
// Make newform 9675.2.a.da in Magma, downloaded from the LMFDB on 06 June 2026.
// To make the character of type GrpDrchElt, type "MakeCharacter_9675_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_9675_2_a_da();".
// 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_9675_2_a_da();".
// 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 := [100, 0, -1388, 0, 7084, 0, -17428, 0, 22796, 0, -17056, 0, 7613, 0, -2052, 0, 326, 0, -28, 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, 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], [6, 0, -7, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 748, 0, -6564, 0, 17298, 0, -22786, 0, 17056, 0, -7613, 0, 2052, 0, -326, 0, 28, 0, -1], [108, 0, -1680, 0, 7148, 0, -12748, 0, 11616, 0, -5928, 0, 1757, 0, -299, 0, 27, 0, -1, 0], [0, 1076, 0, -13808, 0, 58256, 0, -101492, 0, 89752, 0, -44506, 0, 12869, 0, -2147, 0, 191, 0, -7], [268, 0, -3344, 0, 12464, 0, -19524, 0, 15882, 0, -7380, 0, 2028, 0, -325, 0, 28, 0, -1, 0], [372, 0, -3776, 0, 12908, 0, -19706, 0, 15914, 0, -7382, 0, 2028, 0, -325, 0, 28, 0, -1, 0], [-708, 0, 8296, 0, -31348, 0, 50952, 0, -43020, 0, 20624, 0, -5809, 0, 949, 0, -83, 0, 3, 0], [748, 0, -8552, 0, 31556, 0, -51004, 0, 43024, 0, -20624, 0, 5809, 0, -949, 0, 83, 0, -3, 0], [0, -420, 0, 5340, 0, -20270, 0, 32980, 0, -27906, 0, 13431, 0, -3803, 0, 625, 0, -55, 0, 2], [0, -4544, 0, 44432, 0, -150744, 0, 232238, 0, -190528, 0, 89984, 0, -25171, 0, 4103, 0, -359, 0, 13], [0, -5028, 0, 52324, 0, -183208, 0, 286216, 0, -236156, 0, 111678, 0, -31207, 0, 5076, 0, -443, 0, 16], [1836, 0, -20688, 0, 75556, 0, -120380, 0, 100432, 0, -47864, 0, 13459, 0, -2201, 0, 193, 0, -7, 0], [-2068, 0, 22032, 0, -77772, 0, 121892, 0, -100916, 0, 47936, 0, -13463, 0, 2201, 0, -193, 0, 7, 0], [0, 9292, 0, -112496, 0, 419152, 0, -671844, 0, 561724, 0, -267842, 0, 75283, 0, -12299, 0, 1077, 0, -39], [0, 11468, 0, -125984, 0, 453788, 0, -717416, 0, 595836, 0, -283068, 0, 79387, 0, -12951, 0, 1133, 0, -41], [0, 772, 0, -8918, 0, 32958, 0, -52595, 0, 43804, 0, -20812, 0, 5831, 0, -950, 0, 83, 0, -3]];
    Rf_basisdens := [1, 1, 1, 1, 1, 20, 8, 40, 4, 4, 8, 8, 4, 20, 20, 8, 8, 40, 40, 2];
    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_9675_a();"
function MakeCharacter_9675_a()
    N := 9675;
    order := 1;
    char_gens := [7526, 8902, 5851];
    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_9675_a_Hecke( : Kf := Kf)
    return MakeCharacter_9675_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]];
    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], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, -1], [-2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 1], [0, -1, 0, -1, 0, -1, 0, -1, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, -1], [-2, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 1, 0, 0, 0, -1, -1, 0, 0, 0], [-2, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0], [0, -2, 0, 1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 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, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1], [0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0], [0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 1, 0], [0, 0, 0, 0, 1, 0, -1, 0, 1, -1, 1, 1, 0, 0, 0, -1, -2, 0, 0, 0], [-3, 0, -1, 0, 0, 