
// Make newform 8036.2.a.s in Magma, downloaded from the LMFDB on 23 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_8036_a();"
// To make the coeffs of the qexp of the newform in the Hecke field type "qexpCoeffs();"
// To make the newform (type ModFrm), type "MakeNewformModFrm_8036_2_a_s();".
// This may take a long time!  To see verbose output, uncomment the SetVerbose lines below.
// The precision argument determines an initial guess on how many Fourier coefficients to use.
// This guess is increased enough to uniquely determine the newform.
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_8036_2_a_s();".
// This may take a long time!  To see verbose output, uncomment the SetVerbose line below.
// The default sign is -1.  You can change this with the optional parameter "sign".
function ConvertToHeckeField(input: pass_field := false, Kf := [])
    if not pass_field then
        poly := [9, 204, 1130, -2276, -18823, 34656, 37544, -84720, -21992, 82500, -220, -40524, 4748, 10948, -1934, -1644, 348, 128, -30, -4, 1];
        Kf := NumberField(Polynomial([elt : elt in poly]));
        AssignNames(~Kf, ["nu"]);
    end if;
    Rf_num := [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [59952362841513, 738083784597603, -196305191328821, -13852123920661924, 20402313321661661, 28198262762586312, -54976710977041287, -17304021386138605, 55269502351641049, 811667273331286, -27567693836690814, 3042707531442513, 7513711673122948, -1304931363722533, -1134655223791407, 238604415918489, 88680236252730, -20725264188092, -2778645197913, 693771077180], [190983464209108996263, 1555738005610136792040, -2950763457356350118969, -27515570123960339467871, 53967376288662842383274, 55417302249307152484678, -133301820620661470919197, -31996738533222421425408, 129922976197309212858705, -1268832263838809426215, -63775711863953965507911, 7637148660948016713900, 17214742740867450156004, -3055149489179038791221, -2583040292296088360850, 547064973518762056275, 200987274480806224623, -47074158679250201267, -6277851071446228846, 1567892632533415234], [237506550933062053047, 2351603977580673921478, -3540129341608367956689, -41370391953693733063937, 76448600437103562826964, 82085159614420114983234, -192459021916121267807269, -46054021734106426917342, 189167220552118841239433, -3140475534235154283977, -93326413146857308210869, 11815139014102216431238, 25275099625931947407732, -4630220852871028587469, -3801108458647015368204, 822244089607423348755, 296231174702212346977, -70424247764763687101, -9262887357902091940, 2338757660528812226], [620836439810025, 7723657414763231, -1309162504591808, -145789349517861572, 202658302419133080, 305071323257237295, -547047554161970435, -201766431641702593, 548751658773871214, 26102191633898274, -272988213285828381, 24114490412599688, 74233650073598569, -11748441413484831, -11189902694968197, 2229477793619106, 873381091267388, -197062564273797, -27339265673408, 6661373649057], [97226989580590920354, 1234511067892056717935, 137683984888334896715, -23837476286048645159857, 31172753632958704540280, 50327088938842591365967, -85783168225253530008394, -34029275141695079410549, 86537534252271920654531, 5221070179901194950473, -43154858634515689790568, 3498116413657850939414, 11749994362571690048087, -1805440454952041490734, -1772518274441041104831, 347664092105664073677, 138415002843547076609, -30930718070891675108, -4334271434248616952, 1049275988912470441], [606826360165697573025, 8395092563731168662665, 1023954424120529904920, -165493117300867307298002, 223334005665434926549898, 347741351999178390256559, -614376030427052055814071, -230588328077451908360595, 619876660982428449866914, 30268230823871797593612, -309205145409647896750815, 27270563865313329311810, 84209031937717862545217, -13339100027251658888871, -12705398753421574017087, 2533932755487489006282, 992270980545485712530, -224074168773683551559, -31073635796039525650, 7576293982927979121], [392584122713171677173, 4967650318979614979306, -113306502518376301934, -90208099965535405712597, 118753928893976335890255, 188504634894224254795827, -324232804881156119466287, -125963171001350030109214, 326510789581180900501616, 18087044949039785162649, -162744505113663406493844, 13746983099618899161683, 44305336615419018612667, -6916239982613718566301, -6683420464723393238238, 1322869278130680137994, 521906431334303239643, -117320671722447788928, -16342846128512544173, 3972783117852940809], [-221061471807410959458, -2586400883220466564331, 517517724798107266852, 46575172685757514399803, -62888363036257849808159, -97578804334811055019104, 169432892648625526742675, 65568896606482854054425, -169854154542396568640853, -9732855884360263281280, 84464400288516335583243, -6956162240324603946659, -22962070603119437409617, 3543492889243349642386, 3460621390478264793615, -680096131542676025598, -270070665887929370564, 60415489542289066625, 8453306354806390649, -2047786292360142275], [-667661155757941536921, -8943772883317561833176, -880481015365818753984, 180338782805028994078333, -246474731929496125697395, -378819093668096210188203, 676734395670792749969903, 249783826314754461858204, -682452603951447075395134, -31116542935035778457819, 340365600693759113900646, -30703096120479886653617, -92690601820563143085051, 14807867321195626880525, 13984839560922314660460, -2802339477585508903152, -1092181398511623458951, 247380582079000993072, 34202040308351693999, -8356272662031765421], [1039311719576074586769, 11973135027759598136281, -5004868760721322981926, -225340677579528815198014, 333187098654750974129600, 467029295366688741017921, -886587875671824490647875, -299668100923119368276203, 885892877952153906591132, 28483713793780474325016, -440051048998962173817801, 42952487320825958297536, 119580968135206563719079, -19652386941621891075063, -18018706532048828189043, 3665451754025270244468, 1406026625803290483046, -321427966399360503593, -44004533606033770380, 10817735530643672823], [-508723097353615002549, -6622263148757199924236, -395578244725691148738, 129044554135267262643513, -172340908041091230121837, -272203242371124194650313, 472103252678673209814171, 182985431498476594699216, -475532953075794779675528, -26798116659087406948195, 236964510849042737550060, -19717931987831196765635, -64491433648002404390229, 9993361151771601407425, 9725925495596380955028, -1915869049907838609096, -759339338545804496015, 170121063113279701288, 23774153729099490769, -5765110608764984219], [-562332436760355025320, -7045871191970967584026, -20762070898140250163, 137687461555365045233094, -187322137052218898966457, -289687900253439035789069, 511321403595229157488586, 193026483803831537370618, -514564778294223298658171, -26358642828281747248718, 256332262566733625164623, -22128310064864091219739, -69753480654678076097837, 10952270309572306681580, 10518852033194202600960, -2087033475527660694129, -821215965080328317242, 184817918043869208801, 25710747398443785873, -6253881503724915265], [1233943646077998910485, 16097180552095863216408, 343760481474573044810, -315556203763661953628365, 429824287705913693338525, 663248018168538332130329, -1174535280429699515543167, -440588282101994854095084, 1182522905208002117547780, 58703032263898179944719, -589251743429612557666656, 51513448344016378444467, 160381237404775884342221, -25306907459928782093989, -24189115890691711217376, 4812963651580171485534, 1888661390075851423815, -425833794628053440962, -59134751184578330885, 14402308926297643223], [1234585521558462095301, 15402396422972692780726, -3554413158860711081553, -304997202980737096627727, 444117927600826721299226, 635842430113801342281372, -1194877112155448350622119, -410474329960614160479102, 1197582146857521448758737, 41227112868720385687825, -595622318194356679148397, 57379737864677684063536, 161958144182482346030238, -26485294281914839965835, -24412967211259506148740, 4952712998950562047623, 1905411720410527343023, -434846673787457040185, -59642851508940305086, 14645155040509963820], [617682916703533320726, 8099183834371161701361, 321155306165435922256, -161021264521041724703129, 220873751730400091677289, 337911546657425909550568, -604220200791226407993500, -222874255585591719674739, 608602934352236377481532, 27923448863376964351637, -303357063011471710727439, 27275698837548390607893, 82584351503069563769488, -13173947522025534613790, -12457405771199322026019, 2494047510119311879458, 972757216930066495875, -220200766266302213723, -30459378048999778099, 7438783877591216548], [-699634305926123616771, -9235939572202007595577, -1221891996360336135274, 181302476507307694588730, -240832709198133636810616, -381979586086710828489095, 662877997391653078852985, 255826579517142651304643, -668728059025171509164860, -36486799032282948761686, 333503362373389497835863, -28224573672325185426058, -90809978718344201679229, 14168966215045114054639, 13699510172653880436333, -2709600815139216588042, -1069812371476842628582, 240323297279872800415, 33499956946277000400, -8138886928753770041], [829762774988511791610, 10524879908602517748106, -748060606226458740485, -199891469248486819547262, 272777471804394727207141, 419276455516957466764863, -741081009576028826055736, -278897838495269416179886, 744805250324323650729783, 37844023940778257308124, -370826360968046011930875, 32101655974673253786169, 100882261019315843361703, -15856792379304385164044, -15210701217109761007314, 3019802809987906445103, 1187394854241713040880, -267337054794349577899, -37172639749616416747, 9044475989189897959]];
    Rf_basisdens := [1, 1, 1, 8907432980628, 7045699320779922348, 7045699320779922348, 8907432980628, 1006528474397131764, 7045699320779922348, 3522849660389961174, 1761424830194980587, 7045699320779922348, 7045699320779922348, 3522849660389961174, 3522849660389961174, 7045699320779922348, 7045699320779922348, 3522849660389961174, 3522849660389961174, 3522849660389961174];
    Rf_basisnums := ChangeUniverse([[z : z in elt] : elt in Rf_num], Kf);
    Rfbasis := [Rf_basisnums[i]/Rf_basisdens[i] : i in [1..Degree(Kf)]];
    inp_vec := Vector(Rfbasis)*ChangeRing(Transpose(Matrix([[elt : elt in row] : row in input])),Kf);
    return Eltseq(inp_vec);
end function;


// To make the character of type GrpDrchElt, type "MakeCharacter_8036_a();"
function MakeCharacter_8036_a()
    N := 8036;
    order := 1;
    char_gens := [4019, 493, 785];
    v := [1, 1, 1];
    // chi(gens[i]) = zeta^v[i]
    assert UnitGenerators(DirichletGroup(N)) eq char_gens;
    F := CyclotomicField(order);
    chi := DirichletCharacterFromValuesOnUnitGenerators(DirichletGroup(N,F),[F|F.1^e:e in v]);
    return MinimalBaseRingCharacter(chi);
end function;

function MakeCharacter_8036_a_Hecke(Kf)
    return MakeCharacter_8036_a();
end function;


function ExtendMultiplicatively(weight, aps, character)
    prec := NextPrime(NthPrime(#aps)) - 1; // we will able to figure out a_0 ... a_prec
    primes := PrimesUpTo(prec);
    prime_powers := primes;
    assert #primes eq #aps;
    log_prec := Floor(Log(prec)/Log(2)); // prec < 2^(log_prec+1)
    F := Universe(aps);
    FXY<X, Y> := PolynomialRing(F, 2);
    // 1/(1 - a_p T + p^(weight - 1) * char(p) T^2) = 1 + a_p T + a_{p^2} T^2 + ...
