
// Make newform 2151.2.a.k in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_2151_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_2151_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_2151_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 := [1, -56, 640, -1184, -4844, 9108, 10479, -21252, -9429, 23404, 3356, -14020, 229, 4804, -540, -936, 164, 96, -21, -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], [-3, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -5, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2324646198, -16518890109, -59487470803, 62363096099, 196387146324, -75991923150, -233246301320, 44748634260, 110440481462, -9466063919, -8255925475, -5690004117, -10641470398, 4637406235, 3879963697, -1318767164, -526870261, 170049029, 25715994, -8259046], [-1169865603, -3285022906, 42654573730, 78826196104, -182021298167, -189016862749, 340443884242, 168783410560, -335996303347, -59687153306, 190290241568, -1856788512, -63597294912, 7821689951, 12309098593, -2385590232, -1266785187, 303862297, 53211591, -14412353], [4109545279, -63595522316, 80270642859, 573846563225, -476065715156, -1389923753527, 968327695840, 1487550147038, -984891173929, -821292093320, 564343295095, 240555769633, -189004335507, -33169211667, 36468511186, 554113853, -3732397225, 337358422, 155801032, -25152759], [435415269, -15016860419, 13748437164, 114948803841, -138330331238, -238050299893, 343079978087, 204676228239, -385701840578, -69698642148, 233192405803, -4793202241, -80281652938, 10579309020, 15676712010, -3118198456, -1608799145, 389694649, 67002479, -18194582], [-5283572531, 61187604393, -68965179349, -312635355213, 586935486325, 545824666009, -1418565745122, -406229547534, 1607226024841, 70776349317, -988002485813, 79045302167, 346201298514, -53462767366, -68713614510, 14002650970, 7153614242, -1707908090, -301609179, 79748961], [-1325315495, 13079021136, 20700322923, -133521035197, -154604743387, 383186074902, 384965658988, -519105112175, -443707767420, 396206848876, 273459017045, -183140190454, -95322242093, 52196104835, 18748215845, -8936959131, -1930987718, 838637985, 80534179, -32909587], [-234896285, 73661197513, -278185798363, -497624917207, 1712651972849, 950270360355, -3712320960866, -660569594262, 3941510138311, 10235198061, -2312306020795, 223739180405, 781865754296, -125091051332, -150919713262, 30755798996, 15370014952, -3626875370, -636904335, 165811103], [-9584403627, 75649845204, -54991098473, -563447135410, 1006992862467, 1145957832622, -2829691525926, -891165421092, 3370944216337, 148889232756, -2099123586481, 178571636242, 734184616508, -117401664390, -144695688234, 30200134326, 14940203236, -3630490016, -625032345, 167543794], [8319810742, -137345767347, 310811596208, 1041865182955, -2148992184846, -2310123795985, 4777975720548, 2194123680594, -5092905104298, -907371831707, 2979330609416, 55963406827, -1003246916152, 82628335904, 193013398266, -29167126050, -19617511978, 3922186244, 812153314, -191187961], [-6936694175, -20820501810, 265089961095, 90722687714, -1761383572467, 28588928198, 4128749475290, -505963606680, -4601849814699, 806330690734, 2776224670379, -583595480738, -953933229802, 225813453148, 185896992694, -47988197224, -19043970058, 5255031164, 792118541, -230262066], [5574045831, -51667771349, 119016332276, 355842728817, -1073350264885, -658526239498, 2663213045448, 396576234042, -3030189040325, 