0, -1, 0, 0, -1, 2, 1, 0, 0, 0, -1, -1, 0, 0, 0], [0, -2, 0, 2, 0, -1, 0, -1, 0, 0, 0, 0, 1, -1, 1, 0, 0, -1, 0, 1], [-2, 0, 0, 0, 0, 0, -1, 0, -1, 0, -1, -1, 0, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, -1, 2, 0, -1, 0, 0, 0, 3, 1, 0, 0, 0], [0, -3, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, -2, 2, -1, 0, 0, 0, 0, 0], [0, 1, 0, -3, 0, -2, 0, 2, 0, 0, 0, 0, -3, 2, -2, 0, 0, 1, -1, -2], [-3, 0, 1, 0, 0, 0, 1, 0, -1, 1, -1, -2, 0, 0, 0, 0, 1, 0, 0, 0], [0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0], [-3, 0, 1, 0, 0, 0, 1, 0, 0, 1, -2, -1, 0, 0, 0, 1, -1, 0, 0, 0], [0, 1, 0, -1, 0, -2, 0, -1, 0, 0, 0, 0, -2, 1, -1, 0, 0, -1, 1, -2], [2, 0, 1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 3, 0, 0, -2, 0, 2], [-3, 0, 1, 0, -1, 0, -1, 0, -2, -2, -1, 1, 0, 0, 0, 1, -2, 0, 0, 0], [0, -4, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, -3, 2, -2, 0, 0, 1, 1, -1], [0, -2, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, -1, 0], [-2, 0, -1, 0, 1, 0, 1, 0, -1, 2, 0, 1, 0, 0, 0, -1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, -1, 1], [-2, 0, -2, 0, 1, 0, 0, 0, 2, 1, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0], [-6, 0, 2, 0, 2, 0, 0, 0, 1, -1, 1, 2, 0, 0, 0, -1, -1, 0, 0, 0], [-2, 0, 2, 0, 2, 0, 1, 0, -2, -1, 1, 1, 0, 0, 0, -2, -1, 0, 0, 0], [0, 1, 0, 2, 0, 1, 0, 1, 0, 0, 0, 0, -1, -2, 1, 0, 0, -2, 2, 0], [0, -1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1], [0, 1, 0, 1, 0, -2, 0, -2, 0, 0, 0, 0, 0, 2, -4, 0, 0, -2, 2, -3], [4, 0, 0, 0, 2, 0, 2, 0, 1, 0, 2, 0, 0, 0, 0, 1, 3, 0, 0, 0], [0, 2, 0, 4, 0, 1, 0, -1, 0, 0, 0, 0, 0, -1, 3, 0, 0, 0, 1, 0], [-7, 0, -3, 0, -2, 0, -1, 0, 2, -1, 2, 1, 0, 0, 0, -1, -1, 0, 0, 0], [0, 3, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, -3, 2, 0, 0, 2, -1, 0], [-2, 0, 0, 0, -3, 0, 0, 0, -1, 0, -4, 0, 0, 0, 0, 1, 0, 0, 0, 0], [3, 0, 2, 0, 3, 0, 2, 0, 1, 1, 3, 1, 0, 0, 0, 0, 2, 0, 0, 0], [-6, 0, -4, 0, -2, 0, -1, 0, 0, 1, 1, 1, 0, 0, 0, 0, -1, 0, 0, 0], [0, -3, 0, 2, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, -5, -1, 2], [0, 0, 1, 0, 3, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 4, 0, -1, 0, -2, 0, 4, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, -2], [0, 3, 0, 1, 0, -1, 0, 2, 0, 0, 0, 0, -1, 1, -3, 0, 0, 0, 1, -2], [4, 0, 2, 0, 3, 0, 1, 0, 0, -4, 1, 1, 0, 0, 0, -2, -1, 0, 0, 0], [0, 2, 0, -2, 0, -1, 0, -1, 0, 0, 0, 0, -2, -1, 0, 0, 0, 1, 1, -3], [0, 3, 0, -3, 0, -1, 0, 2, 0, 0, 0, 0, -2, 0, -1, 0, 0, 3, -1, -2], [0, 2, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 6, -4, 2, 0, 0, 0, 0, 4], [0, 1, 0, 2, 0, 1, 0, -4, 0, 0, 0, 0, 1, 3, 0, 0, 0, -1, 1, 1], [0, 0, 5, 0, 0, 0, 1, 0, -1, 2, -4, -3, 0, 0, 0, 3, 1, 0, 0, 0], [-12, 0, -2, 0, -4, 0, -3, 0, 1, -2, -3, 1, 0, 0, 0, -3, -3, 0, 0, 0], [0, 3, 0, 3, 0, -2, 0, -3, 0, 0, 0, 0, 1, 2, 3, 0, 0, 1, 0, -1], [-4, 0, 3, 0, -3, 0, 0, 0, -1, -1, -6, -2, 0, 0, 0, 1, -1, 0, 0, 0], [0, 1, 0, -1, 0, 4, 0, -4, 0, 0, 0, 0, 0, -1, 4, 0, 0, 0, 1, 2], [-5, 0, 5, 0, 1, 0, 1, 0, 2, 0, -1, -1, 0, 0, 0, -3, 0, 0, 0, 0], [0, 3, 0, 4, 0, -2, 0, -1, 0, 0, 0, 0, 1, -3, 4, 0, 0, 1, -1, 2], [-9, 0, -2, 0, -5, 0, -3, 0, -3, 2, -1, 1, 0, 0, 0, -2, -2, 0, 0, 0], [0, 1, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 3, 2, -4, 0, 0, 3, -2, -2], [1, 0, -2, 0, -4, 0, -5, 0, 2, -2, -2, 2, 0, 0, 0, -1, -2, 0, 