    R<T> := PowerSeriesRing(FXY : Precision := log_prec + 1);
    recursion := Coefficients(1/(1 - X*T + Y*T^2));
    coeffs := [F!0: i in [1..(prec+1)]];
    coeffs[1] := 1; //a_1
    for i := 1 to #primes do
        p := primes[i];
        coeffs[p] := aps[i];
        b := p^(weight - 1) * F!character(p);
        r := 2;
        p_power := p * p;
        //deals with powers of p
        while p_power le prec do
            Append(~prime_powers, p_power);
            coeffs[p_power] := Evaluate(recursion[r + 1], [aps[i], b]);
            p_power *:= p;
            r +:= 1;
        end while;    
    end for;
    Sort(~prime_powers);
    for pp in prime_powers do
        for k := 1 to Floor(prec/pp) do
            if GCD(k, pp) eq 1 then
                coeffs[pp*k] := coeffs[pp]*coeffs[k];
            end if;
        end for;
    end for;
    return coeffs;
end function;


function qexpCoeffs()
    // To make the coeffs of the qexp of the newform in the Hecke field type "qexpCoeffs();"
    weight := 2;
    raw_aps := [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0], [-1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, -1, 0, 0, 0], [0, 0, -1, 0, 1, 0, -1, 0, 0, 1, -1, -2, -1, -1, 1, 0, 1, 0, 0, 0], [0, -1, 1, 0, -1, 0, 1, 1, 0, 0, 1, 1, 2, 1, 0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0, 0, 0, -1, 0, 0, -1, -1, 0, 0, 0, 0, 0, 1, 0], [0, 0, -1, 0, 0, -1, 1, -1, 0, -1, 0, -1, 0, -1, 1, -1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, -2, -1, -1, -1, 1, 2, 2, -2, 0, -1, 0, 1, 1, -2, 1, 0, 0, 1], [0, 0, 0, 0, -1, 0, 1, 1, 1, -1, -1, 0, 1, 1, 0, 0, 0, 0, 0, -1], [-2, 2, -2, -1, 1, 1, -2, 0, 0, 0, 0, -1, -2, -1, 0, 0, -1, 1, 1, 0], [0, -1, -2, 0, -1, 0, -1, 1, 0, 0, 0, -2, -1, -1, 0, -1, 1, -1, 1, -1], [-3, 0, 0, 1, 1, 1, 0, -2, -1, 1, 1, 0, 0, -1, 0, 1, 0, -1, 0, -1], [0, 2, 1, 0, 0, 0, -1, -1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, -1, 0], [0, 1, 2, 0, -1, -1, 2, 0, 0, -1, 1, 1, 1, 1, -1, 0, -1, 0, -1, 1], [-3, 0, 1, 0, 1, 0, 0, 1, 1, 2, -1, 1, 1, 0, 1, 0, 0, 2, 0, 0], [-3, 0, 1, 1, 1, -1, 0, -1, -1, 2, -1, -2, 0, -1, -1, 0, 0, 0, 0, 0], [1, 1, 1, -1, -1, 0, 0, 2, 0, 0, -1, 0, 1, 1, 1, -1, 1, 1, 0, 1], [-4, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, -2, -1, 0, -1, -1, 0, -1, 0, 1], [-1, 0, 1, -2, -1, 1, 0, 0, -1, 1, 1, 0, 1, 0, 0, 0, 0, -1, -1, 0], [-4, 3, -1, 1, 2, 1, 1, -4, -1, -1, -1, -1, -1, -1, 0, 0, -2, 1, 0, -1], [1, -1, 4, 3, -1, 1, -2, 1, -2, 2, 1, 1, 1, 1, -2, 2, 0, -2, 0, 0], [-2, 0, -1, 2, 2, 0, 2, 0, -1, 0, 1, -1, -1, 0, -1, 1, 0, 0, 2, 0], [1, 0, 1, -1, -2, 0, -1, 3, 1, -1, 3, 4, 2, 2, 1, 0, 0, 0, -1, 3], [-2, 3, -1, 0, 0, 0, 2, -3, 0, -1, -1, -2, -1, -2, 0, 0, -1, 0, 0, -1], [3, 0, 1, -1, -1, 1, -1, -1, 0, 1, 1, 3, 1, -1, -1, 2, 0, 0, -2, -2], [-2, -1, 0, 2, 0, -2, 0, 1, 1, -1, 2, 1, -1, 0, -2, -1, 0, -1, 0, 1], [-1, 1, 0, 1, -3, -2, -3, 1, 1, -1, 1, -1, 1, 1, -1, -1, 2, -2, 0, 1], [-2, -1, 1, 0, 0, -2, 1, -1, 0, -1, 3, 1, 1, 0, 0, -1, 1, -1, -1, 2], [0, -2, -1, -2, -1, 1, 0, 3, 2, 1, -1, -1, 0, 1, 1, -1, 1, 0, 0, 1], [3, 2, 0, -2, -2, 0, -1, 2, 2, -1, -1, 2, 3, 2, 2, -1, 1, 1, -1, -1], [-5, 2, 0, 0, -1, 1, 1, 1, 1, -1, 1, 3, 1, 2, 0, 1, -1, 2, 0, 1], [2, 2, 0, 1, -2, 0, 2, -1, -1, 0, 1, 1, -1, -1, -3, 0, 0, -1, 0, -1], [4, 2, 0, -1, -1, 1, -1, -1, -1, -1, 0, 1, -2, -1, -2, 0, -2, 1, 0, -1], [-3, 1, 0, 0, -2, -2, 2, 2, 2, -2, -1, -2, 0, 2, 1, -3, 1, 0, 0, 0], [-1, 0, 3, 2, 1, -1, -4, 0, 0, 0, 0, 3, 1, 1, -2, 1, -1, 1, 0, 2], [-6, 1, 2, 0, 0, -2, 0, -2, 0, 0, 1, 1, 0, 0, -1, -1, 0, -2, -1, 3], [0, 0, 2, 0, -2, -1, 5, 0, 0, -2, 3, 2, 3, 2, 0, 0, -1, -1, -2, 2], [1, -2, 3, 4, 1, -2, -4, -2, -3, 2, 1, -2, 0, 1, -1, 2, 1, -3, 1, 0], [2, -2, 0, 1, 2, 0, 0, 1, -2, 2, -2, -4, -2, -1, 1, -1, 2, 0, 3, 0], [-2, -1, -1, -3, 2, 1, -3, 1, 2, 2, -3, -2, -1, -2, 2, -1, 1, 0, -1, -1], [-2, -4, 1, -1, 3, -2, -4, 1, 1, 3, 0, 0, -1, -1, 0, 0, 1, 0, 1, 1], [3, -3, 3, 2, -3, -1, 3, 2, 2, -1, 2, 0, 2, 4, -2, 0, 2, -1, 1, 1], [-2, -1, 3, 2, 1, -2, 0, 0, -1, 1, 0, -2, -1, 2, -3, 0, 1, -3, 1, 1], [-9, 1, 1, -2, -1, 0, 2, 1, 2, -2, 0, 3, 3, 1, 2, -1, -2, 4, 0, 1], [1, -3, 0, 3, -1, -2, 0, 1, 0, -1, 2, -2, 2, 1, -1, -1, 2, -3, 1, 1], [-4, -1, -4, -2, 3, -1, 2, -3, -1, 1, -2, -2, -2, -3, 2, -1, 0, 1, 1, -1], [-9, -1, 1, 3, -1, -1, 2, -4, -2, 0, 0, -2, 1, -1, 0, 0, -1, -1, 1, -1], [3, -1, 1, -2, 2, 3, 3, 4, 1, 0, -1, 1, 0, 2, 2, 0, -2, 4, 0, 1], [-2, -2, 1, -2, 1, 2, 0, 0, -1, 1, 1, 1, -1, 0, 2, 3, -1, 3, 0, 0], [-1, 2, 0, -2, 2, 4, -4, -2, 0, 2, -2, -1, -2, 0, 1, 2, -3, 2, 1, -2], [-1, -3, 2, 4, -2, 0, -2, 1, -1, 0, 1, 0, 0, 2, -3, 3, 1, -3, 0, 0], [-2, 2, -2, 2, 2, 0, -1, -1, -1, 0, -3, -6, -4, -3, 2, -2, 1, 0, 0, 0], [-1, 0, -4, -4, 2, 0, -1, -3, 1, -1, -3, -3, -3, 