
// Make newform 6016.2.a.n in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_6016_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_6016_2_a_n();".
// 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_6016_2_a_n();".
// 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 := [-832, -1440, 4720, 1488, -6230, 5, 3358, -438, -840, 163, 96, -22, -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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-5, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-78029720, -180048216, 231304564, 4239486, -20578969, 168487210, -79869654, -76866624, 31578537, 11599664, -4303150, -562332, 195435], [-58768544, 13662280, -126028448, 918870696, -174049953, -962998794, 270408522, 330991582, -97777627, -45195340, 13458666, 2092838, -623713], [-787062208, -2024987008, 4041025704, 3627295322, -4697624803, -2309620130, 2158227746, 647371992, -458324917, -79576928, 45355618, 3467516, -1685943], [1617289984, 3317853968, -6526418140, -6285692652, 7523189915, 4342745078, -3604828890, -1304694094, 808510705, 168699740, -84660434, -7613086, 3310971], [-2287713712, -5579893712, 9846735948, 10612170176, -11777706325, -7237641474, 5748539542, 2135000694, -1296809943, -271736444, 135579006, 12120046, -5277677], [-1239592192, -2653342116, 5597835874, 4970241098, -6541061235, -3390849962, 3098280608, 1003716556, -680556885, -128084672, 69595980, 5722128, -2662843], [-2595295424, -5850552272, 11499346780, 10900737512, -13297330361, -7407724298, 6307230430, 2184691446, -1395734323, -278165356, 144044326, 12412430, -5558529], [2837565520, 6899380648, -12708813292, -12807105642, 14854043917, 8583414246, -7063620194, -2503849628, 1563354275, 316434536, -161260170, -14050128, 6218745], [3128024784, 7844979872, -13398793452, -14883035676, 15486782437, 9972299306, -7403133806, -2884160314, 1655301055, 361687364, -172617142, -15973050, 6720997], [2191670088, 5006051868, -8859575594, -9177455798, 10007495075, 6072541562, -4721593184, -1752869144, 1045460149, 220001744, -108160260, -9726996, 4185187]];
    Rf_basisdens := [1, 1, 1, 16452824, 32905648, 32905648, 32905648, 32905648, 16452824, 32905648, 32905648, 32905648, 16452824];
    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_6016_a();"
function MakeCharacter_6016_a()
    N := 6016;
    order := 1;
    char_gens := [4607, 2821, 3201];
    v := [1, 1, 1];
    // chi(gens[i]) = zeta^v[i]
    assert UnitGenerators(DirichletGroup(N)) eq char_gens;
    F := CyclotomicField(order);
    chi := DirichletCharacterFromValuesOnUnitGenerators(DirichletGroup(N,F),[F|F.1^e:e in v]);
    return MinimalBaseRingCharacter(chi);
end function;

function MakeCharacter_6016_a_Hecke(Kf)