98257492451, 1849614742124, -234690327751, -640863691862, 118362276789, 125696279845, -28156991606, -12943039301, 3269848589, 540557051, -148218686], [-7156850618, 262319755187, -714054374770, -2308907122843, 4162998154950, 5417893882787, -8855184929684, -5421598473634, 9357507914978, 2517671450063, -5493115468418, -396106182055, 1862951048504, -94162854506, -361128470164, 47527928106, 36955819636, -6932521542, -1538748210, 349773159], [7398565297, -243115237582, 731216944173, 1929328806792, -4499164209241, -4170396163194, 9743414760590, 3665469555820, -10319684222695, -1211519056514, 6030009661713, -163978080660, -2030486662212, 237254998916, 390583010652, -69029091930, -39676028714, 8685638574, 1641156191, -409558402], [-14477391829, 330179570559, -909185235221, -2641800836793, 5948526383965, 5831232262335, -13279130648006, -5299261526434, 14360787887307, 1879234764699, -8528444005017, 158040286339, 2909343190140, -323375601322, -565548619752, 97829257148, 57939652746, -12540986368, -2412992855, 598257155], [-10645201535, 184808475650, -421428522916, -1375942998806, 3031788732943, 2968266256213, -7002436929558, -2622318172054, 7712530360549, 836812332066, -4633920382372, 167872279748, 1593298102484, -198680269865, -311403994141, 57068773546, 32022014849, -7181512587, -1337024169, 339515531], [17183676468, -373123885017, 1111002194104, 2848228155609, -7497534043164, -5950105648445, 16858150511980, 4797063610670, -18235080824624, -998078437201, 10809765842264, -772152880431, -3679266043972, 547600302602, 713538822384, -142898221962, -72932486780, 17248139170, 3030854544, -796840493]];
    Rf_basisdens := [1, 1, 1, 1, 615206542, 615206542, 615206542, 307603271, 1230413084, 307603271, 1230413084, 1230413084, 1230413084, 1230413084, 615206542, 1230413084, 1230413084, 1230413084, 615206542, 1230413084];
    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_2151_a();"
function MakeCharacter_2151_a()
    N := 2151;
    order := 1;
    char_gens := [479, 1441];
    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_2151_a_Hecke(Kf)
    return MakeCharacter_2151_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, 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, 0, 0, 0, 0, 0], [1, 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, -1, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 0, -1, 0, 0, 1, -1, -1, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [1, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, -1, -1, 1, 0], [2, -2, 1, 1, 0, -1, 2, 0, -1, 0, 0, 1, 0, 1, 1, 1, 0, -1, 1, -1], [0, -1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, -1, 1, 0], [0, -2, -1, 1, 2, -1, 1, 0, 0, 1, -1, 1, 1, 1, 0, 0, -2, -1, 2, 1], [4, 0, 1, -2, -1, 0, -1, 0, -1, -1, 1, 0, -1, 0, 0, 0, 2, 0, -1, 0], [-2, 3, 0, -1, -1, 1, -2, -1, 1, 1, -1, -2, 1, -2, -1, -2, -1, 2, -1, -1], [2, 0, 0, 0, 2, 1, 0, -1, 3, 1, -1, 1, 1, -1, -1, 0, -1, -1, 0, 0], [1, -1, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 1, -1, 0, 0, 0, 0, 1, 1], [2, -2, 0, -1, 0, 0, 0, -1, -1, -2, 1, 0, -1, 1, 1, 0, 0, 1, -1, 0], [-1, -5, 0, 0, 4, 0, 3, -2, 0, 2, 0, 1, 3, 0, -1, 0, -1, 1, 2, 1], [-1, -1, 1, -2, 1, 1, -1, -1, -1, -2, 0, -2, 1, 0, -1, -1, 0, 1, 1, 2], [1, -2, -1, 1, 1, -1, 2, 0, -2, 0, 1, 0, 1, 1, -1, 1, 0, 1, 1, 1], [2, 2, 0, -1, -2, 1, -2, 1, 0, -2, 1, 1, -1, 0, -1, 0, 1, -1, -1, -1], [1, 2, -1, 0, 1, 0, 0, 1, 3, 3, -1, 1, 1, -2, 0, 0, 1, -1, 0, 0], [-2, 2, 