
// Make newform 6020.2.a.k in Magma, downloaded from the LMFDB on 23 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_6020_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_6020_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_6020_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 := [-4, 105, 20, -1729, 231, 2384, -189, -1201, 37, 268, -2, -27, 0, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-61265760, -483490486, 2815717179, 274187663, -3993847798, 64922637, 1977473357, -29216373, -430739109, 2329850, 42386523, -33962, -1537654], [-407264550, 572663033, 5777558205, -1213473653, -7864942625, 586775704, 3942799622, -53662673, -883869052, -6078641, 90038475, 657965, -3379072], [532793576, 1396689219, -6983810052, -950176204, 9057266266, 327739797, -4449167492, -115849143, 981840509, 19594321, -98400044, -1032220, 3634961], [-56489344, -1743391215, -5196373544, 4641122190, 8198411856, -3114270009, -4477485048, 738896929, 1045858413, -71287003, -108151396, 2428772, 4068317], [-56900248, -2683469426, -3259290077, 5618110765, 6955695027, -3559234085, -4359230160, 830625394, 1081452331, -79451502, -114991907, 2682991, 4383099], [-238977264, 617582318, 3550774102, -998832979, -4827397410, 489147473, 2478773524, -68621002, -567105876, 796160, 58451359, 200934, -2205646], [-115635328, 187215299, 3575600842, 270284028, -5160860541, -452829515, 2625107725, 184521935, -591766125, -27283586, 60374111, 1297400, -2264279], [-20700834, 863773441, -5897264220, -125618964, 9624753738, -125035509, -5328390224, -52366611, 1264513359, 20110413, -133195254, -1334884, 5099437], [238318094, -1616237963, -10622872065, 5346609659, 14426296339, -3705855478, -7046841160, 903358959, 1526692324, -89978475, -149767663, 3173615, 5423260], [-259624920, 1467258677, 9852280555, -2579378641, -13834451127, 1165740178, 6888121624, -135571279, -1520659172, -3476691, 152122251, 759047, -5608450]];
    Rf_basisdens := [1, 1, 1, 42614911, 85229822, 85229822, 85229822, 85229822, 42614911, 42614911, 85229822, 85229822, 85229822];
    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_6020_a();"
function MakeCharacter_6020_a()
    N := 6020;
    order := 1;
    char_gens := [3011, 4817, 4301, 1121];
    v := [1, 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_6020_a_Hecke(Kf)
    return MakeCharacter_6020_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, 1, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 1, 0, 1, 0, -1, -1, 0, 0, 0, 0, 0, 0], [1, 1, 1, -1, -1, 0, 0, 0, 0, -1, 0, 0, 1], [0, 1, 0, 1, 1, -1, -1, -1, -1, 1, 1, 0, -1], [1, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 1, 1], [1, 0, 0, 0, -1, 1, 0, 1, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 1, -1, -1, 0, 0, 0, 0, 1, 0], [2, 1, 0, 0, -1, -1, 0, 0, 1, -1, -1, 0, 1], [-1, 0, 0, 1, -1, 1, 0, 1, 0, 0, 0, 0, -1], [1, 2, -1, 1, 0, 0, 1, 0, 0, -1, 1, 0, 