tomleslie

13876 Reputation

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15 years, 174 days

MaplePrimes Activity


These are answers submitted by tomleslie

to solve something which is pretty simple - so I may have misunderstood something.

The attached code solves your ODE system for one set off parameter values.

Do you need any more than this??


 

restart;

ODEs:= {diff(phi(y), y, y)-Re*Sc*v(y)*(diff(phi(y), y))+Nt*(diff(theta(y), y, y)+(diff(theta(y), y))/y)/Nb = 0,
         diff(v(y), y, y)+(diff(v(y), y))/y-(Ha^2/(1-eta)^2+1/y^2)*v(y)-Re*v(y)*(diff(v(y), y)) = 0,
         diff(theta(y), y, y)+Ec*Pr*(diff(v(y), y)-v(y)/y)^2-Pr*Re*v(y)*(diff(theta(y), y))+Nb*(diff(theta(y), y))*(diff(phi(y), y))+Nt*(diff(theta(y), y))^2 = 0};

{diff(diff(phi(y), y), y)-Re*Sc*v(y)*(diff(phi(y), y))+Nt*(diff(diff(theta(y), y), y)+(diff(theta(y), y))/y)/Nb = 0, diff(diff(v(y), y), y)+(diff(v(y), y))/y-(Ha^2/(1-eta)^2+1/y^2)*v(y)-Re*v(y)*(diff(v(y), y)) = 0, diff(diff(theta(y), y), y)+Ec*Pr*(diff(v(y), y)-v(y)/y)^2-Pr*Re*v(y)*(diff(theta(y), y))+Nb*(diff(theta(y), y))*(diff(phi(y), y))+Nt*(diff(theta(y), y))^2 = 0}

(1)

BCs := {phi(1) = 0, phi(eta) = 1, theta(1) = 0, theta(eta) = 1, v(1) = 0, v(eta) = 1};

{phi(1) = 0, phi(eta) = 1, theta(1) = 0, theta(eta) = 1, v(1) = 0, v(eta) = 1}

(2)

pVals := [eta = .5, Ha = 1, Sc = .8, Nt = .1, Nb = .1, Re = 2, Ec = 0.1e-1, Pr = 10];
sol:=dsolve( `union`(eval(ODEs,pVals), eval(BCs, pVals)), numeric);
plots:-odeplot(sol, [y, theta(y)], y=0.5..1);
plots:-odeplot(sol, [y, phi(y)], y=0.5..1);
plots:-odeplot(sol, [y, v(y)], y=0.5..1);

[eta = .5, Ha = 1, Sc = .8, Nt = .1, Nb = .1, Re = 2, Ec = 0.1e-1, Pr = 10]

 

proc (x_bvp) local res, data, solnproc, _ndsol, outpoint, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](x_bvp) else outpoint := evalf(x_bvp) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(15, {(1) = .5, (2) = .5336121902422217, (3) = .5844381546054477, (4) = .6367246910382582, (5) = .6819813637076192, (6) = .7203576555258304, (7) = .7537947476785826, (8) = .7839983988541166, (9) = .8124715099760172, (10) = .8403819137356267, (11) = .8687377326893805, (12) = .8986394117549072, (13) = .9315548210903578, (14) = .968559697402719, (15) = 1.0}, datatype = float[8], order = C_order); Y := Matrix(15, 6, {(1, 1) = 1.0, (1, 2) = -3.5859482319619707, (1, 3) = 1.0, (1, 4) = 0.5543399786149021e-1, (1, 5) = 1.0, (1, 6) = -3.1809506205094804, (2, 1) = .87725852687241, (2, 2) = -3.7104431361386876, (2, 3) = 1.00086632635465, (2, 4) = -0.7886265467496404e-2, (2, 5) = .8973968055181978, (2, 6) = -2.9299124643506866, (3, 1) = .6858296930287634, (3, 2) = -3.7983843053718003, (3, 3) = .9968477089591101, (3, 4) = -.16570559152242836, (3, 5) = .7569280254304388, (3, 6) = -2.6078034998261606, (4, 1) = .4886788141744435, (4, 2) = -3.7065833064563183, (4, 3) = .9813889571224382, (4, 4) = -.4504788339676847, (4, 5) = .6279799464825064, (4, 6) = -2.3329390514471964, (5, 1) = .3264039127758183, (5, 2) = -3.431721972279278, (5, 3) = .9528825669298234, (5, 4) = -.8321572505352428, (5, 5) = .52706832150995, (5, 6) = -2.1316694336743605, (6, 1) = .20176651191080938, (6, 2) = -3.0391816325972827, (6, 3) = .912958115374231, (6, 4) = -1.2651566036115673, (6, 5) = .4481727229687035, (6, 6) = -1.9831367804400784, (7, 1) = .1075223378352854, (7, 2) = -2.580867202344822, (7, 3) = .8632497112937291, (7, 4) = -1.7189089681714942, (7, 5) = .383820521966699, (7, 6) = -1.86811269574634, (8, 1) = 0.36862305254820406e-1, (8, 2) = -2.0868920283383767, (8, 3) = .8045093401991149, (8, 4) = -2.176905317660935, (8, 5) = .3288334707982209, (8, 6) = -1.7745252963625566, (9, 1) = -0.15290413806119445e-1, (9, 2) = -1.5698532569193275, (9, 3) = .7360580755074047, (9, 4) = -2.6336908365432468, (9, 5) = .2794648903098676, (9, 6) = -1.6944750044895431, (10, 1) = -0.5169322978265776e-1, (10, 2) = -1.0362382622884123, (10, 3) = .6562279081637455, (10, 4) = -3.0857546328110734, (10, 5) = .2331830909505202, (10, 6) = -1.623107293673211, (11, 1) = -0.7333435138812011e-1, (11, 2) = -.49201468875877025, (11, 3) = .5623961600379838, (11, 4) = -3.5275886409827275, (11, 5) = .18810719420548744, (11, 6) = -1.5572794718852523, (12, 1) = -0.7976609128142718e-1, (12, 2) = 0.54627866260378306e-1, (12, 3) = .4504645433427342, (12, 4) = -3.9493942806978732, (12, 5) = .1424951029330242, (12, 6) = -1.4946447563190588, (13, 1) = -0.6894151373662899e-1, (13, 2) = .5882277932627828, (13, 3) = .3138997018819178, (13, 4) = -4.3318490778469, (13, 5) = 0.9433060308421574e-1, (13, 6) = -1.4331769658752087, (14, 1) = -0.3795243066478835e-1, (14, 2) = 1.061035885737002, (14, 3) = .14766342011083522, (14, 4) = -4.626437061503043, (14, 5) = 0.4244154938475846e-1, (14, 6) = -1.3727368303912408, (15, 1) = .0, (15, 2) = 1.3317906480247055, (15, 3) = .0, (15, 4) = -4.7459341712306315, (15, 5) = .0, (15, 6) = -1.3280648427471695}, datatype = float[8], order = C_order); YP := Matrix(15, 6, {(1, 1) = -3.5859482319619707, (1, 2) = -4.29241124272649, (1, 3) = 0.5543399786149021e-1, (1, 4) = -1.555973924135644, (1, 5) = -3.1809506205094804, (1, 6) = 8.0, (2, 1) = -3.7104431361386876, (2, 2) = -3.04159655555617, (2, 3) = -0.7886265467496404e-2, (2, 4) = -2.2712081318866444, (2, 5) = -2.9299124643506866, (2, 6) = 6.973328161356879, (3, 1) = -3.7983843053718003, (3, 2) = -.2191094271112375, (3, 3) = -.16570559152242836, (3, 4) = -4.097526495354406, (3, 5) = -2.6078034998261606, (3, 6) = 5.757981542128251, (4, 1) = -3.7065833064563183, (4, 2) = 3.930050502868366, (4, 3) = -.4504788339676847, (4, 4) = -6.946812582589477, (4, 5) = -2.3329390514471964, (4, 6) = 4.79477796465889, (5, 1) = -3.431721972279278, (5, 2) = 8.29672095085938, (5, 3) = -.8321572505352428, (5, 4) = -9.970518789704158, (5, 5) = -2.1316694336743605, (5, 6) = 4.1201428566394505, (6, 1) = -3.0391816325972827, (6, 2) = 12.140457543418716, (6, 3) = -1.2651566036115673, (6, 4) = -12.563493312469376, (6, 5) = -1.9831367804400784, (6, 6) = 3.631776833962368, (7, 1) = -2.580867202344822, (7, 2) = 15.194694466844348, (7, 3) = -1.7189089681714942, (7, 4) = -14.499297274998137, (7, 5) = -1.86811269574634, (7, 6) = 3.255014533758307, (8, 1) = -2.0868920283383767, (8, 2) = 17.405006190704025, (8, 3) = -2.176905317660935, (8, 4) = -15.7263194921503, (8, 5) = -1.7745252963625566, (8, 6) = 2.9467070050276982, (9, 1) = -1.5698532569193275, (9, 2) = 18.782720425968986, (9, 3) = -2.6336908365432468, (9, 4) = -16.243091305361336, (9, 5) = -1.6944750044895431, (9, 6) = 2.6797089676684482, (10, 1) = -1.0362382622884123, (10, 2) = 19.30931718099608, (10, 3) = -3.0857546328110734, (10, 4) = -16.02408238602015, (10, 5) = -1.623107293673211, (10, 6) = 2.4373370748165213, (11, 1) = -.49201468875877025, (11, 2) = 18.916395122027694, (11, 3) = -3.5275886409827275, (11, 4) = -15.003886500576392, (11, 5) = -1.5572794718852523, (11, 6) = 2.208380962285937, (12, 1) = 0.54627866260378306e-1, (12, 2) = 17.474209410708973, (12, 3) = -3.9493942806978732, (12, 4) = -13.066894823711849, (12, 5) = -1.4946447563190588, (12, 6) = 1.9837050921906823, (13, 1) = .5882277932627828, (13, 2) = 14.768557616409225, (13, 3) = -4.3318490778469, (13, 4) = -10.029649089488705, (13, 5) = -1.4331769658752087, (13, 6) = 1.7541174718260835, (14, 1) = 1.061035885737002, (14, 2) = 10.625903166992163, (14, 3) = -4.626437061503043, (14, 4) = -5.7772366642187984, (14, 5) = -1.3727368303912408, (14, 6) = 1.515782771743526, (15, 1) = 1.3317906480247055, (15, 2) = 6.542639835111612, (15, 3) = -4.7459341712306315, (15, 4) = -1.7967056638809809, (15, 5) = -1.3280648427471695, (15, 6) = 1.3280648427471695}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(15, {(1) = .5, (2) = .5336121902422217, (3) = .5844381546054477, (4) = .6367246910382582, (5) = .6819813637076192, (6) = .7203576555258304, (7) = .7537947476785826, (8) = .7839983988541166, (9) = .8124715099760172, (10) = .8403819137356267, (11) = .8687377326893805, (12) = .8986394117549072, (13) = .9315548210903578, (14) = .968559697402719, (15) = 1.0}, datatype = float[8], order = C_order); Y := Matrix(15, 6, {(1, 1) = .0, (1, 2) = 0.5567591149559529e-9, (1, 3) = .0, (1, 4) = -0.4720178433566516e-9, (1, 5) = .0, (1, 6) = 0.5806238456307002e-11, (2, 1) = 0.2594749531815668e-10, (2, 2) = 0.10438246203626163e-8, (2, 3) = -0.21934507360142496e-10, (2, 4) = -0.8796874640428898e-9, (2, 5) = 0.1539628482016512e-12, (2, 6) = 0.5717965888169809e-11, (3, 1) = 0.5992251035338046e-10, (3, 2) = 0.11925708541839176e-8, (3, 3) = -0.4913589721875806e-10, (3, 4) = -0.9881856955882214e-9, (3, 5) = -0.42377484545175315e-12, (3, 6) = 0.37912390130539474e-11, (4, 1) = -0.14977345101819915e-10, (4, 2) = 0.7606903966640406e-10, (4, 3) = 0.13088748257276803e-10, (4, 4) = -0.6167456079213195e-10, (4, 5) = -0.7213832404795737e-12, (4, 6) = 0.2711671755590121e-11, (5, 1) = -0.29581472668313945e-10, (5, 2) = -0.22505785900536102e-10, (5, 3) = 0.24511870707456357e-10, (5, 4) = 0.1523263250638019e-10, (5, 5) = -0.6680631853736067e-12, (5, 6) = 0.2494497371838201e-11, (6, 1) = -0.28132564850902845e-10, (6, 2) = 0.17623841132090892e-10, (6, 3) = 0.2298862024001426e-10, (6, 4) = -0.1870675793704771e-10, (6, 5) = -0.5814762221025983e-12, (6, 6) = 0.2398392246363883e-11, (7, 1) = -0.25630934707125227e-10, (7, 2) = 0.464417837666462e-10, (7, 3) = 0.2075704845360695e-10, (7, 4) = -0.42096191408218247e-10, (7, 5) = -0.5044805307603398e-12, (7, 6) = 0.23235686264674555e-11, (8, 1) = -0.23241994857474903e-10, (8, 2) = 0.6641278190244896e-10, (8, 3) = 0.18686399062714793e-10, (8, 4) = -0.57832440664354906e-10, (8, 5) = -0.43548662306535644e-12, (8, 6) = 0.22584332393050797e-11, (9, 1) = -0.2079247784589872e-10, (9, 2) = 0.8271773247960182e-10, (9, 3) = 0.1660240138091526e-10, (9, 4) = -0.7033871003740232e-10, (9, 5) = -0.37219532636603117e-12, (9, 6) = 0.2194400771161029e-11, (10, 1) = -0.18146969888012006e-10, (10, 2) = 0.9709240804926876e-10, (10, 3) = 0.14393471145425924e-10, (10, 4) = -0.810332066863477e-10, (10, 5) = -0.31219930318568087e-12, (10, 6) = 0.21336640487388516e-11, (11, 1) = -0.1522072981285547e-10, (11, 2) = 0.10994741572009034e-9, (11, 3) = 0.1198933038629346e-10, (11, 4) = -0.9022224404382198e-10, (11, 5) = -0.2525881426764856e-12, (11, 6) = 0.20721655750009697e-11, (12, 1) = -0.1194863200331772e-10, (12, 2) = 0.12111526364535104e-9, (12, 3) = 0.9344725691772761e-11, (12, 4) = -0.9772544015992493e-10, (12, 5) = -0.19154070588675547e-12, (12, 6) = 0.20111028272235497e-11, (13, 1) = -0.8298349114678449e-11, (13, 2) = 0.1298997578871148e-9, (13, 3) = 0.6441581863400948e-11, (13, 4) = -0.10291220194017138e-9, (13, 5) = -0.12710438218746106e-12, (13, 6) = 0.19414204479209388e-11, (14, 1) = -0.425748905007238e-11, (14, 2) = 0.13576851550915667e-9, (14, 3) = 0.32679276073938085e-11, (14, 4) = -0.10533975377445373e-9, (14, 5) = -0.5745144768422898e-13, (14, 6) = 0.18683030113516307e-11, (15, 1) = .0, (15, 2) = 0.14097193658053773e-9, (15, 3) = .0, (15, 4) = -0.10711280470593468e-9, (15, 5) = .0, (15, 6) = 0.18092580983940886e-11}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[15] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(1.1925708541839176e-9) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [6, 15, [phi(y), diff(phi(y), y), theta(y), diff(theta(y), y), v(y), diff(v(y), y)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[15] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[15] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(6, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(15, 6, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(6, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(15, 6, X, Y, outpoint, yout, L, V) end if; [y = outpoint, seq('[phi(y), diff(phi(y), y), theta(y), diff(theta(y), y), v(y), diff(v(y), y)]'[i] = yout[i], i = 1 .. 6)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[15] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(1.1925708541839176e-9) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [6, 15, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[15] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[15] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(6, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(15, 6, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(6, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0.}); `dsolve/numeric/hermite`(15, 6, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 6)] end proc, (2) = Array(0..0, {}), (3) = [y, phi(y), diff(phi(y), y), theta(y), diff(theta(y), y), v(y), diff(v(y), y)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(x_bvp) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(x_bvp) else _ndsol := pointto(data[2][0]); return ('_ndsol')(x_bvp) end if end if; try res := solnproc(outpoint); [y = res[1], seq('[phi(y), diff(phi(y), y), theta(y), diff(theta(y), y), v(y), diff(v(y), y)]'[i] = res[i+1], i = 1 .. 6)] catch: error  end try end proc

