
// Make newform 6034.2.a.k in Magma, downloaded from the LMFDB on 24 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_6034_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_6034_2_a_k();".
// 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_6034_2_a_k();".
// 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 := [-44, -1040, -557, 25598, -53572, -10051, 118845, -68589, -82713, 84697, 19553, -42069, 2170, 10784, -1963, -1495, 382, 106, -32, -3, 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], [67218999701674198, 5216975976415944925, 41411235428956984938, -181665080056500571426, 27939152610740301313, 404156120962248189289, -220585853219456888561, -316718406459312876665, 230857985966499041093, 109977128581407295541, -107267874290971032547, -14331109638941604574, 26359431408583195074, -1113396279392493815, -3539175730986085457, 531834645279097790, 244497232318481630, -54819832348153622, -6772049431260751, 1884208619073815], [-70564680236336004, -1537307441254348881, -3488125857404902184, 42615529150975749982, -55260926422933630697, -71612347865554683003, 150864790001142980735, 20786416910545552897, -139757278490216706639, 20399478263473531751, 63238650629312797919, -16648452991686642704, -15563451891548516804, 5031539410354637667, 2115406329855661411, -757000768750022846, -148521462379189690, 56342467239727746, 4183343716317277, -1646489955919853], [835262515354061076, 6039841121644550400, -20249899522952731459, -29683598894102148527, 115278628048640600541, 3813604006572639198, -207565952904505687307, 74528931910043807460, 164168401698048247281, -86002892896791014258, -67633902391246240399, 42065511186223993522, 15511667094461435358, -10803722285236563090, -1984932905299763089, 1513198132916894710, 132019632435244250, -108807566211895234, -3540140078642762, 3127104033838755], [537124289860931266, 7172369417865667487, -18133147962913477724, -70981567614451844400, 189757253919079795777, 25255588012663275495, -380635973235985493941, 185972147390093472361, 300975641977135175641, -235459091984761509221, -118727806455225918255, 121093907308705820874, 25322430827364838482, -32271571631138111809, -2935114539028035169, 4657159059159682402, 172548994397585930, -343220790204299614, -3991346206018785, 10065141187344371], [58867169842075096, 2258491597010611886, 1876574736206580737, -33968674222941907429, 35928090013923519289, 57717793420680133428, -95678215384117260935, -22413709883206621946, 87184380574671031621, -9724746283820681574, -38863125151886120345, 10147403027698270934, 9428248289577918396, -3236734930360921036, -1263930365044317699, 499904042406259194, 87597900041745720, -37840877805593040, -2438333220022678, 1119536860327121], [-109311142072143852, -343771353327302546, 10693047212385667203, 20986728065886996523, -170606770584699719105, 91295869333194184928, 368008791233657177981, -307154999607483199868, -302859648982824319957, 301486860612581278080, 123629291047411873291, -141491884224648904880, -27333349626656604218, 35938085817581442262, 3304033166645627703, -5033069516739563416, -204385495015574670, 363424214178179798, 5034051088678948, -10503448216358573], [1194417972855740628, 19638808582601284345, 26838729095394594943, -370408125699181241641, 375056080009787972978, 658177758251583145949, -1026673138313829839246, -287795403625904923975, 941503286636183226728, -78031514542204280329, -420635238281782202832, 100947764831013868166, 102128444313634036454, -33366011599506042935, -13692638884638157382, 5231711985000248940, 948762142305284300, -399380682611257162, -26399200742569021, 11879423578954700], [35268733993435026, 2277763214801098667, -17751734706099632224, -115343226461668973760, 475492920356722312937, -74213307447322281605, -1080397092158436110881, 622042653413978308181, 918068582305768390561, -679216189447299489521, -386842852178757781115, 330325542765500062434, 