0], [1, -1, 0, 1, 2, 0, -1, 0, 0, 1, 1, 0, 0], [1, 2, 1, 0, 0, -1, 0, 0, 0, -1, 0, -1, 1], [3, 0, 1, 0, 1, 0, 0, -1, -1, 1, 1, -1, -1], [-1, 2, -1, -2, -2, 0, 0, 0, 0, -1, -2, 1, 1], [1, -2, -1, 1, 1, 1, -1, 0, 0, 1, 0, 0, -1], [1, 1, 0, -3, -2, 0, 1, 0, 0, -1, -1, 0, 0], [4, -1, 0, 0, 0, 0, 1, 0, -1, 1, -1, -1, 0], [2, 1, 0, 0, 1, -1, -2, 0, -1, 1, -1, 2, 1], [-1, 0, -1, -2, -1, 2, 1, 0, 0, 1, 1, -1, 0], [0, 1, 1, 2, -1, 1, 0, -1, 0, 0, 0, -1, -1], [1, -2, -1, 2, 2, -1, 0, -1, 0, 0, 0, -1, -2], [5, 1, 0, 0, 0, -1, 0, -1, 0, -1, 0, 1, 1], [1, 0, 3, -1, -1, 0, 0, 0, 0, 0, 0, -2, 1], [0, 2, -1, -1, 1, 0, 0, 1, 0, -1, 1, 0, 0], [4, -1, 1, -1, -1, 0, 3, -1, 2, -2, -2, -1, 0], [0, 2, -2, 1, 0, -1, -2, 0, -3, 1, 1, 1, 1], [2, 2, -2, 2, 1, -2, 0, -1, 0, 1, 1, 0, 0], [-2, -2, 1, -1, -1, 1, -1, 0, 0, 1, 1, 0, -1], [1, 0, 1, -1, -2, -1, -2, 2, -2, 1, -1, 0, 0], [3, 1, -1, 0, -1, -1, 1, 1, 2, -1, -1, 1, 1], [1, 0, -2, 0, -1, -1, -2, 1, -1, 0, 0, 2, 0], [4, 3, 0, -2, -1, -1, -1, 1, 0, 0, -1, 0, 2], [-1, -2, -1, 2, 2, 0, 0, 0, 1, -1, 0, 1, 1], [2, 1, -1, -3, 0, 1, 0, -1, -1, 1, 0, 0, -1], [-1, 1, -1, 0, 0, 2, 0, -1, 0, -1, 0, 1, 0], [7, 0, 3, -1, -3, -1, 0, 1, 0, 1, -2, -2, 0], [4, -2, 1, 0, -1, -1, 1, 0, 1, 0, -2, -1, -2], [-1, 2, -1, 0, 1, 0, -1, 0, -1, -2, 1, 1, 2], [-2, -1, 1, -2, 1, 0, -2, 0, -3, 1, 0, 1, 0], [2, 0, -2, -2, -1, 1, 1, 0, -1, -1, 2, -1, 0], [1, 1, -1, 1, 3, 1, 1, -1, 0, 0, 1, 1, -1], [-2, -2, -1, 2, 1, 1, 0, -1, 1, 0, 2, -1, -1], [4, 2, 0, -1, -1, 2, 1, 0, 2, -1, -2, -1, 0], [1, -5, 1, -2, 0, -1, 1, 0, 3, 0, 0, -1, -1], [4, 2, -1, 0, 3, -2, 1, -1, 1, 0, 0, 1, 1], [3, 0, -1, 2, 0, -1, 2, 0, 2, -1, 0, 1, 1], [1, 0, -2, 4, 4, -1, -2, -2, -2, 1, 5, 0, 0], [3, 0, 3, -3, -3, 1, 0, -1, 0, 1, 0, -2, 0], [0, -2, 1, -3, -3, 2, 0, 1, 0, -1, -1, 0, 0], [-3, -2, -1, 1, 1, 0, 2, 1, 1, 1, 0, 0, 0], [3, -3, -1, 2, 1, 0, 0, 0, -1, 1, 2, -2, 0], [0, 1, 1, 4, 1, -1, 0, -2, 1, 1, 1, -2, -1], [5, -1, 0, 2, 1, 2, 2, 0, 0, 0, 2, -2, -3], [8, -2, -2, 2, 2, -1, 1, -1, 0, 0, 0, 0, -3], [2, -3, 0, 2, 1, -1, 0, -2, 0, 0, -1, 0, -1], [-3, 5, 3, -3, -3, 1, 1, -1, 0, -1, 0, -4, 0], [5, 4, -2, 2, -1, -1, -2, 1, -1, 0, 2, 2, 2], [3, -6, 0, 4, 1, -1, -1, 2, 0, 2, 2, -2, -3], [2, -3, 1, -1, -3, 2, 3, 1, 0, 1, -4, -1, -2], [3, -1, -3, -4, 1, 1, 1, 1, 2, -2, -1, 1, 1], [5, 0, 4, -3, -2, -2, 1, -1, 1, -3, 0, 1, 2], [5, 1, 2, -2, 1, -1, 0, -1, -1, 0, 0, -2, 2], [4, 1, 2, 2, -4, 1, 3, 2, 2, 1, -2, -2, -2], [3, 2, 2, 4, 1, -1, -1, 0, -2, 2, 2, -4, 1], [-9, 1, 4, -3, -5, 1, 0, 2, 1, -2, -1, -3, 0], [7, -1, 0, 0, -2, 1, 0, 3, 2, -3, -3, 0, 1], [3, -3, 2, -1, -1, -1, 1, -1, -2, 0, -1, 1, 1], [-5, -3, -4, 0, 0, 1, -1, 0, -1, 2, -2, 3, 1], [0, -4, -1, -2, -2, 1, -2, 2, -2, 0, -1, 1, 3], [-3, -1, 0, -1, 0, -2, 0, -1, 0, 1, 1, -4, 0], [-2, -2, -3, -1, 1, 1, -2, 2, -1, 2, 1, 0, 1], [0, -5, 1, -1, -2, 0, 3, 0, 3, -2, 1, -1, -1], [2, -6, -2, 2, 2, 0, -1, -1, 0, 1, 0, 