0, 3, -1, -1, 2, 1, -2], [1, 2, -3, -3, -1, 1, 4, 0, 1, -1, -1, -1, 0, -3, 4, -3, 2, 1, -1, -1], [-7, 1, 0, -1, 3, -1, 1, -1, -2, 0, 0, -3, -3, -2, 0, -2, -1, 1, 4, 0], [-1, -1, 4, 1, -2, 1, 2, -1, -1, -1, 3, 6, 3, 0, -3, 3, -3, 0, 0, 0], [-3, 6, -7, 0, 3, 3, -2, -4, -2, 2, -4, -8, -5, -6, 2, -1, 0, 1, 1, -4], [-1, -3, -3, -5, 3, 2, -2, 0, -1, 3, -2, -3, -2, -3, 2, 0, 0, -2, 1, -2], [-6, -2, 2, 0, -2, 1, 0, 2, 0, 0, 0, 1, 4, 3, -1, 3, 1, 0, 0, -2], [3, -3, 5, 3, -1, 2, 2, -4, -4, 2, 1, -2, 2, -1, -4, 2, -2, -2, 0, -4], [2, 2, 0, -1, 0, 3, 7, -2, 0, 0, -1, 4, 1, 0, 0, 2, -1, 3, 0, -2], [5, -3, 5, 1, 0, -1, 1, 3, 0, -2, 3, 5, 1, 2, -1, 0, -1, 0, 0, 4], [-4, -2, 0, 2, 2, -2, -11, -4, -2, 3, -1, -3, -3, -4, -3, 1, 0, -3, 2, -3], [-8, -3, -3, -2, 4, -2, -5, 2, 1, 3, -3, -6, -5, 0, 2, -1, 3, -2, 3, 0], [1, 3, -2, -1, 2, 2, -4, 3, -1, 3, -4, -7, -5, 0, 1, -1, 1, -2, 2, -2], [6, -2, 1, 2, -1, 0, 0, -1, 0, -2, 1, 2, -1, -1, -2, 2, 0, 0, 0, 1], [-6, 0, -1, -2, -2, -3, -6, 1, 2, 0, 1, 2, 0, -1, -3, 1, 0, -2, 0, 1], [2, 1, 0, -1, 3, 2, -3, -2, -1, 2, -5, 1, -3, -2, 3, 2, 0, -1, -1, -1], [-4, -4, 0, 1, 3, -1, -3, -1, 1, 3, -2, 2, 0, 1, 0, 1, 0, 0, 2, 0], [-2, 1, -1, -1, -4, -3, 7, 2, 3, -5, 3, 3, 3, 3, 2, -4, 0, 3, -2, 3], [-2, -1, -1, 0, -1, -2, 4, -2, 2, -3, 0, -4, 0, 1, 1, -6, 3, -1, -3, 1], [-7, 1, 3, 5, -3, -1, 0, 0, -1, -3, 2, 0, 2, 2, -3, 1, -1, -2, -1, 2], [-2, -1, 1, -2, -1, -2, 4, 2, 3, -1, -1, 3, 5, 3, 4, -1, -1, 4, -1, 1], [-5, 3, -2, 0, -3, 0, 7, 3, 2, -3, -1, 0, 2, 1, 1, -3, 2, 1, -3, 0], [3, -1, 4, 4, 1, 1, 1, 0, -5, 1, 3, 3, 4, 0, 0, 2, -1, 1, 0, 0], [-1, -1, -1, 1, 1, 3, 3, 0, -1, -1, 0, 6, 1, 1, -1, 3, -3, 5, -1, -1], [4, 4, -3, -3, -4, -1, -4, 1, 2, -2, -2, -3, 0, 2, 2, -4, 1, -1, 0, -2], [-2, -1, -3, -1, -1, 0, 0, 6, 2, -3, 0, 2, 0, 1, 2, -3, 2, 1, 0, 0], [5, 3, 0, -4, -4, 1, 4, 2, 2, -4, 0, 3, 2, 2, 2, -1, -1, 2, -1, -2], [3, 3, -1, 1, 4, -1, 2, -2, 0, 1, -1, -1, -3, -4, 2, -2, -2, 1, 0, 1], [2, -4, 0, -3, 3, 3, -1, -1, -1, 5, -4, -4, -4, -3, -2, 3, 0, -2, 2, -6], [1, -6, 4, 5, -2, 0, -1, 3, -1, 1, 1, 3, 1, 2, -2, 3, 3, -2, 1, 3], [-8, 1, -4, -3, 1, 1, -1, -2, 1, 1, -1, 1, -4, -2, 1, 0, -2, 2, 2, -1], [3, 3, -3, -4, 0, 3, -2, 1, -1, 0, -3, -6, -4, 0, 4, -2, 1, 2, -1, -2], [-3, 3, -4, -3, -3, 3, 1, -1, -2, 0, 1, 0, 3, -1, 0, 0, 0, 0, -2, -4], [1, 0, 3, 1, 0, 0, 1, 1, 0, 2, 1, 1, 1, -1, -2, 0, 0, -4, 0, 1], [5, 0, -6, -4, -3, -2, -4, 5, 3, -4, -2, -3, -4, 1, 2, -7, 4, -3, -1, 2], [2, -5, 4, 1, 3, -1, -1, -4, -5, 2, 3, 2, -1, -1, -1, 1, -1, -2, 1, 0], [-5, 0, 1, 3, 3, -3, 4, -6, -4, 0, 1, -5, -2, -3, -3, -2, 0, -5, 0, 0], [4, 1, 3, 4, -6, 0, 7, 0, 1, -5, 4, 2, 6, 4, -2, 0, -2, 0, -3, 1], [-6, 1, -1, 2, 5, 2, -4, 2, -3, 5, -4, -6, -5, -1, 1, 0, 3, -1, 3, -1], [3, 1, 1, -1, 0, 3, -3, -1, -2, 2, 1, 4, 1, -1, 1, 3, -1, 0, -1, -1], [2, 2, -6, -5, -1, 0, 4, 3, 4, -2, -3, -4, -3, 1, 6, -8, 1, -2, -1, 0], [-2, 1, 2, -3, -4, -1, 4, 0, 3, -5, 0, 4, 0, 2, -2, -1, -2, 4, -1, 0], [2, -1, 6, 2, -4, -1, -1, -1, -1, -5, 3, 3, 3, 4, -2, -1, -2, -1, 0, 3], [2, -7, 0, 1, 2, 0, -6, 0, -4, 3, 1, -4, -3, -2, -5, 2, 0, -1, 4, -3], [1, 3, -2, -9, 1, 3, -1, 2, 0, 0, 0, 6, 2, -3, 3, 3, -1, 2, 0, -3], [0, 0, 2, 1, 2, 1, -6, -1, -2, -2, 2, -1, -2, 0, -4, 0, -1, 0, 0, 2], [2, -6, 0, -3, -1, 0, 0, 4, 0, 1, 1, 2, 1, 1, -2, 0, -1, -1, -1, -1], [-7, -4, 2, -2, 1, 1, 5, 2, 2, 0, 4, 5, 1, 2, 1, 1, -2, 3, -1, 2], [10, -2, 4, 0, -2, 3, 4, 6, 2, 0, 4, 13, 6, 7, -1, 3, -3, 4, 0, 0], [-2, 0, 2, -3, 3, 4, 3, -1, -1, 1, -1, 5, 0, -3, 2, 2, -3, 3, -1, -2], [0, -5, -3, -4, -1, 2, -2, 4, 3, -1, -1, -1, 1, 3, 4, 1, -1, 3, -1, -1], [-9, 0, -5, -3, -2, 5, -1, 2, -1, 1, -2, -2, -1, -2, 0, 1, -2, 3, 2, -4], [-1, 3, -3, -2, 3, -1, -4, -6, 0, 3, -3, -6, -4, -3, 2, 0, -1, 0, 1, -5], [1, -2, 2, 4, 0, 2, 1, 7, 0, -1, 0, 4, 2, 2, 0, 2, -1, 0, 1, 2], [-7, -1, -3, -1, -1, -5, 0, -3, 2, -1, -2, -5, 0, -1, -2, -2, 0, -2, -2, 0], [-11, 4, 4, 6, 1, 0, 2, -9, -4, 0, 3, 0, 1, 1, -5, 4, -2, 1, 1, -1], [5, -6, 3, 1, -2, 1, -8, 1, -2, 4, -4, -5, 0, 0, 1, 4, 3, 0, 1, -1], [-6, -4, 4, 1, 1, -2, 1, -3, 0, 1, 6, 6, 4, 1, -2, 2, -1, 1, 0, 5], [-3, -2, 2, 4, 1, 2, -7, 1, -1, 3, 1, -2, -3, 0, -3, 6, -2, -2, 2, -1], [1, 3, -4, -1, 0, -2, 0, -1, -1, -1, 3, -2, 1, -1, -1, -1, 0, -5, 0, 0], [-4, -2, -6, -7, 1, 2, 0, 3, 3, -1, 0, 1, 2, -1, 5, -1, 0, 6, -1, -1], [0, 0, -5, -2, 5, 2, 0, -3, -1, 1, -3, -4, -2, -3, 5, -1, 2, 2, -1, -3], [-10, -3, 1, 2, 2, 1, -5, 0, -3, 3, 0, -2, -5, 0, -3, 2, 1, -2, 2, 2], [-1, -4, 1, 2, -2, 0, 0, 1, 2, 1, 2, 3, 1, 0, -1, 2, 0, -1, 2, -1], [-4, 3, -8, 3, 5, -1, -1, -5, 0, -1, -4, -6, -4, -3, 5, -2, 3, 0, 2, -1], [-4, 3, 2, 1, 4, -1, -1, -3, -3, 1, -1, 1, 1, -2, 2, -3, 2, 1, 0, 3], [0, -3, 3, 5, -4, -3, 5, 5, 2, -2, 4, 7, 5, 8, -3, 2, 1, -4, 0, 