88702496070239696822, -85136639406827835829, -11198820939293132989, 11994831050850637262, 728957321221247750, -867850713408271494, -19034873443334565, 25085191831479371], [-2220405302942957286, -50629726658386178209, -77202290690818616026, 988854651337288080098, -1014599839635315715593, -1753709700170495919137, 2795731775654655622205, 749482882951131681213, -2568991581728831247401, 226468875709856889979, 1149237242011364868311, -277045272916197744106, -279370097860565801106, 90699297037338387083, 37504207045011304289, -14154077632308236534, -2602117595074175970, 1077136798741435754, 72498357937682183, -31966208645463627], [-249743705922629934, -12266222197926562235, -21990502912283119654, 299198586394309623888, -406200616592431367949, -451109215052237945047, 1078448534742318966363, 14549830779549933435, -976132120602824220979, 267079743961638057517, 431385711403507642631, -175101874019574190308, -103591966370155386702, 50339956735608067405, 13729731111826327841, -7460969028510329990, -940299913509390050, 553852546619031056, 25866429321884853, -16224647473810125], [257541633675664884, -4270452584235103680, -11817748904901276961, 177530071668141828347, -347965140931814392621, -180515428448785359558, 893801568877545104677, -219590243417063266600, -798817401655150548711, 369300234338226285628, 349590177495387192079, -199850736345345756232, -83134202697530401288, 53742761929014228840, 10904462281102297799, -7718195745488889130, -738800036979872060, 563322951257545704, 20104009767025802, -16342144147451935], [1280728335623362936, 27289472051371045745, 41380605186174422011, -547957516221886200967, 573124862483069279336, 978720279096516244953, -1572900099036513843592, -429755687216334791905, 1446833818111464209566, -113001640915608876683, -648698659677830432714, 147817116983655916622, 158132035611333153118, -48785177018579809945, -21292905889765348234, 7628601459071785650, 1481853849782149650, -580666147649447414, -41406843424153057, 17224340615133150], [1805105827288545462, 34708132108877259925, 41583289250618372652, -756258555500456403984, 1016446369826370907787, 1172369235067575467021, -2657866945010579613199, -137061739189064090905, 2401670155483626014147, -575306463072558160851, -1062720649383104752333, 395080134444313106514, 255849454129385894786, -115031029357563459095, -34020153750713470263, 17132798313918081130, 2338285929742575490, -1274413605570467678, -64558827124941099, 37361376400924505], [-292259905165321848, -10012177462068633729, -17550715465077968808, 223107187522592085377, -277526287381350090395, -351730890493329935193, 747063820491258359964, 53864470795574235898, -679374153241403694603, 158285459780581389870, 301201657390889352304, -111679607285072540890, -72537072214922240777, 32793031411241113008, 9640762564957410867, -4905429074201272744, -662073116063725145, 365880217180962962, 18260962849193807, -10746543134042912], [1374880185302607158, 37794653657177039453, 78033602764254232158, -949901414726717269498, 1201151737800137645677, 1514528377374218926757, -3247270958174814193717, -243960778983622631921, 2960230531782877081933, -670170696264940021031, -1315248817160925041811, 475696139112830000294, 317423446216747218470, -139868223871836622291, -42280004014645994737, 20926938449972393498, 2909813195872212810, -1560542818850246142, -80423199849046123, 45818802149595219], [728488020471033914, 14632200301001467927, 14800765298119527046, -301623431917841174850, 403684530372989121723, 469634877785439511647, -1047076905137305110331, -62796098856213684591, 943112291717055668147, -221438087034559720857, -416411828992692958941, 153953951875942323930, 100070008563587669410, -45009368063324320529, -13284570343241530587, 6718854045484071566, 911713206433600330, -500532558632426530, -25137550241914713, 14690039489903837], [2396009442276911106, 65374448727472674843, 100752167824208576356, -1531756924411167399844, 2107844200896181039245, 2263071533214921389091, -5536494816837663198793, 33264134102817150609, 4985914666269938045961, -1466850759779536091305, -2193831028682643821903, 943426197150910256570, 524474375811286138494, -269984520608703321501, -69185942304319470029, 39973839933539256578, 4715623603162141030, -2968108296797542394, -129109586967391609, 87010448442195819]];