4, -3], [-1, 1, 2, 2, -1, 0, 2, 0, 0, 1, 0, -2, 1], [-5, -2, -2, 2, 2, 1, 3, 1, 3, -1, -1, 0, 1], [8, -5, 1, -2, 0, 2, -2, 1, -2, 1, -1, -1, 0], [-2, -1, -2, -2, 1, -2, -1, 1, -2, 1, -4, 3, -2], [6, -3, 0, 0, 2, -2, -2, -2, -3, 3, 0, 0, -2], [0, -7, -1, -3, 1, 3, -1, -1, 0, 2, 1, 2, 0], [5, -3, 0, -2, -1, 3, 1, -1, 4, -4, 0, 0, 2], [3, -2, -2, 0, 4, -3, 1, -1, 0, -1, 1, 2, -1], [5, -8, -2, 2, 0, 3, 1, 1, 0, 1, 1, 2, 1], [-6, -2, -2, 1, 1, 1, 2, 1, 0, -1, 2, 1, -1], [2, -1, 0, 1, 0, -1, -1, 2, 1, 2, 1, -3, -1], [-2, -6, -4, -1, 0, 1, 2, 0, 1, 0, 3, 3, -1], [-7, 1, 0, -4, -5, 1, 0, 2, -1, -4, -2, 0, 1], [1, 3, 0, -1, -2, 0, -2, 1, -2, 3, -3, 0, 2], [2, -1, 4, 0, -7, 2, 1, 2, -2, 0, -1, -4, 1], [2, -1, 2, 0, -1, -1, 3, 1, -1, -1, 1, -2, 0], [-6, 5, -3, 3, 0, 4, 2, 0, 3, -1, 0, 0, -2], [-1, 4, 1, -1, -2, -4, -1, 0, -2, -2, -1, 0, 4], [8, 3, 2, -3, -3, -1, -2, 0, -1, -1, 1, 2, 1], [-2, 4, -2, 0, -4, 1, 1, 1, -2, 0, -3, 1, 2], [2, -3, 2, -6, -3, 1, 3, -1, -3, -1, -1, -2, 0], [-2, 2, 2, 5, 0, -3, -3, -3, 1, 2, 1, 1, 0], [3, -1, -5, 2, 2, -2, 0, -2, 2, 1, 2, 3, -1], [3, 4, -2, 2, 7, -2, -2, -3, -1, 0, 2, 2, -2], [-6, 4, -2, 5, 4, -1, -2, -2, 2, -1, 3, 1, 1], [3, -4, 2, -8, -6, 2, 1, 0, -2, 2, -1, -4, 0], [1, 2, 0, 0, 4, -1, 0, -2, -3, 1, -1, -2, 0], [-2, -2, -1, -1, -3, 0, 2, 1, 3, -5, -1, 0, 0], [1, 0, -3, -2, 0, -1, -2, 0, 3, 1, -1, 2, 2], [-4, 2, 4, 4, -6, 1, 4, 2, 3, 0, -1, -5, -1], [8, -8, -5, -1, 2, 0, 0, 0, 0, 0, 0, 4, -2], [5, -1, -4, -4, 4, 0, -2, -1, 1, 0, -1, 2, -1], [4, 4, 6, -1, 3, -2, -2, -3, -4, 1, 4, -5, -1], [-7, 3, 2, -1, -3, 3, 3, -1, -1, 0, -1, -1, 1], [-9, -2, 7, 3, -4, -1, 0, 0, 0, 3, -1, -4, -2], [5, -5, -1, -3, 0, -2, 0, -1, 0, -3, 1, 2, 1], [-3, 10, 1, -4, 2, -3, -2, -4, -3, 2, 1, 0, 2], [5, 2, 2, 3, -1, -1, 2, 1, 0, 0, 1, -5, 1], [4, -8, -1, 0, 1, 1, 3, 0, 4, 0, 2, -1, -2], [-1, 4, -2, -2, 0, -1, 0, 0, 0, -1, 1, -2, 0], [10, -1, 0, -4, -2, -2, 1, 0, -2, -2, -5, -1, 0], [2, 1, 0, -3, -1, -2, -3, -1, -1, 0, -4, 3, 5], [0, -5, -3, 1, 4, 2, 2, 2, -5, 3, 4, 0, -4], [-6, 0, -1, -2, 3, 1, 0, -1, -5, 3, 0, 1, -3], [-11, 1, 0, 1, 0, -4, -6, -1, -1, 3, -3, 4, 3], [6, -6, -2, 2, 2, -1, -1, -1, -1, 0, 1, 1, -2], [-4, 2, 4, 2, -5, 1, 0, 3, -3, 0, -3, -2, 0], [-9, -4, -4, 2, 2, 2, 2, 1, 0, 1, -3, 2, 1], [-2, 6, 0, -4, -4, 4, 0, 0, 1, -2, -4, 0, 2], [-1, 0, 1, -2, -4, 1, -2, 2, -3, 0, -3, -4, 3], [3, 2, -3, 5, -2, 1, -3, -1, -2, 0, 3, 0, -1], [1, -1, -2, 4, 5, 1, -1, -3, -3, 1, 2, 2, -4], [-2, 0, -3, 1, -2, -2, 0, 2, 6, -3, -2, 2, 0], [-3, 3, 3, -1, -2, -1, -1, -1, -5, 1, 1, -2, -1], [9, 2, 1, 7, 5, -1, -1, 0, 0, 2, 2, -4, -1], [-8, 2, 1, -3, -3, 4, 6, 1, 1, -2, 1, -2, 2], [-14, 2, -2, -1, -3, 3, 2, 1, 2, -2, -4, -1, 1], [1, 1, 6, 3, 0, -2, -1, -2, -4, -1, 1, 0, 1], [-6, -4, 2, -3, -5, 2, 1, 0, -2, 1, -1, 0, 1], [-3, -2, 7, -2, -1, 0, 0, -1, 3, 2, -1, -1, -1], [-5, 7, 4, -6, -3, 1, 2, 0, 0, -5, -1, -3, 0], [9, 0, 0, -2, 2, -2, 0, 