4], [-7, -3, 3, 5, 3, -2, 3, -4, -2, 0, 0, -6, -2, 0, -3, 1, 0, 1, 2, 4], [3, -10, 1, -3, -2, -2, -3, 3, 3, -1, 3, 0, 0, 2, -1, -2, 0, -6, -1, 1], [9, -2, 10, 2, -1, 0, -1, 5, 1, -1, 1, 8, 3, 3, -3, 0, 2, 2, -2, 5], [-1, 2, 1, 6, 4, 2, 1, 0, -1, 3, -2, 0, 0, 1, 1, 4, -2, 4, 4, 1], [1, -3, -1, 0, -2, 0, -5, 6, 5, 0, -1, -2, -4, 1, 1, -1, 1, -3, 1, 1], [-2, -3, 1, 0, 0, 6, 5, 2, -2, 2, 1, 4, 1, 2, -1, 2, 0, 3, 4, 0], [7, -5, -4, 0, 0, 2, 3, 8, 3, 0, 0, 1, -2, 2, 7, -1, 2, 1, 1, 3], [2, 4, -6, -4, -2, 3, 7, 0, 3, -1, -1, 0, -1, -2, 1, -3, -3, 5, -3, -1], [1, -6, -1, 1, 2, -1, -7, -1, -1, 4, -1, -3, 0, -2, 2, -1, 1, -4, 1, -2], [5, -7, -1, -1, -1, -3, -5, 0, -2, 2, 0, -2, -1, -3, 0, 0, 3, -7, -3, -1], [-7, -1, 2, -4, -1, 2, -3, -3, 0, 1, 0, 5, 0, -4, 1, 3, -3, 0, -1, -2], [12, -4, 4, -4, -3, -1, -5, 3, 3, -1, 2, 4, 1, 1, 0, -2, 3, -4, -5, 4], [-7, -2, -4, -3, 0, 0, -5, 0, -2, 0, -2, -3, -2, 0, 3, -2, 1, 3, -2, 3], [0, -7, 2, 3, 4, -5, 4, 1, 1, 0, 1, -7, 2, 3, 1, -2, 3, 3, 3, 3], [-2, 0, 9, 10, 0, 1, 5, -3, -4, 3, 0, 0, 3, 0, -5, 3, -3, 0, -1, 1], [-3, 7, -5, -4, -1, -3, -5, -3, 1, -1, -3, -5, -4, -3, 2, -4, 3, -1, -1, -1], [2, 1, -8, -3, 3, -3, -13, 2, -2, 4, -6, -17, -8, -7, 5, -10, 7, -3, 4, -3], [-1, 3, 3, 3, 0, -4, 5, -7, -1, -2, 4, 0, -1, 0, -4, 0, 0, -5, -3, 2], [-1, 1, -3, -2, -4, 0, 2, 4, 2, -3, -4, -4, 3, 2, 4, -6, 3, 5, 1, -1], [-7, -2, -2, 4, 5, -1, -7, -4, -3, 6, -5, -9, -5, -6, 2, 3, 3, -3, 2, -5], [11, -2, 1, -6, -4, 3, 3, 7, 4, 0, 0, 12, 2, 2, 4, 0, 0, 3, -1, 1], [-3, 5, 3, -1, -4, 1, 5, 7, 2, -5, 2, 4, 7, 6, 4, -4, 2, 2, -2, 5], [8, -2, 2, -2, -2, 3, 5, 2, 2, -2, 1, 9, 4, 2, 1, 5, -2, 4, 1, -2], [-6, 4, -4, -1, -1, 0, 4, 2, 1, -2, 0, 3, 1, -2, -2, -2, -2, 0, 1, -2], [-6, 8, 3, 1, 1, -1, 7, -5, -2, -1, -1, -1, 3, 1, 2, -2, -2, 3, -3, 1], [2, -5, -2, -5, 1, -2, 3, 2, 7, 0, -7, -3, -1, 0, 6, -4, 2, 1, -2, 0], [-3, 5, 7, 3, 0, -3, 2, 1, -2, -1, 4, 2, 1, 2, -4, 2, -4, 4, 2, 3], [-7, -3, -2, 4, 4, -5, -7, -5, -1, -1, 2, -4, -2, 0, -2, -4, 2, -5, 1, 3], [8, -8, 6, 5, 2, -3, 0, -2, -2, 2, 5, 5, 3, 2, -4, 2, -2, -1, -1, 4], [3, 4, 2, -4, 1, 5, 3, 0, -3, -1, 0, 6, 0, -2, -1, 6, -4, 4, -1, -2], [7, -5, 10, -2, -5, 2, 2, 4, 0, 1, 4, 10, 8, 1, -2, 4, -1, 0, -4, 0], [-3, 3, -5, -3, -5, -1, 3, 6, 2, -4, -3, -10, -4, 3, 1, -7, 4, 1, 2, 2], [-3, -5, 2, 3, 3, 0, -1, -1, -5, 1, 1, -3, 0, -1, -1, 2, -3, -1, 5, 0], [-5, 2, -4, -2, 2, 4, 0, -2, -4, 2, -6, -4, -4, -4, 3, 2, 0, 6, 0, -4], [-1, 7, -5, -5, 5, 3, -4, -4, -2, 4, -4, -3, -1, -7, 4, -2, -1, 3, 1, -5], [-3, -9, -3, -5, 2, -2, 1, 1, 3, 2, 0, 1, -2, -1, 3, 0, 0, -4, 1, 0], [-7, 9, -6, -2, -3, 0, 9, -3, 0, -4, 4, 2, 2, 1, 0, 0, -4, 1, -3, 0], [0, -5, 1, 8, 4, 0, -10, -3, -1, 1, -2, -2, -1, -2, -3, 4, -4, 2, 2, -3], [1, 0, -3, 0, 5, 7, -4, -1, 0, 6, -3, -1, -1, -4, 4, 3, -1, 4, 1, -2], [-4, 3, -5, -5, 0, 2, 0, 8, 5, 0, -5, 3, 0, 2, 7, -2, 1, 5, 1, 0], [11, -2, 6, -1, 4, 1, 4, -6, -6, 4, 3, 1, -2, -4, -4, 5, -3, -5, -3, -1], [-9, 6, 1, -2, 5, -2, 9, -5, 4, -1, 0, 4, 1, -1, 0, -1, -5, 7, -1, 1], [-10, 4, -11, -9, -1, -2, 6, 0, 3, -1, -2, -5, -2, -4, 5, -6, 4, 0, -2, -4], [-5, 6, -2, -2, 3, 1, 0, -5, -4, 0, -3, 5, -1, 0, 0, 1, -1, 3, 0, 0], [5, 0, 2, 6, 0, -1, 4, -2, -2, 2, 4, 1, 2, 2, 2, -3, -1, -2, 0, 0], [1, 2, 5, -4, -2, -3, 9, 4, 3, -3, 3, 12, 8, 6, 3, -2, 1, 3, -2, 3], [-11, -1, 5, -4, -4, 2, 4, -1, 0, -2, 4, 12, 8, 4, -3, 3, -4, 3, 1, -3], [4, 1, -4, -2, 0, 4, -3, -4, -1, -1, -2, -5, -6, -2, 1, 4, 0, 0, -1, -7], [-10, 6, -3, -4, -2, -3, 5, -1, 0, -3, 2, 3, 0, -3, -3, 1, -2, -2, 0, -2], [8, -3, 3, 2, -4, 4, -5, 1, -2, 2, 2, 7, 8, 2, 0, 5, -1, -1, -5, -3], [1, -8, 2, 0, -5, 2, 1, 9, 1, -3, 6, 5, 3, 9, -2, 3, 2, 2, 1, 6], [4, 5, 2, 3, -6, -3, -9, -5, 1, -3, 4, 3, 4, 0, -3, 0, 1, -1, -6, -1], [6, -3, 5, -4, 3, 1, 9, -3, -2, 4, 2, 5, 0, -2, 1, 1, -1, 1, -2, -2], [5, 2, 0, 0, 5, 3, 5, 5, 1, -1, 2, 10, -1, 5, 3, 0, -3, 8, 2, 6], [-6, 0, -1, 3, 1, 2, -2, -7, 0, 4, -2, 2, 2, -4, 3, 3, -1, -1, -3, -4], [-1, 1, -8, -2, 5, 1, 5, 5, 0, 2, -2, -9, -2, -2, 5, -3, 1, 6, 6, 0], [2, 4, -5, -5, 0, 3, 4, 2, 1, 1, -1, -3, 1, 2, 3, 3, -1, 1, -2, -3], [-9, 7, -5, 4, 1, -1, 2, 0, 7, -2, -5, -3, -2, 3, 2, -4, 1, 4, -1, 0], [7, 5, -2, -2, -7, 2, 1, 8, 5, -7, 5, 10, 6, 7, 3, -1, -2, 0, 1, 2], [4, 4, 6, 3, -5, 3, -2, 4, -1, 0, 6, 6, 6, 3, -5, 5, -3, -2, -2, 3], [4, 1, 2, 6, -3, -8, 1, 3, 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-4, -4, 2, 2, 0, 0, -5, -3, 4, 2, 2, -2, 2], [8, 0, -3, 1, 4, 5, 0, -3, -2, 4, 0, 7, 0, -6, -2, 6, -3, 2, 2, -6], [10, -14, 4, 1, -1, 0, -4, 6, -3, 4, 3, 1, 3, 1, -2, 6, 7, -5, -1, 0], [3, 6, 2, 6, -4, 3, 4, -2, 0, -2, 1, 2, 4, 2, -5, 2, -1, 2, -7, -1], [-3, -6, 1, 7, -2, -1, -15, 4, -1, 1, 2, -2, -1, 4, -6, 5, 0, -5, 2, -2], [-3, 1, -6, 