0, -2, -1, 2, -3, -2, 0, 0, 0, -1, 1, -2, -1, -2, 1, 3, -1, -1], [4, 4, -1, 0, 1, 2, -2, 0, 1, 2, 0, -2, 3, -2, -2, 0, 0, 0, 0, 0], [0, 0, 1, -2, -1, 1, -2, 0, 0, 0, 0, 0, -2, -2, 1, 0, 2, 2, -1, 0], [-2, -1, -1, 2, 4, 1, 0, -2, 1, 3, -4, -3, 4, -1, -2, -1, -3, 2, 2, 2], [1, 1, 1, 0, -1, -2, 0, 1, 1, -3, 1, 1, -2, -1, 1, 0, -1, -3, 1, 0], [-1, -1, -1, 0, -1, 0, 1, -1, -2, -1, 0, -1, -1, 1, -1, -1, -1, 3, -2, -1], [-1, 1, 1, 1, -2, -1, -1, 0, -1, 2, -1, -2, 0, -1, 1, -1, 0, 0, 0, -2], [3, 2, -1, 0, -2, 2, -1, 1, 1, 0, 2, 1, -3, -2, 2, 2, 3, 1, -3, -1], [-1, -2, 0, 0, 3, 2, 0, -2, 1, 0, 1, 1, 3, -1, -3, 1, 0, 0, 1, 0], [0, 0, -2, 0, 1, -2, -1, 0, -1, 0, -1, -1, 1, 0, -1, 0, 0, -1, 2, 0], [5, 1, 2, -1, -2, 0, -2, 2, 0, 0, -2, -1, -1, 0, 0, 1, 1, -2, 0, -1], [-2, 2, -1, 0, -2, -1, 0, 0, 1, -1, 2, 1, -1, -1, 2, -2, 0, 1, 0, -2], [0, 3, -4, 2, 0, 1, 1, -1, 3, 2, 0, 2, 3, -1, 0, -1, -1, 2, -2, -3], [-1, -7, 0, 1, 0, -2, 3, 0, -3, -2, 0, 2, -1, 3, 1, 0, -1, 0, 0, 0], [-2, 0, 0, 1, 1, 1, 0, 0, -1, 1, -1, 0, 1, -1, -1, 1, 1, 0, 1, 0], [3, -2, 0, 3, -1, 0, 2, 1, -1, 1, 1, 1, 1, 3, 1, 3, 2, -2, -1, -2], [0, -5, 0, 1, 4, 0, 3, -2, 1, 2, 0, 2, 1, 0, 0, 1, 0, 1, 2, 0], [-1, -2, 1, -3, -1, -1, -1, -3, -4, -4, 2, -1, -1, 1, -2, -2, 0, 2, 0, 2], [6, 3, -1, -1, -1, 0, -2, 2, 2, 1, 1, 2, 0, 0, -2, 0, 1, -2, -1, -1], [0, -2, -1, 3, 1, -1, 1, 0, 3, 4, -1, 0, 1, -2, 1, 0, -2, -2, 1, -1], [5, -4, 3, 1, -2, -4, 2, 2, -2, -1, 2, 1, -3, 4, 4, 3, 2, -3, 0, -1], [-4, 0, 0, 1, -1, 1, 0, -1, -2, -1, 0, -3, -2, 0, -1, -2, -2, 3, -2, 1], [0, -1, 1, 1, 1, 0, 0, -1, 0, 1, 0, 0, 2, -2, 0, 0, -1, 1, 3, 1], [-2, -6, 1, 2, 0, -2, 4, -1, -3, -1, 2, 1, 2, 1, 1, 0, 0, -1, 4, -1], [2, 0, 1, -2, 0, 3, -2, 1, 1, -1, -1, 1, -1, -1, 0, 1, 3, -1, 0, 1], [0, -6, -1, 1, 2, -3, 2, 0, 0, 0, -1, 1, 2, 1, -2, -2, -5, -1, 3, 0], [-1, 5, 0, 1, 3, 1, 1, -1, 4, 5, -2, -1, 5, -3, -2, -4, -1, -1, 2, 0], [-1, -4, 1, 0, 3, 1, 2, -2, 0, 2, -3, 0, 2, 0, 1, 2, -1, 0, 2, -1], [2, 1, -2, -2, -1, 2, -3, 0, -1, 0, 1, -2, 1, 0, -2, 1, 4, 2, -1, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, -3, 1, -2, 2, -2, 2, 3, -2, 0, 1, -2, 1, 1, -1, 1, 0, -2, -2], [4, 1, 2, 1, 0, -2, 1, 1, 0, 3, -2, 1, 0, -1, 2, -2, 0, 0, 0, 2], [1, 7, 2, -2, -5, 1, -4, -1, 1, 2, -2, -3, 2, -3, 1, -3, -1, 2, -2, -4], [0, -3, 2, -1, 1, 0, 1, 1, -1, 0, -1, 0, -1, 1, -2, 0, -2, 0, 0, 2], [0, -1, -3, 4, 6, -3, 3, -2, 4, 4, -5, 1, 6, -1, 1, -1, -4, -1, 3, 1], [-3, -4, 1, 0, 2, 2, -4, -1, 2, -1, 0, -3, 2, -2, -2, 0, -1, 2, 1, 2], [6, -3, 0, -2, -1, -2, 1, 2, -1, -4, 4, 1, -3, 2, -2, -2, -3, -3, 1, 3], [4, 4, 0, 1, -1, 2, -2, 2, 0, 0, 1, -2, 2, 2, -2, 2, 2, 1, -3, -1], [-2, 4, -4, 7, 1, 1, 2, 2, 3, 1, -3, 0, 5, 3, -1, 1, -3, 0, 1, -2], [7, 3, -1, -3, -4, -2, -2, 3, 2, -2, 1, 3, -3, 0, 0, -2, 1, -1, -3, -1], [5, 4, 1, -3, -5, 0, -4, 4, 0, 0, 1, -2, -5, 0, 0, 0, 5, 0, -5, -2], [-2, -2, -1, 6, 6, 2, 4, 0, 0, 6, -4, 0, 7, 1, -1, 0, -2, 0, 4, 0], [-4, 1, 3, -2, -1, 0, -2, -1, -3, -5, 0, -3, -1, -1, -1, 0, 2, 1, 0, 3], [0, -5, 2, -1, 3, 1, 0, 0, -1, -6, 0, 1, -1, 2, -2, 3, -1, -2, 3, 5], [-1, -1, 1, 1, -3, 0, 0, 1, -3, -3, 2, -2, 0, 1, 1, -2, 0, 0, 2, 2], [9, 2, 0, -1, -3, -5, 2, 6, -4, -2, 3, 3, -3, 5, 2, 2, 3, -5, 1, -2], [-1, 8, 2, 0, -7, 2, -5, 3, 0, -3, 1, -2, -3, 1, 1, 4, 5, -1, -3, -5], [-3, 0, 4, -3, -6, -1, -2, -3, -3, -4, 1, -3, -1, 0, 0, -1, 2, 4, -2, -3], [1, -1, -1, 1, 6, -3, 1, -1, 3, 3, 0, 1, 2, -3, 0, -4, -5, -1, 4, 2], [-6, 1, 0, 0, 0, 