 

 

 

 

``


 

Download odeProb.mw

by "difference quotient", that you want to compute (1/h)*(f(x+h)-f(x)), then the attached should work

  restart;
  DQ:= proc( expr, var:=x)
             local f:= unapply(expr, var);
             return simplify((f(var+h)-f(var))/h);
       end proc:
##############################################
# Some examples
##############################################
# If no variable name is supplied as a second
# argument to procedure DQ, then 'x' will be
# used as default
#
  DQ(3-x^2-x);
  DQ(a*x^2+b*x+c);
#
# If using a different variable name, then
# variable name has to be specified
#
  DQ((t-3)/(5-t), t);
  DQ((t-a)/(b-t), t);
  DQ((t-3)/(b-t), t);

-h-2*x-1

 

(h+2*x)*a+b

 

2/((-5+t+h)*(-5+t))

 

(-a+b)/((b-t-h)*(b-t))

 

(b-3)/((b-t-h)*(b-t))

(1)

 


 

Download DQ.mw

that you want to find a set of 16 values which makes the expression=0, or as close as possible.

  1. I didn't have any luck with commands from Maple's in-built Optimization package
  2. Using the (free) addon DirectSearch() available from the Maple Application Centre a pretty plausible solution can be found - ie one can find a set of values for the 16 coefficients so that the resulting value of the original expression will be ~10-10

If this is not your intent, then you will have to clarify

NB you will not been able to execute the attached until/unless you have the DirectSearch package loaded :-(

restart;
#
# Coefficients in OP's expression have about 15-16
# digits. Maple's defauly Digits setting is 10, so
# wind it up a little just to ensure that rounding
# issues won't happen
#
Digits:=20:
expr:=1.47449729919434*10^10*c[0, 1]*c[0, 2]*c[2, 2]*c[3, 0]+3.38624318440755*10^8*c[0, 1]*c[0, 3]*c[1, 0]*c[2, 1]+1.54309415817260*10^10*c[0, 1]*c[0, 3]*c[1, 3]*c[2, 0]+1.69527735464914*10^14*c[0, 2]*c[0, 3]*c[1, 3]*c[3, 3]+5.64571777979530*10^11*c[0, 1]*c[1, 3]*c[3, 0]*c[3, 1]+5.64571777979530*10^11*c[0, 1]*c[1, 1]*c[3, 0]*c[3, 3]+3.44365358352662*10^11*c[0, 1]*c[1, 1]*c[3, 1]*c[3, 2]+4.56141047477722*10^11*c[0, 1]*c[0, 2]*c[2, 1]*c[3, 3]+1.47449729919434*10^10*c[0, 1]*c[0, 2]*c[2, 0]*c[3, 2]+1.00292015075684*10^10*c[0, 1]*c[0, 2]*c[2, 1]*c[3, 1]+4.96419365552208*10^14*c[1, 1]*c[2, 3]*c[3, 1]*c[3, 2]+2.41547661753786*10^16*c[1, 1]*c[2, 3]*c[3, 2]*c[3, 3]+3.09237360954284*10^11*c[0, 2]*c[1, 1]*c[1, 3]*c[3, 1]+2.07077209298372*10^13*c[0, 2]*c[2, 2]*c[2, 3]*c[3, 0]+2.77395036220550*10^11*c[0, 2]*c[1, 1]*c[1, 2]*c[3, 2]+3.25883571082134*10^15*c[1, 2]*c[2, 3]*c[3, 1]*c[3, 2]+2.77442234357198*10^11*c[0, 2]*c[1, 1]*c[2, 1]*c[2, 3]+7.80736282336175*10^14*c[2, 0]*c[2, 1]*c[3, 2]*c[3, 3]+3.25883571082134*10^15*c[1, 2]*c[2, 2]*c[3, 1]*c[3, 3]+5.35593751087840*10^15*c[1, 2]*c[2, 3]*c[3, 0]*c[3, 3]+3.63255405301248*10^15*c[1, 1]*c[2, 3]*c[3, 1]*c[3, 3]+3.25883571082134*10^15*c[1, 2]*c[2, 1]*c[3, 2]*c[3, 3]+1.48022406855142*10^13*c[1, 0]*c[2, 1]*c[2, 2]*c[3, 3]+5.19766484559825*10^15*c[0, 1]*c[2, 3]*c[3, 2]*c[3, 3]+3.63255405301248*10^15*c[1, 3]*c[2, 1]*c[3, 1]*c[3, 3]+1.03156027712140*10^14*c[0, 3]*c[1, 2]*c[1, 3]*c[2, 3]+6.84418565576730*10^13*c[1, 1]*c[1, 2]*c[1, 3]*c[3, 3]+1.36253689407226*10^13*c[0, 1]*c[1, 2]*c[2, 3]*c[3, 2]+4.50722523384354*10^11*c[0, 1]*c[0, 2]*c[1, 2]*c[3, 3]+4.63272867590191*10^14*c[1, 1]*c[1, 3]*c[2, 3]*c[3, 2]+9.56722337372450*10^9*c[0, 1]*c[0, 2]*c[1, 2]*c[1, 3]+7.56283392524430*10^14*c[0, 3]*c[1, 1]*c[2, 3]*c[3, 3]+1.51879056084535*10^13*c[0, 3]*c[1, 1]*c[2, 3]*c[3, 1]+8.15436050904650*10^14*c[1, 1]*c[2, 3]*c[3, 0]*c[3, 3]+1.51879056084535*10^13*c[0, 1]*c[1, 1]*c[2, 3]*c[3, 3]+3.05712170936082*10^11*c[0, 1]*c[1, 1]*c[1, 3]*c[2, 3]+2.21942429315476*10^9*c[0, 1]*c[0, 2]*c[1, 0]*c[3, 2]+1.50960286458333*10^9*c[0, 1]*c[0, 2]*c[1, 1]*c[3, 1]+6.37602806091310*10^9*c[0, 1]*c[1, 1]*c[1, 2]*c[1, 3]+2.22015380859375*10^7*c[0, 0]*c[1, 0]*c[1, 1]*c[3, 0]+2.24812825520834*10^6*c[0, 0]*c[0, 1]*c[1, 0]*c[2, 1]+2.24812825520834*10^6*c[0, 0]*c[0, 1]*c[1, 1]*c[2, 0]+4.45556640625000*10^5*c[0, 0]*c[0, 1]*c[0, 2]*c[1, 0]+1.80236816406250*10^7*c[0, 0]*c[0, 2]*c[0, 3]*c[1, 0]+9.99813988095240*10^6*c[0, 1]*c[1, 0]*c[1, 1]*c[2, 0]+1.64310515873016*10^7*c[0, 0]*c[0, 1]*c[1, 0]*c[3, 1]+1.09924316406250*10^7*c[0, 0]*c[0, 1]*c[0, 2]*c[1, 2]+1.22578938802084*10^7*c[0, 0]*c[0, 1]*c[0, 3]*c[1, 1]+6.74438476562500*10^5*c[0, 0]*c[0, 1]*c[1, 0]*c[2, 0]+3.27484130859375*10^7*c[0, 0]*c[0, 1]*c[2, 0]*c[3, 0]+4.96419365552208*10^14*c[1, 1]*c[2, 2]*c[3, 1]*c[3, 3]+1.48022406855142*10^13*c[1, 2]*c[2, 0]*c[2, 1]*c[3, 3]+1.48022406855142*10^13*c[1, 2]*c[2, 0]*c[2, 3]*c[3, 1]+7.00457388588595*10^14*c[1, 2]*c[2, 0]*c[2, 3]*c[3, 3]+9.01806926154510*10^12*c[1, 2]*c[2, 1]*c[2, 2]*c[3, 1]+4.26195329427362*10^14*c[1, 1]*c[2, 2]*c[2, 3]*c[3, 2]+8.70017911044035*10^14*c[1, 1]*c[3, 0]*c[3, 2]*c[3, 3]+1.64960358855012*10^13*c[1, 2]*c[1, 3]*c[3, 0]*c[3, 1]+8.70017911044035*10^14*c[1, 3]*c[3, 0]*c[3, 1]*c[3, 2]+4.11701503132284*10^16*c[1, 3]*c[3, 0]*c[3, 2]*c[3, 3]+1.32823657812862*10^13*c[2, 0]*c[2, 1]*c[2, 2]*c[2, 3]+2.49782355477406*10^13*c[0, 1]*c[0, 3]*c[3, 1]*c[3, 3]+1.86077008928572*10^7*c[0, 0]*c[0, 1]*c[0, 2]*c[0, 3]+4.50750425170068*10^11*c[0, 3]*c[1, 2]*c[1, 3]*c[2, 0]+2.41765159606934*10^10*c[0, 0]*c[0, 2]*c[2, 0]*c[3, 3]+1.28155946659681*10^15*c[2, 0]*c[2, 3]*c[3, 0]*c[3, 3]+7.80736282336175*10^14*c[2, 0]*c[2, 3]*c[3, 1]*c[3, 2]+2.95015059452266*10^13*c[2, 0]*c[2, 3]*c[3, 0]*c[3, 1]+1.64424324035644*10^10*c[0, 1]*c[0, 3]*c[2, 0]*c[3, 1]+7.80736282336175*10^14*c[2, 0]*c[2, 2]*c[3, 1]*c[3, 3]+3.38624318440755*10^8*c[0, 1]*c[0, 3]*c[1, 1]*c[2, 0]+6.83811849201320*10^14*c[0, 2]*c[2, 1]*c[2, 3]*c[3, 3]+4.96419365552208*10^14*c[1, 1]*c[2, 1]*c[3, 2]*c[3, 3]+4.50722523384354*10^11*c[0, 1]*c[0, 2]*c[1, 3]*c[3, 2]+2.74640085129511*10^12*c[0, 3]^2*c[1, 3]*c[3, 0]+4.53797990504672*10^10*c[0, 2]^2*c[2, 0]*c[2, 3]+2.76260943995885*10^10*c[0, 2]^2*c[2, 1]*c[2, 2]+5.63905988420760*10^10*c[0, 3]^2*c[1, 0]*c[3, 1]+2.74640085129511*10^12*c[0, 3]^2*c[1, 0]*c[3, 3]+5.63905988420760*10^10*c[0, 3]^2*c[1, 1]*c[3, 0]+1.67039675031390*10^12*c[0, 3]^2*c[1, 1]*c[3, 2]+1.67039675031390*10^12*c[0, 3]^2*c[1, 2]*c[3, 1]:

#
# Assuming OP wants expr=0, the simplest(?) way is
# probably to minimise expr^2
#
  sol:=DirectSearch:-GlobalSearch( expr^2 );
#
# Although DirectSearch is supposed to order all
# the found solutions, it is safer to check the
# value of expr^2 with each of the solutions in
# turn, then seelct the one which provides the
# minimum residual
#
  ind:=min[index]([seq(eval( expr^2, sol[j,2]), j=1..100)]);
#
# Display the solution with the minimum residual
#
  sol[ind,..];
  eval(expr^2, sol[ind,2]);