0, -2, -5, -4, -9, -3, -1, 1, -7, -4, -5, -5, -1, 4, -9, 1, -3], [2, 3, 0, 3, 5, 4, -9, -4, -6, 4, 2, 3, -6, -2, -7, 8, -6, 0, 5, -1], [10, 5, -12, -7, -2, 1, 4, 4, 4, -2, -5, 0, -6, -1, 3, -6, 3, 2, -1, -1], [-10, 7, -3, 2, 2, -2, -3, -13, -6, 3, -3, -9, -4, -10, -3, 0, 2, -11, 1, -7], [-2, 4, -2, 3, -5, -1, 15, 11, 7, -5, 0, 4, 6, 9, 0, -1, 0, 7, 0, 2], [-3, 5, -2, -4, -3, -1, -5, 11, 6, -5, 6, 9, 6, 5, 8, -2, 2, 3, -2, 8], [3, 9, -5, -3, 4, 5, 5, -8, -7, -2, 3, 4, -2, -6, 3, 1, -4, 2, -2, -2], [-6, 3, -2, 0, 1, 1, -7, -2, -4, 4, 3, -2, 1, -4, -1, 4, 0, 1, 0, 1], [-4, -2, -2, -7, 5, -3, -10, 2, 2, 0, 1, 3, -1, 3, 0, -2, 1, -4, 2, 5], [8, 9, 1, -1, -1, -1, 7, -7, -1, -5, 1, 4, 0, 1, -1, -4, -6, 4, -1, -2], [13, 0, 7, 3, -1, 6, 2, -2, -3, 1, -2, 5, 4, 1, 0, 2, -6, 2, 0, -4], [4, 5, -7, -7, -6, 4, 9, 3, 4, -6, 3, 5, 0, 5, 6, -3, -2, 3, -1, 0], [-1, -4, 7, 2, -5, -2, 6, 8, 3, -2, 5, 8, 10, 9, -5, 4, -1, 3, -1, 6], [6, -5, 1, 2, 5, 3, -13, -2, 0, 2, -6, -1, -3, -1, 1, 2, 0, -2, 1, -2], [-19, 4, 5, 0, 7, 6, -3, -6, -4, 6, -3, 1, -6, -5, -6, 5, -6, 2, 0, -2], [-7, 0, -2, -11, 2, -2, 3, -6, -1, 1, -3, -3, -3, -5, 1, -4, -3, 3, 3, -3], [14, 4, 1, 5, -1, 1, -11, -4, -3, 2, 1, -1, -2, -3, -5, 3, 0, -8, -4, -2], [3, -4, 6, 4, -10, 0, 6, 3, 3, -7, 12, 11, 9, 5, -7, 0, 0, -4, -2, 7], [8, -4, -7, -5, -1, 1, -10, 6, 6, 0, -9, -8, -4, 1, 2, -2, 5, -5, -1, -4], [4, 11, -4, -5, 0, 0, -3, 0, -3, -3, -3, -5, -1, -4, 8, -3, 1, 4, -1, -1], [21, -3, 2, 3, -2, -2, -8, 0, -2, 1, 3, -4, 1, -1, -3, 5, 0, -6, -2, -2], [-2, -2, 3, -1, 2, 0, -7, 5, 3, 1, -4, 3, -5, 2, 1, -3, -2, 4, 2, 3], [2, -2, 2, 5, 3, -7, -3, -6, 1, 2, -2, 1, -3, 1, -3, -1, 3, -7, 0, 2], [-12, 2, -2, 5, 4, 1, 6, -5, 0, -4, 0, -7, -2, 2, 0, 0, -3, 6, 0, 4], [0, -6, 1, 4, -4, -3, 3, 2, -1, -1, 11, -2, 4, 3, -6, 0, -1, -4, 0, 8], [-2, -2, 7, 12, 6, -4, -5, -3, -3, 3, -1, 3, -3, 0, -5, 3, 1, -6, 5, 4], [-5, 5, -5, 1, 5, 7, 6, -5, -8, 5, -4, -7, -6, -7, -1, 2, 0, 4, 1, -5], [-5, -2, -7, -1, -4, -2, 11, 6, 7, -7, -8, -11, -3, 0, 9, -10, 5, 3, -2, 2], [0, 7, -8, 1, 1, -2, -5, -4, 2, -4, -12, -14, -8, -6, 5, -11, 4, 0, 0, -4], [2, 8, -7, -4, 2, 1, 6, 12, 6, -2, -8, -5, -6, 1, 2, -5, 1, 5, 4, 3], [-10, -4, 3, -3, 0, 0, 11, -8, -1, -3, 4, 3, 5, 2, 2, 4, -5, 1, -4, 0], [12, -4, -2, 0, -4, 5, 4, -2, 0, 0, 1, -2, 4, 2, 4, 0, 1, -4, -2, -1], [-5, -3, 7, 2, -6, -3, -9, -1, -6, -2, 8, 10, 6, 1, -2, 2, 2, -5, -1, 3], [-6, -2, 8, 0, -8, -4, -4, 7, 7, -6, 5, 11, 11, 8, 1, -3, 3, 1, -2, 8], [-2, 5, -5, 0, -2, 5, -1, 4, 3, -2, -2, 12, 2, 3, 5, 2, -3, 4, -1, 0], [-6, -7, 1, 3, 7, -3, 0, -6, -1, 5, -1, -5, -4, -3, -1, 0, -1, -2, 3, 5], [9, -1, 9, 13, 0, -4, 5, -4, -3, -5, 4, 7, -1, 2, -9, 3, -2, 0, 4, 1], [15, -7, 0, -3, -1, 6, 9, 5, 3, 1, 2, 8, 4, 3, 4, 3, -1, 5, 0, -3], [9, -18, 0, -3, 3, 1, 3, 6, 2, 4, -3, -3, 0, 2, 4, 2, 3, -2, -1, 0], [8, 7, -3, 4, -3, 4, -5, 1, 1, -2, -1, 3, -3, -1, -1, -1, 0, 3, -1, -2], [6, 2, 2, -6, 2, 6, 5, -6, 4, -2, -2, 12, 2, 2, 4, 4, -4, 8, -4, 0], [6, -4, 2, 1, -1, 0, -3, 6, 3, 4, 1, 0, 1, 5, -6, 2, 3, 3, -1, 0], [7, -2, 8, 4, 3, -1, -1, -8, -1, 6, 1, 6, 3, -2, -4, 5, -1, 3, 0, 3], [11, 11, 0, 0, 3, 4, -1, 1, -1, 1, -2, 5, -5, -5, -4, 3, -2, 0, 1, -2], [-8, 0, -4, 1, 3, -3, 19, -7, -3, -1, 6, -4, 2, -3, 3, -1, -2, -2, -1, 1], [-12, 8, -10, -6, 7, 3, 1, -10, -4, 3, -9, -13, -7, -8, -1, 1, 0, 1, 2, -9], [3, -6, 6, -4, -1, -2, -12, 7, -3, -2, 4, 7, 0, 1, 0, 1, 0, -6, -1, 8], [1, 2, 11, 3, -2, 8, 2, -4, -7, 4, 4, 13, 6, 1, -5, 12, -5, 4, -1, -2], [-2, -9, 13, 2, 7, 8, -15, -3, -7, 12, 1, 3, -3, -3, -6, 11, -4, -4, 2, -1], [-19, 9, 0, -5, -2, -2, 0, -7, 1, -5, -4, 4, -1, 0, -1, -3, -3, 2, -4, -2], [8, 5, 1, -13, -2, -1, -5, 3, 6, -4, 2, 3, 3, 4, 7, -4, 1, 4, -4, 4], [-5, -2, -1, -1, -6, -1, -3, 8, 4, -3, -6, -1, 2, 2, 3, -4, 2, -3, 0, -3], [0, 6, 6, 3, -1, 0, 4, 4, -1, 2, 3, 12, 1, 3, -7, 3, -3, -3, 0, 4], [-9, 7, -3, -3, -2, 3, 23, -8, -1, -5, 2, 6, 5, 0, 4, -1, -6, 5, -1, -4], [5, -5, -1, -5, -4, 0, 11, 2, 7, -1, 0, 5, 5, 5, -1, -4, 3, -1, -4, -2], [-2, -4, 4, 9, 10, -3, 0, -10, -4, 4, 4, 2, -3, -1, -7, 7, -4, -3, 1, 3], [1, -10, 0, 0, 3, -5, 2, 1, -1, 6, -2, -2, 0, -2, 0, 2, 5, -5, 1, 3], [6, -3, 1, 4, -12, -1, -3, 6, 5, -4, 6, 13, 9, 4, -1, -2, 2, -2, -11, 4], [-7, 1, -6, 0, 1, -4, 3, 2, 0, -2, -2, -4, -1, 1, 8, -6, 3, -1, 1, 2], [-4, -1, -5, -5, 0, 1, -3, 7, -2, 0, -2, -17, -7, -3, 7, -4, 5, 2, 1, 0], [14, 6, -1, 0, -3, 5, 3, -1, -1, -1, 0, 1, 2, 1, 3, 5, 2, 1, -3, 1], [0, -7, 8, 6, -2, -6, -3, -1, -5, 1, 7, 1, 5, -1, -2, 5, 1, -6, 4, 5], [-5, 1, -6, -10, 3, 0, 10, -1, 4, -5, 0, 0, -2, -1, 5, -3, -2, 5, -7, 3], [-3, 1, -5, -4, 3, -1, -7, -1, -1, -1, -1, 3, 0, -3, 8, 0, 5, 3, -1, -1], [-11, -2, -1, 3, 6, 0, -25, -4, -3, 5, 1, -5, -1, -3, -1, 4, 1, -4, 3, -5], [1, 