    return MakeCharacter_6016_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], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, -1, -1, -1, 0, 0, -1, 0, 0, -1, -1, 0, 0], [1, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0], [0, -1, 0, 0, -1, 1, -1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0], [1, -1, -1, -1, 0, 0, 0, -1, 0, 0, -1, 1, 0], [1, -1, 0, 0, -1, -1, 0, 0, 0, -1, -1, 0, 0], [1, -1, 0, 0, 0, -1, 0, -1, 1, 0, -1, 1, 0], [0, 0, -1, 0, 1, -1, 1, -1, 1, -1, -1, 0, -1], [-2, 1, -1, -1, 0, -1, 1, 1, 1, -1, 0, 1, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 1, 0, 0, 0, 0, 1, 0, 1, 2, 0, 0], [-2, 0, -1, -1, 0, 0, -1, -1, 1, -2, -2, 0, -1], [1, -1, -1, -1, 1, 0, 1, -1, 0, 0, 0, 1, -1], [-1, -1, -1, -1, 2, -1, 1, -1, 1, 0, -1, 2, -1], [4, 0, 1, 0, -1, 0, 0, 2, -1, 1, 0, -1, 0], [-1, 0, -3, -1, 1, 0, 0, -2, 3, -2, -2, 1, -2], [1, 0, 1, 1, 0, -1, 1, 3, -2, 2, 1, -2, 1], [-1, -2, -2, 0, 0, -1, -1, 0, 1, -1, -1, 2, 0], [2, 2, -1, 1, -1, -1, 1, 1, 1, 1, -1, 1, 1], [-1, 2, 1, 1, -2, -1, 1, 1, -1, 1, 1, -1, 0], [2, -2, -2, -1, -1, 1, -1, -1, 1, -1, -3, 2, -1], [-1, 0, -3, -1, 0, 0, 0, 0, 1, -2, -2, 0, -1], [-4, 0, -2, -1, 0, -2, -1, -1, 0, -3, -1, 1, -2], [0, 0, 1, 2, 1, 1, 0, -2, 0, 0, 1, -1, 1], [1, 0, 0, -1, -2, 1, -1, 1, 0, -1, -1, -1, 1], [3, -2, -1, -2, 1, 0, 0, 0, 1, -1, 0, 0, 0], [1, -3, 1, -1, -3, 0, 0, 1, -1, 0, -2, 0, 0], [4, -2, -3, -2, 1, -1, 0, -2, 1, -2, -3, 3, -1], [-4, 2, 1, 2, 1, 2, 0, 0, 1, 3, 0, 0, 1], [2, -1, 1, 0, 1, 3, -1, 0, -2, 2, 3, 0, 2], [0, 3, -1, 1, 0, -1, 1, 1, 1, 2, 1, 2, 0], [4, 1, 2, 1, -4, 0, 0, 2, -1, 0, 2, -2, 1], [-2, 0, 3, 1, 1, 0, 1, -1, 1, 1, 2, 0, 1], [0, 2, -1, 1, 1, 0, 0, -1, 1, 1, 2, 1, 0], [5, 0, 2, 2, -1, 2, -3, 2, -3, 1, 2, -5, 2], [-7, 0, 0, 2, 0, 2, -1, 2, 0, 1, 1, -2, 0], [2, -2, -2, -2, -2, -1, 0, 1, 1, -6, -3, 1, -1], [4, 0, 2, 1, -1, 1, -1, 2, 1, 4, 3, -1, 3], [1, -2, -1, -1, 1, 0, 1, -3, -1, 1, -2, 2, -2], [0, 1, -1, -3, -2, -2, 0, -1, -1, -1, -2, 0, 1], [3, 1, 1, -1, -2, 1, -2, -1, -3, 0, -1, -1, 2], [-2, 0, -1, -2, -1, -2, 1, 2, -3, 2, 1, 0, 2], [-1, -2, -3, -2, 1, -2, 2, -2, 1, 1, -4, 4, 0], [0, 0, 1, -2, -3, 0, -1, 2, -1, -2, 1, 0, 2], [-4, 1, -1, 0, 2, 1, 1, 0, 2, 1, 0, 0, 1], [11, -2, 2, 3, 0, 1, -2, 4, -4, 2, 3, -4, 1], [5, 0, 1, 0, -1, 0, -2, 1, 1, 0, 0, -1, 2], [0, -2, -3, 1, -1, -2, -1, -1, 1, -1, -4, 1, -2], [-1, 2, -2, -2, 1, -2, -1, 0, 0, -2, 0, -2, -1], [-1, 2, -5, -3, -1, -3, -2, 1, 1, -4, -3, 2, -1], [3, 4, 0, 1, 3, 0, 2, 0, 2, -2, 2, -1, -3], [7, 2, -1, 0, 1, 0, 1, -3, 1, -2, 0, 1, -2], [0, -1, -1, -2, 0, -2, -1, -3, -1, 0, -2, 1, -1], [-1, 1, -2, 0, 0, -1, -2, 1, 1, -2, -1, 1, 2], [7, -2, -2, 1, 0, 0, -1, -2, -2, -3, 0, 0, 0], [-7, 4, -3, -1, 2, -4, 3, -4, 3, -1, -2, 4, -1], [-3, 2, 0, 3, 2, 2, 0, 1, -3, 2, 4, -1, 2], [-2, 1, 0, 2, 0, 0, -2, 0, 0, 0, 0, -2, 2], [5, 3, 3, 3, 0, 1, -2, -1, 1, 0, -1, -1, -2], [6, 2, 0, -2, -4, -3, 0, 3, 0, -2, -1, 1, -1], [8, 2, 0, 0, 2, -1, 0, -1, 1, 2, -1, -1, -1], [-6, 2, -3, -3, 0, -2, -1, 1, 1, 2, -2, 0, 1], [1, -1, 7, 2, 2, 3, 0, 1, -5, 6, 7, -4, 2], [-2, 4, -4, 0, 1, 0, 1, 1, 0, -3, 0, 0, -1], [0, 6, 1, 2, 1, 1, 2, 4, 0, 4, 5, -1, 3], [0, -1, 0, 0, -1, -1, 1, 0, 0, -2, -3, -1, 0], [7, 1, -6, -6, -1, -3, 0, -2, -2, -5, -5, 4, 0], [2, 4, 2, 2, 2, 0, 2, 2, -2, 4, 2, 2, 0], [-3, 4, 0, 1, -2, 