3, -1, -4, 1, -3, -1, -5, 3, -2, -2, -1, -2, 3, 1, 1], [-4, -2, 3, 0, 5, -1, 2, -5, -1, -1, -2, 0, 2, -1, 0, -1, -1, 1, 0, 1], [0, -8, -1, -1, 5, -4, 4, -1, -4, 0, 4, 3, 2, 4, 1, 0, 0, 1, 3, 3], [-5, -5, -2, 1, 5, 0, 3, -2, -1, 0, 0, -2, 2, 2, -6, 0, -3, 2, 1, 6], [-1, -1, 5, -5, -4, 2, -1, -4, -4, -4, 3, 0, -1, -3, 1, -2, 2, 2, -2, -2], [1, -1, 2, -2, 0, 3, -1, 0, -1, 0, -1, 1, 1, 0, 2, 3, 6, 1, 1, -1], [-4, 8, -1, 1, -6, -1, -2, 2, -1, -3, 1, -2, -2, -1, 2, 0, -1, 0, -1, -2], [11, -2, 2, -2, -4, 0, -1, 3, -2, -3, 0, 1, -4, 3, 3, 0, 3, -1, -3, -1], [0, 5, -2, 1, 1, 1, -1, 3, 1, -1, 0, 0, -3, 1, 1, 3, 3, -2, -1, 2], [-5, -6, 3, 2, 6, 4, 3, -6, 0, 1, -1, 0, 7, -1, -2, 2, -1, 1, 3, 3], [-8, 0, -1, 2, 9, 7, -2, -6, 6, 6, -5, -4, 11, -5, -8, 0, -4, 5, 0, 2], [-5, 2, 5, -2, -2, 2, -3, -4, 0, -3, 1, 0, -3, -3, 0, -2, -1, 1, -1, -1], [0, -6, 1, 4, 1, -2, 4, 1, 0, -2, 0, 4, -1, 2, 6, 6, 0, -4, 3, -3], [-8, 5, 2, -3, -5, 1, -1, -2, -2, -8, 3, -2, -4, -1, 1, 0, 2, 4, -5, -3], [-5, -3, 0, 1, 0, -2, 5, 0, -5, 1, 3, 0, 0, 4, 2, 4, 4, -2, 0, 0], [3, 0, -2, -4, 4, 2, -2, -3, 3, 2, -1, -2, 2, -3, -2, -3, -2, 1, 0, 3], [-4, 2, 3, 0, 1, 4, 0, -1, -1, -1, 1, 0, 1, -3, 1, 3, 5, 4, -2, 0], [5, 2, 1, 0, -1, 0, -1, 4, 4, -4, 0, 3, -3, 0, 0, -3, -6, -2, 0, 2], [-3, 2, 0, 0, 4, 2, 2, -4, 3, 3, -1, 5, 4, -2, 2, 0, -3, -1, 1, -1], [1, -4, 3, -2, -3, -1, 3, 0, -3, -4, 3, -1, 0, 2, -1, -1, -1, -2, 3, 1], [0, -1, -2, 2, 1, 1, 6, 4, -3, 1, 1, 4, -2, 4, 1, 5, 5, -2, 0, -2], [4, -4, 1, 1, 0, -1, 2, 5, 2, 4, -4, 2, -4, 0, 4, -2, -4, -2, 3, 0], [-2, -4, -3, 0, 4, -1, -2, -1, 5, 0, -3, 0, 3, -1, -2, 1, -4, -1, 1, 1], [1, -4, 2, -4, 0, -1, -1, -1, -1, -4, 3, 3, -3, 2, -1, 4, 2, -1, 0, 1], [-5, -1, 2, -2, -4, -1, 0, -1, -1, 0, 1, -2, -5, -1, -1, 1, -1, 2, -2, -2], [1, -7, 5, -6, -2, -1, -3, -5, -3, -4, 4, -6, -2, -2, -1, -5, 0, 7, -1, 1], [11, 4, -5, 0, 0, -3, -3, 2, -2, -1, 1, -2, 1, 4, -4, -2, 0, 0, 0, 0], [0, 0, 4, -4, -1, 1, 0, -2, -4, -2, -2, -1, 2, 2, -1, 0, 2, -1, 2, 1], [0, -8, -2, 2, 0, -1, 4, -3, -4, 2, 2, 0, 3, 4, 1, 2, 2, 4, 0, 1], [-10, 13, -1, -4, -1, 3, -4, -6, 3, 5, 2, -1, 5, -7, -2, -6, 2, 7, -4, -4], [3, 5, -4, 2, -3, -4, 1, 7, 0, 6, -2, -2, -3, 3, 0, -5, -5, -2, -1, 1], [3, 0, 1, 2, -6, -2, 1, 5, -8, -1, 4, -5, -3, 4, 2, 2, 3, 1, -3, -3], [10, -11, 3, -2, 4, -5, 4, -1, -4, -4, 3, 4, 0, 4, -2, -1, -5, -4, 6, 4], [-3, 4, -1, -3, -5, 1, -4, 1, -1, -2, 1, -3, -3, -1, -3, -1, 2, 4, -2, 0], [2, 5, -3, 5, 2, 2, 5, 2, 4, 0, 2, 2, 1, 0, -1, 4, 0, -1, -3, -3], [-6, -5, 7, -3, 1, -2, -1, -2, -3, -4, 2, -3, 2, -1, -3, -4, -4, 2, 4, 4], [10, -4, -6, 5, 6, -3, 5, 4, 0, 8, -1, 3, -2, 0, 0, 1, 0, -3, 4, 1], [3, 6, 0, 0, -7, 0, -4, 1, -2, -3, -2, -4, 1, 3, 0, -2, 2, 2, -2, 0], [5, -9, 4, 0, 0, 0, 2, 2, -1, -3, -3, 1, 0, 3, 1, 4, 1, -3, 0, 1], [5, 13, -1, -2, -1, 1, -3, 2, 3, 4, -3, -1, 1, -1, 0, 0, 0, -3, -2, 0], [9, 3, -4, -2, -5, 1, 1, 6, 0, 0, 2, 6, -7, 4, 4, 0, 5, 0, -8, -4], [0, 11, -4, 5, -1, -4, -3, 4, 4, 3, -2, 1, 0, -4, 1, -2, -3, -3, 3, -3], [10, 1, 1, -3, -5, -4, 1, 5, 1, -4, 5, 8, -6, 1, 3, 2, 0, -4, -2, 0], [0, 4, -9, 0, 3, 1, -2, 2, 0, 5, -1, 1, 5, 2, -2, -4, 0, 2, 1, 2], [0, -10, 2, 0, 12, 4, 0, -3, 5, 1, -5, -1, 2, -3, -4, -2, -8, 2, 6, 6], [2, -1, 1, -1, -2, -4, 1, 3, -3, -3, 5, 0, -2, 0, -1, 1, -3, -1, 3, 0], [0, -17, 2, -4, 11, -3, 6, -6, -1, -3, 3, 4, 2, 2, -1, 1, -5, 0, 6, 6], [3, 3, -4, 0, 2, 6, -4, -1, 5, -2, -3, 1, 0, -1, -1, -1, -1, 1, -1, -1], [0, 7, -7, 3, -2, 