0, -2, -1, -4, 1, 1], [-4, 0, -3, 4, 2, 0, -3, 3, 3, 2, -2, -4, -1], [-6, -2, -3, -1, -4, 1, -1, 3, 2, -1, -3, 3, 0], [3, -2, -1, 1, 2, 1, 1, -1, -2, -2, 3, 0, 1], [11, -4, -1, 8, 3, -1, 0, -3, 2, 3, 0, -2, -3], [-3, 1, 4, 7, 0, 0, 1, 2, 3, 2, -1, -2, -1], [-2, -2, 4, -1, 0, 1, -2, -2, 1, 1, 1, 1, -3], [6, -4, 0, -8, 3, 0, 2, -1, 0, -1, -1, -2, 0], [9, 1, 5, -2, 0, -3, -2, -3, 2, 3, 4, -3, 0], [-4, 8, 0, -4, 1, -2, -2, -3, 0, -3, 1, 2, 4], [-3, -7, 2, -2, -2, 1, 1, -1, -1, 2, -5, -2, 1], [0, 3, 9, 3, 3, -2, -1, -2, -3, -1, 3, -4, 1], [-2, -2, -2, 4, 5, -1, 2, -2, 0, 3, -1, 0, -5], [-14, -2, 0, -5, -1, 0, -2, -1, 0, -2, -1, -2, 3], [4, 2, 2, -6, -1, 4, 4, 3, -3, -2, -1, 0, 0], [-7, 2, 1, -2, 0, 3, 2, -1, -1, -2, 2, 3, 4], [-2, 0, -3, -6, 3, 3, 1, 0, -2, 4, 2, 1, -2], [-17, 3, -1, 3, 0, 0, -3, 0, -5, 3, 1, -2, -4], [-1, 4, -2, 0, -3, -3, -5, 2, -2, 0, -2, 8, 3], [0, 6, -1, 3, -3, -3, -1, 2, -1, -2, -1, 0, -1], [-6, 0, 1, 1, 1, -1, 2, -1, 4, 4, 2, -3, -3], [0, 2, 3, -4, -1, -3, 2, -1, 1, 0, 2, -1, 1], [-10, 0, -5, 6, -2, 1, 0, 0, -1, -3, 3, 3, -3], [-2, 7, 0, 2, 1, 2, 4, -1, 2, -1, 3, 0, 0], [-6, 6, 5, 5, -2, -5, -1, 1, -3, -2, -1, 1, 3], [-13, 4, -3, 0, -1, 0, 0, -1, -2, 0, -1, 3, -5], [-2, 3, 4, -5, -6, 2, 0, 1, 1, 0, -3, 1, 2], [-8, -2, -2, -2, 0, 5, 1, 3, -3, 4, 4, -2, -3], [-6, 1, 3, -5, -5, -2, 1, 1, -2, -3, -4, -3, 0], [-1, 2, 4, 1, 1, 2, 1, 2, 3, 0, 1, 3, 2], [-6, 0, 2, 2, -1, -3, 1, 0, 0, -4, -6, -1, 1], [9, 1, 3, -2, 2, 5, -1, 0, -6, 5, 0, -1, 1], [-12, 0, -2, -5, -5, 1, 1, 0, -1, -3, -2, 5, 0], [0, 7, 0, 2, -4, -1, 2, -1, 1, -1, 0, -2, -3], [-5, -3, 1, 1, -6, 0, -1, 2, -2, 1, -5, 2, 0], [-18, 0, -1, 0, 2, 3, -3, 3, -2, 0, 3, 3, 2], [-4, 9, -2, 0, -3, 3, -1, 3, -5, 0, -1, 2, 2], [-3, -1, 3, -2, 1, 0, -2, 2, -2, 3, -2, 4, 1], [2, 7, 3, -4, -5, -2, -5, 5, -2, 1, -2, 3, 3], [-4, -1, 2, -1, 2, -1, 0, -1, -3, 3, 3, 3, 2], [7, 6, -2, 1, 3, -5, 0, 1, 4, -2, -1, -1, -1], [-4, -3, -6, -6, 3, 3, 0, 2, -1, 0, -1, 6, -3], [-3, -12, 1, -1, 3, -1, -1, 0, 0, 2, -2, -4, 1], [-14, -3, 3, 0, -6, -1, 3, 2, 6, -1, -6, 0, 4], [0, -2, -1, -1, 2, -6, -6, 2, 0, 3, 0, 2, 4], [-3, 6, -5, -10, -3, 1, 2, 3, -2, -1, -2, 6, 2], [13, -1, -8, 6, 9, 1, -3, -2, -2, 0, 4, 6, 1], [-17, 0, 4, -4, -6, 1, 3, 3, 4, -7, -7, -2, 3], [7, 10, 2, -1, -4, -3, 2, 0, 0, 0, -2, -3, -1], [6, -1, -5, 11, 8, -1, 0, -1, 3, -1, 6, 0, -3], [7, -1, -8, 3, 5, 3, 2, 0, 1, 1, 3, 3, -4], [-1, 11, 6, -1, -7, -2, 5, 2, -4, -2, 1, -5, 2], [-7, 6, 1, 4, -6, 2, 5, -1, -1, -2, -2, -5, -4], [-7, 7, 3, -1, -2, -4, 1, 0, -2, -1, -3, -2, -2], [-7, -2, 5, -3, -6, -2, 3, -2, 3, -2, -7, -6, 4], [18, 9, 4, -3, -4, 2, 3, 2, 2, -5, 3, -3, 1], [2, 2, -4, 1, 6, 0, 4, -2, 1, -4, 1, 5, -1], [-7, 6, 4, 1, -4, -4, 0, -2, 2, -5, 0, -5, 1], [-2, -9, -2, 3, 8, 1, -1, -4, 6, -1, 2, 6, 0], [-10, 3, 1, -1, 2, 1, -4, -1, -5, -1, 0, 4, 3], [-1, -6, -6, 4, 10, -1, -5, 1, 2, 3, 3, 2, -1], [-6, -10, 2, 7, 2, -3, -4, 