    Rf_basisdens := [1, 1, 1, 113435235445735860, 56717617722867930, 56717617722867930, 113435235445735860, 11343523544573586, 56717617722867930, 56717617722867930, 113435235445735860, 113435235445735860, 56717617722867930, 56717617722867930, 56717617722867930, 113435235445735860, 28358808861433965, 113435235445735860, 22687047089147172, 113435235445735860];
    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_6034_a();"
function MakeCharacter_6034_a()
    N := 6034;
    order := 1;
    char_gens := [1725, 869];
    v := [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_6034_a_Hecke(Kf)
    return MakeCharacter_6034_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 := [[-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], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -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], [-1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [3, -1, 0, 0, 1, 0, -1, 0, -1, -1, 1, 0, -1, 2, 0, 0, 0, 0, -1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0], [-2, -1, -1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 1, -1, 0, 0, 0], [-2, -1, -1, 1, 0, -1, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, -1, 0, 0], [-2, 1, 0, 0, -1, 0, 0, -1, 2, 1, -1, 0, 1, -3, 0, -1, 1, -1, 2, 1], [-2, -1, -2, 0, 0, 0, 2, 0, 2, 1, -1, 0, 0, -3, 0, 1, 2, -2, 1, 0], [-5, -1, -2, 0, 0, -1, 2, 0, 1, 1, -2, 0, 0, -3, -2, 1, 1, -2, 2, -1], [1, 1, 1, 1, 0, 0, -1, 0, 0, 0, 1, 1, 0, 0, 1, -1, 0, 0, 0, 1], [-3, -1, -2, 0, 0, 0, 1, -2, 1, 0, -2, 0, 0, -3, -1, 0, 0, -2, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 1, 1, 1, 1, -1, 0, 1], [-4, 0, -2, 0, 1, -1, 1, 0, 0, 0, 0, -1, 1, -1, -1, 0, -1, 0, 1, -1], [3, 0, 1, 0, 0, 0, -1, 0, -1, 0, 3, -1, 0, 2, 2, 1, 1, 1, -2, 0], [0, -2, 0, 0, 1, 1, 0, 0, 0, 1, 0, -2, 0, -1, -2, 0, 1, 2, 0, 0], [0, 1, 4, 1, 0, 3, -2, 1, 0, 0, 2, 0, 1, 2, 2, -2, 1, 4, -3, 1], [1, 2, 2, 1, -1, 0, 0, 1, 1, 1, 3, 0, 1, 1, 1, -1, 0, 1, -2, 0], [-5, -2, -2, -1, 1, 1, 1, -1, 1, 2, -2, 0, 0, -3, -2, 0, 2, 0, 1, 0], [-2, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, -2, 1, -1, 1, -1, 0, 1, -2, 0], [-1, -2, -3, 0, 3, -1, 1, 2, -2, -1, 2, 0, -2, 3, -1, 3, 0, 0, -1, -2], [4, -1, 3, 0, 0, 1, -1, 1, -1, -3, 1, 1, 0, 2, 1, 1, -1, 2, -1, 1], [-4, 0, -1, 1, -2, 2, 0, -1, -1, 0, -3, 0, 0, -2, 0, -1, -1, -1, 1, 1], [-3, -2, -1, 1, 1, -1, -1, 1, -1, 0, 1, 0, -1, 2, 0, 2, 0, 2, 0, -3], [-2, 1, 1, -1, 0, -1, -1, 0, 0, 0, 2, -1, 1, 1, 0, 0, -1, 1, 1, -1], [0, 1, 1, 0, 0, 2, -1, -1, 0, -2, -2, 1, 0, -1, 0, 0, 0, 0, 0, 0], [-5, 4, 0, -1, -1, -2, 1, 0, 3, 2, 2, 1, 1, -1, 0, -1, 1, -2, 2, -2], [-5, -2, -2, 0, 0, -2, 0, 0, -2, -2, -1, 0, -2, 1, 0, 1, -2, -1, 3, -1], [-3, 0, -1, -1, 0, 0, 1, 2, -2, -1, 0, -1, 0, 0, 0, 2, -1, 2, -2, 0], [1, 1, 5, 2, -1, 2, -2, 2, -2, -1, 2, 1, 0, 4, 1, 0, -1, 3, -2, 0], [0, -1, 1, 1, 1, 2, -1, 0, 2, 1, 3, 1, 1, -1, 0, 0, 1, -1, 0, -1], [4, -3, 5, 2, 0, 5, -4, 1, -1, -2, -1, 2, 2, 1, 2, -1, 0, 4, -2, 2], [-9, 2, -4, -1, 0, -4, 2, -1, 0, 1, -3, -2, 0, -2, 0, 2, -2, -2, 2, 0], [0, 0, -1, -1, 2, -2, 1, 2, 0, 0, -1, 1, 0, 2, 0, 2, 0, -1, 0, -1], [-4, 2, 1, 1, -2, -2, 1, -1, 3, 2, -2, -1, 2, -3, -1, -2, -2, -1, 3, -2], [-2, 0, 4, 0, -2, 3, 0, 0, 1, 1, 1, -2, 2, 0, 1, -2, 0, 2, 0, 1], [6, -3, 1, 0, 1, 2, 0, 0, -2, -2, -1, 3, -2, 2, -1, 2, 1, 0, -1, 1], [1, 0, 4, 0, 3, 0, -3, 2, -2, 0, 4, 3, -1, 4, -1, 1, 1, 2, -1, 1], [-8, 1, 1, -1, -2, 1, -1, -1, -1, -1, -2, -1, 3, -3, -3, -2, -2, 1, 2, 0], [4, -1, -1, -1, 1, -3, -1, 1, -2, 0, 1, 0, -1, 5, 4, 1, -1, 1, -3, 1], [1, 1, 2, 1, 1, 0, -1, 2, -1, -1, 