0, 0], [-4, 0, 5, 0, 1, 0, 2, 0, 2, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0], [0, -7, 0, -2, 0, 3, 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, -3, -1, 2], [-3, 0, -2, 0, 2, 0, -1, 0, -2, 1, 4, 3, 0, 0, 0, -3, 1, 0, 0, 0], [0, -1, 0, 1, 0, -3, 0, 1, 0, 0, 0, 0, -1, 1, -5, 0, 0, -2, 2, -1], [0, 4, 0, -4, 0, 2, 0, 1, 0, 0, 0, 0, 0, -3, -3, 0, 0, 2, -2, 0], [-8, 0, -4, 0, -1, 0, -2, 0, 2, -1, 3, -2, 0, 0, 0, 0, -3, 0, 0, 0], [-3, 0, 2, 0, 1, 0, 1, 0, -1, -3, 0, 1, 0, 0, 0, -4, 1, 0, 0, 0], [-4, 0, -3, 0, 1, 0, 0, 0, 2, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0], [0, -3, 0, 3, 0, -1, 0, -1, 0, 0, 0, 0, -1, 1, 3, 0, 0, -3, 0, 4], [0, 0, 0, -2, 0, 5, 0, 5, 0, 0, 0, 0, 1, 1, -1, 0, 0, -3, 3, -1], [-9, 0, 2, 0, 3, 0, 1, 0, 0, 0, 3, 0, 0, 0, 0, 1, 2, 0, 0, 0], [0, -3, 0, 0, 0, 3, 0, 2, 0, 0, 0, 0, 1, 3, 2, 0, 0, -1, -3, 3], [2, 0, -2, 0, -2, 0, -2, 0, -3, 3, -2, -4, 0, 0, 0, 1, 3, 0, 0, 0], [0, 0, 0, 6, 0, -1, 0, -1, 0, 0, 0, 0, -3, -1, 3, 0, 0, -1, 4, 3], [-4, 0, -4, 0, 1, 0, 1, 0, 0, -2, -1, 3, 0, 0, 0, -2, -1, 0, 0, 0], [0, -1, 0, -1, 0, 3, 0, -2, 0, 0, 0, 0, 1, 2, 5, 0, 0, -1, 2, 2], [-10, 0, -2, 0, 2, 0, 1, 0, -1, 5, 4, 1, 0, 0, 0, -1, 4, 0, 0, 0], [2, 0, 1, 0, 3, 0, 3, 0, 3, 2, 2, -1, 0, 0, 0, -1, 5, 0, 0, 0], [0, 5, 0, -2, 0, -1, 0, 2, 0, 0, 0, 0, -1, -4, -2, 0, 0, 6, 1, -1], [0, 7, 0, -1, 0, 2, 0, -2, 0, 0, 0, 0, 1, -4, 2, 0, 0, 1, 2, 2], [0, 0, 8, 0, 2, 0, 4, 0, -3, 3, -3, -6, 0, 0, 0, 1, 5, 0, 0, 0], [0, 1, 0, 2, 0, -1, 0, -2, 0, 0, 0, 0, -1, 2, 2, 0, 0, -2, 0, 1], [1, 0, 10, 0, 1, 0, 3, 0, 0, 4, 0, -1, 0, 0, 0, 3, 3, 0, 0, 0], [0, 3, 0, 2, 0, 1, 0, 1, 0, 0, 0, 0, 5, -5, 5, 0, 0, 1, -6, 4], [0, 0, 0, -4, 0, 1, 0, 1, 0, 0, 0, 0, 2, -1, -6, 0, 0, 7, -5, 3], [7, 0, 6, 0, 0, 0, 3, 0, -3, 3, -1, -3, 0, 0, 0, 4, 5, 0, 0, 0], [0, 0, 0, 0, 0, -2, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2], [0, 0, 0, 0, -1, 0, -1, 0, -2, 1, 1, 6, 0, 0, 0, -2, -4, 0, 0, 0], [0, -3, 0, -1, 0, 5, 0, 3, 0, 0, 0, 0, 1, -5, 3, 0, 0, -1, 2, 4], [0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, -5, 2, 5, 0, 0, -1, 4, -1], [0, 0, 0, -2, 0, 1, 0, -3, 0, 0, 0, 0, -4, 1, 3, 0, 0, 0, 4, 2], [-5, 0, 2, 0, 1, 0, -2, 0, 2, -2, 3, -2, 0, 0, 0, 1, 4, 0, 0, 0], [-6, 0, -1, 0, -4, 0, 0, 0, 2, -2, -2, -2, 0, 0, 0, 0, -2, 0, 0, 0], [-3, 0, 3, 0, 0, 0, -1, 0, 0, -1, -4, -1, 0, 0, 0, 1, -3, 0, 0, 0], [0, 3, 0, 7, 0, 1, 0, -3, 0, 0, 0, 0, -1, -1, 3, 0, 0, 0, 6, -1], [0, 0, 0, 0, 0, -4, 0, 1, 0, 0, 0, 0, 0, 4, -1, 0, 0, -2, 1, -3], [0, 8, 0, 5, 0, -1, 0, -3, 0, 0, 0, 0, 4, -4, 1, 0, 0, -1, -4, 2], [-3, 0, -2, 0, 2, 0, -3, 0, -2, 0, 4, 6, 0, 0, 0, -1, 0, 0, 0, 0], [-8, 0, -2, 0, 0, 0, 1, 0, -5, 1, 2, -1, 0, 0, 0, 1, -2, 0, 0, 0], [0, 6, 0, 6, 0, 4, 0, 3, 0, 0, 0, 0, 3, -1, 7, 0, 0, 0, -3, 4], [0, -8, 0, -3, 0, 4, 0, 3, 0, 0, 0, 0, -1, -1, -3, 0, 0, 0, 3, -2], [0, -5, 0, -1, 0, -5, 0, -6, 0, 0, 0, 0, -3, 4, -3, 0, 0, -3, 2, -2], [11, 0, 4, 0, 3, 0, 4, 0, -3, 6, -1, -8, 0, 0, 0, 6, 3, 0, 0, 0], [-4, 0, 6, 0, -2, 0, -2, 0, 0, 2, 1, 2, 0, 0, 0, -2, 1, 0, 0, 0], [-7, 0, 8, 0, -6, 0, 1, 0, -3, -3, -7, -5, 0, 0, 0, 0, -3, 0, 0, 0], [0, 3, 0, -6, 0, 2, 0, 2, 0, 0, 0, 0, -2, 0, -4, 0, 0, 7, 0, -4], [-6, 0, -6, 0, 3, 0, 0, 0, 0, 4, 2, 4, 0, 0, 0, 0, 4, 0, 0, 0], [7, 0, 4, 0, 5, 0, 5, 0, -1, 3, 2, 1, 0, 0, 0, 2, 1, 0, 0, 0], [0, 9, 0, 5, 0, 1, 0, -3, 0, 0, 0, 0, 1, -3, 