sol := Array(1..100, 1..3, {(1, 1) = 0., (1, 2) = [c[0, 0] = 90.800618604856040144, c[0, 1] = -80.253806713827979858, c[0, 2] = -26.829207644135640647, c[0, 3] = -704.62180814972478320, c[1, 0] = -49.942273117681432408, c[1, 1] = 6.4300180510788979697, c[1, 2] = -104.42182807135754446, c[1, 3] = -9.9555323416839459324, c[2, 0] = 16.563761214715724811, c[2, 1] = -121.61043459974129950, c[2, 2] = 47.024639117183508658, c[2, 3] = -14.385555211352035714, c[3, 0] = 96.429664101707244401, c[3, 1] = 88.850686272158251943, c[3, 2] = 13.024724301727707363, c[3, 3] = -21.416345078669364685], (1, 3) = 870, (2, 1) = 0., (2, 2) = [c[0, 0] = 448.94799558552258936, c[0, 1] = -82.770589413565433668, c[0, 2] = 617.00266683244143173, c[0, 3] = 616.57043534913041824, c[1, 0] = 78.333417765823178235, c[1, 1] = -54.110649223126769226, c[1, 2] = -81.264427661221162437, c[1, 3] = 5.2286784922524730076, c[2, 0] = -50.436275607882672265, c[2, 1] = 20.280338841521632556, c[2, 2] = 35.925572422756769301, c[2, 3] = -15.096754413320999159, c[3, 0] = -43.162348851173935802, c[3, 1] = 49.006018860827494449, c[3, 2] = 21.007014506308305273, c[3, 3] = -54.793251171212021073], (2, 3) = 3133, (3, 1) = 0., (3, 2) = [c[0, 0] = -121.67423682280960361, c[0, 1] = 12.577922533147690623, c[0, 2] = 3.5152107352064083382, c[0, 3] = 35.549295155417981630, c[1, 0] = -208.15720370356301164, c[1, 1] = -73.452479994076119184, c[1, 2] = -87.664562155391665082, c[1, 3] = -42.681926206001640162, c[2, 0] = -90.954060303820801353, c[2, 1] = -17.386442006301847854, c[2, 2] = -37.787250616184344495, c[2, 3] = -93.541825927414045398, c[3, 0] = 96.441866613005686235, c[3, 1] = 26.436043590318582758, c[3, 2] = -9.9365562444848279505, c[3, 3] = 1.0331122656576359068], (3, 3) = 2309, (4, 1) = 0.196e-19, (4, 2) = [c[0, 0] = -1.8243538810367763440, c[0, 1] = 1.7996826772852573644, c[0, 2] = .18365167026843320790, c[0, 3] = -.11853244312417180297, c[1, 0] = 13.859921608013804918, c[1, 1] = -.21729129933076301149, c[1, 2] = 0.16218969510361195014e-1, c[1, 3] = 0.83933889689887728476e-1, c[2, 0] = -0.12991229066982614778e-1, c[2, 1] = 0.88779183916655130951e-2, c[2, 2] = 0.89640935470539434575e-2, c[2, 3] = 0.27417785779224142601e-2, c[3, 0] = -0.32908967050719276438e-1, c[3, 1] = 0.65400937056718118063e-2, c[3, 2] = 0.30865749527965067239e-3, c[3, 3] = 0.65158888642353488075e-3], (4, 3) = 2297, (5, 1) = .24117921, (5, 2) = [c[0, 0] = -60.312437623223771337, c[0, 1] = 18.093428707227214297, c[0, 2] = 50.296061618997922163, c[0, 3] = 27.434534861585837554, c[1, 0] = -114.14977801857413274, c[1, 1] = -18.467641837049286093, c[1, 2] = -23.888485209989545669, c[1, 3] = -94.572145041945609500, c[2, 0] = 62.618605079923699114, c[2, 1] = 65.180646116961678637, c[2, 2] = -38.532118967301656632, c[2, 3] = 7.7074658310334670483, c[3, 0] = 50.410323045693190337, c[3, 1] = 1.0098716516777567044, c[3, 2] = -47.755623881622784538, c[3, 3] = 0.18581113264929290410e-1], (5, 3) = 1640, (6, 1) = 4., (6, 2) = [c[0, 0] = -60.135361023583978097, c[0, 1] = -23.060788623345666603, c[0, 2] = 41.760238293702591651, c[0, 3] = 37.442540043501672840, c[1, 0] = 114.06361121998335127, c[1, 1] = 84.844079067966027419, c[1, 2] = -13.393452536449261441, c[1, 3] = -5.7641271351115461142, c[2, 0] = 42.312939187316471660, c[2, 1] = -46.827247387085788185, c[2, 2] = 52.813804195725848220, c[2, 3] = -58.765653577441311132, c[3, 0] = -48.425236454009223148, c[3, 1] = -27.948304683756506970, c[3, 2] = -17.163184554513126015, c[3, 3] = -.45684000043856580402], (6, 3) = 1785, (7, 1) = 4.1182208356, (7, 2) = [c[0, 0] = -48.294739787187889064, c[0, 1] = 83.605038535714361324, c[0, 2] = -76.045206362502702975, c[0, 3] = 65.317755799241124955, c[1, 0] = 152.47199784344010281, c[1, 1] = -44.905399615055905655, c[1, 2] = 73.555500097068391851, c[1, 3] = 43.022840966079522287, c[2, 0] = 41.325738619076191899, c[2, 1] = -30.022551465016004496, c[2, 2] = 59.636167179327323360, c[2, 3] = 57.553756907139131753, c[3, 0] = 33.538530237078640690, c[3, 1] = -33.557837605464205548, c[3, 2] = 5.6885773090600926817, c[3, 3] = 3.1608854146982035391], (7, 3) = 1444, (8, 1) = 9.914516293581600100, (8, 2) = [c[0, 0] = 36.375448937126973286, c[0, 1] = 37.185787575902912540, c[0, 2] = .20631254755008981161, c[0, 3] = -5.7615657022519447864, c[1, 0] = -72.268909954011805920, c[1, 1] = 10.484870971664001887, c[1, 2] = 76.600206378645328793, c[1, 3] = 65.928602109201855777, c[2, 0] = 55.849514613719819076, c[2, 1] = 66.536499588510447105, c[2, 2] = 109.96868412094962944, c[2, 3] = 21.769314711467684071, c[3, 0] = -33.186979219014035705, c[3, 1] = 101.43991074226584559, c[3, 2] = 18.907660366670471991, c[3, 3] = -2.6344160291742988514], (8, 3) = 2750, (9, 1) = 79.21, (9, 2) = [c[0, 0] = -106.21951263058552955, c[0, 1] = 23.251069697207610450, c[0, 2] = 1227.8920131963264872, c[0, 3] = -23.490929358290286491, c[1, 0] = 72.148175423309967623, c[1, 1] = -5.2419660088900005292, c[1, 2] = 86.090801014067647082, c[1, 3] = -5.7753523603683559858, c[2, 0] = -7.3408254665658043140, c[2, 1] = 89.367853329467073261, c[2, 2] = -27.046171413520650751, c[2, 3] = 27.909346020296044879, c[3, 0] = 20.786772470683189764, c[3, 1] = -56.643621650685406436, c[3, 2] = -70.530254376407223054, c[3, 3] = -18.651995422991785394], (9, 3) = 2768, (10, 1) = 249.64, (10, 2) = [c[0, 0] = -32.287550541750268689, c[0, 1] = -70.419251792873191498, c[0, 2] = 114.05784350536789027, c[0, 3] = -75.850402853366981696, c[1, 0] = 112.97362706789334491, c[1, 1] = -86.783385147633353202, c[1, 2] = -67.863693066039914153, c[1, 3] = -81.398381248543968388, c[2, 0] = -17.415075818965571016, c[2, 1] = -22.027869574375384273, c[2, 2] = -23.121036020090043707, c[2, 3] = 9.4441777955336236270, c[3, 0] = -58.141514470763869432, c[3, 1] = 53.347282376004536567, c[3, 2] = -53.940419826972393807, c[3, 3] = -.78338381834930826752], (10, 3) = 2934, (11, 1) = 0.4e3, (11, 2) = [c[0, 0] = -29.246922314851986153, c[0, 1] = 68.790712905849014424, c[0, 2] = 25.087807025936773940, c[0, 3] = -60.197253101245386848, c[1, 0] = 99.216003188747697253, c[1, 1] = -93.344952770780150779, c[1, 2] = 20.348714186850253339, c[1, 3] = 72.778794786477493144, c[2, 0] = 97.392767723357634394, c[2, 1] = 33.821685659635278145, c[2, 2] = 89.641572689044976788, c[2, 3] = -9.5672395644583496732, c[3, 0] = -82.055810931721089171, c[3, 1] = -62.048261640857299824, c[3, 2] = 43.829517094655052345, c[3, 3] = 1.8052780534058105510], (11, 3) = 3989, (12, 1) = 501.76, (12, 2) = [c[0, 0] = 80.178195615601903472, c[0, 1] = 76.501537628261452657, c[0, 2] = .67665704836479598959, c[0, 3] = 85.170282139981553340, c[1, 0] = 84.088564936935802978, c[1, 1] = 94.367074083507992096, c[1, 2] = -11.139267964242527960, c[1, 3] = -71.387340237702037706, c[2, 0] = 53.091157839344806536, c[2, 1] = 55.660837230175724893, c[2, 2] = 61.137252113385643286, c[2, 3] = 21.117473745262849635, c[3, 0] = 62.184605600934288117, c[3, 1] = -57.843830390030156252, c[3, 2] = 7.3129671209868175075, c[3, 3] = 2.3060816462920646496], (12, 3) = 1979, (13, 1) = 515.29, (13, 2) = [c[0, 0] = -91.644721390545757470, c[0, 1] = -41.232168224408871020, c[0, 2] = -26.985299714039525633, c[0, 3] = -53.717105755306710207, c[1, 0] = 50.511205253079424941, c[1, 1] = -21.433759588550271105, c[1, 2] = -19.179929605740899365, c[1, 3] = -35.322806505898414548, c[2, 0] = -62.624122810811227345, c[2, 1] = 11.229828612963415592, c[2, 2] = -57.399238547945841807, c[2, 3] = -79.038374535780048006, c[3, 0] = -35.553115129857825058, c[3, 1] = -68.670468102115551671, c[3, 2] = 6.8774494723061011527, c[3, 3] = -6.1398719198666939824], (13, 3) = 2253, (14, 1) = 661.5184, (14, 2) = [c[0, 0] = 98.501017273654006019, c[0, 1] = -92.172739530392424984, c[0, 2] = 99.710757447401871800, c[0, 3] = 36.582184366054164835, c[1, 0] = -51.444468963884437525, c[1, 1] = -30.098631236030971358, c[1, 2] = 46.279117414904037653, c[1, 3] = 5.6823176504709505516, c[2, 0] = -43.433309198128592368, c[2, 1] = 49.546727360418995127, c[2, 2] = 12.894591326528063464, c[2, 3] = -59.591631957167851070, c[3, 0] = 3.3847139558314167306, c[3, 1] = 32.779209127336988501, c[3, 2] = -79.381614702862729801, c[3, 3] = 2.4110238374422745190], (14, 3) = 3451, (15, 1) = 696.537664, (15, 2) = [c[0, 0] = 17.113272850943742227, c[0, 1] = 8.4056720833245272102, c[0, 2] = -47.429934292735373377, c[0, 3] = -58.623912462804706390, c[1, 0] = -3.2955047928835781713, c[1, 1] = -27.116900455473853784, c[1, 2] = -19.412179361842407677, c[1, 3] = -62.493531271770932302, c[2, 0] = -90.360178351823858356, c[2, 1] = -68.939356258260236731, c[2, 2] = -65.327797271408997086, c[2, 3] = -97.823733957390853363, c[3, 0] = -78.184308317751464731, c[3, 1] = 34.127840701403187354, c[3, 2] = -13.157096228917767671, c[3, 3] = -1.1716103579598141206], (15, 3) = 1689, (16, 1) = 712.89, (16, 2) = [c[0, 0] = -25.912798686524559917, c[0, 1] = 54.576811184653132035, c[0, 2] = 10.622905914979616504, c[0, 3] = 25.183061805431547300, c[1, 0] = -16.852315928349245754, c[1, 1] = -83.195549450197025693, c[1, 2] = -69.678981547203731962, c[1, 3] = -51.004187493198882798, c[2, 0] = 28.779433886425432812, c[2, 1] = -38.832548035235959610, c[2, 2] = 65.640117678645798579, c[2, 3] = -31.600752410917695765, c[3, 0] = -47.899100510355055132, c[3, 1] = .77250121504957674832, c[3, 2] = -51.360039650999691165, c[3, 3] = -.14122971706902718597], (16, 3) = 2219, (17, 1) = 1030.6019669401, (17, 2) = [c[0, 0] = -13.535240838571407856, c[0, 1] = -75.669795068435382367, c[0, 2] = 43.302895792337573178, c[0, 3] = -45.209253928372937581, c[1, 0] = -263.74995378311393205, c[1, 1] = -13.212491214877818037, c[1, 2] = 40.025108662543413191, c[1, 3] = -84.939155658164546489, c[2, 0] = 43.615140014123083278, c[2, 1] = 5.4015773631207522541, c[2, 2] = 57.076256694650572086, c[2, 3] = 24.278938255289153164, c[3, 0] = -17.452232074867454726, c[3, 1] = 38.918947873679586426, c[3, 2] = -4.5176564996578759721, c[3, 3] = 93.116349996565713764], (17, 3) = 3230, (18, 1) = 2209., (18, 2) = [c[0, 0] = -60.238373035623518901, c[0, 1] = -55.360530115895468642, c[0, 2] = -21.759757044803952757, c[0, 3] = -88.468771638837724422, c[1, 0] = 101.05530277116416549, c[1, 1] = 40.256652573062585211, c[1, 2] = 59.005870025224393102, c[1, 3] = 10.484596241569103060, c[2, 0] = -75.104567833275602073, c[2, 1] = -9.2803858499802309213, c[2, 2] = 41.832685371623490435, c[2, 3] = 2.2982082745523514905, c[3, 0] = -13.593198420364340422, c[3, 1] = 28.282656064771237058, c[3, 2] = 38.955803966563852051, c[3, 3] = 4.8949065730008302873], (18, 3) = 2146, (19, 1) = 0.36e4, (19, 2) = [c[0, 0] = -49.424328621181850216, c[0, 1] = 22.446899141563983122, c[0, 2] = 68.668904053404299396, c[0, 3] = 89.003508856470585859, c[1, 0] = -50.828968021748779105, c[1, 1] = 40.192531989490129418, c[1, 2] = 9.9547658833412172494, c[1, 3] = 48.868189261183624339, c[2, 0] = 88.572693914318593547, c[2, 1] = -44.947280732299278392, c[2, 2] = 19.225645696419015114, c[2, 3] = 32.395909104030562026, c[3, 0] = 4.2540672781225857476, c[3, 1] = -91.530312289703005713, c[3, 2] = -57.766452737982874536, c[3, 3] = 9.5274387062879784124], (19, 3) = 2101, (20, 1) = 4558.9504, (20, 2) = [c[0, 0] = 15.176789607045411365, c[0, 1] = 22.973942175448400767, c[0, 2] = 97.548474540941671426, c[0, 3] = 13.531238844789944883, c[1, 0] = -65.442655367040818701, c[1, 1] = -28.730486243606739510, c[1, 2] = 62.638897500995603347, c[1, 3] = -12.414984392424474932, c[2, 0] = -29.261382601979747958, c[2, 1] = 68.778661900743331893, c[2, 2] = -99.407740163903229733, c[2, 3] = -74.304275477660867689, c[3, 0] = 73.894045659215350903, c[3, 1] = 44.946525230932098284, c[3, 2] = 52.063710360452390343, c[3, 3] = -23.410507400731097740], (20, 3) = 2062, (21, 