2, 0, -1, 4, -1, 0, 0, 2, 0, -2], [-8, -1, -2, -1, 0, -4, 0, -1, 1, 3, -1, -1, 0, -3, -1, -2, 0, -2, 3, -2], [-3, -2, -1, 0, 0, 2, -2, -1, -3, 0, -2, -2, -2, -1, -1, -1, -1, 3, -1, 1], [2, -2, -1, 0, 3, 2, 0, 0, -1, -1, 1, 0, -1, 0, -2, 0, 1, 3, -2, -2], [-3, 2, 3, 1, -2, 1, 1, 0, 0, -2, 1, -1, 2, 1, 0, -2, -1, 3, -1, 1], [-2, 0, 3, 2, -1, 2, -2, -2, 1, -1, -3, 0, 1, -3, 0, -3, 0, 1, 2, -1], [2, -3, -3, 0, 2, -2, 1, 0, -2, -1, 2, -1, -2, 3, -2, 3, 0, -1, 0, -3], [0, -1, 0, 1, 0, 1, 0, 0, -1, -1, 1, 0, 1, -1, -1, -1, -1, 2, 0, 1], [-5, 5, 0, -2, -4, 3, 6, -3, 2, -1, -6, -3, 2, -5, -1, -2, 0, 0, 0, 2], [8, 2, 3, 1, -1, 1, -1, 1, 1, -2, 4, 3, 0, 4, 5, 0, 0, -1, -1, 0], [-5, -4, -1, -1, 0, 2, 0, -1, -4, -1, -2, -3, 2, -1, -1, -1, 1, 4, -3, 1], [5, 5, 6, 2, -2, 3, -4, 0, 0, -2, 3, 3, 2, 3, 4, -2, -3, 2, -1, 2], [-7, 9, 2, 2, -4, 4, 3, 0, 5, 1, 3, 1, 3, -1, 2, -1, 3, -1, -2, 1], [-2, 5, -3, 0, 2, -6, 0, 1, 0, 0, 7, 1, -1, 4, 2, 0, -3, -4, 1, -3], [-10, -1, -6, -2, -2, -1, 4, -3, 2, 4, -7, -3, 0, -8, -2, 0, 1, -1, 2, -1], [4, -1, 2, 0, -2, 0, 1, -2, -3, 0, -3, 0, -1, 1, 0, -1, -1, 2, -3, 0], [4, -3, -1, -1, 3, -2, -2, 4, -5, -3, 4, -1, -3, 9, 2, 1, -1, 2, -3, 0], [5, -3, -1, 0, 1, 3, -2, 0, 2, 0, -1, 2, 0, -1, 0, -2, 3, 1, -2, 2], [-3, 3, 2, 1, -1, 2, 3, 1, 3, 0, 0, 0, 1, -1, 0, -3, 1, 2, -1, 0], [-3, -4, -2, -1, -2, 0, 4, -3, 3, 4, -9, -1, 0, -8, -3, -3, 1, -1, 1, 4], [-1, 4, 1, 1, 1, -1, 0, 4, -3, -3, -1, 3, -2, 7, 3, 4, -3, 0, -1, 0], [8, -4, 3, 3, 0, 1, -4, 3, -3, -1, 3, 3, -3, 6, -1, 0, -3, 2, -2, -2], [7, 3, 1, -1, 2, -2, 1, 2, -1, -3, 8, 1, -2, 9, 3, 3, -1, -1, -2, 0], [-1, 0, 0, 3, 2, -1, -2, 2, 1, -1, 3, 1, -3, 4, 2, 1, -1, -2, -1, -3], [1, -4, -1, 1, -1, 1, 0, 1, -2, -1, 1, -1, -2, 1, 2, 3, -1, -1, -1, -1], [-11, 4, -3, -3, 1, -4, 3, -1, 2, 3, -3, -5, 2, -5, -1, -1, 0, -1, 2, 1], [4, -1, 4, 2, 0, -2, -2, 3, 1, 0, 4, 4, -2, 3, 6, -1, 1, -1, 0, 2], [-8, -1, -3, -1, -2, -2, 1, -5, 1, 1, -6, -1, 0, -6, -3, -3, 0, -4, 3, -1], [-4, -5, -7, -2, 1, -4, 1, -2, -1, 1, -1, -2, -3, -3, -2, 1, -2, -5, 4, -3], [-2, -5, -5, 0, 4, -2, -1, 4, -7, -2, 3, -1, -6, 9, -2, 3, 0, 2, -5, -3], [-2, -2, -2, 0, -1, 2, 0, -1, -4, 0, -4, -3, -2, -1, -3, -2, -3, 1, 2, -1], [4, -2, 2, 0, -1, 2, -2, -1, -5, -3, 0, -1, 0, 3, -2, -2, 0, 3, -3, 0], [-11, 5, -4, -4, -1, -3, 2, -2, 2, 1, 0, -2, 2, -5, -1, -1, -2, -3, 5, -3], [-8, 2, -2, -2, 0, 0, 4, 0, -2, 1, -2, -2, -1, 1, -1, 1, 2, 3, -4, -2], [0, -1, 0, -2, 2, -3, -1, 2, -4, 0, 2, -3, -1, 4, 1, 0, 1, 3, 0, 0], [-5, 2, -2, -2, 1, -4, 2, 0, -1, 0, 2, 1, 0, 3, 2, 5, 0, 0, -1, 1], [3, 7, 2, -2, 1, 0, 2, 1, 2, 0, 3, -1, 2, 2, 2, -1, 0, 2, -4, 2], [-2, -2, -3, 0, 1, 0, 2, -2, 3, 3, 0, 2, -2, -4, -3, 2, 3, -5, 1, -3], [6, -4, 0, -2, 2, -3, -4, 3, -2, 1, 9, 1, -3, 8, -1, 4, -2, -3, 1, -5], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 2, 4, 3, -3, 1, -3, 0, 2, 1, 2, 3, -2, 4, 1, -2, -2, 0, -2, 1], [-8, 7, -1, -1, 1, -5, 1, -2, 4, 1, -1, 0, 2, -2, -1, 0, -1, -4, 6, -2], [11, 0, 8, 2, 2, 5, -4, 4, -6, -2, 5, -1, 2, 9, 4, 1, -1, 9, -6, 1], [-10, 4, 1, 1, -2, -2, 0, 1, 3, 0, 0, 2, 1, 0, 2, -1, 1, -2, 0, 1], [5, 3, 2, 3, -1, 3, 4, 0, 4, 0, 3, 1, 3, -3, 2, -1, 4, 2, -4, 0], [12, -1, 5, 0, 3, 0, -1, 3, 3, -4, 7, 5, -1, 5, 2, 4, 4, -3, -1, 2], [-6, 4, -3, -3, 2, -6, -1, -3, 1, 3, 3, -2, 1, -1, -1, -3, -2, -4, 3, -1], [-1, 1, -1, -4, -1, -3, 1, 0, -2, 2, -2, -2, -2, 0, -4, -3, 1, 3, 0, 1], [-10, 3, -1, -1, -4, 5, 4, -2, 0, 1, -3, -4, 6, -8, -1, -3, 0, 1, 0, 0], [-2, 1, 0, -1, 0, 4, 0, 2, -3, 2, 0, -3, 1, -3, -2, -3, 2, 3, -2, 2], [-4, 0, -1, 0, 2, -5, 2, 4, -2, 2, 2, -3, 0, 3, -1, 0, 1, 4, -1, -1], [-2, 5, -4, 3, -3, -6, 1, -2, 3, 2, -6, 1, 0, -5, 1, -2, -2, -8, 7, 2], [7, -5, 2, 4, 1, 2, -6, 4, -6, -5, 1, 8, -3, 8, 4, 3, -4, 1, -5, 5], [13, -7, 6, 3, 1, 4, -7, 3, -8, -7, 1, 3, -6, 12, 5, 3, -3, 6, -4, 3], [-11, 2, -1, -1, 4, -4, -1, 2, 0, 1, 1, 1, -1, 1, -2, 2, 0, -2, 4, -2], [8, 6, 1, -1, 0, -3, 2, 1, 