3, 0, 0, -1, 6, -4], [-5, 0, 4, 0, -2, 0, 3, 0, -5, -1, -1, -1, 0, 0, 0, -2, -1, 0, 0, 0], [0, 0, 0, -4, 0, 4, 0, -3, 0, 0, 0, 0, -3, 1, 3, 0, 0, 2, -1, 2], [0, -4, 0, -11, 0, -2, 0, -1, 0, 0, 0, 0, -1, 7, -10, 0, 0, 4, -7, -6], [0, 3, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 3, -3, -5, 0, 0, 2, 2, 1], [-10, 0, -7, 0, -6, 0, -6, 0, 3, -4, -2, 4, 0, 0, 0, -1, -3, 0, 0, 0], [-1, 0, -2, 0, -3, 0, 0, 0, -1, 5, -1, -4, 0, 0, 0, 4, 4, 0, 0, 0], [0, -10, 0, -6, 0, 2, 0, 4, 0, 0, 0, 0, 0, -2, -4, 0, 0, 0, 2, 0], [0, -2, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, -6, 4, 1, 0, 0, -2, 7, -3], [1, 0, -4, 0, -6, 0, 0, 0, -5, 3, -3, 2, 0, 0, 0, 4, 2, 0, 0, 0], [0, 5, 0, -4, 0, -1, 0, 4, 0, 0, 0, 0, -3, 0, -2, 0, 0, -2, -2, 1], [-4, 0, -1, 0, 0, 0, 3, 0, 0, 2, -6, -3, 0, 0, 0, 2, 0, 0, 0, 0], [0, 9, 0, -4, 0, -3, 0, 5, 0, 0, 0, 0, -5, 0, -3, 0, 0, 3, -3, -1], [-6, 0, -6, 0, 0, 0, 2, 0, 2, -1, 2, 6, 0, 0, 0, 0, -2, 0, 0, 0], [-8, 0, 4, 0, 2, 0, 6, 0, -3, 6, 0, -2, 0, 0, 0, 3, 0, 0, 0, 0], [0, 0, 2, 0, 1, 0, 1, 0, -1, -2, -1, -2, 0, 0, 0, -1, -1, 0, 0, 0], [0, -5, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 1, 3, -2], [-2, 0, -8, 0, -5, 0, -3, 0, -3, 4, 5, 0, 0, 0, 0, -1, 1, 0, 0, 0], [-10, 0, 4, 0, -4, 0, 0, 0, -3, 4, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0], [0, -3, 0, -11, 0, 0, 0, 2, 0, 0, 0, 0, -1, -2, -8, 0, 0, 7, -1, -2], [4, 0, 4, 0, 4, 0, 4, 0, 1, 0, 0, -4, 0, 0, 0, -3, 1, 0, 0, 0], [0, -4, 0, 6, 0, 0, 0, -3, 0, 0, 0, 0, 1, -5, 4, 0, 0, -2, -3, 4], [4, 0, -2, 0, -6, 0, -2, 0, -2, 0, 2, 0, 0, 0, 0, -4, -4, 0, 0, 0], [0, 1, 0, -4, 0, -2, 0, -3, 0, 0, 0, 0, 0, -4, -5, 0, 0, 3, 3, -3], [0, 7, 0, 6, 0, -5, 0, 0, 0, 0, 0, 0, -3, 2, 6, 0, 0, -6, 6, 1], [2, 0, -2, 0, -5, 0, -2, 0, -1, 2, -2, -2, 0, 0, 0, -3, -4, 0, 0, 0], [0, 5, 0, -7, 0, -4, 0, 1, 0, 0, 0, 0, -3, 8, -9, 0, 0, -1, -2, -7], [2, 0, 3, 0, 0, 0, 8, 0, -3, 0, -1, -8, 0, 0, 0, 1, 4, 0, 0, 0], [0, -3, 0, -2, 0, -2, 0, -2, 0, 0, 0, 0, -8, 8, 0, 0, 0, -4, 5, -5], [2, 0, 2, 0, -1, 0, 7, 0, -6, -2, -7, -5, 0, 0, 0, 6, 1, 0, 0, 0], [0, 11, 0, 1, 0, -1, 0, -1, 0, 0, 0, 0, 1, 5, -5, 0, 0, 3, -4, -2], [0, 0, 1, 0, -1, 0, 2, 0, -2, -1, -3, -1, 0, 0, 0, 4, 1, 0, 0, 0], [0, 3, 0, -1, 0, 2, 0, 6, 0, 0, 0, 0, 6, -3, 2, 0, 0, 0, -3, 0], [-2, 0, -4, 0, 4, 0, -2, 0, 3, 2, 0, 3, 0, 0, 0, 1, -2, 0, 0, 0], [0, -3, 0, -4, 0, -3, 0, -2, 0, 0, 0, 0, -2, 6, -6, 0, 0, -1, -3, 0], [-12, 0, -3, 0, -3, 0, -4, 0, -5, 3, 4, 4, 0, 0, 0, 1, 3, 0, 0, 0], [0, 6, 0, -4, 0, 0, 0, 2, 0, 0, 0, 0, -2, 1, -8, 0, 0, 3, -1, 0], [-10, 0, -3, 0, 0, 0, -2, 0, 3, 0, 1, -4, 0, 0, 0, 1, 0, 0, 0, 0], [0, -3, 0, 2, 0, 3, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 3, 1, 4], [-3, 0, -1, 0, 1, 0, -1, 0, 0, 4, 1, 3, 0, 0, 0, 5, 2, 0, 0, 0], [0, -2, 0, -2, 0, 0, 0, 6, 0, 0, 0, 0, -1, 6, 2, 0, 0, -5, 1, 3], [2, 0, -5, 0, 4, 0, 2, 0, 2, -4, 6, -4, 0, 0, 0, -4, 0, 0, 0, 0], [0, -3, 0, -1, 0, 1, 0, 5, 0, 0, 0, 0, -2, 1, 3, 0, 0, -4, 2, 3], [-6, 0, -6, 0, -6, 0, 2, 0, -1, 2, 2, -2, 0, 0, 0, -1, -2, 0, 0, 0], [0, -4, 0, -1, 0, 9, 0, -1, 0, 0, 0, 0, 2, 2, -5, 0, 0, -1, 4, -2], [0, -3, 0, -8, 0, -3, 0, 3, 0, 0, 0, 0, -7, 4, -5, 0, 0, 4, 0, -6], [0, -4, 0, -4, 0, -6, 0, 4, 0, 0, 0, 0, 2, -2, -7, 0, 0, 6, -6, -4], [6, 0, 5, 0, 4, 0, 2, 0, -3, -4, -3, 2, 0, 0, 0, -1, -2, 0, 0, 0], [0, 2, 0, -1, 0, -1, 0, -2, 0, 0, 0, 0, 2, 0, 