3, 0, 2, 3, -2, 3, 0, -1], [0, 3, -1, -1, -1, 0, -2, -2, 3, 1, -2, 2, 2], [4, 0, -3, -1, 2, -4, 4, 1, 3, -1, -2, 4, -1], [3, 2, -1, -1, 3, -2, 3, -1, 0, -1, 0, 2, -2], [8, 1, 7, 2, -3, 1, -1, 2, 0, 0, 5, -4, 0], [6, -4, 4, 2, -1, 5, -3, 1, 1, 0, 1, -1, -1], [3, 4, 6, 5, 2, 4, 0, 3, 0, 6, 8, -5, 4], [-5, 3, 0, 0, 1, 1, 1, -2, -2, -3, -1, 3, -1], [-2, -1, -1, 0, 6, 0, 0, -6, 2, -2, -3, 2, -2], [10, 0, 0, -1, -1, -3, -1, -2, -3, -1, -1, 1, -1], [-5, 0, -2, -1, 2, -2, 1, 4, 2, 5, 0, 0, 4], [1, 0, -4, -2, -2, -4, 0, 1, 2, -9, -4, 2, 0], [3, 5, 0, -2, -1, 1, 0, 2, 4, 0, -2, -1, 2], [7, -4, 2, 1, 2, 0, 1, 0, 0, 1, 2, 0, 0], [1, -8, -1, -4, 0, -1, -2, -2, 0, -6, -3, 0, 1], [15, -3, 3, 3, -2, 3, -2, 4, -2, 4, 4, -2, 3], [0, 0, -5, -3, -1, 0, -2, -3, -3, -3, -4, 3, -2], [0, 3, 1, 1, 0, -3, 2, -3, -1, 2, 1, 1, -3], [-5, 2, -4, 2, 4, -2, 0, -3, 2, -4, -2, 2, -4], [-1, -2, 0, 3, -1, 3, 3, -1, -5, 3, 1, -1, -1], [-9, -3, -3, -1, 1, -2, 0, -3, -1, 0, -2, 4, -2], [6, 1, 6, 2, 1, 1, 1, -4, 0, 0, 2, 0, 0], [8, 1, 1, -3, 2, -1, 1, 1, -1, 0, 3, 0, 2], [8, 1, 0, 0, -3, -1, -3, 1, 1, 1, -2, 0, 3], [4, -1, -3, -2, -5, -3, -2, 3, -3, -2, -1, 0, 1], [-3, 1, 6, 4, -1, 5, -2, 1, 1, 8, 7, -4, 1], [-1, -1, -1, -1, -1, 2, -1, -3, 4, 0, -2, 1, 1], [5, 2, 3, 2, -3, -2, 1, 0, -3, -1, 4, -3, -1], [3, 1, 0, -1, 5, 0, 1, -3, -1, -1, -1, 0, -2], [1, -2, 5, 1, 3, 2, 0, 1, -1, 7, 2, -3, 3], [12, 0, 1, 4, 3, -1, 4, 2, -1, 4, 3, 1, -3], [-1, -1, -2, -4, 0, 0, 0, -1, -2, 1, -2, -2, 2], [-2, -2, 6, 0, 0, 3, 2, 1, -2, 6, 3, -1, 3], [-10, -1, -5, -1, 2, -1, -2, -3, 3, -4, -3, 1, -1], [1, -2, 0, -3, -4, -2, -5, 2, 4, -3, -4, -2, 2], [0, 4, 4, 2, -2, 6, -2, 6, 2, 4, 6, -4, 6], [-12, 3, -11, -5, 3, -2, -1, 0, 4, -5, -6, 1, -3], [-3, -1, 0, -5, 1, -1, 1, 1, -4, 1, 1, 2, 0], [9, -5, 3, -3, -7, 0, -3, 5, -4, 2, 2, -5, 3], [10, -8, -1, -1, -3, 0, -1, 1, -7, 1, 2, -1, -2], [-8, 2, -6, -4, 0, -1, 1, -3, 9, -8, -7, 4, -4], [10, -6, 2, -1, 0, 0, 1, -1, 0, 0, 0, 2, 0], [-2, 4, 0, 2, 0, 0, 4, 0, 8, 6, -2, 4, 0], [8, 0, 7, 3, -4, 0, -5, 5, -7, 0, 4, -8, 5], [2, 1, -4, -2, 3, -4, 3, -3, 2, -6, -4, 4, -7], [2, -3, -1, 0, -1, -3, 5, 2, 0, 6, -1, 2, 4], [-8, 5, -2, -2, -2, -2, 2, 4, 0, -6, -2, -2, 0], [6, -1, -3, -4, -1, -1, -3, 0, 6, -6, -9, 2, 0], [4, -2, 0, 2, -4, 6, -5, 5, -2, -1, 4, -3, 6], [-8, 2, 0, 4, 2, -2, 1, 1, -3, 1, 4, -3, -2], [1, -5, -1, -3, -1, -2, -2, -5, 1, -8, -6, 4, -2], [13, -1, -4, -3, -1, -1, 0, -1, 10, -5, -3, 5, -1], [7, 2, -1, 1, -1, -1, 4, 1, 0, 4, -1, 2, -1], [-5, 9, 1, -1, -1, 4, -3, 1, 4, 2, 0, -1, 3], [10, -3, -4, -5, -2, -2, -1, -4, 0, -2, -8, 5, 0], [-10, -3, 1, 0, 0, -1, 2, 0, 1, 6, -1, 0, 2], [-6, -4, 0, -1, -3, 1, -1, 3, 1, -1, -1, 2, 3], [-9, 7, -3, -1, 3, 0, 0, -5, 5, -2, -2, 4, -4], [-1, -5, -1, -2, -2, 5, -3, 2, -7, 2, 1, -5, 0], [-2, 2, -1, 4, 3, 8, -1, 2, 1, 3, 0, -1, 0], [-6, -1, -5, -2, 2, -4, 1, 1, 2, -3, -3, 1, -6], [-2, 9, 3, 2, -2, 3, -1, 2, -4, 2, 3, -1, 5], [-6, 3, -5, 0, -3, 0, -2, -1, 1, 0, -4, 2, 0], [-2, -2, -2, 3, 1, -1, -1, -1, 3, -1, -1, 