3, 2, 3, 3, 4, 0, 0, 2, 3, -3, 1, 1], [-3, 2, -1, 0, 1, 3, 3, -1, 1, -1, 3, -1, 3, -4, 1, 1, 1, -1, -1, -2], [6, -3, 1, 4, 0, 4, -2, -4, -2, -2, -4, 2, -4, -1, 1, 1, -3, -3, -1, 2], [-14, 3, -1, -1, 0, 1, 5, -4, 6, 1, -2, -3, 5, -10, -1, -1, 2, -3, 0, 1], [-10, -4, -5, -5, 2, 1, 6, -3, 6, 5, -6, -1, 2, -12, -9, 2, 6, -6, 5, -1], [2, 1, 3, -1, 2, 0, -2, 2, -5, -2, 5, 0, -2, 5, 0, -2, 0, 4, -4, 1], [0, 5, 1, -2, -1, 4, 1, -2, -2, 0, -4, -2, -2, -2, -1, 2, 0, 1, -3, 3], [8, -5, 5, 2, 4, 8, -4, 6, -2, -3, 1, 2, -1, 5, -1, 2, 2, 6, -3, -1], [17, 2, 9, 0, 0, 5, -5, -1, -2, -4, 2, 2, -1, 8, 0, -3, 1, 2, -3, 4], [-3, -4, -4, 0, 2, 1, 1, 3, -1, 1, -10, 0, -1, -1, -4, 1, 0, 2, 0, 0], [-14, -1, -2, -1, 2, -5, 0, 3, -6, 1, -4, 0, -2, 4, -2, 2, -3, 1, 1, 0], [-6, 1, -7, -1, -1, -7, 6, 0, 3, 6, -1, 2, -5, 0, 2, 6, 0, -10, 3, -2], [-1, 11, -2, 0, -1, 0, 2, 0, 2, 1, 1, -2, 1, -2, -1, -1, 0, -3, -1, 1], [-7, 3, 2, 1, -2, -2, -3, 2, -3, 3, 2, -3, 2, 1, 4, -3, -4, 1, 1, -2], [0, -8, -3, 1, 6, -6, 4, 3, 3, 3, 8, 2, -1, -2, -3, 2, 6, -4, 1, -4], [1, -4, -6, -2, 5, -5, -1, 1, -2, -1, -1, -2, -2, 4, 0, 3, 0, -5, 1, 2], [6, 4, 4, -3, 0, 4, -1, 2, -3, -4, 0, -1, 3, 1, -2, -3, 1, 7, -4, 3], [-16, 8, 0, 1, -5, -4, 2, -5, 3, 2, -3, -2, 4, -2, 1, -2, -3, -3, 5, -4], [-4, -1, -5, -4, -2, -4, -1, -5, 0, 0, -6, -3, 0, -2, 0, -2, -4, -3, 2, 1], [0, -1, 4, 0, 4, -1, -4, -1, 2, 2, 2, 4, 2, 0, -1, 0, 5, 1, 1, -1], [-12, 4, -9, -1, 1, -2, 7, -1, 4, 4, -2, 0, -1, -8, 0, 2, 1, -6, 1, -2], [-13, -10, -5, 3, 4, -2, 2, 3, -3, 0, -3, 0, -2, -1, -3, 4, 1, 0, 1, -4], [-12, -7, -10, -3, 3, 2, 5, -4, -2, -2, -7, -4, -4, -8, -5, 7, 1, -2, 2, -3], [-5, 1, -3, 5, -3, -2, -1, -1, -1, 0, -7, 3, -1, -1, 0, 0, -6, -5, 0, -2], [6, 5, -2, 1, -4, -5, 2, -3, 5, 4, 1, -2, 2, -3, 3, -4, 1, -6, 2, 1], [-19, 2, -2, -6, -7, 0, 6, -7, 7, 5, -10, -8, 7, -13, -3, -3, 0, -3, 6, 0], [6, 0, 3, 0, -3, 7, 0, 0, 1, -3, 0, 2, -1, -1, -2, 1, 1, 3, 0, 1], [2, -2, 0, -1, -1, 8, -4, 0, -2, -4, 1, -2, -3, 4, -5, -1, -3, 5, -5, -1], [7, 8, 1, 4, -6, 6, 5, -3, 6, 0, 1, 1, 5, -9, 3, -1, 2, -1, -3, 2], [4, 7, 4, 1, -2, -2, 0, -3, 3, 0, 1, 3, 0, 7, 8, 0, -1, -2, -3, 5], [-12, -4, -1, 0, 0, -5, 2, 1, 3, 2, -5, 0, 2, -4, -2, -1, -2, -1, 8, -1], [23, -9, 1, 1, 7, -3, -7, 4, -8, -7, 3, 5, -7, 14, 1, 1, -1, 3, -2, -1], [7, 6, 10, 1, -5, 1, -7, -2, 2, 0, 3, 0, 2, 2, 6, -8, 1, 2, 1, 6], [-18, -6, -9, -4, 0, -4, 3, -1, -1, 0, -10, -3, 2, -6, -1, 4, -3, -3, 9, -3], [-3, 4, 6, 3, -6, 3, -1, -2, 5, 1, -4, 3, 3, -3, 2, -8, 1, 0, 1, 2], [4, 7, 3, 3, 5, -5, -4, 5, 0, -6, 12, 5, 0, 13, 5, 2, -3, -1, 0, -5], [1, 8, 2, -3, 0, -5, 4, -2, 9, 2, 5, -1, 7, -3, 1, -2, 4, -2, 2, -1], [-6, 6, 4, 1, -9, 4, -3, -7, 5, 2, -8, 3, 3, -10, -1, -4, -4, -5, 3, 3], [-5, 0, -4, -1, -1, 3, 1, -4, 1, 2, -7, -4, 1, -5, 1, 0, 2, 1, -2, 5], [16, -4, 11, 1, 2, -2, -6, 3, -5, -4, 8, 1, -2, 10, 4, 2, 1, 4, -3, 0], [8, -11, -1, 2, 6, 2, -8, 2, -11, -7, -1, 1, -7, 14, 1, 6, -5, 2, -3, 0], [-18, -2, -10, -2, 3, -6, 4, 2, 5, 5, -7, 0, 0, -11, -8, 1, 0, -10, 7, -3], [6, -1, 6, 3, 2, -1, -4, 1, -2, -1, 8, 2, 2, 1, 1, -3, 0, 0, 0, 0], [15, 2, 0, -3, 6, -4, 1, 7, -4, -4, 13, -1, -2, 12, 2, 2, -2, 6, -8, -1], [1, 10, 9, 3, -5, 3, -3, -1, 6, -1, 10, 2, 3, 6, 5, -3, 0, 3, -3, 1], [-6, 1, -1, 0, 0, 0, 6, 2, 2, -2, -4, 0, 2, 1, -1, 3, 1, 1, 1, -2], [3, -8, -4, -2, 2, -6, -1, 2, -1, 1, -1, 1, 0, 2, -2, 0, -1, -2, 5, 2], [-2, -5, 8, 2, -2, 4, -4, -1, -2, -1, -2, 6, -1, 4, 3, -2, 4, 5, -4, 3], [-9, -7, -7, 3, 3, -3, -1, 4, -2, 1, 3, 1, 0, -3, -1, 3, -1, -1, -1, -3], [1, 6, -1, 1, -1, 1, 1, -1, 1, 1, -2, 2, 1, -5, -2, 2, -1, -8, 8, -1], [-1, 3, -6, -2, -2, 1, 9, -6, 9, 4, -5, -1, 4, -15, -3, 3, 5, -7, 1, -1], [-13, 0, 4, 0, -6, 10, 3, -5, 7, 7, -9, -1, 5, -15, -2, -9, 5, -1, 2, 5], [12, 5, 2, 0, 0, 0, -2, -2, 4, -1, 7, 3, 5, -1, 7, -5, 2, 0, -2, 3], [9, -10, 1, 0, 5, 0, -9, 5, -8, 0, 10, 0, -5, 13, 6, 0, 0, 4, -7, 4], [8, 1, 3, -1, 3, 6, 0, 3, 1, -3, 