1) = 6241., (21, 2) = [c[0, 0] = 14.058645920176532806, c[0, 1] = 98.871915337298485565, c[0, 2] = -53.010227338235577302, c[0, 3] = 101.87731347051023748, c[1, 0] = 64.566140734275907674, c[1, 1] = -26.296636265712736043, c[1, 2] = 35.437473717053035507, c[1, 3] = -1.0492728927095834515, c[2, 0] = -56.615258233145873952, c[2, 1] = 56.760902878982181548, c[2, 2] = -28.359159756704594984, c[2, 3] = -19.798423197493386969, c[3, 0] = 82.648675461134898978, c[3, 1] = -14.406973476883212200, c[3, 2] = -72.299795149875013973, c[3, 3] = -12.034022573794797270], (21, 3) = 3440, (22, 1) = 7691.29, (22, 2) = [c[0, 0] = 51.255196919320746401, c[0, 1] = 93.173313102812333677, c[0, 2] = 8.4302171565401233236, c[0, 3] = -81.573604056381647508, c[1, 0] = 3.7988917381315229500, c[1, 1] = -42.593576199137662379, c[1, 2] = 25.165862398168646890, c[1, 3] = 14.887143031324055183, c[2, 0] = 26.540029805960939435, c[2, 1] = -11.446429961217790134, c[2, 2] = -40.770149501229288241, c[2, 3] = 39.736651910847942400, c[3, 0] = -28.291915670643608210, c[3, 1] = 81.407972265291893327, c[3, 2] = -19.448029934988709637, c[3, 3] = -41.807558778288236305], (22, 3) = 2670, (23, 1) = 0.1e5, (23, 2) = [c[0, 0] = -51.346636414835292414, c[0, 1] = 52.202526457178011497, c[0, 2] = -5.6503063403998577468, c[0, 3] = 12.336597812609529671, c[1, 0] = -46.044629192128233602, c[1, 1] = 46.594159170525007991, c[1, 2] = 39.705672264530025190, c[1, 3] = 92.059486341969740800, c[2, 0] = -69.038214720162062270, c[2, 1] = -64.670686381082062590, c[2, 2] = -98.440867242461532168, c[2, 3] = 85.738085086508489753, c[3, 0] = -7.9886657989456412055, c[3, 1] = 85.516725154884315584, c[3, 2] = 22.378208728811683144, c[3, 3] = -71.426982654931815076], (23, 3) = 1619, (24, 1) = 11273.3366054409, (24, 2) = [c[0, 0] = 92.400665355428942819, c[0, 1] = -100.19492640683331028, c[0, 2] = 97.681336143088319184, c[0, 3] = -23.472631780539951078, c[1, 0] = -39.072627750103453591, c[1, 1] = -15.613451574460163622, c[1, 2] = -69.526994179002076556, c[1, 3] = 5.0005235054022527675, c[2, 0] = 69.851276973984300705, c[2, 1] = -52.581501280521045486, c[2, 2] = -13.421828562277267851, c[2, 3] = 83.032984186516257277, c[3, 0] = -65.439515061736903154, c[3, 1] = 42.116121453317235571, c[3, 2] = -76.686628949486419686, c[3, 3] = -6.9395400991016093423], (24, 3) = 2664, (25, 1) = 11881., (25, 2) = [c[0, 0] = -65.684419614002139591, c[0, 1] = 77.218499527054358856, c[0, 2] = -37.952691962414468827, c[0, 3] = -103.00723796858668436, c[1, 0] = 84.625588525517030278, c[1, 1] = -.20508782559432363222, c[1, 2] = 41.080176176141981639, c[1, 3] = -61.684072730046058846, c[2, 0] = 92.399702754733011705, c[2, 1] = -.54935277602811020992, c[2, 2] = 52.874147791784922384, c[2, 3] = -77.550402560200309806, c[3, 0] = -23.375657115697225718, c[3, 1] = 48.670303919776533323, c[3, 2] = 70.452434456132739762, c[3, 3] = 18.141502260899910193], (25, 3) = 2837, (26, 1) = 12254.49, (26, 2) = [c[0, 0] = 5.7523053395936659186, c[0, 1] = 31.714085493675499045, c[0, 2] = -70.797600903472879982, c[0, 3] = 55.721794319542100789, c[1, 0] = 6.8496226205038162324, c[1, 1] = 89.624697929207594070, c[1, 2] = 24.848513954229184553, c[1, 3] = -56.266518231245094449, c[2, 0] = -57.242646863660951348, c[2, 1] = 52.576434268388575752, c[2, 2] = 18.191164870112636904, c[2, 3] = 76.620024403025380241, c[3, 0] = 96.146449764907641565, c[3, 1] = -25.489288167292698444, c[3, 2] = 21.220487741182655042, c[3, 3] = -66.482561390780152708], (26, 3) = 1894, (27, 1) = 12321., (27, 2) = [c[0, 0] = 49.307956172620140436, c[0, 1] = -20.379135789022763645, c[0, 2] = -68.176677305079771622, c[0, 3] = 29.024641803576895854, c[1, 0] = 51.835895640924004596, c[1, 1] = 40.260276937388809588, c[1, 2] = 16.288135600157152335, c[1, 3] = -42.316932491193683003, c[2, 0] = 44.889311047249786933, c[2, 1] = -79.530394280745045227, c[2, 2] = -77.517535396156503928, c[2, 3] = 30.453588488205694054, c[3, 0] = 90.636717026773342262, c[3, 1] = 5.6175378881587716038, c[3, 2] = 52.587932445748320140, c[3, 3] = -.46865184053963290968], (27, 3) = 1911, (28, 1) = 17658.5561102500, (28, 2) = [c[0, 0] = 75.225473506904261362, c[0, 1] = -20.342407445872084765, c[0, 2] = 86.007350191833927225, c[0, 3] = 94.389395195016381470, c[1, 0] = 49.710626128755479956, c[1, 1] = -7.1401551159327582769, c[1, 2] = 58.064466557008266829, c[1, 3] = -15.800598031116308744, c[2, 0] = -50.312430007333422200, c[2, 1] = -56.249303926976225279, c[2, 2] = -53.937198831030710385, c[2, 3] = 16.941348931258175397, c[3, 0] = -192.08430001619774342, c[3, 1] = -35.342398623127173585, c[3, 2] = 74.701156746197530784, c[3, 3] = 1.7308821755341776268], (28, 3) = 3227, (29, 1) = 0.225e5, (29, 2) = [c[0, 0] = -83.758879813765853904, c[0, 1] = 79.685489033184376810, c[0, 2] = -56.360442632492202993, c[0, 3] = -253.76140456692629380, c[1, 0] = 59.344038021438947700, c[1, 1] = 63.837713125119949785, c[1, 2] = 14.599688709659845088, c[1, 3] = -37.907145891689868062, c[2, 0] = 33.415743059778587675, c[2, 1] = -7.2079390377100069890, c[2, 2] = -20.762840710757925292, c[2, 3] = -72.726055862342212202, c[3, 0] = 73.913092733308917634, c[3, 1] = 42.874983735897241739, c[3, 2] = 66.683146951224638251, c[3, 3] = -1.1943457205549593118], (29, 3) = 2147, (30, 1) = 0.256e5, (30, 2) = [c[0, 0] = -31.233567449522687181, c[0, 1] = -54.912847538393026135, c[0, 2] = 27.789410397217638286, c[0, 3] = .80968757567594991044, c[1, 0] = -18.195780780382136814, c[1, 1] = -79.463923012062527880, c[1, 2] = 68.918402439166970822, c[1, 3] = -69.278062811093507248, c[2, 0] = -45.953119808537230156, c[2, 1] = -77.122025950057194860, c[2, 2] = 95.588266061548724446, c[2, 3] = 86.437938391709369384, c[3, 0] = 20.804027722444139304, c[3, 1] = 42.100646314694055188, c[3, 2] = -49.807925583312766025, c[3, 3] = 1.5669682861945424672], (30, 3) = 2912, (31, 1) = 28900., (31, 2) = [c[0, 0] = -29.225405753068435041, c[0, 1] = 47.922455628844450665, c[0, 2] = -30.315901306258153598, c[0, 3] = 50.504304544557607094, c[1, 0] = 81.681051734651343861, c[1, 1] = 23.602315869609707726, c[1, 2] = -66.791289797513256431, c[1, 3] = -36.517177021297352642, c[2, 0] = 14.326255422083166516, c[2, 1] = -68.557788956999603913, c[2, 2] = 9.5987620035861555473, c[2, 3] = 77.138868089781894083, c[3, 0] = 20.091636925218490481, c[3, 1] = 64.127462372039741498, c[3, 2] = -20.528226641181987473, c[3, 3] = 52.767037104875493670], (31, 3) = 2542, (32, 1) = 33489., (32, 2) = [c[0, 0] = 27422.339954225403967, c[0, 1] = -87.197151659806294634, c[0, 2] = -10.626782533805216733, c[0, 3] = -99.203723126768418905, c[1, 0] = -13.946412479756463546, c[1, 1] = -31.504037738960575596, c[1, 2] = -53.806036048920930758, c[1, 3] = -.59618219602771010914, c[2, 0] = -2.4028698532256949527, c[2, 1] = -6.3107890629086702396, c[2, 2] = 22.112641795950952474, c[2, 3] = 39.560086785799778578, c[3, 0] = 69.135285531382502866, c[3, 1] = 2.4994989875110179424, c[3, 2] = -15.584813936093174601, c[3, 3] = 164.91079906241586654], (32, 3) = 3978, (33, 1) = 39322.89, (33, 2) = [c[0, 0] = -95.702788554165941930, c[0, 1] = -14.641348971992663010, c[0, 2] = -130.72645438164521053, c[0, 3] = 58.338460880590419873, c[1, 0] = -4.0048860379084875169, c[1, 1] = -11.919316574742432921, c[1, 2] = -75.190922627841335431, c[1, 3] = 88.840935678431325518, c[2, 0] = -3.8947820469285939209, c[2, 1] = 64.234342949648557335, c[2, 2] = 41.076073134114294260, c[2, 3] = 11.446633813777842698, c[3, 0] = 91.826544976809669971, c[3, 1] = -30.461837482453072469, c[3, 2] = 86.059025828635388639, c[3, 3] = .45053552974725572647], (33, 3) = 2126, (34, 1) = 0.4e5, (34, 2) = [c[0, 0] = -84.418883080295358220, c[0, 1] = -14.181325333796575314, c[0, 2] = 91.670030366005611354, c[0, 3] = -13.871053870326704879, c[1, 0] = 87.749461374683084835, c[1, 1] = -38.891691440493641759, c[1, 2] = 17.221169186599975177, c[1, 3] = -44.321734021761627326, c[2, 0] = -16.406581241816469871, c[2, 1] = -49.186113287109070830, c[2, 2] = -41.847103712377427728, c[2, 3] = -48.899612223837859521, c[3, 0] = -89.848754172688479029, c[3, 1] = -89.780305169921928577, c[3, 2] = 4.0686014543676093555, c[3, 3] = -38.661037350061297376], (34, 3) = 3763, (35, 1) = 0.4e5, (35, 2) = [c[0, 0] = -98.134217046133282225, c[0, 1] = 36.037020030709123229, c[0, 2] = 26.929763929185811153, c[0, 3] = -.74468170173594536153, c[1, 0] = -29.746055582061070446, c[1, 1] = -51.957915612849029688, c[1, 2] = -42.454918803650065784, c[1, 3] = 16.395826649354195228, c[2, 0] = -46.210607646689233058, c[2, 1] = 51.182496972008990327, c[2, 2] = 19.069172092976541729, c[2, 3] = 18.142817453777494451, c[3, 0] = 44.714908558553725486, c[3, 1] = -20.581941352535067047, c[3, 2] = -59.747217461771143905, c[3, 3] = -57.280049464132936762], (35, 3) = 3248, (36, 1) = 0.4e5, (36, 2) = [c[0, 0] = 70.107150363252095212, c[0, 1] = 81.963409356985784258, c[0, 2] = 46.176569471776085583, c[0, 3] = -41.013475297030994447, c[1, 0] = 80.002920967560250220, c[1, 1] = -29.928907330996542989, c[1, 2] = 95.701449261459809912, c[1, 3] = 26.137600049458289332, c[2, 0] = 86.421484780964409721, c[2, 1] = -27.297913159062894573, c[2, 2] = -69.561068200302809557, c[2, 3] = -12.091300563328876708, c[3, 0] = 45.238410565766470382, c[3, 1] = -96.868838486325902378, c[3, 2] = -69.476176420576847923, c[3, 3] = -32.425793740092342180], (36, 3) = 1760, (37, 1) = 42436., (37, 2) = [c[0, 0] = -26.061238632656593963, c[0, 1] = 39.555479467301048768, c[0, 2] = -38.656038519012016855, c[0, 3] = 71.082848055863485105, c[1, 0] = 73.945131536503261801, c[1, 1] = 31.019122720892791114, c[1, 2] = -64.183779889725133501, c[1, 3] = -21.585054030817641075, c[2, 0] = -66.506129714231454658, c[2, 1] = 37.418263632591115002, c[2, 2] = -16.338245136693923785, c[2, 3] = -79.784528671435177817, c[3, 0] = 37.764392416491424340, c[3, 1] = 53.200629262893103099, c[3, 2] = 9.2155883996809719393, c[3, 3] = 15.400776152789733126], (37, 3) = 3004, (38, 1) = 0.441e5, (38, 2) = [c[0, 0] = 40.905299663309554826, c[0, 1] = 59.943304029732646560, c[0, 2] = -28.135338221832956380, c[0, 3] = 14.874402006412265249, c[1, 0] = -80.962098163529047498, c[1, 1] = -39.247843761542869769, c[1, 2] = -17.408250626539693380, c[1, 3] = -76.220648286054395523, c[2, 0] = -41.868081609209187117, c[2, 1] = 35.716210836313349913, c[2, 2] = -6.2636805841918008560, c[2, 3] = 60.787801850044960214, c[3, 0] = -56.135209061737628207, c[3, 1] = 81.292478160722600761, c[3, 2] = 81.881679445510639671, c[3, 3] = 1.1305805951844424899], (38, 3) = 2218, (39, 1) = 51347.56, (39, 2) = [c[0, 0] = 20.474297580219444966, c[0, 1] = 13.108979773704390241, c[0, 2] = 91.867562486355892889, c[0, 3] = 82.473809915461289145, c[1, 0] = 26.833175629856818966, c[1, 1] = -23.901857024315308412, c[1, 2] = 2.2753639553523505780, c[1, 3] = 60.474668548115657536, c[2, 0] = -9.7647569511562182900, c[2, 1] = 32.728831839948808934, c[2, 2] = 88.186441738999422712, c[2, 3] = -77.541470360476491528, c[3, 0] = -25.790330593676473194, c[3, 1] = 39.419323114506537307, c[3, 2] = 44.557426798802499341, c[3, 3] = 8.4411036003811368752], (39, 3) = 1968, (40, 1) = 55225., (40, 2) = [c[0, 0] = 64.557682805583362766, c[0, 1] = -52.174220129739672253, c[0, 2] = 10.653727907083803890, c[0, 3] = 44.791394485079704974, c[1, 0] = -61.356479094340195126, c[1, 1] = -72.046132295500272601, c[1, 2] = -62.123513740998179836, c[1, 3] = 48.608081827861586723, c[2, 0] = -26.497356600582659568, c[2, 1] = 11.421758558907780848, c[2, 2] = -45.006332478631226152, c[2, 3] = -3.2458376886346430761, c[3, 0] = -27.672202662212533473, c[3, 1] = -72.163887866857094722, c[3, 2] = -20.696904361828743178, c[3, 3] = -25.288520206554348121], (40, 3) = 2133, (41, 1) = 64009., (41, 2) = [c[0, 