0, -1, 4, 1, -1, 2, 3, 1, 6, -1, 2, -1, -5, -1, 1], [7, -1, 4, 0, -1, 1, -1, -2, 2, 3, 2, -1, 1, 1, 2, 6, 7, -3, -1, -2], [8, 7, 6, -2, -15, -3, -4, 7, -6, -6, 2, -4, -9, 2, 3, 0, 6, 0, -4, -3], [-1, -7, 4, 1, -2, -2, 5, -2, 0, 1, 3, 1, -1, 0, 4, 3, -1, -2, -1, -1], [-14, 0, -5, 5, 7, 1, -1, -2, 3, 0, -5, 1, 5, -2, 2, -1, -4, 1, 4, 1], [4, -5, 0, -1, 2, -2, 3, 2, 0, -4, -1, 5, -4, 1, 2, -2, -2, -1, -1, 0], [6, 2, 5, -3, -10, -1, -1, 3, -6, -4, 3, -1, -10, 1, 5, 1, 8, 1, -2, -6], [1, 8, -4, 1, 5, 0, 4, -2, 7, 7, -4, 4, 6, -1, -1, -6, -4, -2, 1, 1], [5, 6, -7, 2, -3, -2, -2, 7, 5, 0, 0, 4, -4, 0, 1, 0, -2, -2, 0, 0], [-2, -7, 2, 0, 4, -1, 1, -2, -3, -5, 3, 2, 0, 0, 1, 3, -1, -5, 4, 4], [-8, 11, -1, 4, 3, 2, -1, -2, -1, 4, -4, -1, 5, -4, 1, -3, -1, 3, -1, 2], [-11, 5, -1, 6, 6, 4, 1, -8, 4, 8, -3, -2, 12, -7, 0, -4, -3, 3, 2, -2], [-3, 1, -2, -5, 4, 4, -1, -1, 4, 0, 3, 4, -5, -5, 0, -1, 3, 3, -4, 2], [5, -15, 3, 3, -2, -6, 5, 1, -10, -1, 3, 0, -8, 7, 4, 2, 3, 3, 0, 0], [3, 0, 6, -6, 1, 3, -4, -3, 2, 1, -1, 1, -5, -3, 2, 0, 3, 3, -5, 4], [13, 6, 8, 3, -4, 1, 0, 1, 3, 1, -3, 0, -1, -5, 4, 1, 4, -3, -3, -3], [2, 10, -5, 6, 3, 2, 2, 5, 4, 4, -2, 4, -1, 0, 0, 6, 2, -8, 3, -3], [11, 5, -1, 3, -7, 3, -2, 8, -6, 0, 1, -3, -7, 4, 1, 3, 6, 0, -5, 0], [-3, -5, 10, -6, -1, -1, -1, -7, -4, -9, 3, -2, -2, 0, 1, 2, 2, 2, 0, -1], [11, 5, 0, 4, -1, -3, 5, 6, 3, 0, 2, 10, -4, 4, 4, 5, 2, -5, -3, -3], [2, -3, -6, 5, 6, 3, 5, -4, 6, 0, 1, 8, 4, 0, 1, 3, -1, 3, -5, -3], [7, -1, 0, 4, -2, 1, 3, -1, 2, 3, -1, 2, 3, 3, -2, 2, 0, -2, -3, -5], [-1, -8, 1, 0, 5, 3, 4, -6, 1, 1, -2, -3, 6, -2, -7, -2, -6, 1, 4, 0], [-6, -3, -6, -3, 1, -2, 0, -4, -1, -3, -1, 0, 2, 2, -4, -2, -3, 4, -1, 0], [-7, 4, -3, 2, 1, 2, -2, 1, 2, 3, -4, -2, 6, 0, -3, -2, 0, 2, 2, 4], [0, 0, 0, 4, -5, -6, 2, 6, -3, -1, 0, 1, -4, 3, 1, 0, -2, -1, 1, 2], [9, 1, 7, 0, -10, -5, 0, 10, -5, -6, 2, -1, -4, 5, 2, 3, 3, -8, 4, -2], [4, -10, -2, 1, 3, -2, 4, 1, -2, -4, 1, 2, -3, 5, 0, 2, -2, -1, 5, 4], [11, 0, 2, 2, -3, 0, 2, 6, -2, -8, 5, 4, -13, 2, 7, 4, 3, -2, 0, 1], [0, 9, -5, 2, 7, 4, -3, -1, 12, 4, -7, 0, 6, -5, -5, -6, -10, 0, 4, 5], [-7, 3, -3, 0, 0, 3, 0, -4, 2, 2, 2, -5, 3, -4, -1, -5, -2, 3, 0, 1], [9, 1, 3, -4, -6, 0, -1, 0, 2, -1, -1, -1, -4, 0, -2, -2, 1, 0, -1, -2], [13, -2, 0, 2, 0, 0, 1, 2, 7, 0, 0, 3, -6, -2, 2, -2, -5, -3, 0, 1], [0, -8, 10, -7, 1, 1, 4, -8, -1, 1, 5, 2, -3, -5, 3, -3, 3, 4, -5, 0], [7, 7, -3, -6, -7, -1, -6, 5, 3, -6, 2, 3, -13, 0, 2, -5, 3, 2, -8, 0], [3, 0, 4, 1, 1, 0, 2, 0, 5, 1, 0, 6, 1, -1, 1, -2, -2, -6, 1, -5], [-10, 2, -7, 5, 5, 1, 0, -5, 5, 6, -2, 4, 7, -1, 2, 0, -3, 1, 2, -3], [4, -4, 1, 0, 2, -5, 4, -2, 2, -1, 6, 6, -2, 2, 2, 4, -2, -6, 1, 0], [11, 7, -7, 2, -7, 1, -3, 4, 3, -2, 1, -2, 0, -2, -2, -2, -1, 1, -2, -6], [1, 8, 5, -1, -7, 1, -4, 4, 0, -3, -2, 1, -8, -1, 5, 2, 5, 0, -4, -7], [2, -5, -2, -1, 8, 1, 5, -3, -6, 7, -1, -1, 2, 1, -3, -4, -2, 5, 2, 5], [-2, -3, 2, -2, 0, 3, 1, 4, -5, 3, 0, 3, -1, 0, 4, 5, 7, -1, -1, 2], [10, 2, -6, 2, -2, 2, 0, 5, -2, -5, 0, 1, -4, 3, 0, 4, 4, -1, -3, -1], [0, 1, 5, 1, -6, -5, 1, 1, -7, -1, 2, 0, -3, 2, 8, 3, 5, 0, 1, -7], [10, -4, 1, 2, -1, -2, 0, 6, -5, -9, 7, 1, -8, 5, 1, 6, 4, -8, 2, 2], [14, 3, 6, 0, -7, 6, 1, -1, -3, -5, 7, 5, -3, 3, 4, 6, 9, -2, -4, -5], [-3, 5, -2, 2, -2, 1, -3, -4, -1, 2, 3, -3, 3, 0, -2, 3, 4, 3, -5, -5], [-2, -13, -3, 0, 1, -1, 6, -2, 1, 1, 6, 3, 1, 1, 0, 0, -2, 1, 2, 0], [-1, -8, 6, 2, 0, -1, 3, -3, -3, -4, 