279105*x52 - 0.00287641*x53 - 0.000965771*x54
        + 0.0113336*x55 + 0.0357203*x56 + 0.0145296*x57 + 0.00272192*x58
        + 0.0121424*x59 + 0.0146222*x60 - 0.0077883*x61 + 0.0198609*x62
        + 0.0218181*x63 + 0.00828497*x64 + 0.00989917*x65 + 0.016393*x66
        + 0.0125003*x67 + 0.0127107*x68 + 0.0222552*x69 + 0.0106646*x70
        + 0.0267494*x71 + 0.0406248*x72 + 0.0188454*x73 - 0.00483593*x74
        + 0.0063483*x75 + 0.00782909*x76 + 0.00640522*x77 + 0.00697773*x78
        + 0.0292966*x79 + 0.0279531*x80 + 0.00530393*x81 + 0.000223223*x82
        + 0.00363753*x83 + 0.00924268*x84 - 0.00425863*x85 + 0.0328297*x86
        + 0.0166774*x87 + 0.000189871*x88 + 0.0249229*x89 + 0.00673929*x90
        + 0.0245795*x91 + 0.0145509*x92 + 0.0137895*x93 + 0.0102735*x94
        + 0.0121398*x95 + 0.0127301*x96 + 0.0425572*x97 + 0.00641426*x98
        + 0.246306*x99 + 0.00353612*x100 - 0.00520827*x101 =E= 0;

e103..  - x50 + 0.00588268*x52 - 0.00540049*x53 + 0.0157379*x54
        + 0.00992279*x55 + 0.0381607*x56 + 0.00606395*x57 + 0.00300911*x58
        - 0.00299957*x59 + 0.00920343*x60 - 0.00313691*x61 + 0.0242712*x62
        + 0.0268327*x63 - 0.0189632*x64 + 0.0228823*x65 - 0.00100315*x66
        - 0.00578404*x67 + 0.0134156*x68 + 0.00180371*x69 - 0.0157855*x70
        + 0.0178498*x71 - 0.00265226*x72 + 0.0261119*x73 + 0.00268557*x74
        + 0.000150809*x75 + 0.0385547*x76 + 0.000393756*x77 + 0.00248209*x78
        - 0.00126318*x79 + 0.0110346*x80 - 0.00585743*x81 + 0.0131328*x82
        + 0.00102053*x83 + 0.00369864*x84 + 0.0100274*x85 + 0.0235991*x86
        + 0.0332544*x87 + 0.00118145*x88 - 0.000623048*x89 + 0.00450472*x90
        - 0.00658672*x91 + 0.0109233*x92 + 0.00376129*x93 - 0.0164264*x94
        - 0.000692501*x95 - 0.00399355*x96 - 0.0154741*x97 + 0.0200771*x98
        + 0.00353612*x99 + 1.25224*x100 + 0.0259038*x101 =E= 0;

e104..  - x51 + 0.0171354*x52 + 0.0133618*x53 + 0.0187837*x54 + 0.00909239*x55
        + 0.0203578*x56 + 0.00747571*x57 + 0.0133916*x58 + 0.00907044*x59
        + 0.0199828*x60 + 0.0264584*x61 + 0.0138048*x62 + 0.0203605*x63
        + 0.0101028*x64 + 0.017772*x65 + 0.0101386*x66 + 0.0225237*x67
        + 0.00882735*x68 + 0.00323067*x69 + 0.0165385*x70 + 0.0295494*x71
        + 0.0216914*x72 + 0.0236217*x73 + 0.0264927*x74 + 6.68242E-5*x75
        + 0.0147477*x76 + 0.0123718*x77 - 0.00975878*x78 - 0.0099048*x79
        + 0.00696769*x80 + 0.0197286*x81 + 0.0100911*x82 + 0.0252622*x83
        - 0.00445725*x84 + 0.00728145*x85 + 0.0470289*x86 + 0.0151416*x87
        + 0.00362186*x88 + 0.0135896*x89 + 0.0152845*x90 + 0.00527527*x91
        + 0.00930651*x92 + 0.00807619*x93 + 0.0105885*x94 + 0.00371111*x95
        + 0.00993756*x96 + 0.0155463*x97 - 0.0157458*x98 - 0.00520827*x99
        + 0.0259038*x100 + 0.389181*x101 =E= 0;

* set non-default bounds
x52.up = 1;
x53.up = 1;
x54.up = 1;
x55.up = 1;
x56.up = 1;
x57.up = 1;
x58.up = 1;
x59.up = 1;
x60.up = 1;
x61.up = 1;
x62.up = 1;
x63.up = 1;
x64.up = 1;
x65.up = 1;
x66.up = 1;
x67.up = 1;
x68.up = 1;
x69.up = 1;
x70.up = 1;
x71.up = 1;
x72.up = 1;
x73.up = 1;
x74.up = 1;
x75.up = 1;
x76.up = 1;
x77.up = 1;
x78.up = 1;
x79.up = 1;
x80.up = 1;
x81.up = 1;
x82.up = 1;
x83.up = 1;
x84.up = 1;
x85.up = 1;
x86.up = 1;
x87.up = 1;
x88.up = 1;
x89.up = 1;
x90.up = 1;
x91.up = 1;
x92.up = 1;
x93.up = 1;
x94.up = 1;
x95.up = 1;
x96.up = 1;
x97.up = 1;
x98.up = 1;
x99.up = 1;
x100.up = 1;
x101.up = 1;

Model m / all /;

m.limrow=0; m.limcol=0;
m.tolproj=0.0;

$if NOT '%gams.u1%' == '' $include '%gams.u1%'

$if not set MINLP $set MINLP MINLP
Solve m using %MINLP% minimizing objvar;


Last updated: 2022-08-11 Git hash: f176bd52
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