0, -3, 9, 1, -3, -7], [5, 5, 3, 1, -6, 4, -1, 2, -3, 3, 3, -2, 4], [-7, -5, 1, 5, 9, -6, -5, -3, -2, -1, 2, 8, 0], [-4, -1, 2, 4, 4, 1, -3, -2, 3, 3, 6, 2, 4], [4, 0, 1, 1, -1, -1, -1, -3, 0, 3, -3, 2, -2], [-15, 0, -7, -2, -3, 0, -3, 4, 1, 1, -1, -1, 4], [8, -9, -2, -6, 2, 4, 4, 1, 0, 0, 2, 0, 1], [12, 0, 0, 8, 0, 2, 6, 0, 4, 1, -2, -6, -4], [-14, -9, -4, 4, 3, 7, 1, -1, -3, 4, 5, -2, -4], [0, -1, -8, 1, 1, 0, -1, -1, -2, 1, 2, -1, -1], [-3, -4, -1, 6, -5, 2, 2, 5, 6, -4, -3, 1, 3], [-15, -1, -3, -1, 3, -2, -1, -3, -1, 4, 2, 4, -2], [4, -3, 1, -5, 2, 5, -4, 1, -3, 4, 0, 4, 3], [-17, 4, 3, -1, 2, -3, -1, -1, 2, -1, -3, -2, -3], [-2, -2, -3, -3, 5, -3, -4, 1, -2, -5, 0, 5, 3], [-17, -10, 0, 0, 4, 5, -2, 2, 4, -2, 1, 4, 0], [-4, 6, 3, 1, 0, -4, -3, -3, 2, 3, 2, -4, -1], [17, 7, 0, 9, 1, -1, -3, 1, -2, -1, 3, -1, -1], [-5, 8, -1, -8, -2, -3, -1, 1, -4, 3, -2, 1, 4], [-16, -3, -2, 9, 1, -4, -7, -1, -5, 5, 2, 1, -3], [7, -3, -2, 4, 9, -5, 2, -2, 1, 3, 1, 1, -2], [3, 6, 3, 4, -3, -10, -4, -1, -4, -4, 3, -1, 3], [1, -4, -4, 5, -2, 3, 2, 3, 1, -3, -2, -3, -6], [-3, 3, -3, -2, -7, 0, 2, 2, 4, -1, -6, 0, -2], [-17, -4, 1, 2, 4, -2, -2, -4, 2, -1, 2, -3, -1], [-4, -18, -3, 4, 8, 4, 0, -2, 0, 4, 6, 2, 0], [4, 10, -1, 1, -3, 1, 2, -1, -5, 4, 3, -2, 2], [2, -1, 0, 7, 0, -3, -2, 1, 1, -1, 6, -2, 0], [-7, -11, 0, -11, -4, 6, 1, 4, -1, -3, -3, 2, 5], [-6, -6, -2, 3, 4, -5, -5, 3, -1, 3, -1, -1, 0], [-19, -6, -4, -2, 3, -1, 4, 1, 5, 2, 0, 4, 0], [4, -14, -4, 3, 10, 1, 5, -3, 8, 1, 5, 1, -6], [-3, 4, 4, 1, 3, 0, 1, -2, -2, -3, 1, 1, 0], [8, 2, 7, -3, -6, 1, 7, 0, 4, 1, -2, -6, -2], [4, 0, 3, 3, 1, 4, 4, -5, 2, -2, -1, -4, -2], [0, 2, 6, -2, -5, 1, -2, 1, -4, -1, 4, -5, 2], [-1, -4, 6, -5, -1, -5, 1, 0, 4, -3, -6, -2, -2], [-5, 0, -1, 0, -3, -2, -6, 1, -1, 3, -3, 5, 5], [-1, 6, 1, -7, -8, 7, 3, 3, 0, -1, 5, -8, 3], [8, -3, 4, 0, -4, 3, 4, 3, 6, -2, -2, -6, 3], [20, -6, -1, 6, 7, -2, 0, -3, 7, -1, 1, 0, 0], [-2, 9, 1, 3, 0, -7, -7, 0, -2, 2, -4, 4, 4], [2, 3, -7, -1, 5, -3, 0, 0, -3, 2, 1, 4, 1], [-11, -6, -2, -1, -2, 1, 4, 2, -3, 0, 1, -4, -6], [-9, -11, -1, -6, -3, 4, -1, 5, 3, 2, -3, 5, 1], [6, -7, -2, -8, 3, 1, 4, 2, 8, 1, -5, -2, 3], [-1, -10, -5, -4, 0, 0, -3, 1, 3, 0, -2, 7, 2], [16, 9, -7, 2, 2, 0, 1, -4, 0, 3, 5, 3, 3], [-7, -6, -2, 5, 5, -4, -5, 0, 5, 2, -3, 1, 0], [0, 10, 7, -3, -6, 1, 3, 0, -4, 1, 2, 0, 0], [1, -7, -4, 1, 1, 3, 0, 2, 0, 8, 1, -3, -4], [-9, -3, -1, -2, 4, -1, -5, -4, -4, 1, 4, 3, -3], [-3, 2, -4, 6, 1, 2, 2, -3, 2, 8, 5, -5, -6], [10, -2, 0, -2, -5, 0, 7, 2, 4, 0, -7, -2, 5], [-6, -5, -7, 11, 2, 1, -3, 0, -3, 3, 4, 0, 0], [9, -9, -2, -4, -4, 4, 0, 5, 0, 1, -5, 6, 3], [-1, 3, 5, -5, -5, 6, 6, 6, 6, -3, -2, -2, 1], [-2, -6, -11, 1, 4, 6, -3, 3, 2, 3, 0, 10, -1], [10, -2, 1, -6, 0, 5, 6, -2, -3, 3, 3, -1, -1], [-2, -3, -4, 6, 2, -3, -2, -1, -9, 1, 2, 4, 1], [10, 1, -2, -3, -2, 1, 0, 3, 2, 1, -7, 1, 0], [-16, 3, 7, -7, -7, 