5, 1, 4, -1, 4, 2, 5, 5, -6, 2], [-6, 7, -2, -5, -2, 4, 6, -2, -2, 1, -9, -10, 3, -8, -5, -4, -3, 4, -4, -2], [4, -2, -2, -2, 1, -4, -1, -4, 0, 1, -4, 4, -5, 0, 1, 4, -2, -9, 9, 2], [-7, 2, -3, -3, -3, -4, 8, -2, 9, 6, 4, -4, 4, -10, -2, 5, 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[-11, 8, -1, 0, -4, -3, 4, 1, 0, 9, -3, -3, -2, 3, 2, -10, -6, 8, -5, 1], [18, 6, 11, -2, -1, -2, -11, -6, -9, -1, -1, 0, -2, 3, -4, -11, -7, 3, 4, 2], [4, 13, -2, -6, -6, 4, -4, -4, -3, -1, 4, -12, 0, 3, -3, -9, -1, 7, -1, 1], [-20, 1, -7, -4, -6, 3, 4, -9, 3, -1, -9, -8, 2, -15, -7, -1, -7, -6, 11, 0], [8, -7, 0, -1, -2, -8, -2, -1, -4, -1, 3, 7, -7, 12, -1, 2, -6, -6, -2, -2], [13, -15, -5, 5, 8, -4, -8, 1, -9, -5, -2, 8, -8, 4, -4, 3, -7, -3, 0, -5], [-19, -7, -5, 1, 1, -1, -7, 5, 0, 1, -6, 0, -3, 2, 3, 1, -5, -2, 4, 6], [10, 5, 0, 4, -3, -1, 0, 2, -4, -7, -4, 0, -7, 9, 6, 3, -7, 6, -7, 0], [0, 10, 1, 0, -6, 4, 3, -2, 0, 6, -4, -9, 8, -6, 5, -12, 1, 11, -5, 11], [4, 11, -4, 3, -2, -11, 2, 5, 7, -2, 3, 10, -7, 7, 8, 2, -6, -11, 3, 0], [-4, 3, -7, 5, 9, 0, -1, 5, -5, -8, 8, 0, 1, 3, 3, 3, -4, 3, -4, -2], [16, -1, 4, 6, 0, 6, -4, 8, -6, -2, 14, 3, 2, 11, 4, 6, -2, 6, -11, -2], [-3, 6, -2, 2, -3, 12, 4, -4, 1, -10, -4, 2, 2, -8, 2, 0, -1, -5, 7, 0], [0, -20, -10, 2, 12, -9, 0, 9, -5, 2, 7, 4, -2, 9, -8, 5, 1, -5, 1, -10], [9, -6, -4, 2, 6, -8, 1, 4, -5, -5, 5, 8, -12, 8, -4, 12, 0, -8, 4, -8], [-5, 5, 11, 8, -4, 11, -1, 1, 9, 5, 0, 3, 7, -14, -1, 0, 5, -6, 6, 3], [10, 1, 11, 0, -4, 12, 3, 5, 4, -3, -3, 4, 4, -1, 4, 3, 6, 4, -6, 12], [16, 7, 2, -4, 4, 4, 6, 6, -2, -2, 11, 3, -2, 14, 0, 9, -1, 7, -11, 1], [33, 2, 15, 4, 0, 13, -5, 0, -1, -1, 0, 8, -2, 9, 0, -6, 8, 6, -10, 11], [-23, -16, -2, -3, 4, 4, 6, -3, 2, 5, -7, 0, -1, -12, -14, 3, 6, -7, 10, -2], [4, -14, -10, -6, 4, -1, -4, -3, -10, -5, -4, -4, -6, 13, -8, 4, 0, 2, -7, -4], [0, -5, -7, -4, 2, -2, 5, 0, 2, 1, -7, -2, 4, -11, -3, 4, 2, -3, 2, -1], [-1, 0, -2, 0, -3, -3, 1, -2, 1, 8, -12, 3, 3, -7, -2, 0, -1, -7, 2, 7], [-22, -12, -9, 1, -2, -1, 4, -5, -4, 11, -13, -9, 1, -19, -9, -5, 1, 1, 4, -2], [-13, -6, 10, -3, -6, 6, 5, 0, 9, 6, -4, 3, 8, -11, 1, 0, 9, 0, 1, 6], [-16, 18, 5, -5, -4, -2, 7, -2, 8, 7, -3, -5, 8, -13, -11, -10, 3, -1, 5, -1], [7, 7, 7, -7, -1, 7, 5, -2, 7, -1, -1, 0, 5, -1, -7, 0, 2, 6, 0, -1], [5, 14, 5, 2, -6, 6, 4, 2, 8, 1, 0, 3, 9, -4, 10, -13, -1, 2, -2, 9], [9, 9, 0, -1, -3, 1, 4, 4, -2, -9, 2, 2, 1, 4, 9, 13, 1, 0, -7, 4], [14, -5, 7, 4, -3, -7, -11, 4, -8, -5, 12, 9, -12, 22, 18, 6, -7, 3, -10, 3], [10, -2, 10, 5, 0, -1, -10, 8, -7, 3, -1, 4, 1, 13, -1, -11, -2, 11, -7, 2], [-16, -6, -10, 2, 9, -5, -4, 6, -1, 1, -3, -5, -3, 1, -4, 0, -1, -3, 0, -4], [-7, -1, -3, -3, 0, -13, 7, 2, -3, 0, 2, -3, -2, 2, -1, 5, 1, -2, 5, -1], [21, -11, -4, 3, 6, -5, -2, 6, -4, -6, 14, 7, -11, 14, 1, 13, 6, -6, -3, -4], [2, 3, 12, 3, 0, 1, -4, 10, -2, -6, 5, 0, 6, 16, 9, -9, -7, 15, -6, -1], [1, 0, -1, -7, 0, 4, -1, -9, 5, 7, -14, -5, 2, -13, -6, -16, -1, 6, 2, 7], [0, 4, 5, 3, -7, 0, -3, -8, 1, -1, -2, -5, 2, -8, 9, -5, -3, 1, 2, 2], [23, -13, 0, -5, 0, -1, -10, -2, -12, 0, 0, -1, -9, 11, 7, 2, -4, -2, -3, 3], [5, -7, 8, 8, 0, 10, -12, 1, -3, -1, -10, 3, 1, -1, 8, -5, 1, 10, -2, 6], [-17, 3, -8, -1, -12, -9, 13, -3, 2, 1, -7, -7, 2, -8, 4, -1, -2, -8, 3, 0], [-2, 7, -2, -5, -4, 0, 7, -7, 8, 4, -11, 0, 0, -7, -6, -7, -2, -6, 7, -1], [-1, 18, 6, 1, -11, 5, 11, 1, 10, 6, -11, 2, 11, -16, -4, 3, 2, -4, 3, 3], [-10, 13, 6, -4, -5, 1, -1, -3, 3, 4, -1, -1, 13, -6, 7, 2, -10, 0, 6, 4], [-9, -3, 2, -9, -1, 6, -8, -6, -6, -3, -8, -5, 3, 0, -3, 2, 0, 4, 0, 2], [-6, -7, -3, -5, 6, 5, -2, -1, -5, 3, 5, -9, -3, 0, -3, -7, 6, 6, 0, 0], [23, 4, -3, -1, -1, 2, 3, 3, -6, -4, 4, -2, 1, 5, 0, 0, -4, 8, -8, -4], [-6, -6, -7, -5, 7, -5, 1, -6, -8, -2, -6, -8, -1, -6, -8, -5, -4, 4, 0, -4], [-12, -1, 4, -2, 6, -4, -8, 2, -4, -6, 7, 1, -5, 11, 3, -11, -4, 7, 4, -3], [-30, 12, -9, 1, -13, 