2, 0, 0, -4, 9, -2], [0, -9, 0, -8, 0, -3, 0, 5, 0, 0, 0, 0, -1, 2, -7, 0, 0, 3, 3, -5], [0, 16, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, -2, 2, 0, 0, 4, -2, 6], [-10, 0, 2, 0, 2, 0, 2, 0, -2, 1, -2, 1, 0, 0, 0, 0, 5, 0, 0, 0], [-18, 0, -6, 0, 6, 0, 2, 0, 3, 2, 0, 0, 0, 0, 0, 3, -2, 0, 0, 0], [2, 0, 2, 0, 1, 0, -3, 0, 5, -3, -1, 1, 0, 0, 0, -3, 0, 0, 0, 0], [0, -9, 0, 2, 0, 3, 0, 5, 0, 0, 0, 0, 5, 0, 1, 0, 0, -5, -7, 1], [0, 2, 0, 2, 0, 1, 0, -1, 0, 0, 0, 0, 4, 5, -5, 0, 0, -2, -1, -4], [-3, 0, -2, 0, -3, 0, 0, 0, 1, 0, 1, -2, 0, 0, 0, 4, 5, 0, 0, 0], [0, 3, 0, -5, 0, -1, 0, 9, 0, 0, 0, 0, -2, 5, -7, 0, 0, 6, -1, -3], [3, 0, -5, 0, 4, 0, 5, 0, -1, 5, 5, -4, 0, 0, 0, 2, 1, 0, 0, 0], [8, 0, 4, 0, 0, 0, 1, 0, -3, -8, -3, -5, 0, 0, 0, 1, 3, 0, 0, 0], [0, 5, 0, 3, 0, -2, 0, -5, 0, 0, 0, 0, -3, -1, 3, 0, 0, 2, 9, -3], [0, 0, 4, 0, 1, 0, -2, 0, 2, 5, -4, -2, 0, 0, 0, 6, -1, 0, 0, 0], [0, 7, 0, -5, 0, -4, 0, -12, 0, 0, 0, 0, -2, 0, -10, 0, 0, 4, 0, -3], [-26, 0, -10, 0, -2, 0, -2, 0, 0, 10, 6, 4, 0, 0, 0, -2, 0, 0, 0, 0], [-8, 0, -10, 0, -4, 0, -6, 0, -2, -8, 0, 4, 0, 0, 0, -4, -2, 0, 0, 0], [3, 0, -4, 0, 1, 0, -1, 0, -2, 1, -4, 9, 0, 0, 0, -1, -3, 0, 0, 0], [0, 2, 0, -5, 0, -3, 0, 0, 0, 0, 0, 0, -10, 7, -6, 0, 0, 1, 4, -8], [-27, 0, -6, 0, -3, 0, -7, 0, -3, -3, 0, 7, 0, 0, 0, -6, -9, 0, 0, 0], [0, 5, 0, 12, 0, 3, 0, -3, 0, 0, 0, 0, 3, -5, 12, 0, 0, -5, 8, 6], [0, -2, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 1, -3, -7, 0, 0, 2, -5, 0], [0, 6, 0, 0, 0, -1, 0, 3, 0, 0, 0, 0, -4, 3, -1, 0, 0, 0, 2, -8], [-9, 0, -4, 0, -1, 0, 2, 0, -3, 1, 1, 0, 0, 0, 0, 6, 8, 0, 0, 0], [-2, 0, -14, 0, 4, 0, 1, 0, 0, 3, 2, 3, 0, 0, 0, 2, 4, 0, 0, 0], [-2, 0, 2, 0, 7, 0, 1, 0, 6, -4, 4, 3, 0, 0, 0, -4, 0, 0, 0, 0], [0, 12, 0, 2, 0, 1, 0, 1, 0, 0, 0, 0, 6, -1, 7, 0, 0, 0, -5, 4], [-3, 0, 1, 0, 2, 0, 3, 0, -2, -5, 4, 1, 0, 0, 0, 3, 7, 0, 0, 0], [0, 5, 0, 2, 0, 1, 0, -4, 0, 0, 0, 0, 0, -6, 6, 0, 0, 3, 3, 4], [4, 0, 4, 0, 5, 0, 0, 0, -6, -6, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0], [0, 9, 0, 5, 0, 6, 0, 0, 0, 0, 0, 0, 6, -10, 6, 0, 0, -2, -3, 11], [0, 5, 0, 7, 0, 5, 0, -4, 0, 0, 0, 0, 2, -2, 4, 0, 0, -7, 5, 2], [0, -7, 0, -3, 0, -3, 0, -1, 0, 0, 0, 0, -3, 5, 5, 0, 0, 1, 4, -6], [2, 0, 5, 0, -4, 0, -2, 0, -1, -4, 0, -8, 0, 0, 0, 1, -1, 0, 0, 0], [-7, 0, 1, 0, 3, 0, 5, 0, -1, 4, -2, -8, 0, 0, 0, 4, 6, 0, 0, 0], [0, 3, 0, 4, 0, -2, 0, -11, 0, 0, 0, 0, -4, 4, -1, 0, 0, -3, 7, -3], [0, 3, 0, 5, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, -5, -3, 4], [0, -2, 0, -3, 0, -7, 0, 5, 0, 0, 0, 0, -6, 0, -3, 0, 0, 1, -6, -6], [7, 0, -10, 0, -3, 0, -2, 0, 1, -9, 3, 5, 0, 0, 0, -4, -4, 0, 0, 0], [-3, 0, 6, 0, 7, 0, 1, 0, 3, -2, -5, 5, 0, 0, 0, 2, 0, 0, 0, 0], [-10, 0, -4, 0, 2, 0, 0, 0, 2, 4, 8, 0, 0, 0, 0, -2, -2, 0, 0, 0], [0, 7, 0, 3, 0, 1, 0, -1, 0, 0, 0, 0, 6, -3, -5, 0, 0, 4, -1, 1], [0, 1, 0, -4, 0, -7, 0, 2, 0, 0, 0, 0, -4, 4, 1, 0, 0, 1, 1, 0], [10, 0, 8, 0, -4, 0, 0, 0, -1, 0, 2, -1, 0, 0, 0, 1, 6, 0, 0, 0], [0, 10, 0, 5, 0, -3, 0, -4, 0, 0, 0, 0, 5, -3, 0, 0, 0, -1, -3, 0], [0, 7, 0, 3, 0, 1, 0, 1, 0, 0, 0, 0, -2, -3, 7, 0, 0, -8, 0, 5], [-4, 0, 1, 0, 5, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [3, 0, 0, 0, 3, 0, -1, 0, -1, -7, 0, -3, 0, 0, 0, -6, -3, 0, 0, 0], [0, 2, 0, 8, 0, 0, 0, -4, 0, 0, 0, 0, 8, -5, 2, 0, 0, 1, -3, 10], [8, 0, 1, 0, 1, 