5, -3, -2, 0, 1, -2, 0, 7, 0, -1], [-6, 9, -2, 1, 5, 3, -4, -1, -2, 0, 1, -1, 5, -4, -3, 0, 1, 1, 3, 5], [1, -8, -8, 5, 10, 0, 7, 1, 2, 2, -1, 3, 5, 1, -3, 4, -5, -2, 7, 3], [-5, 11, -3, -4, -3, 3, -6, -1, 7, 4, 0, -3, 4, -7, 0, -6, -1, 4, -6, -5], [-12, 1, 1, -1, 0, 5, -3, -4, 1, 2, -1, -2, -1, -8, -1, 0, 2, 4, -3, -1], [-1, -5, -6, 0, 10, 3, -2, -3, 5, 12, -5, -4, 5, -5, -3, -1, -1, 4, 2, 4], [0, -9, -3, -3, -3, -3, 1, 4, -4, -5, 1, -1, -7, 5, 2, 2, 4, -1, -2, -1], [-6, 1, -2, 5, 5, 8, 3, 0, 4, 8, 0, 0, 1, -1, 0, 2, 2, 7, -7, 2], [18, -6, 6, 3, 2, -1, 5, 6, -7, -6, 1, 3, 1, 4, -1, 3, -1, -4, 4, 6], [-4, -15, -3, 1, 10, -2, 6, -5, 2, 0, -1, 3, 6, 2, -4, -4, -13, -1, 6, 1], [2, -9, 6, -3, 7, 1, -1, -4, 1, 3, -1, -1, 1, -8, 0, -1, 1, 6, 0, 7], [2, -10, 4, 5, 6, -1, 6, -5, 0, 6, -5, 1, 8, 0, 5, 0, -3, 3, 1, 1], [13, 1, 5, -3, -3, -4, 3, 1, -6, -6, 4, 4, -3, 6, 2, 6, 1, -4, -5, -2], [4, 3, -5, -3, -4, 0, -3, -1, 3, 2, -1, 0, 1, 0, 4, -2, 2, 0, -5, -6], [-10, -2, -6, -1, 4, 1, -2, -2, 3, 8, 2, 1, 9, -4, -4, -5, -4, 3, 1, 1], [0, 3, -1, -6, 2, 1, -3, -4, 3, 8, 0, 1, 1, -8, -1, 0, 5, 7, -6, 1], [2, 5, 3, -3, -5, -3, -3, -1, 1, -7, 3, -1, -1, -3, 3, 1, -1, -2, -2, -4], [12, 1, -1, 1, -3, -8, 4, 9, 6, 3, 0, 8, -8, 0, 10, -4, -3, -11, 1, 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6, -5, -12, 2, 4, -3, 1, 10, -12, -5], [6, 7, -3, -8, 6, 2, -4, 2, 8, 9, 0, 8, -4, -2, -6, -2, -3, -5, -2, 2], [1, 4, -1, 3, -5, -3, -2, 0, 7, 7, -6, -6, 2, -2, 1, 0, -2, -6, 5, -3], [11, 8, 5, -6, -19, -6, -10, 6, -5, -16, 1, -9, -14, 5, 1, -4, 2, 2, -6, -2], [-25, -10, 2, -10, 9, 9, -4, -18, -5, -2, 2, -7, 10, -9, -6, -5, 2, 13, 3, 7], [-18, 12, -12, 7, 5, 7, -6, -1, 8, 16, -9, -1, 15, -7, 2, 2, 1, 1, 2, -1], [4, 2, -11, 0, -2, 8, -2, 3, 6, 4, -4, -4, -5, 1, -3, -2, -10, 4, -6, -1], [-4, -6, 1, 6, 0, 1, 3, -4, -3, 4, -2, 1, 7, 6, -2, 2, 5, 3, -1, -5], [-22, 9, 4, -5, -3, 8, -11, -6, 9, 8, -4, -3, 7, -12, -8, -6, -4, 2, -2, 0], [14, -28, 12, -3, -6, -11, 4, 3, -8, -6, 3, 7, -19, 8, 9, 0, 3, -3, -3, -1], [-24, -3, -3, 4, 8, -3, 1, -2, 9, -2, -6, 0, 5, -2, -5, -5, -15, -4, 6, -2], [5, -5, 5, -3, 3, -5, -3, 2, -1, 5, -4, 0, 1, -4, -3, -1, -4, -1, 11, 6], [-8, 0, 11, 11, 9, 2, 4, -4, 4, -1, -9, 1, 14, 0, 1, 2, -6, -10, 12, -1], [3, 2, -1, 0, -5, -3, -8, 5, -2, 13, -6, -6, 0, -2, -1, -6, -1, -3, -1, 3], [12, 4, 6, -13, -7, -3, -7, 9, 0, 3, 1, 1, -16, 1, 1, 3, 1, -10, 2, 4], [-5, 25, -9, -6, -8, 5, -11, 0, 1, -2, 3, -5, -7, -10, -3, -16, 2, 17, -13, 2], [6, -17, 0, -4, 3, 7, 5, -9, -8, -12, 5, -3, 6, 5, -8, -3, 0, 13, -1, 7], [10, -11, 5, 3, 0, -1, 5, 6, -5, -2, 1, 8, 1, 4, 7, 4, 2, -12, 11, 5], [2, -13, -10, 4, 22, -6, 15, -8, 3, 11, -4, 0, 11, 8, -8, -5, -19, 2, 12, 7], [18, -18, 5, 11, -3, 2, 10, 7, -8, 1, 0, 8, -4, 9, 5, 8, 6, -2, -2, -3], [-3, -1, 3, -2, 7, 5, -2, -7, 13, 8, -8, 1, 18, -5, -8, -5, -4, -5, 6, -2], [5, -5, -3, -10, 7, 5, 0, -5, 9, 6, 4, 3, -4, -7, 0, -5, 0, 7, -6, 4], [30, -14, 11, -13, -12, -5, -6, 6, -13, -12, 5, -1, -19, 7, -2, -3, 5, -1, -2, 1], [16, 15, 10, -15, -18, 0, -7, 0, -5, -18, 7, 0, -16, 0, 4, -4, 12, 10, -18, -4], [-17, -4, -5, 2, -2, -9, 5, 1, 2, 4, 5, 1, -9, 1, 4, 2, -4, -7, 5, -3], [-7, -8, 3, -2, 5, -3, 3, -4, 7, -6, -1, 1, -5, 6, -1, 0, -4, 1, -3, 2], [-15, -9, 3, 0, 9, 4, 7, -8, -14, 0, 8, -3, 9, 1, -8, 2, 5, 7, 2, 10], [-24, -20, 3, -3, 14, 1, 6, -14, -8, 3, -8, -11, 12, 3, -9, -3, -6, 11, 5, 13], [3, 5, 10, 6, -3, -4, 2, 14, -2, -4, 3, 7, -9, 