1, 1, -1, 5, -4, -5, 4, 0], [3, 0, 7, 2, 0, -4, -3, -3, -1, 0, 0, -3, 4], [4, -8, 0, 6, 6, 0, 5, -3, 1, 1, -2, 2, -7], [-1, -3, -5, 5, 0, -4, -2, -1, 3, 2, 1, -2, -1], [18, -4, 6, -2, -3, 0, 2, 3, 0, -1, -5, 0, 4], [-9, -1, -3, 6, 5, -1, -4, 0, 4, -1, 3, 5, -2], [4, 9, 5, 0, 3, -2, 1, -5, -2, 0, 2, -5, -5], [1, 4, 2, 7, -4, -4, -2, 2, 7, -1, -6, 1, 1], [1, -1, -1, -3, 1, 0, -3, -1, -10, 2, 6, 0, -2], [10, 2, 2, -10, -5, 2, 4, -1, -2, -2, -3, -6, 4], [19, 11, 5, -6, -8, -5, -4, -3, -4, -5, -2, 3, 8], [-2, -4, 3, -3, -9, 1, 0, 6, -1, -2, -7, -4, -1], [4, -5, -2, 8, 11, -4, -2, -2, 1, 2, 6, 1, 2], [2, -10, 2, 0, 0, 6, 3, -1, -6, 0, 0, -4, -7], [16, 2, -5, -1, 2, -3, -4, 1, -5, 4, 0, 0, -1], [1, -1, 0, 6, 2, -2, -2, 1, 5, -3, -3, 0, -1], [0, -1, 1, -4, 5, 4, 1, -1, 1, 1, 2, -1, -1], [8, 10, -1, 3, 1, -6, -5, -2, -1, -2, -3, 0, 1], [4, -1, 9, 2, -12, 2, 1, 4, 2, -1, -5, -7, -1], [11, 9, 0, 6, -1, 5, 3, -3, 1, -1, 3, -5, -1], [1, -10, 3, -4, -5, 3, 6, 0, 2, 0, 3, 3, 2], [-4, -16, 2, 6, -1, -3, -3, 0, 2, 7, 0, -1, -3], [14, -4, 5, 0, 1, 5, 2, 1, 1, -1, 6, -1, 1], [10, 4, -2, 8, -3, 3, 3, 2, 3, -2, -1, -2, -3], [-2, -8, 2, 4, -1, 2, -1, 2, -8, 3, -1, 2, -1], [-3, -10, 2, 10, 2, 5, 1, 1, -2, 5, 1, -2, -3], [-17, -7, -1, -1, 3, 1, 1, 0, 4, 4, 0, 2, -3], [-2, -10, -3, -7, 2, 8, 2, 0, -5, 7, -2, 2, -4], [-4, -4, -7, -5, -6, 8, 7, 7, 6, -7, -6, 6, 5], [-12, -13, -1, 1, 0, 3, -2, 1, -5, -3, 0, 0, -3], [1, 0, 2, -1, 2, -4, -5, 3, -5, 2, 0, -5, 2], [-23, -6, 1, 0, -4, -2, -6, 0, 1, 1, 0, -3, 1], [-7, -7, 5, -2, -8, 0, -2, -1, -5, 2, 2, 1, 4], [13, 0, -6, 7, -4, 6, 5, 1, 4, -4, -4, 3, -2], [5, 3, 0, 6, 4, -10, -7, -4, 1, -4, 3, -2, 2], [3, -8, -3, 7, 2, 1, -1, -1, -1, 2, -1, 0, -1], [27, 13, -5, 1, -5, -1, -4, 4, 1, -7, -1, 7, 5], [10, 0, 2, -7, -9, 4, 2, 3, 4, -3, -12, -5, 1], [2, 1, 2, 0, 1, 3, -2, -4, -6, 0, 5, -2, -5], [11, 5, 9, -15, -7, 5, 6, 1, -3, -2, -2, -8, 2], [17, 3, 6, -7, -11, -2, 2, 2, 4, 1, -12, -8, 4], [8, 4, -8, 9, 7, 0, -3, 2, 0, 0, 0, 9, 2], [-1, 4, -10, 4, 8, -2, -10, 1, -6, -1, 1, 8, 1], [6, 3, -1, -6, -1, 7, 7, 0, 4, -11, 0, -1, 2], [-11, -3, -2, 1, -6, 2, -1, 0, -7, -2, 1, 0, -1], [10, 12, 4, -4, -8, -2, -7, 1, -8, 1, -2, 0, 3], [-5, -2, 2, -2, -3, 0, 7, 1, -4, -6, 2, -4, 2], [3, -1, 0, -1, -3, -5, 0, 0, 1, 2, 1, -5, -6], [1, -2, -11, 10, 4, -2, 0, -2, 7, 3, 0, 1, -1], [16, -4, 5, -6, -2, 3, 1, -1, 3, -1, -3, 1, 4], [5, 6, 2, 3, 9, -1, 0, -2, 3, 2, 7, 1, -4], [11, -7, -2, -3, 0, 3, -1, 6, 2, 3, 0, 7, -1], [2, -12, 2, 1, 2, 2, 2, -2, 0, 3, -2, -6, -7], [-35, -4, 0, -6, -4, 9, 8, 2, 3, -3, -3, -2, 2], [26, 7, 0, -6, -1, -2, 1, -1, -3, 0, -3, 2, -2], [-18, -6, 4, 4, -1, 0, -3, 0, -3, 0, -1, 0, 3], [20, -4, -3, -1, 3, -5, -4, -3, -5, -7, 4, 3, 2], [20, -5, -3, -1, -6, 0, -2, 1, -4, 0, 1, -1, -1], [-17, 10, 4, -5, -1, -1, -1, 0, -5, -7, 4, 2, -1], [14, -3, -6, 0, 2, -6, 0, -1, -1, -1, -1, 1, 2], [0, 5, 2, 0, -2, -4, 4, -1, 