2, 17, -13, 15, 5, -19, -7, 7, -23, -4, 0, -1, -14, 7, -3], [0, -15, -7, 2, 13, -8, -10, 3, -8, 2, 7, -1, -3, 3, -7, -1, 0, 0, 0, -7], [-14, 6, 2, 0, 1, -11, 4, 6, 3, -1, 11, 5, 1, 6, 6, 13, 0, -4, 4, -3], [-7, -13, -1, 5, 1, 8, -11, -7, -1, -5, -7, 3, -3, -6, 0, -2, -2, -5, 6, 0], [-8, -14, -4, 0, 7, -4, -1, -2, -5, -5, 3, 0, -4, 6, -7, 12, -1, 1, 5, -7], [-17, -4, 7, -3, -8, 3, -3, 2, -8, -3, -3, -7, 5, 5, 1, -4, -12, 13, -9, -1], [5, 1, 4, 8, -9, 3, 3, 2, 2, -8, -2, 3, -3, 2, 2, -4, -3, -7, 3, 2], [-1, -13, -4, -2, 6, -8, 2, 1, -1, 3, 4, -4, -4, -1, -12, 0, 8, 2, 4, -7], [-8, -6, -9, 3, 2, -12, -1, -2, 6, 6, 4, 7, -7, 3, 0, 9, -2, -18, 10, -8], [1, -6, -3, -2, 4, -11, -5, -3, 4, 0, 3, 3, -7, -6, -3, -1, 6, -15, 14, 3], [1, -2, 0, 4, 7, -5, -4, 9, -7, -7, 4, 4, 1, 11, 5, 5, 1, 9, -12, 0], [-8, -3, 2, -4, -5, 2, 6, 2, 2, 2, -5, 5, 1, -14, -1, 5, -1, -1, 1, 1], [10, -5, -8, -3, 11, -5, -8, -6, -12, -4, -9, -2, -9, 2, -5, 0, -6, -1, 5, 1], [-21, -1, -19, -1, 6, -5, 10, 0, 0, -2, -13, 2, -4, -8, -6, 8, 0, -13, 6, -6], [-17, 13, -6, -7, -6, -8, 10, -6, 14, 7, -4, -5, 8, -16, 2, -7, 6, -2, 2, 0], [-3, -8, -5, 6, -1, 6, -1, -9, -6, 0, -10, -5, -6, -2, -8, -5, -5, 0, 3, 4], [5, 11, 20, 1, -1, 11, -10, 11, -8, -6, 14, 10, 4, 14, 10, -6, -1, 16, -14, 4], [4, -1, 6, -1, -1, 6, -5, 1, -4, -1, -8, 3, 0, -1, -8, -7, -4, 8, 1, 3], [-33, -6, -5, 5, 0, 9, 6, -4, 6, 3, -3, -3, 0, -11, -8, 4, 0, -3, 2, -10], [-22, -12, -1, 5, -5, -2, -1, -11, 7, 4, -8, -5, 0, -18, -3, -3, 3, -8, 8, 1], [0, -2, -2, 3, -1, -8, -4, 1, -11, -1, 6, 1, 1, 10, -2, -8, -9, 4, -5, -9], [11, 9, 9, 1, 3, -4, 0, 5, 3, -2, 18, 5, 3, 5, 12, -3, 7, -4, 4, 2], [-12, 8, 1, 1, 1, 7, 0, 3, -5, -5, 15, -3, -3, 14, 2, -4, 1, 8, -13, 0], [8, -5, 3, -3, 0, 4, -2, -14, 2, -4, -9, -3, -4, -9, -7, -9, 5, -1, 4, 0], [9, -13, -1, -7, 3, 6, 4, -2, 2, 7, 4, -2, 3, -11, -5, -3, 12, 3, -1, 0], [8, 23, 16, -1, -2, -1, -3, 0, -2, 0, 16, -1, 6, 4, 0, -3, -2, 4, 2, -3], [-27, 19, -2, -4, -3, -2, 12, -10, 10, 10, -9, -7, 6, -18, -4, -14, 1, -2, 2, 4], [-9, -15, -1, 7, 0, 4, -7, -8, -1, 1, -11, 6, -11, -6, -6, 0, -5, -8, 8, -1], [-11, -1, -8, -2, 9, -9, 10, -1, -1, 0, 8, -7, -5, 4, -2, 1, 8, 2, -4, -7], [-30, 7, -7, -4, 5, -13, 3, 4, 6, 7, 12, -7, 3, -1, -6, -6, 3, -2, 10, -12], [1, 11, 16, -2, -8, -6, -4, 4, 1, 0, 2, 5, 5, 1, 7, -4, 4, -2, 4, 7], [-8, 12, 3, -6, -5, -1, 7, -8, 10, 5, 8, -7, 9, -7, -4, -10, 3, 3, 4, -7], [-22, -11, -3, -6, 4, -2, -2, -4, -1, -1, -9, -3, -2, -6, -13, -1, -1, -1, 13, -3], [-9, 4, 8, 3, -2, 1, -6, -3, 1, 4, 5, 1, 5, -3, 6, -9, -9, 3, -4, 2], [9, -5, 4, 5, 5, 5, -6, -3, -1, -3, 10, 12, -7, 5, 4, -1, 4, -7, -6, 8], [5, -15, -3, 1, 3, 3, 0, -4, 4, 6, -7, 8, -3, -8, -6, 0, 3, -3, -1, 4], [-7, 2, -3, 9, -6, 5, 5, -5, 10, -1, -8, 7, -5, -13, 2, 1, 0, -15, 6, 1], [-3, 8, 2, 2, 5, -6, -2, 8, -5, -3, 11, -1, -9, 15, -4, -4, -3, 7, -4, -10], [-18, 1, -10, -11, -5, -8, 6, -7, -5, 5, -7, -15, 2, -11, -8, 2, -7, 1, 4, -14], [14, 11, 4, 7, 2, 0, 0, 10, 2, -7, 13, 7, 5, 6, 8, 3, 1, 4, -5, 0], [-13, 2, -3, -11, 5, -9, -1, 3, -4, 7, 12, -11, -1, 6, -7, -2, -6, 7, -1, -5], [33, -4, 3, -2, 5, 4, 1, -3, -3, -5, 8, -3, -4, 6, -1, -8, 5, -2, -1, 3], [-40, 6, 7, 4, -3, 8, 4, 0, 17, 5, 2, 1, 9, -13, -2, -11, 9, 1, 4, 1], [12, -15, 18, 6, 4, 12, -20, 7, -22, -13, 3, 4, -8, 29, 1, -2, -10, 25, -9, 7], [1, 8, 10, 3, 0, -7, -1, 4, 5, 4, 8, 0, 4, -1, -4, -6, 2, -4, 11, -6], [1, 11, 14, -3, -4, -10, -8, 3, -5, -2, 13, -6, 5, 19, 5, -8, -15, 8, 1, -1], [15, 4, 18, 10, 1, 11, -9, 2, 0, -8, 6, 14, 0, 12, 1, -5, 1, 1, -3, 1], [-26, 5, 4, -3, -11, 1, 10, -12, 13, 9, -23, -11, 13, -30, -8, -9, 2, 6, 14, 3], [5, -13, -2, 5, 7, -2, 5, 4, 2, 5, 5, 6, -1, 1, 6, 1, 11, -1, -6, 4], [17, 7, 11, 13, -7, 2, -4, 1, 8, -3, 1, 18, -1, 1, 11, -7, 2, -7, 2, 8], [4, 3, 18, 7, -4, 7, -3, 1, 2, -3, 12, 6, -6, 14, 7, -4, 0, 12, -9, 5], [14, 1, 1, -1, 10, 5, -5, 0, 3, 2, 12, -2, 8, -1, 6, 0, 6, 4, -1, 7], [5, 