0, 2, 0, -1, 7, 2, -4, 0, 0, 0, -1, -1, 0, 0, 0], [0, -14, 0, -8, 0, 2, 0, 11, 0, 0, 0, 0, 0, 2, -7, 0, 0, -2, -5, 3], [0, 0, 0, 6, 0, 1, 0, 3, 0, 0, 0, 0, 6, -3, -3, 0, 0, 2, -1, -2], [2, 0, -7, 0, 9, 0, 0, 0, 7, 2, 6, 8, 0, 0, 0, -3, 5, 0, 0, 0], [6, 0, -2, 0, -2, 0, -4, 0, 4, -2, 1, 2, 0, 0, 0, -4, -5, 0, 0, 0], [0, 6, 0, -4, 0, -1, 0, 3, 0, 0, 0, 0, 5, -5, 3, 0, 0, 3, -3, 1], [0, -7, 0, 7, 0, -5, 0, -6, 0, 0, 0, 0, 0, 0, 8, 0, 0, -9, 5, 0], [0, 11, 0, -2, 0, -3, 0, -4, 0, 0, 0, 0, -3, -4, -2, 0, 0, -3, 0, -6], [7, 0, 10, 0, 1, 0, 0, 0, 1, -8, -1, -4, 0, 0, 0, -2, -3, 0, 0, 0], [0, 0, 6, 0, -3, 0, -1, 0, 5, 0, -2, -1, 0, 0, 0, 7, 1, 0, 0, 0], [0, -5, 0, -9, 0, -3, 0, -5, 0, 0, 0, 0, -7, 7, -7, 0, 0, 5, 3, -6], [-4, 0, 1, 0, -4, 0, -8, 0, 5, -4, -7, -2, 0, 0, 0, 3, -4, 0, 0, 0], [0, 0, 0, -2, 0, -2, 0, 3, 0, 0, 0, 0, 1, -7, 9, 0, 0, -2, 1, 2], [2, 0, 7, 0, 8, 0, 1, 0, 2, 2, -4, -5, 0, 0, 0, 6, 6, 0, 0, 0], [0, -7, 0, 8, 0, 3, 0, -2, 0, 0, 0, 0, 3, 2, 14, 0, 0, -9, 2, 6], [0, 10, 0, -2, 0, -1, 0, -7, 0, 0, 0, 0, -4, 7, 1, 0, 0, -4, 3, -2], [3, 0, -6, 0, -3, 0, 1, 0, 0, 0, -8, -3, 0, 0, 0, -3, -3, 0, 0, 0], [0, 3, 0, 3, 0, -1, 0, -5, 0, 0, 0, 0, 4, 7, 3, 0, 0, -4, -5, -1], [-10, 0, -4, 0, -8, 0, -2, 0, 1, -5, -9, 2, 0, 0, 0, 3, -5, 0, 0, 0], [-4, 0, 5, 0, -4, 0, -6, 0, -2, 6, 2, 6, 0, 0, 0, -2, -2, 0, 0, 0], [0, 0, -11, 0, -3, 0, -11, 0, 1, -8, 4, 7, 0, 0, 0, -5, -7, 0, 0, 0], [0, 2, 0, 6, 0, 2, 0, 2, 0, 0, 0, 0, -2, 0, 6, 0, 0, -8, -1, 0], [0, 0, -5, 0, -4, 0, -2, 0, -1, -4, -5, -2, 0, 0, 0, -1, 4, 0, 0, 0], [0, -2, 0, 10, 0, 1, 0, -4, 0, 0, 0, 0, -3, -8, 18, 0, 0, -6, 2, 8], [-2, 0, -4, 0, -6, 0, -6, 0, -5, -13, 0, 4, 0, 0, 0, -1, -5, 0, 0, 0], [0, -9, 0, 1, 0, 4, 0, 7, 0, 0, 0, 0, -6, 1, 11, 0, 0, -8, -2, 5], [0, 1, 0, 1, 0, -1, 0, 3, 0, 0, 0, 0, 6, -1, -9, 0, 0, 0, -9, 1], [0, -4, 0, 4, 0, 5, 0, -9, 0, 0, 0, 0, 2, -1, 8, 0, 0, -9, 1, 5], [0, -3, 0, -5, 0, -1, 0, -6, 0, 0, 0, 0, -4, 4, -2, 0, 0, -3, 9, -4], [7, 0, 8, 0, 3, 0, 6, 0, 7, 3, -1, -5, 0, 0, 0, 2, 0, 0, 0, 0], [-13, 0, -8, 0, -2, 0, 1, 0, -3, 11, 1, -3, 0, 0, 0, 2, 11, 0, 0, 0], [-2, 0, 2, 0, -5, 0, 1, 0, 0, 2, -6, -1, 0, 0, 0, 0, 4, 0, 0, 0], [0, 4, 0, 1, 0, 10, 0, 1, 0, 0, 0, 0, 5, -7, 4, 0, 0, 2, 3, 4], [0, -10, 0, -7, 0, 4, 0, 8, 0, 0, 0, 0, 8, 1, -3, 0, 0, 0, -13, 5], [14, 0, 6, 0, 4, 0, 11, 0, 0, 3, -1, -7, 0, 0, 0, 0, -3, 0, 0, 0], [0, -11, 0, 4, 0, -2, 0, -7, 0, 0, 0, 0, -1, 1, 0, 0, 0, -9, 5, -4], [8, 0, 1, 0, 0, 0, 7, 0, -7, 6, -4, -7, 0, 0, 0, 1, 7, 0, 0, 0], [0, 17, 0, 0, 0, -2, 0, 5, 0, 0, 0, 0, -2, -2, 9, 0, 0, 0, 0, 4], [-6, 0, -6, 0, -11, 0, 0, 0, 1, -3, -4, -5, 0, 0, 0, 3, -5, 0, 0, 0], [0, 10, 0, -4, 0, -2, 0, -6, 0, 0, 0, 0, 0, -1, -6, 0, 0, 5, 3, 0], [0, 7, 0, 4, 0, 5, 0, 3, 0, 0, 0, 0, -5, 2, 1, 0, 0, 2, 0, 0], [14, 0, 8, 0, -3, 0, 1, 0, -2, 2, -1, 3, 0, 0, 0, 2, 1, 0, 0, 0], [0, 4, 0, 1, 0, 2, 0, 10, 0, 0, 0, 0, 0, -10, -2, 0, 0, 2, -10, 8], [0, 0, 0, -2, 0, -1, 0, -5, 0, 0, 0, 0, 2, 7, -1, 0, 0, 4, -7, 2], [6, 0, -6, 0, 0, 0, -4, 0, 2, -4, -2, 8, 0, 0, 0, 2, -2, 0, 0, 0], [10, 0, -7, 0, 1, 0, -8, 0, -1, -9, 0, 4, 0, 0, 0, -3, -1, 0, 0, 0], [0, -2, 0, -6, 0, -12, 0, 6, 0, 0, 0, 0, -4, 6, -6, 0, 0, 4, 2, -6], [1, 0, 5, 0, 5, 0, 7, 0, 5, 6, 4, -6, 0, 0, 0, -2, 4, 0, 0, 0], [23, 0, 8, 0, -3, 0, 2, 0, -2, -10, -6, -6, 0, 0, 0, 3, -1, 0, 0, 0], [0, 14, 0, 7, 0, -2, 0, -4, 0, 0, 0, 