8, -5, 5, -1, 3], [14, -6, 0, -3, 5, -9, -9, 0, -1, 0, -4, 1, -2], [2, 16, 0, -2, -1, 4, 4, -5, 1, -6, 5, -2, 4], [5, -1, -6, -4, 7, 4, -4, 0, -3, 4, 6, 12, 3], [1, -1, 6, -6, -5, 3, 9, -2, -1, -8, 0, -2, 3], [-1, 13, 2, -2, -2, -3, -6, -1, -6, 7, -2, -1, 1], [28, 0, -1, -9, -4, 4, 4, 4, 0, -4, 0, 2, 2], [10, -1, 11, 0, -4, -4, -1, -2, 6, -1, 3, -7, 1], [2, 3, -6, 6, 8, -3, -1, -2, -3, 0, 0, -2, -6], [-5, -4, 4, -6, -6, 4, -2, 2, -9, 4, 4, -1, -1], [12, -1, -2, 3, -1, 0, 3, 3, 0, -5, 6, 1, 1], [-10, -12, -2, -9, -1, 7, 1, 0, 0, 5, 2, 3, -2], [-7, -19, 4, -7, -1, 7, 2, 0, -5, 4, -1, 5, -6], [-3, 18, 5, 0, 0, 2, 3, -3, 3, -3, 4, -7, 2], [6, 3, 0, -12, 1, 0, -2, 0, -3, 0, 0, 5, 6], [-16, -6, 8, 2, -2, 1, -1, -2, -3, 7, 2, -4, -6], [14, 4, -11, 8, 6, -5, 1, -1, -3, -3, 5, 1, -4], [15, 2, -2, 4, 3, 0, -1, 2, 1, 6, 1, 1, -3], [11, 8, 6, -8, -3, 0, -1, -2, -4, 1, 3, 1, 4], [7, 1, 7, -7, -2, -4, 2, 3, 2, -2, -5, 2, 3], [-3, -14, -1, -9, -1, 1, -1, 2, -2, 2, -2, 2, 3], [15, 9, 5, -1, 1, 2, 3, -3, -5, -1, 0, 2, 0], [1, 0, 10, -8, -5, 2, 0, 1, -2, 1, -7, -9, 1], [13, -5, 1, -3, 4, -3, -1, -2, 1, 2, -4, -1, -1], [-23, 4, 11, -2, -7, -4, -5, 4, -3, 0, -5, -3, 2], [-1, -4, 4, -5, -6, -5, 0, -2, 1, 0, -10, -5, 3], [23, 0, 7, 4, 4, -1, 2, -4, -4, -1, 1, -8, -7], [21, 14, -4, 10, 5, -3, -6, -1, 0, 7, 0, 4, 2], [-8, 3, -1, 3, -3, -2, 5, 4, 12, -7, -5, 0, 5], [-7, 1, 7, 7, -3, -4, -5, -1, 0, 5, -4, -4, -6], [21, -8, -1, -4, -9, -5, -5, 1, -4, 2, -3, -1, 7], [10, -8, -3, -4, -3, 1, -3, 2, -5, -5, -6, -1, 6], [-15, -6, -1, -4, 0, 0, 5, 5, 9, 1, -4, -1, -4], [9, 4, 2, -3, 2, -6, -3, -5, 5, -5, -4, 5, 6], [8, 2, 0, -5, -4, 11, 9, -1, 5, 2, 3, -5, 2], [25, -1, 5, -1, -4, 8, 3, 0, 1, -1, 3, -8, -4], [11, 13, 2, -6, 1, 5, 3, 3, 2, -6, 5, -1, 4], [4, 10, 1, 15, 1, -3, -2, -3, 0, -1, 10, 1, 1], [-8, 4, -3, -3, -3, 0, -2, 5, -2, 3, 1, -4, -2], [6, 11, 1, 0, 0, -7, -2, -5, 0, -3, 1, 1, 0], [-4, 8, 1, -4, -5, -1, 8, 1, -1, -5, 2, -3, 5], [-6, 5, -8, 12, 6, -6, -6, -3, -8, 7, 9, 5, -3], [21, 1, -4, -3, -2, 7, 9, 2, 3, -3, -2, 1, -1], [13, -2, 5, 0, 2, 1, 4, -2, 9, -3, 1, -4, -4], [-11, 1, -12, 4, 5, 0, -3, 1, 2, 2, -2, 4, -6], [-16, 2, -6, 4, 14, 3, -2, -2, -2, 6, 1, 1, -6], [-4, -3, -11, 9, 1, 7, -5, 3, -3, 4, 5, 0, -6], [9, 5, -1, 5, 3, -1, 5, -3, 1, 1, 3, -5, 3], [-1, 10, -11, 5, 6, -3, -3, 3, -5, 2, 5, 0, 1], [14, 1, 4, -11, -3, 1, 6, 0, -5, 1, 1, -6, 0], [0, 6, -7, 3, 0, 3, 2, -2, 1, 2, 3, 7, 0], [-13, -1, 4, -3, -8, -9, 3, 0, 6, -5, -12, 1, 1], [-6, -2, 0, 0, -1, -8, -4, -3, 3, -5, -5, 2, 2], [-4, -2, 0, -5, -3, 6, -2, 7, 3, -2, -2, -3, -1], [-14, 13, -1, 2, 4, -7, -2, -6, -6, 0, 1, 7, 1], [13, 2, -1, 9, -2, -7, -5, -3, 1, -1, -1, -4, 1], [-6, 1, -5, 10, 12, -10, -3, -6, -6, 2, 1, 3, -9], [-2, 8, -13, 0, 3, -1, -3, -4, 1, 5, 2, 9, 0], [-5, 11, 6, -8, -14, 5, -1, 5, -1, -5, -9, 4, 3], [-22, 7, -2, 3, 2, -3, -6, -1, 3, -3, 0, 2, -2], [12, 1, 0, -3, 1, 0, 4, 