22, 23, 3, -10, 12, -7, -2, 9, -8, -3, 10, 12, -2, 7, -11, -8, 0, 5, 11], [-3, 5, -2, -8, 5, -14, -2, 7, -12, 0, 11, -2, -7, 15, -2, 9, -9, -2, -6, -4], [-21, 4, -4, 14, -4, -13, 1, 3, 9, -1, 2, 10, -2, 2, 8, -1, -4, -15, 8, -3], [4, 9, 1, -6, 4, -2, 4, -9, 17, 9, 19, -4, 7, -10, 5, -9, 9, -10, 2, 2], [8, -4, 1, 2, -4, 9, 1, 2, -5, -6, -4, 3, 2, 3, 4, 6, 6, 5, -7, 4], [-9, 3, -2, -7, 0, -12, -2, 11, -1, 9, 0, -5, -1, 2, 4, 1, 2, 2, 3, -1], [29, 15, 10, -6, -8, -3, 3, 1, 8, -3, 5, 5, 7, 4, 8, 3, 0, -11, 2, 10], [-11, 10, 13, 5, -7, 8, 2, 1, 13, -4, -9, 9, 2, -6, 1, 0, -3, -2, 8, -4], [25, -9, 2, -2, 7, -2, -3, 1, -9, -5, 9, 0, -5, 18, -7, 0, -12, 8, -4, -12], [-14, 12, -4, -4, -7, -10, 10, -4, 11, 5, 10, -6, 8, -13, 4, -9, 10, -11, 8, 2], [-21, -4, -11, -3, 4, -8, 2, 1, 0, -1, -7, 9, -4, -3, -8, 2, -6, -11, 13, -2], [22, 12, 19, 2, -1, 13, 0, 1, 1, -1, 1, 2, 4, 4, 4, -11, 9, 19, -15, 9], [6, -14, 6, -4, 5, -1, -11, 4, -13, -5, 6, 8, -2, 16, 0, 4, -4, 6, -5, -4], [-4, -5, -4, -4, 10, 7, -3, 6, 1, 0, 10, 4, 5, -11, -4, 6, 15, -6, 2, 2], [22, 2, 16, 4, 3, 3, -9, 12, -4, -3, 13, 8, -2, 21, 0, 0, -6, 8, -9, -3], [32, 14, 18, 4, -4, 13, -2, 3, -2, -11, 19, 14, -4, 21, 17, 7, 4, -1, -14, 9], [-4, -10, -1, -4, 4, 8, -1, -2, -10, 4, -9, -13, -2, -8, -10, -9, -4, 20, -12, 0], [15, -3, 13, 7, 3, 6, -9, 14, -3, 2, 18, 6, 5, 14, 4, 1, 1, 6, -5, -7], [4, 1, 10, 5, -16, 12, 3, -2, 12, 1, -6, -1, 1, -13, 6, -13, 4, 3, 4, 8], [17, -15, 6, 1, 6, 15, -7, 9, -20, -12, 10, -4, -4, 24, 3, 1, 4, 20, -19, 3], [-16, -8, -6, -9, -9, 6, 3, -1, -3, 6, 1, -10, 5, -5, 1, 3, -4, 7, -9, -2], [35, 2, 7, 6, 13, 4, -2, 10, -1, -10, 26, 4, 1, 17, 0, 1, 4, 0, -10, -8], [9, 2, -1, 5, 1, 6, 5, 4, 4, -1, -3, 5, 4, -13, -3, -13, 7, 2, -3, 4], [-9, -1, -6, -3, -3, -14, 7, -3, 1, 12, 2, -5, 0, -4, -6, -3, 3, -3, -2, -5], [-16, -16, -7, 3, 3, 4, -9, -3, -6, -1, -9, -4, -8, 2, -3, 3, -4, -2, -5, 4], [14, -7, -2, -4, 6, 1, -7, -1, -1, 0, 10, -3, 3, -9, 1, 1, 0, -1, 2, 7], [-11, 6, -7, -2, 6, 2, 7, 0, 10, 0, -2, 12, 3, -12, -3, 5, -1, -5, 3, -1], [18, -9, 1, 0, 8, 11, -2, -4, -6, -6, -11, 4, -6, 1, -4, 1, 7, 9, 3, 6], [-3, 5, -4, -3, 4, 6, 8, -3, 0, 2, -13, 5, 5, -12, -9, 2, 5, -11, 4, 11], [0, 5, 7, -6, 1, 2, 3, 0, 8, 6, 18, -2, 0, 1, -1, 0, 14, 2, -5, -6], [-40, -1, 6, 7, 7, 2, -1, 3, -1, 0, -1, 8, -3, 3, -3, 5, 2, 0, 3, 2], [-7, 10, 3, 2, -6, -14, -1, -4, 5, -1, -5, 5, -3, 0, -6, -1, -9, -16, 21, -7], [17, -4, -10, -6, 8, 6, -1, 0, -14, -7, -1, -11, -5, 10, 0, 3, 1, 4, -13, -1], [14, -2, -5, 7, 6, 4, 1, 4, 3, -2, 12, -2, 0, -1, 2, -2, 16, 1, -5, -2], [-16, -3, -4, -1, 2, 7, 6, -9, 1, 1, -11, -14, 12, -23, -7, -12, 7, 10, 0, 2], [16, -1, 5, -5, 3, 8, -6, -2, -7, -11, -3, -2, -5, 5, 0, -4, -12, 4, -2, -4], [3, 1, 8, 5, -1, 3, -13, -1, -4, -10, 13, 8, -7, 20, 0, -6, -3, 5, -5, 2], [-17, 2, -1, 1, -8, 3, -2, 4, 4, 0, -5, 2, 4, 2, 3, 2, -6, 8, -5, 1]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_6034_a_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_6034_2_a_k();".
// 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_6034_2_a_k(:prec:=20)
    chi := MakeCharacter_6034_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_6034_2_a_k();".
// 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_6034_2_a_k( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_6034_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![-44, -1040, -557, 25598, -53572, -10051, 118845, -68589, -82713, 84697, 19553, -42069, 2170, 10784, -1963, -1495, 382, 106, -32, -3, 1]>,<5,R![966416, -3333152, -3597448, 9924904, 6282929, -11316028, -5901853, 6577300, 3095103, -2211515, -961393, 454003, 183752, -57392, -21794, 4327, 1557, -177, -61, 3, 1]>,<11,R![-13416128, -96945536, -271782544, -344567160, -110909679, 193983814, 197800086, 8598801, -66049827, -21685673, 8554867, 4909954, -370002, -502911, -16139, 26931, 2216, -733, -80, 8, 1]>],Snew);
    return Vf;
end function;