0, 0, -4, -2, 0, 0, 4, -2, -4], [-8, 0, -8, 0, -2, 0, 2, 0, -9, -4, 2, -2, 0, 0, 0, -3, 1, 0, 0, 0], [-30, 0, 2, 0, -1, 0, 2, 0, 1, 7, 0, -1, 0, 0, 0, -1, 7, 0, 0, 0], [0, 15, 0, 14, 0, 3, 0, 0, 0, 0, 0, 0, 0, -4, 8, 0, 0, 3, -3, 6], [-16, 0, -16, 0, 3, 0, -1, 0, 6, 5, -1, 4, 0, 0, 0, 2, 4, 0, 0, 0], [0, -1, 0, 3, 0, -4, 0, 4, 0, 0, 0, 0, 2, -6, 10, 0, 0, -10, 9, 3], [0, -17, 0, 6, 0, -3, 0, 2, 0, 0, 0, 0, 1, -5, 10, 0, 0, -7, -1, 11], [-6, 0, 0, 0, -6, 0, 0, 0, -6, 14, -1, -8, 0, 0, 0, 10, 1, 0, 0, 0], [0, 11, 0, 0, 0, -1, 0, -14, 0, 0, 0, 0, -5, 0, -2, 0, 0, 3, 6, -6], [-12, 0, 1, 0, -2, 0, -5, 0, -7, -4, 0, 3, 0, 0, 0, 1, 1, 0, 0, 0], [1, 0, -10, 0, -9, 0, -1, 0, -2, 1, -5, 1, 0, 0, 0, -1, -2, 0, 0, 0], [1, 0, -16, 0, -5, 0, -9, 0, -1, -6, 9, 9, 0, 0, 0, -2, -4, 0, 0, 0], [10, 0, 8, 0, 0, 0, 3, 0, 1, -4, 5, 5, 0, 0, 0, -5, -1, 0, 0, 0], [7, 0, 2, 0, 1, 0, -1, 0, 4, 0, 3, -2, 0, 0, 0, 5, 2, 0, 0, 0], [-16, 0, -6, 0, -4, 0, -7, 0, -4, -4, 0, 11, 0, 0, 0, -8, -8, 0, 0, 0], [0, 13, 0, -2, 0, -1, 0, 7, 0, 0, 0, 0, 1, 2, -9, 0, 0, 4, 0, -12], [-1, 0, 4, 0, 4, 0, 1, 0, 9, 2, -2, 7, 0, 0, 0, 2, 4, 0, 0, 0], [4, 0, -1, 0, 4, 0, -4, 0, -1, 4, 4, 4, 0, 0, 0, -3, 1, 0, 0, 0], [0, -8, 0, -6, 0, -11, 0, 1, 0, 0, 0, 0, -4, 1, -3, 0, 0, -2, 5, -4], [0, 5, 0, -1, 0, -5, 0, -4, 0, 0, 0, 0, -3, 3, 8, 0, 0, -1, -2, 3], [-8, 0, -2, 0, -3, 0, 6, 0, -8, 4, 2, -6, 0, 0, 0, 2, 6, 0, 0, 0], [0, -2, 0, 1, 0, 6, 0, 2, 0, 0, 0, 0, 4, 5, -4, 0, 0, 7, -5, -4], [-9, 0, 2, 0, -1, 0, -2, 0, -5, 2, -7, 4, 0, 0, 0, 4, -3, 0, 0, 0], [3, 0, -8, 0, -3, 0, 1, 0, -4, 7, -1, -3, 0, 0, 0, -1, 6, 0, 0, 0], [0, 2, 0, -8, 0, 6, 0, -2, 0, 0, 0, 0, -3, 4, -6, 0, 0, 5, 7, -5], [-4, 0, -7, 0, -1, 0, -8, 0, 4, 1, 5, 1, 0, 0, 0, -6, -3, 0, 0, 0], [0, 3, 0, 8, 0, -3, 0, -3, 0, 0, 0, 0, -3, 7, -1, 0, 0, -3, 2, -6], [34, 0, 18, 0, 3, 0, 5, 0, -4, -9, -1, -8, 0, 0, 0, -2, 2, 0, 0, 0], [0, -7, 0, -1, 0, 8, 0, 7, 0, 0, 0, 0, 1, 0, 9, 0, 0, -3, 2, 9], [0, -1, 0, 6, 0, -5, 0, 2, 0, 0, 0, 0, -7, 5, -4, 0, 0, -1, 9, 3], [0, 9, 0, 6, 0, -3, 0, -5, 0, 0, 0, 0, 7, 0, -3, 0, 0, 2, -2, -4], [0, 9, 0, -15, 0, 4, 0, 8, 0, 0, 0, 0, -4, -1, -10, 0, 0, 10, -7, 0], [0, -9, 0, -13, 0, -2, 0, 6, 0, 0, 0, 0, -6, 6, -12, 0, 0, 12, -2, -11], [-8, 0, -9, 0, 0, 0, 2, 0, 6, -2, -2, -5, 0, 0, 0, 4, 4, 0, 0, 0], [0, -14, 0, -13, 0, -5, 0, 1, 0, 0, 0, 0, -6, 6, -11, 0, 0, 9, 2, -4], [-2, 0, -1, 0, 4, 0, 6, 0, -2, 8, 0, 2, 0, 0, 0, 4, 6, 0, 0, 0], [0, -3, 0, 8, 0, -6, 0, 0, 0, 0, 0, 0, 6, 0, -2, 0, 0, 1, -8, -2], [0, 5, 0, -6, 0, 1, 0, 5, 0, 0, 0, 0, 3, 0, -3, 0, 0, 1, -3, -3], [36, 0, 6, 0, -3, 0, 6, 0, 0, 3, -5, -4, 0, 0, 0, 4, 3, 0, 0, 0], [-10, 0, 7, 0, 5, 0, 4, 0, 8, 5, 1, -3, 0, 0, 0, 4, 3, 0, 0, 0], [0, -5, 0, 4, 0, 7, 0, 2, 0, 0, 0, 0, 2, -4, 1, 0, 0, -3, 3, 10], [-10, 0, -9, 0, 1, 0, 0, 0, -2, 0, 0, -6, 0, 0, 0, -2, -2, 0, 0, 0], [0, -11, 0, -11, 0, -5, 0, -2, 0, 0, 0, 0, -3, 3, -18, 0, 0, 9, 0, -9], [-1, 0, 8, 0, 1, 0, 1, 0, -1, 9, 4, -3, 0, 0, 0, 2, 11, 0, 0, 0], [0, 0, 10, 0, -10, 0, -3, 0, -3, 0, -17, -9, 0, 0, 0, 9, -1, 0, 0, 0], [0, -21, 0, 1, 0, 1, 0, -2, 0, 0, 0, 0, 7, -7, -4, 0, 0, -1, -2, 5], [-10, 0, -2, 0, -5, 0, -5, 0, -2, -4, -3, -5, 0, 0, 0, 2, -3, 0, 0, 0], [0, 19, 0, 21, 0, 2, 0, -8, 0, 0, 0, 0, 7, -16, 14, 0, 0, -7, 5, 8], [5, 0, 14, 0, 3, 0, 7, 0, -1, -4, -3, 1, 0, 0, 0, -2, 4, 0, 0, 0], [0, -18, 0, 5, 0, -4, 0, 8, 