4, -1], [11, -2, -5, -3, 1, 2, -6, 1, -3, -5, -2, 1, -1], [8, -1, 7, -2, -2, 0, 1, 5, -4, 3, 7, -1, 4], [14, -10, -4, -4, 0, 1, 0, -1, -2, -2, -5, 5, -3], [-3, -2, 0, -2, -1, -2, -1, 8, -2, 4, 0, -4, 1], [-6, 8, 4, 8, -2, -1, -3, 0, 3, 1, 3, -4, -1], [-4, -5, -4, -6, 5, -1, 0, -10, 5, -5, -9, 6, -5], [10, -4, 1, -1, -4, -6, 1, 3, 3, -6, -2, 0, 1], [2, -1, -1, 0, -4, -4, -2, -4, -2, -6, -5, 0, -4], [-3, 4, 2, 2, -4, -2, 1, 0, -4, 2, 2, -3, 2], [-5, -7, -4, -4, -2, 1, 2, -1, -1, 0, -3, 3, 2], [2, 4, -5, -2, -3, -1, -2, 2, 7, -6, -7, 1, 1], [2, -3, -1, -1, -2, -1, 2, 1, -5, 2, 3, -1, -1], [1, -7, -1, -4, -2, -2, -1, 0, -1, -5, -2, -1, -3], [-9, 5, 5, 7, 0, 1, 3, 1, 0, 5, 6, -1, 1], [4, 0, -1, -2, -1, -6, 4, -3, 3, -4, -2, 8, -8], [6, -9, -1, -1, 5, 4, 0, -6, 1, 3, 2, 4, -2], [1, -2, 1, -3, -5, -2, -3, 3, 7, -1, 0, -4, 2], [10, -1, 6, 2, 3, 3, 2, 2, -5, 1, 5, -2, -1], [7, -3, -4, -4, -1, 0, -1, 4, -2, 3, -4, 4, 5], [4, 0, 5, 0, -5, 0, 3, -2, -1, 1, -2, 3, 2], [-3, 1, 6, 4, -4, 0, -1, 2, -6, -2, 2, -5, 4], [-6, 4, 2, 2, -2, -5, 1, 6, 0, -3, 1, -2, 3], [2, 2, 1, -2, 0, 4, 0, -7, 2, 1, -2, 0, -2], [4, 3, 4, 2, -7, -3, 2, 4, 3, -5, -1, 0, 1], [-4, 2, -2, 0, 0, -1, 0, -3, 0, -2, -5, 1, -1], [4, -10, 0, -3, 1, -4, -2, -5, 2, -3, -6, 7, -5], [-9, -9, -2, 1, 1, -1, 1, -7, 6, -4, -8, 7, -8], [2, -2, 7, 7, -6, 1, 2, 6, -6, 11, 7, -6, 3], [2, -3, 0, 3, -3, -1, -4, 3, 0, 3, 1, -5, 2], [3, -5, 2, -4, -1, 0, -1, 4, 2, 1, 0, 2, -3], [-10, 0, -5, -2, -1, -8, 2, -3, 6, 0, -2, 6, -2], [-4, 4, -1, -2, 1, -3, 3, -3, -5, 1, -5, -2, 1], [0, 4, 7, 6, -7, 4, 0, 3, -6, 4, 8, -4, 2], [3, 8, 2, 4, 1, 0, -3, 4, -4, 8, 8, -4, 3], [2, 5, 6, 7, 2, 4, 2, 4, -7, 6, 6, 0, 1], [11, -14, 0, -7, 0, 0, -2, -1, 2, -4, -6, 3, -2], [2, -8, -3, -6, 3, 4, 0, 3, -3, 0, 2, 4, 2], [-4, 9, 8, 5, 1, 7, 0, 9, 0, 7, 13, -3, 6], [14, 4, 4, 0, -6, -3, -1, 6, -4, -3, 7, -10, 1], [15, -3, 0, 2, -2, 2, -2, -3, -12, -1, 0, 0, 0], [13, 0, 1, -3, 2, -1, -2, -4, 0, -5, -1, 3, -1], [1, 9, 10, 8, -1, -1, 4, 8, -2, 5, 7, -4, 2], [4, 1, -1, -6, -4, -7, 0, 5, -6, 0, -6, 1, -1], [-16, 4, -12, -10, 2, -6, 0, -2, 2, -9, -6, 4, 2], [1, -5, 2, 1, -1, 3, -4, 7, -6, 1, 5, -5, 3], [2, 1, -4, 1, 2, -2, 0, -4, 1, -4, 4, 0, -5], [7, 3, 5, 0, 2, 4, -4, -3, -3, -8, 2, -2, 3], [-7, -5, -2, 2, 5, 1, 2, 0, 10, 5, 1, 4, -2], [-7, -5, 0, 4, 0, 3, -4, -3, 3, 8, 3, -1, 0], [-14, 4, -1, -2, -4, -4, 0, -1, 0, -3, -2, 0, 2], [5, -8, 4, 0, -3, 2, -3, 2, -4, -4, 2, -2, 1], [-11, -5, -3, 0, 0, -3, 2, 1, 1, -2, -3, 4, 0], [9, -5, 0, 3, 1, 5, -3, 1, -4, -1, 1, -6, 4], [6, -5, -2, -4, -3, -2, -1, -4, -2, 0, -6, 5, 1], [-5, -2, 14, 5, 0, 2, 1, 1, -6, 8, 8, -4, 1], [19, 1, 7, 2, -2, 3, -4, 4, -15, 2, 7, -10, 3], [-1, -6, -2, -2, 7, -2, 3, -6, 5, -9, -4, 3, -10], [-6, 0, -4, -2, 3, 0, -1, -5, -4, 3, -4, 0, -5], [3, 2, -5, -3, 5, -5, 6, -2, 2, -1, -1, 10, -6], [20, -2, 5, 0, -1, 3, -1, 5, -7, -1, 5, -4, 1], [3, -8, 7, 1, -1, 3, -5, -4, -6, 5, 1, -3, 3], [-12, -6, 0, 2, -1, 6, -7, 1, 1, 6, 0, -5, 6], [-15, 1, -5, -3, 5, -1, 6, -6, 4, 