0] = -18.780208763049236462, c[0, 1] = 83.260453836439284943, c[0, 2] = -39.110742030695957425, c[0, 3] = 57.895831025321309111, c[1, 0] = -47.433983884968131663, c[1, 1] = 44.666097432064934532, c[1, 2] = -32.067705906390724086, c[1, 3] = 33.067129727491175672, c[2, 0] = 42.017043916050447804, c[2, 1] = 27.242542738350456623, c[2, 2] = -40.108135804285772589, c[2, 3] = 65.425680196331849354, c[3, 0] = 86.243713571611753207, c[3, 1] = -24.033009710975821385, c[3, 2] = 3.7749312529274131447, c[3, 3] = -26.878809219503630912], (41, 3) = 3058, (42, 1) = 75625., (42, 2) = [c[0, 0] = 45.928672924804760615, c[0, 1] = -11.098743269504097591, c[0, 2] = 35.021059470344706314, c[0, 3] = -74.895937768965332484, c[1, 0] = -63.914864192513464381, c[1, 1] = -34.942395161814440367, c[1, 2] = -18.542298950906482979, c[1, 3] = -61.523900167909974158, c[2, 0] = 89.124920916663057487, c[2, 1] = 34.562778747884909650, c[2, 2] = 53.979003275376085307, c[2, 3] = -44.320982427578665518, c[3, 0] = 14.808226126602546418, c[3, 1] = -78.730470640075957815, c[3, 2] = -60.181393341206890425, c[3, 3] = 20.313806196139507605], (42, 3) = 1186, (43, 1) = 77479.936667456761, (43, 2) = [c[0, 0] = -91.607607325304172983, c[0, 1] = -53.355725121828870886, c[0, 2] = 20.679020596690451415, c[0, 3] = 6.9343537154749671468, c[1, 0] = -16.065265689268682383, c[1, 1] = -93.057521270712617863, c[1, 2] = 13.368409880010006270, c[1, 3] = -18.796793589229217120, c[2, 0] = 59.280201177740913882, c[2, 1] = -12.695964777972757668, c[2, 2] = 3.8627088076495983160, c[2, 3] = 73.480541797623928870, c[3, 0] = 82.922555441960944826, c[3, 1] = -29.407318416532424851, c[3, 2] = -81.916513320380230941, c[3, 3] = -0.11311571149216559560e-1], (43, 3) = 1928, (44, 1) = 0.9e5, (44, 2) = [c[0, 0] = 62.167682976157663350, c[0, 1] = 46.678622343107582078, c[0, 2] = 44.522473126711954192, c[0, 3] = 35.676873590781197602, c[1, 0] = 85.497342434669115811, c[1, 1] = 20.088771836884160079, c[1, 2] = -96.641373249487286580, c[1, 3] = -74.306478382054913988, c[2, 0] = -85.308083960063906963, c[2, 1] = -38.722775257515541216, c[2, 2] = 2.0625644570410611875, c[2, 3] = 86.767886609981581739, c[3, 0] = 11.892704700065358101, c[3, 1] = 79.595502207076433263, c[3, 2] = 76.279669972438309207, c[3, 3] = 47.730501859912953281], (44, 3) = 3528, (45, 1) = 0.1024e6, (45, 2) = [c[0, 0] = 14.227929981045579670, c[0, 1] = 80.808933504147603569, c[0, 2] = -48.375572643333304451, c[0, 3] = 21.507079123025194083, c[1, 0] = 59.465019809106659924, c[1, 1] = 44.487910889222627700, c[1, 2] = -75.882166332393229084, c[1, 3] = 10.870610300410751579, c[2, 0] = 57.912061874006501733, c[2, 1] = -83.001584797095525775, c[2, 2] = -40.189314229078111382, c[2, 3] = -18.172197126624217946, c[3, 0] = 85.103622900141072474, c[3, 1] = 57.650274798888501417, c[3, 2] = 91.986671316900116967, c[3, 3] = -6.9707083862784957037], (45, 3) = 2326, (46, 1) = 109627.21, (46, 2) = [c[0, 0] = 51.722488166169555735, c[0, 1] = -14.473051140521224259, c[0, 2] = -37.487689861025013757, c[0, 3] = 26.347261841983861001, c[1, 0] = 101.92889650147884752, c[1, 1] = -72.759263903172653871, c[1, 2] = 51.181946561737007937, c[1, 3] = 15.881433135574244967, c[2, 0] = 38.269061693102730579, c[2, 1] = -64.340457599160156224, c[2, 2] = 50.243608256244983752, c[2, 3] = 74.924948758982125282, c[3, 0] = 67.995768035508700240, c[3, 1] = -57.265072682617133698, c[3, 2] = 54.280355046125793827, c[3, 3] = -14.094885638606044010], (46, 3) = 3895, (47, 1) = 110822.41, (47, 2) = [c[0, 0] = -1.7528608148821668914, c[0, 1] = -60.442999044899155637, c[0, 2] = -98.778227020855904954, c[0, 3] = 1.1364233359989203651, c[1, 0] = 48.326703012419976179, c[1, 1] = -2.8411604281316028488, c[1, 2] = 54.486608834439404648, c[1, 3] = 7.7883404734343749434, c[2, 0] = -1.7586303479036426888, c[2, 1] = -106.75366257354137849, c[2, 2] = 24.644789720206465248, c[2, 3] = -8.7504479975518368783, c[3, 0] = 9.8249924754394863800, c[3, 1] = -62.468436672163772742, c[3, 2] = -17.337887178778755473, c[3, 3] = 42.230623340972695548], (47, 3) = 2803, (48, 1) = 113434.24, (48, 2) = [c[0, 0] = -35.400677277961690349, c[0, 1] = 8.1204220234147490887, c[0, 2] = 63.721217846739061866, c[0, 3] = 39.075306873985406133, c[1, 0] = 90.471318463020414447, c[1, 1] = -4.9055611555288766469, c[1, 2] = -17.271720119294297770, c[1, 3] = -9.3949122514664370379, c[2, 0] = -40.093631257611506994, c[2, 1] = 51.587905926337154398, c[2, 2] = 62.634598659094974256, c[2, 3] = -50.557543127232664851, c[3, 0] = 42.741988041619448340, c[3, 1] = -29.784237796951447355, c[3, 2] = 9.9273350844745308567, c[3, 3] = 6.5114313527562694599], (48, 3) = 1536, (49, 1) = 160504.3969, (49, 2) = [c[0, 0] = -82.596152129335315734, c[0, 1] = -61.978988519523851726, c[0, 2] = -71.352229891853232746, c[0, 3] = 10.253020398965900270, c[1, 0] = 60.576454908342157144, c[1, 1] = -2.2318102672442725628, c[1, 2] = 10.145818512775947971, c[1, 3] = 84.138307785619194376, c[2, 0] = -42.036505979267914387, c[2, 1] = 26.996646457775986610, c[2, 2] = -61.997956828063186292, c[2, 3] = 70.932861247923443387, c[3, 0] = 10.098011468328613832, c[3, 1] = -39.510874145778481481, c[3, 2] = 48.565010705853457300, c[3, 3] = -36.101501763400687757], (49, 3) = 2069, (50, 1) = 161604., (50, 2) = [c[0, 0] = 25.523620903669083955, c[0, 1] = -5.7223249121918035300, c[0, 2] = 27.767332025052812929, c[0, 3] = 99.106346141688925240, c[1, 0] = -29.372444074824720556, c[1, 1] = -46.157528620469803691, c[1, 2] = 26.913374705291975240, c[1, 3] = -58.153343934636948672, c[2, 0] = 1.6678657550029520398, c[2, 1] = -78.309136488786825936, c[2, 2] = 72.959384010748674202, c[2, 3] = 61.436657717246952797, c[3, 0] = -42.739294125025821496, c[3, 1] = -96.786705977546844245, c[3, 2] = 38.195568640360845241, c[3, 3] = -41.094162195411310312], (50, 3) = 1888, (51, 1) = 0.1681e6, (51, 2) = [c[0, 0] = -66.767870578621696223, c[0, 1] = 54.383024457226848559, c[0, 2] = -733.73059676025107998, c[0, 3] = 32.797590650714459232, c[1, 0] = 58.877858713288425830, c[1, 1] = -93.946510055130546758, c[1, 2] = -74.725334330349445688, c[1, 3] = 18.323995106398166258, c[2, 0] = 56.563468178652498294, c[2, 1] = 1.8528849538119637944, c[2, 2] = 15.773233716845607935, c[2, 3] = -23.536316519720931109, c[3, 0] = 29.344404204091347755, c[3, 1] = 54.246947794754221169, c[3, 2] = -17.205348868841084474, c[3, 3] = -11.333049740289960375], (51, 3) = 1880, (52, 1) = 178892.623849, (52, 2) = [c[0, 0] = -26.147829906768394871, c[0, 1] = 22.896540063243297472, c[0, 2] = 12.680958034055743625, c[0, 3] = 48.509822974577477649, c[1, 0] = -4.3917298214399136970, c[1, 1] = -62.724204358602846803, c[1, 2] = 81.569517540060261000, c[1, 3] = -44.516903505913171814, c[2, 0] = -84.417852961093329964, c[2, 1] = 81.750468645294336607, c[2, 2] = -66.211110760023762025, c[2, 3] = 73.739182364152131489, c[3, 0] = -61.319572772110673213, c[3, 1] = -2.8218770889750933246, c[3, 2] = 8.0008929768962548491, c[3, 3] = .49781743492755102571], (52, 3) = 1656, (53, 1) = 200890.2409449961, (53, 2) = [c[0, 0] = -88.701616905214952949, c[0, 1] = 78.754119319727187032, c[0, 2] = -63.907910003916784961, c[0, 3] = .43941869057464726149, c[1, 0] = -20.640797044226752892, c[1, 1] = 27.664238870977955302, c[1, 2] = 12.445667094524151616, c[1, 3] = -10.015110965470083645, c[2, 0] = -86.831285173554485785, c[2, 1] = -89.811484844176302025, c[2, 2] = 13.581495846329428249, c[2, 3] = .47745459822421753409, c[3, 0] = -1.7386694361409798645, c[3, 1] = 71.706379468591181189, c[3, 2] = -92.693599209455998211, c[3, 3] = 14.199252918660895116], (53, 3) = 1962, (54, 1) = 223918.24, (54, 2) = [c[0, 0] = 78.109379611911289392, c[0, 1] = -58.843056250979078619, c[0, 2] = -76.165830745339705803, c[0, 3] = -97.151711085542030929, c[1, 0] = -22.374401306895613731, c[1, 1] = -30.851478084987301614, c[1, 2] = -73.457852559480396207, c[1, 3] = -16.035381198563281778, c[2, 0] = 37.727191692548017910, c[2, 1] = 58.687520158301742663, c[2, 2] = -50.037826022035595028, c[2, 3] = 44.406266062779121602, c[3, 0] = 39.648992242208901652, c[3, 1] = 97.676168593342244218, c[3, 2] = -2.9612661199795379890, c[3, 3] = 11.593915631427431186], (54, 3) = 1980, (55, 1) = 240341.284648345609, (55, 2) = [c[0, 0] = 97.376557512525972225, c[0, 1] = 45.855097687501381311, c[0, 2] = 41.371377064977143963, c[0, 3] = 98.980870851200643563, c[1, 0] = 11.656552300864280669, c[1, 1] = -51.306721771424557984, c[1, 2] = -39.905121485776824297, c[1, 3] = 27.855547588865344206, c[2, 0] = -34.103462130517696292, c[2, 1] = -83.023954397792141220, c[2, 2] = -88.986620265469011603, c[2, 3] = 20.348457753434224534, c[3, 0] = -14.376316018143391815, c[3, 1] = 78.823845544836613839, c[3, 2] = 55.947310331295943416, c[3, 3] = -20.076826539903434482], (55, 3) = 2401, (56, 1) = 255025., (56, 2) = [c[0, 0] = -17.338078394303318243, c[0, 1] = -49.717242527006902171, c[0, 2] = -85.917718471910734489, c[0, 3] = 80.530289002124585082, c[1, 0] = -43.893342262892049633, c[1, 1] = -84.432957983744230828, c[1, 2] = 29.270306299567535559, c[1, 3] = -79.116342900658953544, c[2, 0] = 48.605041988339029935, c[2, 1] = 1.5793282421312377638, c[2, 2] = 70.250300576422797629, c[2, 3] = 64.062263303900175309, c[3, 0] = -43.692966386224709905, c[3, 1] = 66.583294609730546785, c[3, 2] = -39.989919539473854524, c[3, 3] = -18.276465515246381860], (56, 3) = 1941, (57, 1) = 296372.689426290841, (57, 2) = [c[0, 0] = 97.153585788831794155, c[0, 1] = 43.393923163420216577, c[0, 2] = 45.053109281324814049, c[0, 3] = -18.691388659241808359, c[1, 0] = 60.967189733297022447, c[1, 1] = -8.1836615972919503041, c[1, 2] = -99.589328301533479512, c[1, 3] = -52.489178211299182563, c[2, 0] = -31.798294254751999192, c[2, 1] = 31.047276402766848666, c[2, 2] = 63.604851856046072257, c[2, 3] = -75.139276230815351727, c[3, 0] = -53.448496282532935589, c[3, 1] = -10.733650830645261807, c[3, 2] = -93.757054014010960360, c[3, 3] = 2.4996184602629491632], (57, 3) = 2333, (58, 1) = 0.36e6, (58, 2) = [c[0, 0] = 26.585888375581205660, c[0, 1] = -23.543984386504929623, c[0, 2] = -57.983616541606226131, c[0, 3] = -7.2096387875242587283, c[1, 0] = -28.957179093567535077, c[1, 1] = -5.0531481059545304793, c[1, 2] = -24.090080033916050162, c[1, 3] = 23.266604397775919803, c[2, 0] = -95.104274066786685662, c[2, 1] = -87.778416199621295126, c[2, 2] = -89.521812619478644757, c[2, 3] = -54.539131441206676153, c[3, 0] = 73.410950268822938911, c[3, 1] = 58.634659472573169987, c[3, 2] = -70.904666809910162226, c[3, 3] = -7.0763849650077999609], (58, 3) = 3634, (59, 1) = 0.36e6, (59, 2) = [c[0, 0] = 17.598770594992803102, c[0, 1] = -70.423861179316766872, c[0, 2] = -99.818655104554446782, c[0, 3] = -81.446505121238469826, c[1, 0] = -76.323063757471990134, c[1, 1] = -32.407144693730097524, c[1, 2] = -29.507760192444617997, c[1, 3] = 12.216608424199704378, c[2, 0] = 92.664857789001338199, c[2, 1] = 21.199476378152656824, c[2, 2] = -55.075982387509956068, c[2, 3] = 23.214755385617339271, c[3, 0] = 56.197517123489111263, c[3, 1] = -35.255947798985886047, c[3, 2] = -82.154353578450564413, c[3, 3] = -39.303122297403841816], (59, 3) = 3198, (60, 1) = 404496.00, (60, 2) = [c[0, 0] = 32.699659644465138630, c[0, 1] = -42.638706901246465673, c[0, 2] = 33.536234799241766046, c[0, 3] = -45.159553511585047443, c[1, 0] = 7.6897181101132017194, c[1, 1] = 47.170747490334655143, c[1, 2] = -1.7083930431214036298, c[1, 3] = -56.211900838276774294, c[2, 0] = -46.437109318689755227, c[2, 1] = 90.092351149813797320, c[2, 2] = -85.395968342988486673, c[2, 3] = 20.270462724816534752, c[3, 0] = 2.7207815032142374201, c[3, 1] = 20.795192067235159712, c[3, 2] = 26.029741078852948126, c[3, 3] = 68.735025706744143937], (60, 3) = 1853, (61, 1) = 0.4225e6, (61, 2) = [c[0, 