0, -1, 1, -2, -4, 2, 1, 1, 2, -3, -1, -2, 2, 1, 0, 3, -1, -3, 6], [-7, -4, 2, 3, 7, -4, 15, -3, 1, -1, -4, -4, -2, -1, 2, -5, -1, 1, -2, 1], [-4, -2, -3, 10, 5, -2, 10, -3, 0, 0, -5, -8, -9, -3, 0, -4, 4, 1, 0, 5], [-6, 2, -3, 6, 3, 0, 5, -3, -1, -3, 3, 0, -8, -3, -2, 4, 0, -5, 4, 5], [9, -11, 14, 6, -4, 1, 8, -7, -3, -1, 6, 6, 6, 5, -6, 4, -8, 1, -1, 1], [3, 9, -6, 0, -3, -1, -1, -4, -2, 0, -5, -12, -7, -7, 0, -4, 2, -7, -2, -5], [5, 3, 0, 8, -4, -1, 11, -10, -6, -4, 6, -5, 0, -2, -4, 2, -5, -2, 1, -4], [9, -4, -5, 2, 1, -6, 7, -1, 2, -1, -1, -2, -6, -3, 1, -4, 2, -5, -1, 7], [-6, 4, -7, -8, 8, -3, 2, -9, 3, 3, -7, -9, -8, -8, -1, -3, -1, 1, 0, -1], [-15, 8, -2, -6, -4, -3, 2, 5, 7, -7, -4, -1, 0, 8, -2, -5, -2, 9, 1, 7], [15, -5, 0, -1, -2, 7, 4, 4, 0, 0, 3, -1, -1, 4, -1, 6, -2, -1, 7, -2], [8, -4, -7, 1, 1, -6, -12, -7, 4, -2, 0, -2, -4, -4, -1, -5, 3, -5, 0, 2], [-13, -7, -7, -5, 8, 2, 3, -10, -7, 7, -3, -15, -4, -10, 8, 2, -1, 4, 6, -5], [13, 12, -4, 5, -7, -1, 15, -6, 1, -9, 0, 2, 4, 2, 0, -5, -1, -2, -2, -3], [-11, 5, -9, 0, 3, 7, -2, 0, -2, -1, -2, -10, -4, -4, 0, 2, -2, 3, 5, -5], [8, -4, 0, 0, 8, 3, -4, -10, -6, 8, -2, 3, 2, -10, 1, 3, -5, 4, -1, -6], [6, -4, -3, -7, -5, -5, -10, 6, 3, 1, 2, -2, 1, 5, -2, 0, 2, -7, 2, 1], [9, 6, -9, -3, 8, 4, 1, -6, -2, 3, -6, -3, -5, -8, 4, 1, 3, 7, -1, -7], [5, 1, 1, -10, 2, 2, -9, 4, 1, 4, -2, 1, 0, 0, 3, 1, 4, 1, 1, 1], [-4, 20, -3, -2, -4, -5, -7, 7, 6, -6, 1, 1, 0, 5, 0, -9, -2, 1, 0, 4], [1, -7, 6, 3, 2, -3, -10, -1, -5, 3, -4, -7, -5, 3, 2, 2, 1, -4, 7, -3], [1, 14, -1, -4, 6, 6, 6, -8, -6, 4, -10, -2, -1, -10, 6, 1, -6, 10, -1, -8], [4, -8, 4, -2, 0, 7, 10, 6, 2, 0, 3, 8, 4, 6, -3, 5, -2, 2, 1, -2], [-13, 3, 7, 3, 2, 1, -15, -2, -5, 6, 5, 8, -2, -2, -7, 7, -6, -4, 2, 4], [13, -1, 4, 5, -3, 0, 0, 0, -3, 0, 1, -11, 1, 0, -1, 3, 3, -4, 1, 0], [11, -9, 7, -3, -6, -2, 1, 2, -3, -1, 6, -1, 7, 4, -3, 1, 4, -2, -4, -1], [8, 4, 7, 1, -7, 0, 10, 3, 0, -2, 5, 9, 6, 4, -8, 0, -7, 3, -3, 3], [14, 5, 1, -2, -6, 1, 1, 1, 2, -2, -3, -1, 4, 8, 4, -1, 4, -3, -4, 4], [4, -9, 14, 11, -4, -4, 1, 3, -5, 4, 2, 3, 10, 7, 0, 3, 1, -5, -2, 5], [1, 0, 9, -4, 2, -4, -9, -2, 1, 7, -3, -7, 0, -4, 4, -3, 0, -4, -2, 4], [2, 8, -1, 1, -3, -3, 16, -12, 1, -11, 2, 10, 2, -5, 0, -7, -5, 2, -7, -2], [0, -3, -3, 4, 2, 0, -6, -2, -1, 5, -5, -5, -1, -8, -2, 5, 1, 0, 3, -6], [-16, -1, 7, 5, 1, -6, 0, -3, 2, -1, 7, 4, 2, 3, -8, -1, -1, -1, -2, 7], [21, -8, 11, 9, -3, -1, 12, 4, -5, 0, 10, 18, 10, 5, -6, 1, 3, -3, 1, 2], [19, -14, 9, 0, -13, 0, -8, 9, 6, -6, 5, 11, 8, 11, -5, 4, 3, -6, -5, 2], [0, 1, -2, -7, -8, 3, 3, 9, 3, 0, 4, 4, 8, 2, 4, 1, 5, 2, -6, -2], [2, 5, 5, 8, 2, 2, -4, -3, 2, -1, -5, 0, -1, 4, 2, 0, 3, -3, -2, 1], [-4, -14, 5, -8, -4, -6, -2, 6, 3, 0, 5, 7, 3, -2, -1, -3, 2, -2, -2, 6], [-28, -1, -7, 2, 6, -3, -1, -8, 1, 7, -4, -20, -7, -8, -5, 0, 5, -4, 2, -6], [-4, -5, -3, 1, 7, -5, -15, -1, 0, 7, -4, -8, -5, -5, 2, -5, 4, -4, 2, -3], [5, 10, -6, -2, -1, -1, 0, -2, -1, -3, -1, 0, 1, 3, 3, -6, 5, 5, 1, -3], [-6, 7, -8, 3, 13, -2, -11, -3, -7, 9, -12, -16, -12, -8, 7, -5, 1, 1, 4, 1], [-9, -5, 7, 4, -11, -5, 8, -6, -6, -3, 9, -1, 6, -1, -9, 3, 1, -10, -8, 1], [14, 6, -4, -7, -3, 1, -11, -1, 0, 1, 1, 1, 3, -3, 6, 2, 2, 6, 1, -5], [5, -1, -3, 1, 3, 1, 23, 2, -2, 2, -2, -9, -2, -1, 6, -4, 1, 6, 1, 0], [-7, -11, 0, 0, -1, -1, 8, 4, -3, 1, 9, 4, 5, 0, 0, -2, 2, -5, 3, 0], [-3, 12, 0, 2, 4, 3, -5, -3, -3, -3, -3, -9, -7, -1, -2, 1, -4, 0, 3, -3], [-19, 2, -7, -4, 4, 3, 11, 1, 2, 1, -7, 4, -1, -4, 10, -7, 2, 9, 0, 0], [-3, 6, -1, 13, -1, -2, -2, 2, 2, -6, -3, -6, -5, 2, -3, -1, 4, 2, 5, -3], [-19, -2, 9, 4, 4, 0, -5, -2, 1, 1, 4, 12, -4, 1, -7, 6, -6, 0, 0, 1], [-10, -4, -1, -2, 4, -4, 11, 0, 6, -3, -1, 10, 6, 2, 8, 0, -3, 1, -6, 5], [-19, 8, 2, -7, 7, 6, 8, -6, -3, 7, -6, 0, -2, -9, 1, 6, -4, 7, -1, -3], [2, 2, 1, -2, 7, -4, -1, -2, 3, 11, -10, -11, -4, -5, 1, -1, 5, -5, -1, -5], [12, 2, 6, 5, 1, 4, -8, 4, 3, 2, -1, 3, 1, 3, 2, 2, 5, -1, -3, 4], [8, -2, 1, 7, -4, -2, -1, 10, 0, -3, 2, 6, 13, 4, 7, -3, 4, 5, -2, -3], [5, -1, -3, -11, -1, 1, 3, 6, 5, 4, 1, 8, -1, -1, 3, -5, 5, 1, 1, 4], [-10, 9, -4, -9, 1, -2, 1, 6, 10, -4, -8, -1, 0, 6, 7, -4, 0, 2, -3, 3], [-14, -6, 2, 6, -2, -10, 10, -10, -1, -7, -1, -14, 1, 2, 0, -6, -1, 0, -1, 1], [17, 8, 2, 1, -1, -1, -7, -5, -5, -3, 9, 6, 2, -2, -4, 1, 2, -11, -5, -2], [-13, 0, 7, 6, -2, 0, 1, 9, 4, 0, 5, 16, 4, 6, -6, 3, 0, 0, -4, 6], [11, -5, -5, -5, -3, 0, 6, 3, 3, 1, -1, -1, -1, -2, 0, -4, 9, -2, -1, 0], [-8, 2, -6, -1, 7, 4, -4, 5, -1, 1, -10, -11, -10, -1, -1, -1, 2, -2, 9, -1], [-2, -4, -5, -3, 1, -2, -5, 5, 4, -3, -1, -6, -7, 4, -5, -5, 5, -6, 6, 1], [-1, 6, -6, -4, -7, -4, 7, 3, 2, -6, 5, -3, 3, 5, -1, -2, 0, 3, 3, 1], [4, -9, 16, -2, -1, 