1, 1, 8, -4], [5, 2, -6, 0, 7, -2, 1, -2, -5, -1, -2, 3, -4], [-19, 2, 6, 2, -6, -2, 4, 3, 4, 4, 2, 0, 0], [-11, -8, 3, 1, -1, 0, 2, -4, 4, 2, 2, 1, -4], [0, -8, 3, 1, -3, 4, -5, 5, -5, 3, 6, -3, 8], [-10, -2, -4, -4, -1, 2, 3, 3, -2, 3, 0, 0, 1], [11, 1, 4, 1, -3, -4, -1, 2, 0, 3, -2, -1, -1], [11, 1, 0, 1, -1, -3, 1, 3, -2, -1, -1, 0, -6], [-4, -2, 0, -2, 1, -2, 1, 3, -2, -7, 8, -2, -1], [11, 6, -1, 1, 3, -2, 5, -1, -1, 1, 0, 4, 0], [-3, 5, -2, 0, 1, 1, 2, 0, 6, -10, -4, -1, -8], [2, -5, 3, 2, -1, 0, 4, 7, -5, 6, 4, 0, 4], [-8, -4, -4, -7, 1, -1, 5, 1, -7, 1, 1, 8, -3], [-1, -3, 9, 5, 5, 3, 4, 4, -4, 3, 9, -2, -4], [10, -5, -7, -7, 0, -3, 0, -1, -5, -4, -5, 3, 1], [-4, 1, -8, 2, -1, 5, -6, -2, 3, -1, -3, -2, 1], [-6, -6, -1, -2, 1, -1, -2, -2, 1, -4, -1, 3, -7], [-4, 4, 2, 4, 0, -2, 0, -6, 6, -2, -4, 6, -2], [8, 0, -7, 0, -1, -8, 2, 1, -3, 0, -8, 8, -2], [-14, -3, -2, -2, -1, 2, 3, -3, 4, 2, -2, 8, -3], [2, -8, 3, 0, -1, 0, 0, 1, -2, -2, 0, -2, 6], [-8, 4, 0, -5, -1, -9, 3, 1, -3, -3, -3, 0, 3], [-3, 11, 0, 1, -2, 7, -2, 6, 5, -5, 5, -3, 0], [2, -10, 0, 2, -2, 0, -2, 2, 0, 0, -2, -4, -2], [-14, 1, 3, -4, -4, 3, 0, 4, 3, 6, 1, -2, 4], [3, 2, -7, -1, 4, 4, -1, -2, -1, -3, -4, 0, 1], [14, -3, 5, 2, -2, 4, -1, -1, -8, 1, 1, -7, 2], [-1, 4, -4, -1, 0, 4, -6, -3, 2, -2, -2, 3, -4], [6, 10, 1, 5, -5, -4, -2, 3, -5, 1, 6, -5, -2], [-13, 3, -6, -3, -4, -5, 0, -6, 7, -6, -7, 1, -4], [-10, 2, 5, -7, 1, 0, -1, -3, 7, 1, 0, 0, 3], [-1, 4, 1, -1, 1, -1, 2, -1, -10, 6, 3, 2, -3], [10, -5, 0, -2, 0, -2, 0, -4, 8, -6, -6, 6, -8], [2, -7, -11, -5, 5, -6, -3, -8, 9, -10, -12, 4, -6], [8, -4, 10, 1, 0, 1, 5, 3, -11, 7, 7, -7, -2], [0, 12, -7, 1, 3, -8, 4, -7, 9, 0, -5, 6, -8], [-2, -1, 9, 4, -6, 1, 2, 2, -13, 14, 5, -8, 2], [-1, 12, -8, -3, 2, -3, 4, 2, 10, -5, -1, 4, -1], [10, -14, 3, 0, -4, -2, 2, 1, 0, -3, 0, 2, 2], [7, -4, 8, 2, -6, 11, -9, 4, -11, 7, 7, -8, 10], [10, -4, 8, 4, 0, 2, -4, 6, -10, 9, 6, -6, 4], [2, -10, 0, -3, -6, -6, 7, 1, -4, -3, -5, 5, -2], [-11, 2, -9, -1, 4, 2, 1, -2, 5, -3, 2, 6, 1], [-6, 9, -8, -2, -3, -3, 1, 10, -4, -1, 3, -1, 2], [-2, -2, -2, -2, 2, 6, -3, -9, 7, 1, -6, 7, -2], [-3, -4, -9, 0, 6, -2, 4, -4, -4, 0, -6, 2, -4], [-6, 6, 7, 2, 1, -4, 4, 2, 5, 1, 0, -3, 0], [-4, -3, -3, -1, 1, -3, -4, 9, -4, 0, 3, 0, 6], [-5, 8, 0, 5, 0, -2, 2, 1, 12, -1, -3, 0, 2], [-5, 4, 4, 0, 4, 3, -5, -2, -1, 1, 5, 0, 8], [14, -9, -3, 2, 4, 2, -1, 1, -1, 2, 2, 5, -1], [-12, -1, 7, 4, 0, -3, 4, 1, -10, 8, 0, 1, -1], [-8, 6, -4, 0, 3, -7, 5, -5, 1, 4, 5, 5, -1], [-10, 2, -3, -12, 3, -6, 2, -4, 5, -5, -6, 5, 0], [-14, -4, -9, -10, -1, -4, 4, -13, 7, -4, -14, 12, -8], [-4, -4, 2, -2, -2, 1, 0, 5, 7, 0, 5, 3, 3], [-14, 6, 6, 8, -3, 6, 3, 7, 4, 9, 10, 0, 1], [24, -1, 3, -2, 6, 3, 0, 1, 0, -6, 6, 1, -1], [26, -1, 6, 1, -1, 3, -3, -1, -12, 7, 7, -6, 7], [-3, -11, -7, -7, 0, -3, -2, -8, 2, -6, -8, 10, -3], [-15, 5, 5, 0, 4, -3, 4, 3, 3, 2, 1, 0, -6], [8, -11, -1, 2, 0, 6, -3, -1, -1, -4, 2, -5, -1], [-10, 10, -2, -1, 4, 0, 2, -9, 6, -2, 0, 5, -1], [-7, 