0] = 42.163574804167090017, c[0, 1] = 52.840108887916465546, c[0, 2] = -67.480912584467382572, c[0, 3] = 55.333554555601728841, c[1, 0] = 10.564156029000417617, c[1, 1] = 54.686927406427212171, c[1, 2] = -37.726413868691919453, c[1, 3] = -45.761573948955029196, c[2, 0] = 32.199282369828430343, c[2, 1] = -31.785435633111218200, c[2, 2] = -30.981243685827381212, c[2, 3] = 42.786388811105130315, c[3, 0] = 47.020389977036052970, c[3, 1] = 31.786001885746209884, c[3, 2] = -68.088023024858394924, c[3, 3] = -11.049182980141918179], (61, 3) = 1937, (62, 1) = 450411.18167824, (62, 2) = [c[0, 0] = 52.598298578800394024, c[0, 1] = 72.254510348396363135, c[0, 2] = 18.964310903029288299, c[0, 3] = 14.323198599790138852, c[1, 0] = -5.7536488007112474203, c[1, 1] = 62.467314631740615692, c[1, 2] = 23.027111162421988321, c[1, 3] = -39.376450058579289454, c[2, 0] = 83.177833695404208956, c[2, 1] = 77.672230780427064402, c[2, 2] = -65.125294093884697961, c[2, 3] = -44.981241582312421785, c[3, 0] = 91.041533408644541194, c[3, 1] = -34.266800179202700244, c[3, 2] = 65.006210628665987415, c[3, 3] = 2.3633901224301847634], (62, 3) = 3806, (63, 1) = 455319.0873656896, (63, 2) = [c[0, 0] = -58.178284846695921351, c[0, 1] = -83.237641187775667048, c[0, 2] = 39.827322000690950557, c[0, 3] = -95.478196323684466298, c[1, 0] = 74.369224583023810970, c[1, 1] = 72.020692849062037861, c[1, 2] = 83.817188187045166421, c[1, 3] = 78.189235890628696413, c[2, 0] = 3.6015455688254952645, c[2, 1] = -97.358728809802010895, c[2, 2] = 1.3400832563899070840, c[2, 3] = 57.548631029856036787, c[3, 0] = -7.1387420935765438513, c[3, 1] = 95.992172001465462245, c[3, 2] = 23.309088699448020324, c[3, 3] = 28.923788045278140023], (63, 3) = 3820, (64, 1) = 476100., (64, 2) = [c[0, 0] = -39.250699517102446090, c[0, 1] = -58.212443854021271882, c[0, 2] = 57.775780816815825152, c[0, 3] = 95.496512026657791873, c[1, 0] = -15.999015101156983213, c[1, 1] = 66.287639288881165620, c[1, 2] = -58.264412979475006539, c[1, 3] = 26.919598262848317096, c[2, 0] = 57.323640104556280126, c[2, 1] = -44.906763665377044840, c[2, 2] = 4.9204256815336038019, c[2, 3] = 33.352908155916249206, c[3, 0] = -56.711195518469038340, c[3, 1] = 68.167548518756009094, c[3, 2] = 27.759353565436886554, c[3, 3] = 95.140921995578576989], (64, 3) = 3203, (65, 1) = 0.49e6, (65, 2) = [c[0, 0] = 46.048767977023642762, c[0, 1] = 31.956506046850376979, c[0, 2] = -74.512454572955121033, c[0, 3] = 55.013236454731557064, c[1, 0] = -47.796484415757013388, c[1, 1] = 74.534660920928207192, c[1, 2] = -49.987857204872195454, c[1, 3] = 82.116793310613709105, c[2, 0] = 36.110829885558722968, c[2, 1] = -89.266762136172655420, c[2, 2] = -4.4312094113012989913, c[2, 3] = 69.834001435942307524, c[3, 0] = 22.697462800764793938, c[3, 1] = -94.145708729254717581, c[3, 2] = -3.3485711605321537156, c[3, 3] = 83.098109991090022536], (65, 3) = 2053, (66, 1) = 636804., (66, 2) = [c[0, 0] = -24.046930335186463812, c[0, 1] = -72.918314962673052833, c[0, 2] = 50.234720699283914201, c[0, 3] = -34.979506526627357430, c[1, 0] = 50.368354220255082507, c[1, 1] = -72.932672152772871437, c[1, 2] = -68.356515750271156488, c[1, 3] = -.67170994079831396858, c[2, 0] = -45.671873957183971068, c[2, 1] = 34.250094823948113032, c[2, 2] = -27.842291162102820144, c[2, 3] = -27.331893135512946791, c[3, 0] = 1.4105433544481164374, c[3, 1] = -86.060315293970832716, c[3, 2] = 38.092978461886047889, c[3, 3] = 70.799575915784060830], (66, 3) = 1514, (67, 1) = 701104.7824, (67, 2) = [c[0, 0] = 66.703470764471672943, c[0, 1] = 31.516100406083167918, c[0, 2] = 33.505766268170130185, c[0, 3] = 35.949683814184960328, c[1, 0] = -27.875946014850712437, c[1, 1] = -91.113447898717553083, c[1, 2] = -90.555438730980735320, c[1, 3] = 50.547857969614712710, c[2, 0] = -54.705808653464359760, c[2, 1] = 39.332252140547537679, c[2, 2] = 11.055340813591171920, c[2, 3] = -99.601206285842528984, c[3, 0] = -58.600510992481937271, c[3, 1] = 38.742712592267470813, c[3, 2] = -27.630732274855979068, c[3, 3] = -10.016301043565766827], (67, 3) = 2183, (68, 1) = 0.81e6, (68, 2) = [c[0, 0] = -.57189359169989906257, c[0, 1] = -60.005432969655670177, c[0, 2] = 54.171163976048027119, c[0, 3] = -33.617992744395010001, c[1, 0] = 23.875208232139501394, c[1, 1] = 73.783383090779758206, c[1, 2] = 82.925416666268159305, c[1, 3] = 78.557235338290532114, c[2, 0] = 93.165458395299109791, c[2, 1] = -15.273038179818765867, c[2, 2] = 73.178254019231595825, c[2, 3] = 38.590467432827231350, c[3, 0] = -37.261112051202262389, c[3, 1] = 60.783136306103307422, c[3, 2] = 12.593299316777343427, c[3, 3] = -27.653822338923233507], (68, 3) = 2527, (69, 1) = 993585.12079876, (69, 2) = [c[0, 0] = -73.202383945977300243, c[0, 1] = -70.826881700431151909, c[0, 2] = 33.888031318904446389, c[0, 3] = 1413.0717352143669507, c[1, 0] = 107.28133596123154594, c[1, 1] = -23.362851626363447233, c[1, 2] = -80.317248880874145434, c[1, 3] = -40.594111404972933986, c[2, 0] = -35.431667967466868193, c[2, 1] = -20.830643341436170756, c[2, 2] = -36.468023375276840915, c[2, 3] = 48.012856062232844667, c[3, 0] = 7.1093147324343676351, c[3, 1] = 95.941898969577532435, c[3, 2] = -9.5640065477275095794, c[3, 3] = -51.384542029145940808], (69, 3) = 2552, (70, 1) = 0.144e7, (70, 2) = [c[0, 0] = -29.653369912417381491, c[0, 1] = -68.252252576843107101, c[0, 2] = -4.1475839776056479548, c[0, 3] = -66.352393403148233780, c[1, 0] = -73.370645887633527791, c[1, 1] = -63.623493385728441959, c[1, 2] = 54.013608573618980349, c[1, 3] = 37.458547493463882951, c[2, 0] = 19.875606675841696123, c[2, 1] = -77.350576346274700340, c[2, 2] = -93.505823775464119662, c[2, 3] = 35.046714905218043006, c[3, 0] = 36.169216668184052269, c[3, 1] = -22.400599588824181946, c[3, 2] = 45.404989220932055088, c[3, 3] = 63.073963935741207993], (70, 3) = 2964, (71, 1) = 1643524., (71, 2) = [c[0, 0] = 75.626509516583397994, c[0, 1] = -97.377971930817851127, c[0, 2] = 52.809175698449390360, c[0, 3] = -88.403364422494226393, c[1, 0] = -93.603203818991190944, c[1, 1] = 90.305679706013910104, c[1, 2] = 84.964883167154534781, c[1, 3] = -43.417415718018309696, c[2, 0] = 28.906589521490675547, c[2, 1] = 63.615930448428200901, c[2, 2] = -64.109951171540963281, c[2, 3] = -96.588495879998922205, c[3, 0] = -98.261729295393079302, c[3, 1] = -30.930544359725522823, c[3, 2] = -83.487941327626559563, c[3, 3] = 22.246592768936325882], (71, 3) = 2185, (72, 1) = 1861587.36, (72, 2) = [c[0, 0] = -77.588362482278857486, c[0, 1] = 96.400562034302953648, c[0, 2] = -34.928610068004995202, c[0, 3] = -64.375147356980831416, c[1, 0] = -75.931770666824817185, c[1, 1] = -64.504922022252941488, c[1, 2] = 87.216244578487577139, c[1, 3] = 15.016624737067500245, c[2, 0] = 23.700277089096495046, c[2, 1] = 31.936897570378539020, c[2, 2] = -71.466030481061492044, c[2, 3] = -40.446337235126902951, c[3, 0] = 68.540187306498693223, c[3, 1] = -58.302945078114150900, c[3, 2] = -46.191421209569383255, c[3, 3] = -4.6414792159573781907], (72, 3) = 1803, (73, 1) = 0.21025e7, (73, 2) = [c[0, 0] = -95.712995279019992612, c[0, 1] = -91.778572662451003007, c[0, 2] = -43.293517372763789172, c[0, 3] = 61.835069817976848316, c[1, 0] = 94.347754323205368193, c[1, 1] = -19.052080027626626224, c[1, 2] = -7.0706226138728670063, c[1, 3] = 78.413233530501609336, c[2, 0] = 68.833027908908505647, c[2, 1] = 79.975812702874651189, c[2, 2] = 59.656802997129697648, c[2, 3] = 86.820649863017924312, c[3, 0] = -39.870396279266283778, c[3, 1] = -.96506820885929635630, c[3, 2] = .23637893829894144689, c[3, 3] = .40653157950281848204], (73, 3) = 1810, (74, 1) = 2322576., (74, 2) = [c[0, 0] = -73.880961085890490878, c[0, 1] = -25.148102569069935318, c[0, 2] = 192.98613843467946628, c[0, 3] = 71.676461594745167250, c[1, 0] = 30.546384392068361468, c[1, 1] = 80.367114884543248022, c[1, 2] = 39.270064500080002868, c[1, 3] = 7.9129418282218143280, c[2, 0] = 57.118711136320438082, c[2, 1] = -62.489949643975115909, c[2, 2] = -34.583658143870111306, c[2, 3] = 11.147472307598066737, c[3, 0] = 16.661426719985813556, c[3, 1] = -4.1710505050700764946, c[3, 2] = -6.2933497617126873198, c[3, 3] = 68.083139618281905649], (74, 3) = 2058, (75, 1) = 2679769., (75, 2) = [c[0, 0] = -101.64527277728529413, c[0, 1] = -40.205227806108012141, c[0, 2] = -74.271632314168941653, c[0, 3] = 61.688973451086776226, c[1, 0] = -1.7188094607874522308, c[1, 1] = -97.040943179268524474, c[1, 2] = -91.959345517951325405, c[1, 3] = -94.702841695130133627, c[2, 0] = 30.619012023791464359, c[2, 1] = 23.851580225701605865, c[2, 2] = -20.192514241532964912, c[2, 3] = -4.3895318456985792475, c[3, 0] = 1.2694109852882516695, c[3, 1] = -60.908711275367316280, c[3, 2] = 22.470092493059051299, c[3, 3] = 97.279222996019407319], (75, 3) = 2062, (76, 1) = 0.400e7, (76, 2) = [c[0, 0] = 54.601553141573227146, c[0, 1] = -9.3788973861148514832, c[0, 2] = -14.744391207519524344, c[0, 3] = -52.067656500456440206, c[1, 0] = 62.232545161745598654, c[1, 1] = 19.207629817426507586, c[1, 2] = -70.787721810162111039, c[1, 3] = -16.729025397040231846, c[2, 0] = 40.895391990212507332, c[2, 1] = 55.453138021592806928, c[2, 2] = -37.631917895571610575, c[2, 3] = 49.682926103819448722, c[3, 0] = -66.250887869986243700, c[3, 1] = 40.841150673733174265, c[3, 2] = -18.792632369053268052, c[3, 3] = -51.096355117365002513], (76, 3) = 2017, (77, 1) = 4008004., (77, 2) = [c[0, 0] = 51.374072994897292509, c[0, 1] = -53.374898796471483928, c[0, 2] = -77.142391794802530988, c[0, 3] = -89.781649932374459834, c[1, 0] = -8.0164313043559443701, c[1, 1] = -28.278573427261115981, c[1, 2] = -88.852952348118956740, c[1, 3] = 56.773627498767255747, c[2, 0] = -27.225877724436914599, c[2, 1] = 79.605106917550252418, c[2, 2] = -31.438017766619988683, c[2, 3] = -63.435907995055029988, c[3, 0] = 6.7089128413430060859, c[3, 1] = -82.202302595626938436, c[3, 2] = 73.355064163168178440, c[3, 3] = 96.781720737454279774], (77, 3) = 1947, (78, 1) = 5362373.8624, (78, 2) = [c[0, 0] = 27.462229320148594281, c[0, 1] = -7.9239039725952033084, c[0, 2] = -68.911324252543880429, c[0, 3] = 29.586488198588365030, c[1, 0] = 12.932970819638586353, c[1, 1] = 66.533082684314241901, c[1, 2] = -48.554804781671650627, c[1, 3] = 24.843419323565561348, c[2, 0] = 32.139959127226313519, c[2, 1] = -30.298924311674202545, c[2, 2] = -83.089925627169589204, c[2, 3] = 63.560184980125544977, c[3, 0] = -70.251058781723839610, c[3, 1] = 91.346769372248113579, c[3, 2] = 20.063994672730983210, c[3, 3] = 5.3243548884902351003], (78, 3) = 2932, (79, 1) = 0.62001e7, (79, 2) = [c[0, 0] = -83.253611140006684842, c[0, 1] = -90.706340375992744913, c[0, 2] = 292.25404521804511976, c[0, 3] = 74.368054435781950485, c[1, 0] = 74.552194007552951696, c[1, 1] = -91.008685842131685946, c[1, 2] = -89.695602012103693567, c[1, 3] = -20.230891035885022782, c[2, 0] = 20.660910731982507024, c[2, 1] = -52.730448856910717185, c[2, 2] = -35.356077366657426273, c[2, 3] = 63.146375108318335908, c[3, 0] = -28.831805882288447883, c[3, 1] = -80.131390140272330861, c[3, 2] = 11.924075704108494798, c[3, 3] = 19.001092877619039438], (79, 3) = 719, (80, 1) = 8596624., (80, 2) = [c[0, 0] = -32.755300840311167516, c[0, 1] = 12.676685449289096633, c[0, 2] = 33.115035402676608594, c[0, 3] = -65.413492267152395790, c[1, 0] = 56.789448938631313079, c[1, 1] = 75.656890691526065046, c[1, 2] = 83.313474775307064449, c[1, 3] = 83.468147026541093220, c[2, 0] = 71.811699600233723826, c[2, 1] = 57.630064621857879888, c[2, 2] = -12.236578928981841914, c[2, 3] = -23.445379468006258451, c[3, 0] = 6.6168619125457538983, c[3, 1] = -70.168666191487331037, c[3, 2] = 76.018577425544151278, c[3, 3] = 66.581226297200495261], (80, 3) = 1746, (81, 1) = 12054784., (81, 2) = [c[0, 0] = 