4, 2, -4, 0, -1, -4], [-7, -1, -4, 4, 0, 4, 3, 0, 2, -2, 3, -8, -8], [10, 13, 8, 11, -1, -5, -1, -5, 2, 0, 9, -4, 3], [-4, -5, 7, -2, -4, 0, -2, -1, -1, 6, 5, -9, -2], [12, 9, -3, 6, 3, -3, -4, -1, -2, 3, 6, -3, -5], [0, -8, 2, 1, 4, 1, 2, 0, 8, 0, -1, -3, 5], [10, 17, 3, -5, -11, -2, 3, 1, -4, -8, -2, 3, 3], [23, 17, 4, -6, -3, 4, 2, -4, -4, 0, 6, 2, -1], [-26, -3, -6, 8, 8, -2, 0, -5, 3, 0, 4, 2, -3], [-18, -1, -5, -6, 8, 2, 1, -2, -8, -5, 3, 3, -3], [3, -4, -2, -3, -3, 11, 12, -3, 7, -2, 0, -2, -1], [-13, 8, 0, 3, 1, 2, -6, 5, -7, 3, 1, 3, 3], [9, 12, 1, -8, -3, -2, 0, -1, -5, 1, -3, 9, 5], [-6, 11, 2, -1, -1, -2, -4, 0, -2, 3, -6, -3, 0], [4, -1, 0, 11, 7, -7, -12, -4, -8, 14, 5, -2, -6], [-3, 8, 3, 2, -3, 12, 9, 2, -1, 0, 3, -5, -4], [-2, -10, 1, -3, 3, 6, 3, 2, 8, -1, -1, 8, 1], [1, 8, -9, 3, 2, -9, 0, 0, -2, -8, -3, 2, 0], [13, -9, -10, -3, 1, 2, 4, 1, 0, -5, -1, 5, -3], [6, 11, -2, -6, 0, -4, -5, 0, 3, 1, 0, -4, 2], [-21, -8, 1, -7, -13, 1, -2, 7, 0, -6, -14, 4, 6], [-4, -2, -1, -1, 0, 4, 8, 6, 8, -13, 0, 0, 6], [17, -3, -2, -11, -6, 6, 7, 2, 1, -2, -9, 0, -1], [0, 1, 7, 4, -4, -4, -2, 3, 9, -1, -9, -1, -4], [6, 5, -2, 4, 9, 0, 0, 0, 9, 1, -2, 1, 2], [3, -7, 6, -6, -1, 6, 3, 5, 7, 1, -10, -4, 0], [13, 12, 1, 7, -3, 4, 0, -3, -14, 6, -1, -5, 0], [14, -6, -1, -4, -6, 4, 6, -2, -2, -10, -1, -5, 1], [5, -2, 0, -5, -7, 4, 3, 6, 3, -2, -7, -5, 4], [23, 11, -5, -1, 0, 4, 4, 3, 1, -2, -1, -6, 3], [13, 14, -1, 7, 6, -6, 1, -3, -1, 2, -5, 0, -5], [0, 15, 8, 2, -4, -3, -1, 2, 5, -2, 4, -6, 0], [-13, -2, 6, -7, -5, 2, 6, 1, 10, -3, -7, 3, -3], [-14, 12, 12, -4, -6, -8, -9, 1, 0, -3, -4, -8, 7], [20, -5, -6, 1, 8, -3, -8, -3, -1, 8, 7, 3, -4], [-1, -3, 9, 2, 5, -4, -3, -1, -3, 8, -12, -2, 0], [12, -12, 5, 3, 5, -2, -2, -1, 5, 1, 7, -4, -2], [12, -5, -1, 4, 8, -12, -10, -3, -2, -5, 1, 3, -2], [9, 13, 6, -10, -6, -2, 0, -1, -1, -4, -5, 2, 3], [7, -1, -15, 1, 1, -5, -7, 1, -2, -4, -4, 14, 2], [2, 5, 3, -3, -8, 3, 0, 3, 4, -1, -2, -2, 1], [-20, 8, 2, -4, -12, 2, -1, 5, 1, 1, -10, 0, 9], [18, 2, -3, 3, 5, -6, -6, 3, -4, 5, 7, 0, -4], [-13, 7, 3, -4, -6, -7, -4, 1, 2, -12, -8, 1, 8], [12, -7, 4, -4, -4, 3, 2, -5, -3, 3, -4, -6, 1], [3, 2, 0, -5, -6, 6, 4, 0, 3, -3, -2, -11, -3]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_6020_a_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_6020_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_6020_2_a_k(:prec:=13)
    chi := MakeCharacter_6020_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_6020_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_6020_2_a_k( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_6020_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![-4, 105, 20, -1729, 231, 2384, -189, -1201, 37, 268, -2, -27, 0, 1]>,<11,R![1212800, -3233168, 2734016, -203300, -818440, 276481, 83075, -43924, -3472, 2953, 50, -90, 0, 1]>],Snew);
    return Vf;
end function;