11, -2, 4, 2, -3, 2, -5, 11, 6, 1, 1, -4], [7, 1, 4, 1, -3, -6, 7, 6, 0, -5, 0, 5, -1], [14, -6, -3, -2, -5, -7, -2, 4, 5, -4, 1, 5, -3], [-11, 1, 3, -1, 9, 0, 2, -5, -1, 0, 0, 0, -2], [7, 13, 2, 5, -1, 2, -1, -2, 0, -3, -2, -3, -1], [1, 2, 6, 3, 4, 3, 2, -4, 4, 6, 7, 6, 5], [-1, 2, 11, 7, 5, 6, 6, -1, -7, 11, 6, -5, -3], [18, -3, 4, 0, -5, -1, -3, 1, 1, -5, -4, -4, 3], [-8, -15, 1, 1, 2, 2, 0, 3, -3, 1, 4, -4, 1], [-3, 5, 2, 2, -6, 6, -2, 7, 0, -9, 6, -4, -4], [-26, 5, -5, -2, 3, -1, 6, 1, 7, 4, 5, 8, 5], [4, 0, 0, -3, 2, -8, 7, 1, 4, -6, -4, 2, -8], [-12, -6, 8, 2, -4, 0, 1, 3, -8, 5, 4, -5, 6], [16, 0, 7, 0, -5, 6, -3, 6, 3, 3, 2, -3, 6], [-3, 4, -1, -1, 2, 6, -1, -8, 11, -3, 0, 2, -3], [-1, 6, 8, 2, -5, 2, -7, 6, -1, -7, 6, -9, 2], [-1, 0, 8, 3, -4, 10, -1, 8, -10, 11, 10, -10, -2], [5, -4, 8, 0, 2, 1, 3, 4, -9, 11, 7, -8, 2], [7, -2, -2, -5, -1, -1, 7, 5, -3, 4, 1, 5, 1], [25, -12, -1, -8, -3, 0, -4, -4, 5, -9, -8, 6, 2], [-10, 9, 1, 7, 1, -3, 2, 1, 2, 6, -1, 4, 4], [6, -7, -3, -3, -4, -4, 6, 7, 3, 7, -4, 2, 1], [-7, 10, 4, 2, -6, 5, -3, 12, -7, 5, 7, -2, 6], [-2, 3, -9, 3, 8, -5, 3, -9, 13, -8, -7, 6, -10], [12, 0, 0, 0, 2, 1, 1, -8, 8, -1, -3, 0, 1], [7, -5, 3, 3, 4, -4, 0, -3, -4, -2, -1, -3, -4], [3, 21, 3, 1, 6, 1, 6, -1, -5, 0, 7, -1, -2], [-10, -4, -3, 1, 3, 0, 7, -3, 1, 7, -2, 5, 0], [9, 12, 7, 5, 0, 1, -2, -2, 4, -1, 5, -1, 1], [-1, -4, -13, -7, 4, -4, 3, -6, 7, -9, -14, 14, -11], [12, 2, 3, 0, -5, -3, 2, -2, 1, -4, -9, 3, -3], [-10, 6, 8, -2, -5, -4, 1, -1, -2, 1, 4, 2, 1], [-8, -1, 3, 2, -3, 7, -3, 6, 2, 2, 9, 0, 0], [8, 7, -9, -6, 8, -4, 5, -7, 4, -5, -7, 5, -8], [-3, -4, 2, 6, 4, 4, -2, -3, 4, 8, 0, 0, 4], [14, -5, 0, -6, 3, -5, -5, 1, -1, -9, -4, -2, -5], [2, -6, -5, -8, 1, 0, -1, 2, 1, -4, -5, 2, 0], [13, -8, 4, -3, 0, 8, -2, 1, 4, 9, 5, 6, 6], [-15, 10, 15, 7, 3, 1, 4, 7, -3, 6, 11, -2, 3], [0, 0, -1, -4, 7, 1, 6, -4, 12, -6, -5, 7, -3], [8, 1, 2, 2, -1, -4, -3, -5, -2, 6, -4, -2, 1], [-5, -14, -1, -3, -1, -4, -1, 1, -7, -2, -7, 7, -2], [3, 1, -8, 4, 10, -2, 8, -1, 4, -1, 0, 4, -4], [5, 4, -11, -3, 11, -6, 7, -13, 13, -7, -12, 12, -16], [-15, 1, -4, -2, 8, 0, 10, 1, 4, 7, 2, 6, -2], [-12, 14, -4, 3, 5, -3, 3, -5, -1, 13, 1, -2, -1], [1, 6, -5, 4, 7, -6, 10, -11, 13, -8, -2, 9, -4], [19, 1, 6, 7, -5, 8, -7, 2, -12, 7, -2, -9, -1], [1, -5, 4, 6, -3, 6, -5, -2, -4, 7, 6, -6, -5], [24, 0, -5, -6, -2, 0, -4, -1, 0, -1, -2, 2, -2], [4, -12, -4, 0, 0, -5, -2, -5, 2, -2, -7, 11, 3], [10, -12, 8, 1, -10, 6, -2, 9, -8, 10, 8, -7, 5], [-2, 7, 4, 0, -3, 1, 5, 10, -12, 9, 7, -5, 0], [-1, -15, 1, -2, -2, 1, 2, 1, -1, 2, 1, 0, 4], [-4, -4, -3, -4, -1, 4, -8, 0, 5, -5, 0, 2, -3], [8, -7, 0, 2, 1, 3, 1, -6, -6, -3, -5, 1, -6], [17, 0, 8, 5, 0, 4, 2, 7, -10, 12, 6, -7, 4], [21, -4, -3, -4, 2, -2, -4, -12, 4, 2, -6, 0, -4], [9, -2, 5, 7, 2, 6, 1, -4, -7, 9, -2, -4, 3], [-4, 10, 5, 6, 3, -6, 5, 8, -9, 15, 6, 3, -4], [-1, -5, 0, -1, 5, 2, 0, 4, -5, 8, -1, -1, 0], [15, 0, -1, -1, -8, -1, -7, -1, 6, 0, -11, 0, 1], [-6, 2, 5, 6, 3, -4, 