6, -3, 8, -2, 4, 6, 10, 5, 8, -1, 8, 1, 3, 3, 4], [13, 1, 2, -2, -1, 2, 16, 2, 2, -3, -2, 12, -2, 5, -3, -2, -5, 2, -1, 1], [2, -11, 8, -4, -10, -4, 10, 8, 4, -2, 9, 7, 18, 6, -5, 3, -4, 4, -5, 3], [-9, -3, -4, -1, 4, -4, -16, 0, -1, 6, -4, -11, -4, -10, 0, 4, 4, -3, 2, -2], [-2, -15, -5, -10, 1, 1, 0, 9, 5, 2, 2, 1, 7, 1, 9, 4, 4, 1, -5, 0], [-20, 4, -4, 3, -1, -2, 7, -9, 3, -7, -5, -11, 0, 3, 6, -4, 5, -3, -5, 0], [17, -7, 3, 4, 7, 3, -9, 0, -10, 11, 3, 1, -4, -3, -2, 6, 3, -10, 3, -1], [-4, 1, -1, -2, 6, 0, 2, -1, -5, 5, -1, -2, -4, -6, 4, -1, -1, 0, 4, -3], [18, 2, 3, 2, 0, 2, 4, 4, -2, -2, -4, -12, -2, 2, 5, -4, -2, 2, 3, -3], [-8, 3, 13, 5, -5, -9, 0, 4, 1, -5, 5, 15, 10, 7, -1, -4, 1, -4, -6, 13], [2, -11, 3, -4, -2, -5, 5, 1, 7, -1, 0, 10, 11, 4, 8, -3, 0, 7, -6, 5], [16, 4, 7, 2, -2, -3, -16, 16, 2, 0, 6, 15, 6, 9, -6, 3, 3, 4, -2, 11], [-9, -5, 2, 0, 0, 2, 6, -3, -2, 1, 3, 4, 5, -2, -2, -4, 1, -2, 2, 1], [-15, -3, -4, -12, 2, 4, -5, 2, -4, 6, -1, -4, 2, -4, 3, 7, -3, -4, 2, -10], [7, 4, -5, 1, 5, 2, 8, 2, -4, 0, -7, -14, -9, 0, 7, -1, 0, 4, 1, 5], [13, -1, -4, 0, -5, -1, 1, 8, 4, -4, 2, 3, -5, 3, -5, 5, -2, -1, -1, 6], [19, -5, 7, 3, -4, 2, 12, 6, 5, -1, 3, 11, 11, 4, -1, 5, -4, -1, -5, 3], [0, 3, 0, -5, -8, 5, 8, 7, 3, -1, -4, 3, 5, 5, 3, 4, 5, 2, -4, -1], [4, -5, 6, 15, -3, -9, 5, 2, -2, 0, 10, 5, 6, 3, -11, 2, 1, -8, 0, 9], [-3, -4, 1, 12, -2, 2, 0, 0, -3, 1, 8, 0, 1, 4, -9, 6, -4, -10, 4, -1], [3, -8, 10, -1, -2, 0, -2, -10, -6, 10, 2, 8, 10, -6, -3, 6, -1, -1, -2, -7], [-10, -9, -3, -6, 4, -2, -9, -11, -2, 1, 7, 7, 0, -6, -3, 6, -6, -9, -3, -1], [-8, 2, -13, 1, -3, 2, 0, 0, 3, -3, -2, -13, -6, -2, 5, -2, 0, 2, 0, -2], [4, -12, 6, 3, 2, -5, -3, -13, 1, 1, 3, 0, -1, 1, -11, 3, 1, -7, 1, -4], [-10, 8, -6, 3, 13, -3, 6, -1, 0, 8, -1, -8, -7, -4, 3, 1, -2, 3, 6, 6], [-10, 7, -5, 4, -4, -3, 8, -3, -2, -7, -5, -7, -11, -3, -2, -9, 4, 4, 2, 0], [-9, 17, -4, -12, 1, 8, 18, -8, 2, 1, -4, 6, -4, -7, 2, -2, -9, 11, 0, -4], [-7, 5, -7, -9, 0, 13, 0, 0, 4, 1, -9, 1, -1, 0, 12, -4, -6, 11, -6, -1], [2, -3, 11, 3, 0, 1, -5, -7, -6, 4, 1, 18, 7, 1, -8, 15, -9, -4, 0, -1], [-3, -3, 4, 12, 5, -4, -11, -11, -3, 1, 2, 5, 0, -3, -6, 0, -1, -4, -4, 5], [22, -1, 2, -5, -4, 6, 0, 2, 4, -3, 3, 18, 7, 3, 5, 7, -3, 8, -11, 3], [-9, -7, -12, 1, 2, -5, -16, 2, 2, -4, -3, -7, -11, -4, -3, -4, 4, -5, 7, -2], [3, 3, 4, 10, 2, -2, 0, -3, -2, 0, 8, -2, 8, 0, -4, 10, -4, 6, 0, 2], [16, 4, 4, 5, 1, -2, 13, -2, -4, -6, 2, 3, -4, 0, -3, -4, -2, 2, 3, -3], [-3, -5, 1, 5, 2, 1, 7, 1, 5, 4, -4, 0, -2, 2, 1, -1, 5, 3, -1, 1], [-8, 8, 6, -11, -3, -2, 6, 0, 0, -4, 7, 8, 7, 6, -3, -1, -4, 4, 3, 1], [-9, -11, 5, 0, -3, 4, 1, 8, 5, 4, -8, 3, 1, 9, -4, 4, -2, 5, 1, 0], [5, 2, 12, -5, -7, -2, 1, -6, -2, -4, 12, 23, 8, -1, -6, 8, -4, -6, -7, 3], [0, -5, 7, 4, 3, 4, 1, -3, 0, 0, 2, 10, 2, 3, -4, 6, 0, 6, 5, -2], [-3, -11, -7, -2, -3, 1, 9, 8, 10, -2, -6, -8, -7, 3, 0, -2, 1, 1, 0, -4], [13, 4, 2, -6, -6, 2, 13, 7, 1, -7, 9, 21, 11, 4, 1, 6, -3, 5, -4, 1], [6, -10, 4, -1, -2, -2, 20, -4, -3, 3, 4, 0, 4, 0, -5, 3, -4, -8, 1, -3], [-5, 4, -1, 0, 4, 8, 4, -6, -3, 9, -7, 2, 3, -5, 7, 10, -1, 3, -1, -8], [0, -12, 8, 6, 6, 0, 10, 0, 4, 8, -6, -2, 0, -2, 0, 2, 0, -3, -2, -2], [-8, 4, 3, -1, -2, 0, -4, 8, -3, 3, 3, 8, -1, 1, -6, 4, 4, -4, -3, 3], [-17, 6, -10, -6, 2, -7, -2, 10, 10, -8, -4, -7, -8, 6, 6, -9, 3, 2, 8, 10], [3, 7, -3, -3, -4, 7, 9, -4, -1, 5, 2, 6, 7, 0, 4, 7, -2, 5, -1, -10], [-1, -6, -11, -8, 1, -4, -6, -5, 2, -2, -1, -8, -9, -5, -1, -8, 2, 2, 6, -2], [-4, 6, -6, -1, 7, 5, -9, -9, -3, 3, -8, -18, -10, -15, -3, 3, -2, -1, 7, -7], [6, -6, -7, 1, -3, 2, -5, 3, 3, -3, -4, 7, 2, -2, 8, 0, -1, 0, -6, -5], [15, -3, 3, 11, -4, -2, -5, 3, 4, -4, 3, 2, 9, 5, -1, 1, 0, -3, 0, 1], [-18, -7, -3, 3, 0, -8, 5, 5, 4, -6, 1, -1, 1, 4, 7, -4, 6, 0, 2, 3], [-3, 21, -3, -1, -6, -11, -4, -2, -1, -11, 6, 3, 3, 4, 0, -10, 6, -7, -4, 7], [-12, 2, 5, 3, -6, 4, -1, 0, -1, 0, 8, 8, 3, 2, -8, 8, -6, -3, 3, -2], [11, -10, 5, 2, 3, -1, -16, 14, 1, 9, -2, -11, -9, 2, -3, -1, 6, -3, 6, 3], [-20, -1, 5, -3, 7, 5, -5, -12, 0, 8, -6, -1, -2, -7, -9, 10, -7, -6, -2, -9], [13, 5, -14, 2, 6, 4, -8, -5, 1, -1, -1, 6, -8, -5, 0, 4, -1, -1, 0, -3], [10, 0, -2, 2, -9, 1, 5, 10, 7, -6, -1, -6, 5, 7, 10, -8, 5, 2, -8, 4], [5, -2, 6, 2, -10, -3, -6, 12, 4, -4, 10, 15, 18, 7, 0, 5, -1, 4, -5, 2], [-12, -4, -10, -1, -6, -6, 3, 2, 4, -3, -3, -7, 1, 0, 3, -13, 8, -5, -4, -3], [3, 2, 1, -2, 1, 7, 4, -5, 3, -6, -1, 12, -5, 5, -8, 7, -11, 3, 1, -2], [-1, 1, 7, 3, -3, -5, 2, -5, 0, -7, 8, 19, 6, 5, -3, -2, -6, -2, -5, 7], [12, 4, 6, -2, 0, 0, 3, 6, -3, 0, -2, -9, -6, 4, 1, -5, 5, 5, 1, 2], [-3, 14, -6, 9, 11, 4, 3, -11, -9, 7, -8, -10, -12, -8, 4, 5, -3, -3, 6, -3], [-14, -6, -3, -1, -3, 