12.454581299514751185, c[0, 1] = -42.650779493491922450, c[0, 2] = 94.495683935134140688, c[0, 3] = 55.300611851932165382, c[1, 0] = 81.771424726855575039, c[1, 1] = -34.678808551748851056, c[1, 2] = -20.277221517877176618, c[1, 3] = 81.223547385699839559, c[2, 0] = -5.3637049615500663654, c[2, 1] = 44.158107439661329189, c[2, 2] = 13.466849250186605951, c[2, 3] = -38.693601592296131984, c[3, 0] = -20.945308481181761098, c[3, 1] = -91.034697342823827933, c[3, 2] = -59.901749487271856226, c[3, 3] = -22.579832784684251009], (81, 3) = 2449, (82, 1) = 0.1444e8, (82, 2) = [c[0, 0] = -27.477129068013872948, c[0, 1] = -43.921180119830054365, c[0, 2] = 91.426134308538415976, c[0, 3] = 46.857562016747384088, c[1, 0] = -56.718867626167090408, c[1, 1] = 17.638279789074849172, c[1, 2] = 31.254331396641787940, c[1, 3] = 54.028788570212174503, c[2, 0] = 65.983719560118689966, c[2, 1] = 97.467473684345759829, c[2, 2] = 34.751493785895015705, c[2, 3] = -69.314479582666774963, c[3, 0] = 79.292284445320610834, c[3, 1] = 8.4086550447121856131, c[3, 2] = 9.4148764230541832507, c[3, 3] = -17.777155521041022350], (82, 3) = 2653, (83, 1) = 0.16e8, (83, 2) = [c[0, 0] = 55.821332036533313176, c[0, 1] = -17.644067216991302989, c[0, 2] = -91.582794202861760094, c[0, 3] = 45.048052933794030671, c[1, 0] = -38.954170419493636612, c[1, 1] = 41.709874106529832968, c[1, 2] = 5.9792781835713275147, c[1, 3] = -27.003964306511120746, c[2, 0] = -85.070956519000024178, c[2, 1] = 99.561503363948508300, c[2, 2] = -32.381311105396711080, c[2, 3] = 56.999370614671926912, c[3, 0] = 53.843051214218363813, c[3, 1] = -27.055565966143558128, c[3, 2] = -48.172669030963905407, c[3, 3] = 66.873614523109369617], (83, 3) = 2318, (84, 1) = 0.2401e8, (84, 2) = [c[0, 0] = -32.179579704700081794, c[0, 1] = -51.778984670467313276, c[0, 2] = -92.706198471228160213, c[0, 3] = 80.930746362583378113, c[1, 0] = 34.609123546941305631, c[1, 1] = -19.948365883686964510, c[1, 2] = -34.872939265438449877, c[1, 3] = 23.837419832635940683, c[2, 0] = -72.709355766884880889, c[2, 1] = -98.092287506527267561, c[2, 2] = -93.020822446512186585, c[2, 3] = -14.396905353893587143, c[3, 0] = 39.628266211225960722, c[3, 1] = -10.701144127175931857, c[3, 2] = .79165067309766652655, c[3, 3] = 58.111822411188688045], (84, 3) = 1963, (85, 1) = 24356453.746337898025, (85, 2) = [c[0, 0] = -85.340214123654970229, c[0, 1] = -8.7495831569222903472, c[0, 2] = -76.818999263640236466, c[0, 3] = -48.490380717437771725, c[1, 0] = 17.018220954150510355, c[1, 1] = -86.827953939260934272, c[1, 2] = -16.385766917775583845, c[1, 3] = 25.719493461105965544, c[2, 0] = -65.735590108461467534, c[2, 1] = 91.982951829114666130, c[2, 2] = 39.765296713567096946, c[2, 3] = 53.002915145618834514, c[3, 0] = 59.001435506005643271, c[3, 1] = 58.453081309376584457, c[3, 2] = -25.935789913900557406, c[3, 3] = -67.703912284876824048], (85, 3) = 3092, (86, 1) = 0.3136e8, (86, 2) = [c[0, 0] = -70.348025310646516266, c[0, 1] = -92.958911545631759182, c[0, 2] = -90.779173094034544500, c[0, 3] = -34.616304751430625737, c[1, 0] = 110.27068752484166926, c[1, 1] = 29.237022814779390910, c[1, 2] = 23.955621959671746110, c[1, 3] = 14.780979147686208207, c[2, 0] = 89.207796313870892518, c[2, 1] = -89.951255632867354220, c[2, 2] = -21.333898212400293437, c[2, 3] = 18.925571947675350169, c[3, 0] = -12.954823171790562023, c[3, 1] = -66.869570553381650229, c[3, 2] = 21.696644354494615993, c[3, 3] = 57.465962738575783339], (86, 3) = 2198, (87, 1) = 0.36e8, (87, 2) = [c[0, 0] = -19.159200968769569714, c[0, 1] = -79.717895991096605793, c[0, 2] = 106.25000542030449858, c[0, 3] = 23.946283785791708238, c[1, 0] = 81.480513390646430137, c[1, 1] = -10.516307827972496208, c[1, 2] = -23.318789194139995327, c[1, 3] = -10.871466105004750975, c[2, 0] = 20.535084998589754251, c[2, 1] = -68.866947328969133265, c[2, 2] = -22.691022797632049232, c[2, 3] = 68.674280626289505994, c[3, 0] = -96.563974980955446129, c[3, 1] = 69.625393613522926036, c[3, 2] = -76.602361121941419656, c[3, 3] = -78.660990240135092676], (87, 3) = 2254, (88, 1) = 45420051.5136, (88, 2) = [c[0, 0] = 66.472246715289586920, c[0, 1] = 94.827857759631421450, c[0, 2] = 15.525055116741586669, c[0, 3] = -10.884752467284969708, c[1, 0] = -14.086933988280666139, c[1, 1] = -82.494074505394937401, c[1, 2] = -84.680003007848759792, c[1, 3] = 95.337674876714763687, c[2, 0] = -81.569404852514497938, c[2, 1] = 50.129093711545280584, c[2, 2] = -63.054341432183478463, c[2, 3] = -82.391127139886540894, c[3, 0] = 12.898783578461084444, c[3, 1] = -77.471922542957394511, c[3, 2] = 41.198784474693937605, c[3, 3] = 67.563136816560254949], (88, 3) = 1280, (89, 1) = 53860921., (89, 2) = [c[0, 0] = 22.941049363214815019, c[0, 1] = -50.581436496363758717, c[0, 2] = -28.673561327755564766, c[0, 3] = 79.473049991997235528, c[1, 0] = 89.676856015371681232, c[1, 1] = 37.230744961310849523, c[1, 2] = 32.841242709591598960, c[1, 3] = 9.2481691344533191173, c[2, 0] = -85.378031583854795250, c[2, 1] = -60.885914538493882215, c[2, 2] = 2.6753505288497710315, c[2, 3] = -96.298162474036142371, c[3, 0] = 56.116720783775651049, c[3, 1] = 84.944842928993863757, c[3, 2] = -65.089871692439574383, c[3, 3] = -39.736547584971662590], (89, 3) = 2086, (90, 1) = 63567672.821077075225, (90, 2) = [c[0, 0] = 60.738898877009828238, c[0, 1] = -67.479679271433074270, c[0, 2] = 73.470366839792134263, c[0, 3] = -30.160215119437648825, c[1, 0] = 74.244443741731493903, c[1, 1] = 41.128218253563933022, c[1, 2] = -12.218423796207646317, c[1, 3] = -75.411085431047809719, c[2, 0] = 44.021529845045630108, c[2, 1] = 92.141787015176527843, c[2, 2] = 51.594469375022978299, c[2, 3] = -16.391981233752469060, c[3, 0] = -34.857861809304447748, c[3, 1] = 42.988149488763737412, c[3, 2] = 59.957521708659942822, c[3, 3] = -1.2394698299872601776], (90, 3) = 2922, (91, 1) = 69891424.3311049921, (91, 2) = [c[0, 0] = -69.498083005546958130, c[0, 1] = -13.921872928359925566, c[0, 2] = 83.710422966066068955, c[0, 3] = -50.805310462195507617, c[1, 0] = -53.816789930172874020, c[1, 1] = 7.3401614353579680162, c[1, 2] = -31.224228927406828537, c[1, 3] = 65.053544456820367323, c[2, 0] = 23.510607790579735357, c[2, 1] = 75.456953333933896085, c[2, 2] = -87.549018688349264410, c[2, 3] = -69.149045690075641564, c[3, 0] = 58.413686123869492842, c[3, 1] = -6.1528824255865578819, c[3, 2] = -.71200097173805728471, c[3, 3] = 65.530532793425985077], (91, 3) = 2197, (92, 1) = 72169974.237874524804, (92, 2) = [c[0, 0] = -89.419484000350368272, c[0, 1] = -59.693204475052383049, c[0, 2] = -3.9034957177233262336, c[0, 3] = 90.319706456530478339, c[1, 0] = 57.460707688066280663, c[1, 1] = 45.505928754881089778, c[1, 2] = 82.928489535440087286, c[1, 3] = -10.763909421900913303, c[2, 0] = -46.981643579096212645, c[2, 1] = 28.792504197301298631, c[2, 2] = 3.8008334000208936102, c[2, 3] = 77.025236133507162191, c[3, 0] = 77.453633208690554683, c[3, 1] = -16.981775708959493531, c[3, 2] = -77.348576656196894707, c[3, 3] = 48.056308644136171823], (92, 3) = 2370, (93, 1) = 0.81e8, (93, 2) = [c[0, 0] = 78.664207426515743309, c[0, 1] = -54.077131316912370334, c[0, 2] = 38.449969290714504525, c[0, 3] = 22.651914032192602460, c[1, 0] = -15.153947734477788931, c[1, 1] = -66.924071358399461158, c[1, 2] = 38.678668259426164419, c[1, 3] = 63.629591748531303684, c[2, 0] = -26.488472209028761636, c[2, 1] = -91.754288659622689876, c[2, 2] = 71.185917309914995848, c[2, 3] = -79.014448965366192811, c[3, 0] = -58.955398276495735154, c[3, 1] = -92.684797407461007568, c[3, 2] = -80.138662028444902336, c[3, 3] = 75.685538785914344258], (93, 3) = 2572, (94, 1) = 0.100e9, (94, 2) = [c[0, 0] = 62.376815236126336860, c[0, 1] = 49.583710572775169616, c[0, 2] = -7.0803603099654115786, c[0, 3] = -8.0961332641418489868, c[1, 0] = 61.353767545970733986, c[1, 1] = -13.303434372351399237, c[1, 2] = 60.226586294882419908, c[1, 3] = -38.760185470075889260, c[2, 0] = 86.354502628951982665, c[2, 1] = 70.343149178589692878, c[2, 2] = -67.676008709864704500, c[2, 3] = 90.066196354223547040, c[3, 0] = -46.334639564143780046, c[3, 1] = -33.968809257990398091, c[3, 2] = 3.5802375309676973899, c[3, 3] = -43.191485893987181999], (94, 3) = 2781, (95, 1) = 0.22801e9, (95, 2) = [c[0, 0] = -80.431925238057597468, c[0, 1] = -39.283676412345531416, c[0, 2] = -71.300290504722916960, c[0, 3] = 96.972355159248711128, c[1, 0] = 101.46561572576117674, c[1, 1] = -7.3243653227083432480, c[1, 2] = -64.472343684586069526, c[1, 3] = 59.424348186689005724, c[2, 0] = 77.343972756288310536, c[2, 1] = -86.627383529857743117, c[2, 2] = -71.285817445240593133, c[2, 3] = 52.216918282270729194, c[3, 0] = 7.5070962764002442146, c[3, 1] = -16.852032421077242307, c[3, 2] = -7.3174025511277917471, c[3, 3] = -36.037335489013100709], (95, 3) = 2239, (96, 1) = 0.36100e9, (96, 2) = [c[0, 0] = 45.103243687394462269, c[0, 1] = 94.749537827616656480, c[0, 2] = 357.36482476777914284, c[0, 3] = -70.991419175100723153, c[1, 0] = -5.8401824234572238771, c[1, 1] = -27.084171790950550801, c[1, 2] = 28.379344249132874145, c[1, 3] = 21.538752088342123235, c[2, 0] = -38.765706273372822854, c[2, 1] = 72.593659850506387877, c[2, 2] = 3.0364358053205252915, c[2, 3] = -45.770206819543181299, c[3, 0] = -43.319058971947085838, c[3, 1] = 80.012028501829187689, c[3, 2] = 1.2103213590265963698, c[3, 3] = 49.485620359583677666], (96, 3) = 1987, (97, 1) = 636300625., (97, 2) = [c[0, 0] = -29.117303468196568776, c[0, 1] = -98.156509553668763165, c[0, 2] = 42.072679056467706781, c[0, 3] = 52.821022744402024318, c[1, 0] = 34.032720923965147263, c[1, 1] = -38.085834344474329718, c[1, 2] = 60.342210712913580681, c[1, 3] = -54.395793539484970393, c[2, 0] = 47.553761630091054175, c[2, 1] = 53.262939788115732596, c[2, 2] = -21.891627088498742214, c[2, 3] = 83.236827016039134071, c[3, 0] = -40.829788475375034558, c[3, 1] = -25.693428069206686232, c[3, 2] = -34.377811130651585930, c[3, 3] = -77.401732251658078268], (97, 3) = 1847, (98, 1) = 2868364169.7294454641, (98, 2) = [c[0, 0] = -82.169927229903924728, c[0, 1] = -57.024064764812575676, c[0, 2] = 50.039709445802309926, c[0, 3] = 58.714361710936949566, c[1, 0] = -58.372964509872248755, c[1, 1] = -50.573680143916741869, c[1, 2] = -48.438639694849804776, c[1, 3] = 5.1658058254067325611, c[2, 0] = -93.082126054508756088, c[2, 1] = 89.021143541547427349, c[2, 2] = 42.657337344917108754, c[2, 3] = -20.644278042870672438, c[3, 0] = -29.661318686120945283, c[3, 1] = 18.235677980502507108, c[3, 2] = 15.065569536428333261, c[3, 3] = 4.7376927647532264808], (98, 3) = 2302, (99, 1) = 3311139306.25, (99, 2) = [c[0, 0] = 6.2464837055084406563, c[0, 1] = 46.950110689177822003, c[0, 2] = -65.033096822968561423, c[0, 3] = -18.025890078421069160, c[1, 0] = -45.488928496433509653, c[1, 1] = -60.522142955187728339, c[1, 2] = 33.548644594048872764, c[1, 3] = 28.042918479339986407, c[2, 0] = -100.31568741542168828, c[2, 1] = 63.561450756452567379, c[2, 2] = 54.107406978283635893, c[2, 3] = 68.427573226793115285, c[3, 0] = 79.099386705948312303, c[3, 1] = 4.1940083886550545714, c[3, 2] = 59.312608032482091313, c[3, 3] = -90.539402450170768499], (99, 3) = 2175, (100, 1) = 0.609961e10, (100, 2) = [c[0, 0] = 55.128620821038850807, c[0, 1] = -75.051961486056216840, c[0, 2] = -74.469141508816587523, c[0, 3] = 60.978359749044808184, c[1, 0] = -10.718666306255245174, c[1, 1] = 98.751239512522376067, c[1, 2] = 90.783443131633681197, c[1, 3] = 22.168107219216155502, c[2, 0] = -15.692954429900699053, c[2, 1] = 81.990559686820294843, c[2, 2] = -71.600540412083296935, c[2, 3] = -38.719650355183216820, c[3, 0] = 28.882250794549899178, c[3, 1] = 87.943926970871510534, c[3, 2] = -82.711640713847402002, c[3, 3] = 51.630944389083471277], (100, 3) = 2734})