0, 7, 3, 8, 8, -4, 4], [20, 4, -3, -6, 1, 5, -8, 0, -3, -2, 3, -3, 5], [-4, 12, -5, 3, -2, 8, -3, 5, -3, 6, 2, -2, 1], [12, -2, 2, -1, -4, 2, -2, 3, 6, -6, 2, -3, -1], [-12, -7, -6, 3, 5, -5, 4, -3, 2, -3, -7, -1, -8], [29, -2, -11, -4, 3, 2, -5, -7, 3, -12, -4, 3, -4], [-9, 4, -7, -4, -1, -8, 3, 7, 1, -6, -4, 7, 0], [-6, 0, 6, 5, 5, 7, -3, 5, 3, 1, 9, 0, 9], [-21, 4, 1, 7, 7, 2, 3, -1, -5, 3, 6, -2, 6], [-10, -1, 4, 2, -4, -4, 4, 0, 14, -6, -6, 0, 2], [-14, -6, -7, -9, -8, -10, 1, -3, -1, -4, -14, 2, 5], [23, 0, 14, 5, -6, 4, -6, 5, -20, 5, 7, -12, 10], [8, -10, -8, 0, -2, 12, -11, -3, 3, -1, -8, -1, 0], [12, 5, -12, -6, 4, 1, 2, -9, 5, -12, -11, 4, -4], [-27, 4, -12, -7, 0, -10, 0, -14, 12, -7, -14, 8, -6], [-4, -4, -8, -6, 0, -8, 2, 0, 16, -18, -8, 8, -10], [12, 4, 7, 4, -2, 2, 2, 1, 6, -1, 2, 2, 2], [20, -10, 5, -4, -13, 4, -5, 6, -9, 9, 2, -1, 8], [5, -14, -11, -5, 2, -13, 0, -10, -2, -11, -17, 11, -13], [-20, 3, 8, 5, -2, 11, -8, 1, 11, 16, 9, -1, 6], [8, -6, 6, 2, 12, 4, 1, -5, -7, 7, 2, -5, -4], [-5, -3, 2, 0, 7, -5, 2, 1, 11, 4, 1, 2, -1], [36, -6, 8, 4, -8, 1, -1, -2, -7, -3, -3, -10, -1], [4, 13, 0, -1, 7, 1, 2, -1, 6, 0, 4, -4, -2], [-5, -6, -14, -12, -2, 7, -9, 2, 3, -5, -9, 0, 2], [8, -4, -3, -2, -2, -2, 0, 5, -4, -1, 2, -10, 2], [-14, -8, 7, 3, 6, 0, -5, -1, -5, 8, 4, -8, 1], [-26, 13, 8, 4, 5, 4, 3, -4, -4, 10, 4, -3, -3], [14, -21, -6, -6, -9, -5, -8, -2, -5, -14, -8, -1, -1], [-7, -5, -4, -7, 7, 1, -3, 1, 10, 1, 3, 4, -6], [-2, -6, -9, 4, 5, -3, 7, 3, -6, 3, -1, 2, -7], [-7, 12, 9, 3, 7, 2, 8, 6, 1, 12, 14, -5, 2], [3, 0, -4, -1, 7, 4, 4, -8, 2, -2, -2, 5, -11], [7, 2, 18, 10, 3, 10, 3, 6, -8, 4, 20, -4, -1], [19, 0, 3, 1, -7, 0, -2, 0, -11, -2, -4, -1, 0], [30, -12, -2, -3, 6, 2, -1, -13, -2, -6, -6, 2, -8], [8, -13, 4, 0, -5, 1, -1, 3, -15, 3, 4, 0, 3], [13, 14, 3, 7, 1, 4, 1, -5, 5, -7, -2, 0, -10], [-1, -6, 2, -5, 7, -3, 7, -1, 11, -1, -1, 5, -3], [25, 0, -2, -4, -2, -10, 3, 2, 4, 1, -7, 4, -2], [-5, -1, 12, 5, 7, -3, 3, 3, -6, 16, 8, 1, 6], [-2, 6, 4, 2, -2, -1, 0, 9, 0, -6, 3, -5, 3], [3, -5, -5, -5, -4, -4, 2, 1, 0, -4, -5, 5, -8], [-2, 3, 1, 1, -1, -9, -2, -3, 6, 0, 1, 4, 0], [-12, 8, -5, 2, 3, 7, 1, -5, -5, 5, 1, 2, 1], [-14, -9, -6, -2, -5, -3, -3, 0, -2, -4, -6, -2, -2], [-19, -1, 10, 6, -5, 5, -2, 3, -1, 6, 3, 0, 1], [-9, 0, -10, -10, 4, -10, 7, -8, 12, -12, -10, 11, 2], [8, 11, 9, 4, -4, -4, 2, 12, -10, -4, 3, -6, 6], [3, 12, 7, 0, 7, -4, 4, 0, -3, 1, 6, -2, 2], [-11, -1, -6, 3, 7, 1, -3, 6, -5, 1, 8, -7, 3], [-13, -5, -8, -8, -5, 3, -2, -4, 2, -4, -8, 7, -4], [12, 5, -10, -5, 0, -3, 2, 5, -3, -4, -5, 7, 0], [14, 11, -5, 1, 3, -1, 3, 4, 0, 1, 9, 1, -4], [5, 11, -13, -14, -4, -1, 6, 5, 3, -12, -5, 10, 0], [3, -7, 1, 4, 10, 3, 2, -3, 5, 12, 3, 8, -4], [2, -1, 2, -3, 2, 2, 4, -4, 3, 12, 6, 2, 5], [-7, 8, -5, 5, 4, 2, -1, -5, 3, -5, -10, 5, -9], [3, -5, -8, -7, -5, 1, -1, 3, 8, 1, -5, 2, 4], [13, -10, -8, -3, -4, -13, -2, -4, 0, -13, -3, 4, -7], [-3, 4, 8, 2, 1, 0, -3, 2, -12, -6, 2, -4, 5], [28, 7, 5, 