6, 12, 10, 6, -12, 1, -1], [2, 2, 16, -7, -20, -1, -2, 7, -8, -15, 5, 0, -17, 0, 7, 0, 8, -3, -8, -7], [13, -19, 13, 2, -4, -5, 5, 6, -6, 5, -2, -5, -5, 10, 5, 4, 3, -1, 1, -3], [-7, -8, -15, 4, 22, -5, 6, -4, 12, 14, -2, 10, 7, -6, -6, -8, -12, -2, 7, 6], [5, -5, -10, 4, -1, -1, 1, 1, 1, 7, 3, -2, 8, -2, -2, 1, 2, 0, -4, -3], [17, 0, 1, 6, -5, -5, 6, 12, 2, 2, -3, 4, -14, -2, 9, 0, -1, -6, 4, -1], [8, 3, -4, 2, 4, -7, 13, 4, 5, 13, 3, 15, 1, 0, 6, 7, 6, -7, 1, -7], [8, -1, 10, -6, -14, 5, -4, 5, -12, -16, 11, -4, -17, 7, 5, 3, 15, 10, -12, -2], [12, -6, 0, -8, 5, -1, 0, -6, 8, -7, -1, 5, 2, 0, -8, -7, -12, -4, 4, 10], [-4, 5, -7, 5, -5, -4, -5, 6, 2, 1, 2, 5, -6, 1, 3, 6, 2, -12, 2, 0], [-7, -10, 14, -8, -8, -10, 4, -4, -15, -10, 2, -2, 2, 6, 6, 2, 8, -8, 4, 0], [-2, -10, 5, 5, -2, 2, 2, -3, 7, -7, -1, 4, -9, 1, 3, -4, -5, 6, -3, -1], [10, 13, -6, 2, 11, 13, 0, -10, 16, 10, -5, 8, 10, -12, 3, 1, 1, 2, -4, -2], [1, 5, 11, -7, -17, -8, -8, 13, -7, -13, 8, 0, -20, 7, 6, -2, 6, -6, -5, -5], [7, -6, -7, -5, 0, -3, 7, 2, -7, 2, 10, 5, -8, 8, 3, 0, 4, 6, -4, -3], [-12, -14, -8, 3, 6, -2, 7, -4, 3, 12, 1, 6, 6, -6, 4, -4, -4, -4, 6, -3], [-25, 12, -11, -1, 6, 0, -14, 1, 9, 9, -7, -13, 7, -12, -12, -11, -12, 2, 9, 3], [-11, 6, 10, -4, 0, 4, -6, -1, -1, 0, 1, -9, 12, -5, -6, -2, 6, 6, 0, 0], [-3, -9, 1, -4, 7, -8, -1, -9, -5, -12, -5, -10, 10, 6, -4, 1, -4, -2, 15, 9], [-5, 7, -5, -7, -6, 3, -8, -8, -8, -4, 2, -7, 2, -8, -3, -10, 4, 9, -5, -1], [-10, 23, -1, -8, -4, 8, -12, -6, 6, -9, -4, -6, 6, -4, -12, -9, -2, 2, -8, 3], [7, -12, 2, 11, 23, 6, 11, -10, 21, 20, -14, 6, 15, -3, -3, 4, -11, -8, 8, 2], [20, -2, -1, 9, 1, -5, 9, 2, 0, 5, -6, 6, -1, 3, -2, 3, -5, -10, 2, 2], [-7, -6, 4, 1, 2, 7, -4, -6, -7, -14, -3, -12, 10, 0, -2, -4, 0, 9, 0, 1], [-14, 28, -7, 7, -8, 10, -8, 3, 8, 8, -3, -2, 13, -12, -3, 2, 0, 3, -7, -11], [-5, 21, -16, 9, 5, 3, 6, 5, 10, 12, 2, 11, 3, 2, 5, 0, 2, -5, 0, -8], [8, -10, -7, -2, -7, -2, 1, 0, -1, -1, -3, 2, -5, 4, -2, -7, -3, 3, -5, -5], [0, 6, 5, -10, -10, 0, -3, 3, -1, -9, 4, -3, -11, 6, 0, -2, 3, 3, -13, -3], [5, -7, 5, -1, -4, 4, 5, 9, -13, 0, 4, 0, -4, 6, 6, 6, 11, 2, 2, 5], [14, -13, 5, 5, 11, 2, 4, 0, 6, 3, -3, 0, 10, 2, -2, 5, -2, -5, 3, -2], [-4, -16, 9, -2, 0, -8, 0, 3, -9, -13, 0, -1, -7, 7, 5, 6, -2, -11, 4, -1], [-8, -5, -4, 19, 19, 7, 9, -7, 1, 16, -17, -8, 15, -1, -4, 2, -8, 8, 7, 3], [7, -4, 5, 3, -11, -5, 7, 4, -4, 0, 0, -6, 1, 5, 4, -1, -3, 0, -4, -4], [1, 4, -2, 6, -9, -10, 6, 11, -6, 6, 0, 2, -8, 2, 13, 0, 3, -3, 0, 1], [2, -24, 8, -3, 3, -3, 6, -6, -5, -14, 4, 4, -3, -2, 5, -3, 0, -2, 0, -1], [-21, 14, -2, 6, 10, 1, -8, -1, 4, 6, -10, -3, 10, -4, -8, 0, -5, 0, 6, 2], [9, 8, 1, 8, -1, 6, -5, 6, 9, 16, -6, -5, 2, -9, 0, -6, 1, 5, -9, -1], [4, 3, 9, 5, -11, 3, 1, 4, -10, -5, -1, -3, -2, 1, 0, 2, 4, 3, -10, -3], [-10, 8, -13, 3, 3, 4, -2, -6, 7, 15, -7, -5, 9, -6, -1, -3, 1, 9, -1, -2], [-10, -18, 14, -1, 2, -10, 6, -6, -9, -7, 3, 3, 3, -1, 0, -3, -1, -3, 9, -1], [-2, 20, 4, -1, -15, 5, -5, 6, 8, -3, 10, 8, -10, -8, 7, -3, 7, 0, -12, -16], [24, -2, 2, -6, -3, -4, -2, 0, 8, 1, -1, 4, -13, 1, 2, -2, -6, -1, -5, 4], [32, 6, -1, 0, -3, -2, 9, 3, 3, -5, 3, 16, -4, 8, 6, 4, -5, -11, -5, -1], [0, -5, 1, 8, -3, 4, 3, 6, -7, 1, 1, -7, -7, 4, 5, -5, 0, 5, 2, -3], [-7, 20, -2, -1, 5, 2, -5, 4, 12, 11, -6, 1, 10, -7, -7, -12, -5, 3, -4, 2], [9, 11, -4, 14, 11, -2, 0, 4, 2, -2, -9, -1, 19, 4, -4, 7, -7, -15, 17, 0], [15, -2, 3, 