1, 4, -1, 5, -6, 1, 5, -1, 1, -5, -5, -6, 2, -1, 1], [-14, -2, -10, -21, 2, 2, -10, -3, 8, 2, -2, -2, -2, -5, 4, -1, 0, 3, -4, -3], [-19, 3, -9, 4, 5, -5, -6, -6, -5, -6, 0, -7, -7, -3, -3, 3, 0, -4, 9, -2], [-17, 11, -7, 3, 5, -4, 12, -6, 0, -4, -7, -7, -7, -1, 5, -5, 1, 3, 2, -3], [-11, 16, 1, -3, 1, -1, 4, 7, 8, -5, -5, 8, 4, 3, 8, -11, -6, 8, 1, 7], [-18, -12, 5, 6, 2, 3, 4, 2, -5, 4, 7, 0, -1, 3, 1, 10, -5, -7, 2, -1], [9, -8, -6, -2, 3, -6, 3, 4, 4, 6, -6, -18, -7, -1, 0, -4, 7, -7, 4, -4], [-8, -9, 6, 8, 9, 2, -6, -11, -4, 8, -1, 3, 5, 0, 0, 7, -4, 6, 1, -3], [3, -2, 0, 6, 5, -5, -23, -2, -4, 2, -5, -4, -11, -8, -8, 0, 2, -7, 0, 1], [10, 7, 2, 7, 0, 7, -16, -4, -6, 1, 3, 5, -3, -4, -1, 8, -8, 2, 1, 0], [-15, 18, -8, -13, 5, 2, 2, -11, -2, 4, -5, 0, -7, -11, -2, -3, -4, -2, -3, -4], [-25, 3, -13, -4, 7, -6, 0, -4, -5, -1, 0, -18, -11, -12, 0, -12, 5, -9, 9, -3], [-18, -4, -3, -15, -2, -4, -5, 3, 8, 1, -2, 2, 1, 2, 4, -4, 7, 2, -7, -1], [-19, 13, -2, 4, 7, 7, 4, -5, -2, 1, -3, -9, -6, 2, 2, 2, -3, 10, 4, 4], [-6, -3, -3, -14, -3, 6, -3, 13, 0, 0, -4, -2, 2, 1, 14, 0, 2, 11, -1, 0], [-17, -4, -1, -3, 8, -7, -7, -6, 1, 9, -7, -6, -10, -6, 3, -8, 7, -1, -2, 5], [4, 1, 8, 8, -3, 1, 8, 1, -2, 0, 4, -10, 6, 11, -5, 2, 4, 3, -2, 4], [7, 0, -6, -1, -2, -5, -19, 8, 4, 0, -3, -11, -3, 2, 5, -4, 10, -5, 5, 4], [-10, 6, 0, -1, 6, 6, -11, 4, 0, 1, -4, 4, -3, 1, 4, 2, -1, -2, 0, 2], [19, -22, 11, 13, 1, -2, -13, 11, -4, 3, 7, 0, 3, 8, -2, 1, 5, -7, -1, 10], [-22, 3, -6, -4, 2, -2, -16, -1, 9, -1, -9, -10, -6, 6, 1, -6, 3, 1, -1, 7], [11, -12, 1, 5, -4, -4, 3, 4, 1, -5, 5, 2, -1, 7, -2, 3, 7, -7, 0, 5], [-15, 6, -4, -11, -2, 1, -4, 5, 11, -6, 0, 0, 0, 7, 6, 1, 0, 3, -3, 5], [-12, -4, 1, 0, 0, -2, -1, 1, 5, 3, -9, 3, 5, 0, 11, 1, 1, 4, -7, -2], [-10, 4, -3, 0, -4, -4, 9, 9, 8, -6, -6, -9, 2, 4, 2, -9, -1, 7, 0, -1], [-13, -2, 6, -6, -4, -10, 14, 4, 7, -6, 5, 19, 7, 6, -4, -3, 0, 6, -5, 9], [11, 8, -3, -9, -4, 7, -17, 11, 4, 4, -6, -3, 1, 4, 6, 2, 5, 8, -2, 0], [-8, -6, -12, 0, 5, 1, -7, 1, 0, 3, -12, -15, -14, 0, 3, -3, 0, -2, 4, -2], [3, -4, 10, -4, 1, 0, 8, 5, 2, -4, 1, 7, 1, 3, 3, -8, -2, 5, -5, 9], [6, -4, -2, -5, -5, 3, -13, 10, -4, 9, 2, -2, 2, -1, -2, 4, 4, -12, 1, -3], [0, 5, 5, 6, -1, 1, 7, 4, -1, 1, 0, 1, -3, 5, 4, -1, 4, -5, 0, 5], [-6, -1, 2, -10, -1, 1, -11, 2, 8, -2, -5, 8, 5, 6, 3, -4, 2, -1, -4, -3], [5, 12, -15, -15, -3, 7, -8, 1, 6, 2, -7, -4, 0, -8, 12, -1, 4, 9, -8, -7]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_8036_a_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_8036_2_a_s();".
// This may take a long time!  To see verbose output, uncomment the SetVerbose lines below.
// The precision argument determines an initial guess on how many Fourier coefficients to use.
// This guess is increased enough to uniquely determine the newform.
function MakeNewformModFrm_8036_2_a_s(:prec:=20)
    chi := MakeCharacter_8036_a();
    f_vec := qexpCoeffs();
    Kf := Universe(f_vec);
    // SetVerbose("ModularForms", true);
    // SetVerbose("ModularSymbols", true);
    S := CuspidalSubspace(ModularForms(chi, 2));
    S := BaseChange(S, Kf);
    maxprec := NextPrime(2999) - 1;
    while true do
        trunc_vec := Vector(Kf, [0] cat [f_vec[i]: i in [1..prec]]);
        B := Basis(S, prec + 1);
        S_basismat := Matrix([AbsEltseq(g): g in B]);
        if Rank(S_basismat) eq Min(NumberOfRows(S_basismat), NumberOfColumns(S_basismat)) then
            S_basismat := ChangeRing(S_basismat,Kf);
            f_lincom := Solution(S_basismat,trunc_vec);
            f := &+[f_lincom[i]*Basis(S)[i] : i in [1..#Basis(S)]];
            return f;
        end if;
        error if prec eq maxprec, "Unable to distinguish newform within newspace";
        prec := Min(Ceiling(1.25 * prec), maxprec);
    end while;
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_8036_2_a_s();".
// This may take a long time!  To see verbose output, uncomment the SetVerbose line below.
// The default sign is -1.  You can change this with the optional parameter "sign".
function MakeNewformModSym_8036_2_a_s( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_8036_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![9, -204, 1130, 2276, -18823, -34656, 37544, 84720, -21992, -82500, -220, 40524, 4748, -10948, -1934, 1644, 348, -128, -30, 4, 1]>,<5,R![12352, -235520, 407840, 830656, -1634000, -1246176, 2306216, 1182288, -1529332, -722896, 520870, 262804, -91327, -54740, 7012, 6276, 7, -360, -28, 8, 1]>,<11,R![795136, 120320, -17304448, 17490304, 46093056, -46853696, -42825048, 43231200, 17460648, -17911096, -3515418, 3626040, 446089, -391008, -40552, 22880, 2418, -680, -78, 8, 1]>],Snew);
    return Vf;
end function;