5, -8, -3, -1, 1, -5, -2, 3, -2, 0], [11, 4, -6, -1, -6, -2, 0, -3, 6, -6, 4, 3, 2], [11, 8, -6, -7, -4, -8, 1, 0, 7, -3, -8, 8, 4], [-18, 14, -4, 2, -3, 2, 1, -1, 12, 3, -2, 0, 5], [0, -1, -10, 4, 7, -4, -1, -5, 0, 6, -4, 2, -1], [21, -20, 4, 3, -4, -4, -4, 9, -16, 4, 4, -9, 4], [6, -11, 1, -2, 11, 5, -1, -8, 0, 8, -3, 2, -4], [-30, 7, -11, -4, 14, -1, 5, -6, 9, 0, -3, 11, -7], [18, -18, -5, -1, 6, 6, -5, -1, -13, 4, 4, -2, 7], [21, -9, 2, 3, 0, 2, -1, 7, -6, -1, 8, -5, 8], [-29, 1, 1, 0, 0, 2, 2, -9, 3, 0, 0, 8, -3], [5, 7, 6, 6, -5, 1, -6, 4, -12, -3, 11, -14, 2], [31, 9, 4, -3, -4, 1, -2, 1, -9, -1, 1, -4, 6], [-1, -17, 12, 3, -5, -1, 0, 7, -2, 1, 7, -1, 7], [-11, 8, 3, 9, 3, 9, -4, 1, 0, 18, 7, -12, 7], [-3, 1, -3, -1, -2, 1, 3, -5, -2, -1, -10, 1, 3], [5, -7, 6, 0, 6, 9, -1, 2, -4, 12, 9, -3, 3], [-26, 8, 2, 10, 10, 2, 10, -6, 6, 0, 8, 4, 0], [-16, 17, 19, 13, 2, 8, 0, 5, -7, 13, 14, -8, -1], [3, 9, -2, 3, 1, 12, -1, 4, 6, 3, 0, -5, -1], [28, -27, 0, -7, -6, 8, -9, 4, -4, 6, -6, 1, 6], [-21, 5, 4, 2, 4, 3, 12, 1, 9, 12, 3, 7, 4], [12, 3, 0, 0, 3, -1, -1, -2, -10, 10, 5, -9, 6], [-1, 2, 9, 10, -3, 12, 2, 2, -5, 12, 7, -11, 6], [21, -22, 7, 1, 3, 6, -4, -5, -3, -7, -2, -3, -13], [8, 2, 3, -2, -13, 3, -8, -2, -7, -12, -5, -7, 1], [-30, 8, -10, -3, 1, -9, 3, -1, 11, -15, -13, 8, -3], [-13, -3, 8, 5, 1, 3, -4, -3, -8, 3, 9, -15, -1], [-4, -3, -5, -6, 2, -5, -4, -4, 9, 1, -2, 5, 2], [-4, 18, 4, 9, -3, -4, 8, 12, -8, 3, 10, -8, 3], [10, 7, -8, 0, 1, -14, 6, -1, 7, -6, -7, 8, -8], [-3, 11, 6, 8, -9, -3, 2, 13, -17, 14, 13, -8, 5], [-1, -2, 4, -2, 6, -4, 1, -2, 0, -2, -2, 3, -2], [11, 6, -1, 3, -3, -7, -2, -5, -5, 4, -1, -4, 7], [4, 3, 2, 7, 0, 2, -1, -6, 12, 2, 4, 5, 6], [40, -7, 11, 4, -5, -3, 1, 10, -6, 12, 7, -4, 4], [2, 1, -9, -3, 2, -10, 2, -3, 7, -1, -14, 6, 3], [-10, -1, 7, 0, 6, 7, -4, -8, 3, 6, 5, -4, 6], [17, -9, 14, 2, 5, 15, 0, -3, 3, 12, 5, -4, 5], [8, 14, 12, 14, 8, 9, 2, 5, 8, 14, 19, -3, 3], [-2, 7, 2, 4, 3, 7, -6, 4, -13, 6, 8, -13, 11], [-16, -17, 8, 2, -1, 3, 2, -2, 1, 7, 7, 0, 3], [10, -9, 0, -4, -1, -7, -3, 4, -6, 8, -1, -5, 12], [-13, -1, 3, -4, 0, -9, -1, 0, 3, -3, 2, -2, 2], [-13, 8, -19, -19, 3, -8, -1, -5, -7, -21, -14, 10, -4]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_6016_a_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_6016_2_a_n();".
// 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_6016_2_a_n(:prec:=13)
    chi := MakeCharacter_6016_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_6016_2_a_n();".
// 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_6016_2_a_n( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_6016_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![832, -1440, -4720, 1488, 6230, 5, -3358, -438, 840, 163, -96, -22, 4, 1]>,<5,R![1216, -9768, 14632, 14608, -23656, -4436, 11072, -76, -2184, 198, 190, -26, -6, 1]>,<13,R![6740768, -19224520, 12691488, 1908872, -3872192, 431576, 413124, -78184, -20200, 4540, 462, -112, -4, 1]>],Snew);
    return Vf;
end function;