 

ind := 4

 

Array(%id = 18446744074372250670)

 

0.1375929e-19

(1)

#
# If one is being pedantic I suppose one ought to
# evaluate the residual of the original expression
# (ie expr, rather than expr^2
#
  eval(expr, sol[ind,2]);

0.1173e-9

(2)

 

Download optProb.mw

has managed to transfer this from a "post" to a "question", but in doing so has mislaid my original comment/answer, which is now available here

https://www.mapleprimes.com/questions/226450-Sets

My original response stands, but I have been somewhat amused by subsequent contributions. I have therefore (reluctantly) decided to provide an explanation which the casual user of the tolerances() package might actually understand.

So the following is intended for the casual user

#########################################################################################################

When one loads a Maple package such as Tolerances, a few things can happen. The most obvious is that some "new" commands become available: this is pretty obvious. Slightly less obvious, and generally not so clear from the documentation, is that some "existing" commands (and operators) are redefined. This redefinition is referred to by a variety of names such as "overloading" or "rebinding". The drawback with such redefinition is that the casual user may not evan be aware that it has taken place!!!

It is possible to check newly-available commands, and redefinitions by using the exports() command. So for example

restart:
with(Tolerances):
exports(Tolerances);

will return

NominalValue, ToleranceValue, `&+-`, `+`, `*`, `-`, `^`, sqrt, sin, cos, tan, cot, csc, sec, arcsin, arccos, arctan, arccot, arccsc, arcsec, sinh, cosh, coth, tanh, csch, sech, arcsinh, arccosh, arccoth, arctanh, arccsch, arcsech, abs, exp, ln, Ei, FresnelC, FresnelS, Fresnelf, Fresnelg, GAMMA, Psi, LambertW, Zeta, dilog, erf, erfc, Precision, _pexports

Reading this list, it is fairly obvious that a large number of basic Maple commands get redefined/rebound when the Tolerances package is loaded. The most relevant rebindings for the current problem are `+`, and  `*`.

Let's be brutally clear: once the Tolerances package is loaded simple addition and multiplication are redefined. However neither the add() command (which must contain a '+' operator somewhere!) not the elementwise operator (~) is respecting these redefinitions.

So congratulations! In the one simple statement

Z := add([3, 2] *~ [x, y]);

you managed to come up with two bugs.

Including my original response, there are many ways to work around these two bugs which I have summarised in the attached. You are of course perfectly free to use whichever you find most convenient/understandable

  restart:
  with(Tolerances):
  x := 10 &+-1:
  y := 20 &+- 2:
  z := 3*x+2*y;
  NominalValue(z);      # returns 70 as expected
  ToleranceValue(z);   # returns 7 as expected
  add([3, 2] *~ [x, y]);
#
# My original suggestion
#
  Z:=evalr( add([3, 2] *~ [x, y]));
#
# Acer suggestion
#
  Z:=`+`(zip(`*`,[3,2],[x,y])[]);
#
# Carl Love suggestion
#
  Z:=subsindets(add([3, 2] *~ [x, y]), {:-`*`, :-`+`}, e-> `if`(e:::-`*`, `*`, `+`)(e));

INTERVAL(63 .. 77)

 

70

 

7

 

3*INTERVAL(9 .. 11)+2*INTERVAL(18 .. 22)

 

INTERVAL(63 .. 77)

 

INTERVAL(63 .. 77)

 

INTERVAL(63 .. 77)

(1)

 

Download tolProb2.mw

as in the attached - although I'm not exactly sure why this "extra" evaluation stage is necessary

restart:
with(Tolerances):
x := 10 &+-1:
y := 20 &+- 2:
z := 3*x+2*y;
NominalValue(z);      # returns 70 as expected
ToleranceValue(z);   # returns 7 as expected
add([3, 2] *~ [x, y]);
Z:=evalr( add([3, 2] *~ [x, y]));
NominalValue(Z);
ToleranceValue(Z);

INTERVAL(63 .. 77)

 

70

 

7

 

3*INTERVAL(9 .. 11)+2*INTERVAL(18 .. 22)

 

INTERVAL(63 .. 77)

 

70

 

7

(1)

 

Download tolProb.mw

Maybe you and your professor have different typesetting 'levels' set. From the menus try

Tools->Options->Display->TypesettingLevel

whatever you have this set to, "Standard" or "Extended", toggle it to the other setting to see if it makes any difference

  1. 'if' clause should be if...then...fi rather than if...the...fi
  2. there is an extra '(' in the then clause: either needs to be deleted, or a matching ')' added, depending exactly on what you are trying to calculate

The attached will execute

  Fract := proc(P::posint, Q::posint)  
         local p,q:
         for p from 1 to P-1 do
            for q from 1 to Q-1 do
                if   (P-p)*q-P*(Q-q)=1
                then return p/q, (P-p)/(Q-q):
                fi:
            od:
         od:  
         end:
  #debug(Fract);
  Fract(5, 13);
  Fract(77, 200);

4/11, 1/2

(1)

``

Download fracProc.mw

why you want to do this - I mean do you literally just want to print, maybe for headers in a table or something??? Assuming that this is all you wish to achieve then the the simplest way is shown in the attached

printf("\t\t"):
seq(printf( "op\(S\[%d\]\),    ",j), j=1..5);

                op(S[1]),    op(S[2]),    op(S[3]),    op(S[4]),    op(S[5]),    

 

 

NULL

Download oddPrint.mw

If you use the VectorCalculus (rather than the Student[VectorCalculus]), package then you can define (almost?) any coordinate system you want. So if you don't like default 'spherical' definition, you can change it.

Consider the attached

restart;
with(VectorCalculus):
assume( r>0,
        0<=theta, theta<=2*Pi,
        0<=phi,     phi<=Pi
      );
AddCoordinates( mypolar[r, theta, phi],
                [ r*cos(theta)*sin(phi), r*sin(theta)*sin(phi), r*cos(phi)]
              ):
PlotVector( VectorField( <0, theta, 0>,
                         mypolar[r, theta, phi]
                       ),
            r = 0 .. 1,
            theta = 0 .. 2*Pi,
            phi = 0 .. Pi,
            view = [-5..5, -5..5, -10..10],
            arrows = THICK,
            color = black,
            grid = [10, 10, 3],
            view = [-1..1, -1..1, -1..1]
          )  

 

 

 

 


 

Download VFplot.mw

  1. In your final expression you have used square brackets (ie '[]') to group terms in an expression. You should only use round brackets (ie '()') to achieve this. Square brackets in Maple designate an indexable quantity (ie list, Array, table, whatever), which I'm pretty sure(?) you don't want
  2. I don't understand why you are plotting 'Re(u)' rather than just 'u'. The latter expression  is real for all specified values of the independent variables 'x' and 't, so plotting 'Re(u)' isn't wrong, just superfluous
  3. The way you have defined the plot ranges in your original post, ie plot3d(Re(u), x = -20 .. .20, t = -20 .. .20); implies that x will vary from -20.0 to +0.2. The spacing of the '.' characters is important. This might be a cut-and-paste problem, particularly if your original worksheet was written using 2D-math input). I have assumed that you actually want both independent variables ro vary from -20.0 to +20.0
  4. There is a lot of structure on this plot over the required range which is dominated by the values of +/-1500 at a few points, so I have added a plot which 'zooms' into the z-range -100..100 just to make this detail more visible

See the attached

  restart:
  A[0]:= 0:
  A[1]:= sqrt(2*(k[1]^2-w[1]^2))/sqrt(lambda):           
  A[2]:= sqrt(2*(k[2]^2-w[2]^2))/sqrt(lambda):           
  c[1]:= 1: c[2]:= 1: c[3]:= 1: c[4]:= 1:
  c[5]:= 1: c[6]:= 1:
  k[1]:= 10.5:k[2]:= 3.5:
  w[1]:= 5.05:w[2]:= .5:
  m:= 1.9:
  lambda:= 1.75:
  xi[1]:= -t*w[1]+x*k[1]:
  xi[2]:= -t*w[2]+x*k[2]:
  a:= m/sqrt(k[1]^2-w[1]^2):
  b:= m/sqrt(k[2]^2-w[2]^2):
  g:= a*(c[2]*cos(a*xi[1])-c[3]*sin(a*xi[1])):
  h:= c[1]+c[2]*sin(a*xi[1])+c[3]*cos(a*xi[1]):
  G:= b*(c[5]*cos(b*xi[2])-c[6]*sin(b*xi[2])):
  H:= c[4]+c[5]*sin(b*xi[2])+c[6]*cos(b*xi[2]):
  u:= A[0]+A[1]*(g/h)+A[2]*(G/H);
  plot3d(u, x = -20..20, t = -20..20);
  plot3d(u, x = -20..20, t = -20..20, view=[-20..20, -20..20, -100..100]);

9.841457496*(.2063907138*cos(1.042273105*t-2.167102495*x)+.2063907138*sin(1.042273105*t-2.167102495*x))/(1-sin(1.042273105*t-2.167102495*x)+cos(1.042273105*t-2.167102495*x))+3.703280398*(.5484827558*cos(.2742413779*t-1.919689645*x)+.5484827558*sin(.2742413779*t-1.919689645*x))/(1-sin(.2742413779*t-1.919689645*x)+cos(.2742413779*t-1.919689645*x))

 

 

 

 

 

Download badpars.mw

but you can control Maple styles from the dropdown menus using (for example)

Format->Styles->Heading1->Modify

This will permit you to adjust (for example) the lineSpacing within, spaceAbove and spaceBelow for all occurrences of the style 'Heading1'

If you wish you can also create your own paragraph styles

So which functionality (exactly) are you missing

 

You say that you are

trying element-wise addition of two arrays

How else would arrays add - other than elementwise?? If you have two arrays 'A' and 'B' then 'A+B' will add them (elementwise). So will 'A+~B', but it is just superfluous

In your code, you run a loop 100 times. On each iteration you generate 5000 samples from a Cauchy distribution, add these to a pre-existing array and the throw away the result (since it is never assigned to anything). Thius the array 'AA' will be the same after the loop has terminated as it was before the loop was executed. Is this intentional?

In the Sample() command of your code, you generate samples with the default output format of Vector(), then use these to initialise an Array(), before doing the array addition - seems a very inefficient way to do things??? Either use Vectors throughout, or ensure that the options to the Sample() command are set to automatically return an Array.

Exactly what constitutes too much memory? Maple's memory usage has increased by about 30MB after the calculation. Is this too much?

See the attached for assorted fixes to the above, where (in some cases) I have "guessed" your actual intentions

##############################################
# Use Vectors for storage probably(?) the most
# efficient
##############################################
  restart;
  with(Statistics):
#
# Get start time
#
  t1:=time():
#
# Function to obtain "memory usage" in MBytes
#
  getMem:=()-> add
               ( k[3],
                 k in kernelopts(memusage)
               )/(1.0*10^6):
  ss:= 2:
  MaxIt:= 5000:
  AA:= Vector[row]
       ( MaxIt,
         [ seq
           ( i,
             i = 1 .. MaxIt
           )
         ]
       ):
#
# Get memory usage before calculation
#
  M1:= getMem():
  for i to MaxIt do
      AA:= AA+Sample
              ( Cauchy(0, ss),
                MaxIt
              ):
      ss:= ss-1/MaxIt:
  end do:
#
# Get elapsed time
#
  t2:= time()-t1;
#
# Get memory usage after calculation
#
  getMem()-M1;
#
# Force a garbage collection, then
# check the memory again
#
  gc();
  getMem()-M1;

4.882

 

33.75100000

 

29.58872000

(1)

##############################################
# Using Arrays rather than Vectors for storage
##############################################
  restart;
  with(Statistics):
#
# Get start time
#
  t1:= time():
#
# Function to obtain "memory usage" in MBytes
#
  getMem:=()->add( k[3],
                   k in kernelopts(memusage)
                 )/(1.0*10^6):
  ss:= 2:
  MaxIt:= 5000:
  AA:= Array
       ( 1..MaxIt,
         [ seq
           ( i,
             i = 1 .. MaxIt
           )
         ]
       ):
#
# Get memory usage before calculation
#
  M1:= getMem():
  for i to MaxIt do
      AA:= AA+Sample
              ( Cauchy(0, ss),
                1..MaxIt
              ):
      ss:= ss-1/MaxIt:
  end do:
#
# Get elapsed time
#
  t2:=time()-t1;
#
# Get memory usage after calculation
#
  getMem()-M1;
#
# Force a garbage collection, then
# check the memory again
#
  gc();
  getMem()-M1;

20.561

 

29.66483200

 

29.70122400

(2)

 


 

Download cauchySample.mw

 

Same problem as the last time you asked this at

https://www.mapleprimes.com/questions/226422-Gaussian-Distribution-Error

If you want to fail quickly, then try the attached which will 'Error' in less than one second - and it errors when you ask for samples from a normal distribution with zero variance - essentially the same problem as your previous post.

Try thinking!

restart; UseHardwareFloats := false; with(Statistics); XG := RandomVariable(Normal(0, h)); SXG := Sample(XG, method = [envelope, range = -1 .. 1]); h := 1; MaxIt := 1000; randomize(); P := Matrix(MaxIt, 5); t1 := time(); for i to MaxIt do h := h-1/MaxIt; P[i, () .. ()] := SXG(5) end do; time()-t1

Error, (in unknown) numeric exception: division by zero

 

.889

(1)

P; i; h

RTABLE(18446744074181361662, anything, Matrix, rectangular, Fortran_order, [], 2, 1 .. 1000, 1 .. 5)

 

1000

 

0

(2)

``


 

Download doGauss.mw

I have no idea why/how 2D-math+ palette entry can come up with something this wrong, but it does.

In case you haven't noticed, the incorrect numbers being generated are not "random" but are

0.7656967841e-3 =1/1306.

0.4743833017e-3=1/2108.

0.1008064516e-2=1/992.

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