3, -3, -9, 7, 10, -9, 6, 0, 0, -1, 8, -1, 2, -1, -8, 6, 4], [0, 9, -6, -6, -15, -5, -9, 0, 1, -11, 4, -1, -9, -4, 3, -1, 1, 3, -8, -6], [32, -8, -7, 0, -5, -6, 5, 5, -5, 9, 3, 2, 2, 6, 0, -2, 3, -1, -3, -5], [14, -10, 8, 0, 5, -7, 12, -5, -7, -6, -3, -4, -1, 3, 1, 3, -11, -2, 9, 4], [-25, -8, -3, -2, 2, -1, 3, 0, -8, -11, 5, 4, 5, 4, 2, 8, 4, -4, 8, 4], [31, 10, 14, -1, -24, -6, 2, 17, -15, -14, 8, 1, -18, 12, 15, 5, 8, -11, -6, -10], [4, -2, 3, 12, -2, -2, -2, -2, 15, 5, -8, 0, 3, -5, 7, -2, -10, -2, 6, -4], [-5, -1, -1, -15, -5, -4, -7, -5, -2, -9, 6, -1, -3, -5, -5, -8, -1, 1, -3, 5], [24, 17, 2, -1, 7, 6, -4, 4, 16, -2, -1, 5, 8, -6, -5, 2, 1, -13, 2, 3], [-10, -2, 1, -8, 0, 4, 3, -3, -3, -3, 0, -5, 7, -2, -2, -6, 1, 13, -1, 1], [15, 12, -2, -7, -9, 10, -4, 2, -4, 1, 2, -8, -8, -2, 1, 6, 15, 3, -8, -3], [18, -3, -2, 5, 9, -4, 4, -2, 12, 8, -3, 3, 16, -4, 6, 2, -7, -15, 11, -4], [21, 0, 1, 3, -7, 5, 1, -2, -4, -7, -6, 0, -1, 6, 8, 9, 7, 2, -3, -2], [16, 3, -3, -1, -4, -6, -3, 8, 4, 1, 6, 5, -1, -1, 5, 0, 0, -10, 2, 3], [23, -22, 5, -3, 0, -6, 5, -1, 2, -9, 7, 10, -7, 3, 2, 8, -3, -13, 10, -1], [11, -4, -1, 9, 17, -5, 4, 6, 8, -2, -6, 4, 2, 6, -5, 2, -15, -9, 9, 9], [13, -10, 2, -9, -11, -8, -2, 7, 3, -6, 6, 2, -16, -1, 6, 0, 3, 3, -9, 3], [18, 8, 13, -14, -11, 0, -6, 7, -11, -5, 6, 7, -19, -1, 10, 8, 22, -5, -7, -1], [-20, -4, -9, 4, 18, -1, 3, -6, 13, 0, -2, 9, 11, 1, -4, -2, -9, -9, 7, -1], [6, -6, -3, -1, 15, -2, 3, -3, 3, 0, 1, 6, -2, -4, -8, 0, -10, -4, 11, 10], [4, 17, -12, 5, 1, 4, -6, 7, 15, 8, -8, -4, -1, -5, 1, 6, -1, -5, -1, -1], [-4, 2, 0, -7, -3, 3, 0, 1, -1, -12, 6, 1, 4, 1, -4, -1, 0, -3, -1, 1], [-9, -3, -12, 4, 3, 2, 4, -8, 3, -1, -3, -1, 6, 0, -4, 2, -7, 3, 1, 5], [14, 6, -10, 9, 8, -13, -3, 6, 3, 12, -5, 3, 3, 4, -1, -5, -11, -6, 6, 6], [15, -12, 0, 0, 1, -4, -1, -3, 6, 2, 4, 3, -3, -1, -1, 2, 1, 7, -10, -2], [9, 10, 3, -5, -4, 4, -9, -2, 8, 4, -5, -3, -3, -16, 0, -2, 3, -6, 1, -6], [-11, 3, -7, 4, 9, 7, -7, -5, 3, 6, -6, -12, 21, 0, -7, 7, -2, -5, 9, 8], [-9, 21, -1, 7, 1, 0, -1, 0, 7, 13, -13, -5, 6, -10, -2, 1, -7, -4, 1, -9], [3, 15, -4, 7, -5, 4, -1, 6, -1, -1, 0, -5, -5, 4, 2, 8, -2, -4, 2, 4], [-18, 20, -1, -2, -11, 2, -6, 3, 13, 0, 5, 3, 1, -10, 9, -3, 3, -1, -1, -8], [-8, 12, -3, -16, -6, 6, -9, -9, -6, 1, 5, -6, -4, -11, -5, -3, 9, 13, -11, -4], [11, -28, 1, 4, 1, -8, 7, 1, -4, -11, 6, 6, -5, 9, -4, 11, -4, -9, 7, 7], [6, -17, -12, -1, -3, -10, 8, -4, -14, -5, 3, 1, -7, 10, 5, -4, -5, 11, -3, 7], [17, -6, 2, 6, -4, -12, 10, 8, -9, 1, -3, 11, -6, 12, 14, -2, -3, -13, 9, -3], [12, -12, 0, 7, 5, 6, 15, -1, 4, -4, 6, 11, -2, 1, 10, 6, -2, -4, -1, -2]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_2151_a_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_2151_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_2151_2_a_k(:prec:=20)
    chi := MakeCharacter_2151_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_2151_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_2151_2_a_k( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_2151_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![1, -56, 640, -1184, -4844, 9108, 10479, -21252, -9429, 23404, 3356, -14020, 229, 4804, -540, -936, 164, 96, -21, -4, 1]>,<5,R![-78784, 446336, -539584, -1119728, 2771933, -315580, -3183445, 1814628, 1367627, -1358932, -125829, 434624, -72922, -62284, 22471, 2548, -2271, 212, 67, -16, 1]>],Snew);
    return Vf;
end function;