0, 0, 0, 0, -2, 2, -8, 0, 0, -4, 0, 0], [0, -9, 0, -7, 0, 6, 0, 2, 0, 0, 0, 0, -1, 2, 4, 0, 0, 5, -6, -4], [0, 5, 0, -8, 0, 7, 0, 2, 0, 0, 0, 0, 3, 1, -2, 0, 0, -1, -7, -3], [-2, 0, 0, 0, -2, 0, -5, 0, 6, -6, 2, 1, 0, 0, 0, 0, -4, 0, 0, 0], [0, 9, 0, -5, 0, 4, 0, 4, 0, 0, 0, 0, 10, -5, -2, 0, 0, 3, -8, 1], [-4, 0, -7, 0, -1, 0, -9, 0, 3, -2, 6, 1, 0, 0, 0, 3, 5, 0, 0, 0], [0, 3, 0, 16, 0, -6, 0, -7, 0, 0, 0, 0, -3, -14, 12, 0, 0, -6, 4, 10], [0, -11, 0, 12, 0, -2, 0, -15, 0, 0, 0, 0, -1, 2, 4, 0, 0, 0, 0, 2], [13, 0, 15, 0, -2, 0, -1, 0, 0, -9, 2, -3, 0, 0, 0, -3, 3, 0, 0, 0], [0, -23, 0, -3, 0, 4, 0, -12, 0, 0, 0, 0, 4, 4, -2, 0, 0, 0, -5, 3], [-16, 0, -7, 0, -7, 0, -11, 0, -5, -2, 2, 3, 0, 0, 0, -3, -7, 0, 0, 0], [9, 0, -6, 0, -5, 0, -8, 0, 1, -13, -5, 4, 0, 0, 0, 0, -4, 0, 0, 0], [0, -5, 0, -7, 0, 2, 0, 2, 0, 0, 0, 0, 1, -6, -10, 0, 0, 7, 6, -6], [-16, 0, 2, 0, 8, 0, 4, 0, 2, -6, 8, 6, 0, 0, 0, -8, 2, 0, 0, 0], [0, 9, 0, -10, 0, 9, 0, 7, 0, 0, 0, 0, 5, -3, -4, 0, 0, 3, 2, -2], [-4, 0, 5, 0, 5, 0, -1, 0, 4, -4, 4, 3, 0, 0, 0, -2, 2, 0, 0, 0], [5, 0, 0, 0, 1, 0, 2, 0, 0, 14, 7, 7, 0, 0, 0, -3, -1, 0, 0, 0], [17, 0, 7, 0, 8, 0, 1, 0, 6, -7, -2, -3, 0, 0, 0, -9, 1, 0, 0, 0], [0, -5, 0, 2, 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, -12, 0, 0, 2, -3, 5], [0, -9, 0, -2, 0, 9, 0, 2, 0, 0, 0, 0, 0, 2, -1, 0, 0, 3, -3, 2], [-6, 0, -8, 0, 8, 0, 2, 0, 4, 6, 14, 12, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 5, 0, -1, 0, -3, 0, 0, 0, 0, 3, 1, 9, 0, 0, 4, 6, 1], [-6, 0, -10, 0, 3, 0, 5, 0, 4, -5, 3, -2, 0, 0, 0, 6, 2, 0, 0, 0], [0, -13, 0, -14, 0, 5, 0, -8, 0, 0, 0, 0, -4, 10, -4, 0, 0, 5, 5, -6], [-2, 0, 4, 0, -7, 0, 8, 0, -2, 6, -4, -2, 0, 0, 0, 2, 0, 0, 0, 0], [0, -13, 0, -13, 0, 3, 0, 16, 0, 0, 0, 0, -7, 1, 0, 0, 0, 3, -4, 3], [9, 0, 16, 0, 6, 0, 15, 0, -5, 10, -2, -9, 0, 0, 0, 10, 8, 0, 0, 0], [0, 2, 0, -6, 0, 8, 0, 16, 0, 0, 0, 0, 8, 2, 7, 0, 0, -8, 0, 8], [-19, 0, 8, 0, -1, 0, 0, 0, -1, 2, -1, -2, 0, 0, 0, -6, -9, 0, 0, 0], [21, 0, 4, 0, -3, 0, 2, 0, 2, 5, -2, 4, 0, 0, 0, 1, -5, 0, 0, 0], [-6, 0, 1, 0, 9, 0, -4, 0, 4, -5, -3, 5, 0, 0, 0, 0, -9, 0, 0, 0], [0, -5, 0, -7, 0, -1, 0, -4, 0, 0, 0, 0, 8, 2, -8, 0, 0, 7, -7, -2], [0, -12, 0, 10, 0, 2, 0, -2, 0, 0, 0, 0, -4, -2, 6, 0, 0, 0, -4, 2], [5, 0, 10, 0, -6, 0, -1, 0, 6, 0, -2, -6, 0, 0, 0, -1, -6, 0, 0, 0], [0, -11, 0, -3, 0, 2, 0, 7, 0, 0, 0, 0, 8, 3, -1, 0, 0, -6, -8, 7], [0, 25, 0, -2, 0, 0, 0, -3, 0, 0, 0, 0, -1, -5, 0, 0, 0, 11, 3, 2], [-14, 0, -2, 0, 7, 0, -3, 0, 7, -5, 3, 7, 0, 0, 0, -1, 4, 0, 0, 0], [4, 0, -16, 0, 1, 0, 0, 0, -2, 5, 5, -2, 0, 0, 0, 6, 7, 0, 0, 0], [0, -6, 0, 6, 0, 4, 0, -2, 0, 0, 0, 0, 10, 0, 2, 0, 0, -4, 6, 0], [0, 15, 0, 4, 0, -1, 0, -4, 0, 0, 0, 0, -1, -2, -8, 0, 0, 1, 4, 4], [-6, 0, -18, 0, -2, 0, 0, 0, -2, -2, 4, 12, 0, 0, 0, 0, -8, 0, 0, 0], [2, 0, 0, 0, 4, 0, -6, 0, 3, -2, 4, 8, 0, 0, 0, -9, -10, 0, 0, 0], [0, -13, 0, 11, 0, -6, 0, -3, 0, 0, 0, 0, 5, -5, 7, 0, 0, -8, -1, 3], [21, 0, 2, 0, 5, 0, 9, 0, 10, 10, -2, -3, 0, 0, 0, 5, 3, 0, 0, 0], [8, 0, 8, 0, 7, 0, 2, 0, -1, -10, -6, 6, 0, 0, 0, -3, 1, 0, 0, 0], [0, -15, 0, 1, 0, 5, 0, -7, 0, 0, 0, 0, -1, 1, -2, 0, 0, 5, -2, 0], [0, 4, 0, 14, 0, 1, 0, -9, 0, 0, 0, 0, -2, -3, 15, 0, 0, -6, 3, 2], [0, -2, 0, -2, 0, 9, 0, 15, 0, 0, 0, 0, -5, 1, 7, 0, 0, -3, 4, 5], [0, 11, 0, 2, 0, -4, 0, -12, 0, 0, 0, 0, -2, 4, 4, 0, 0, 5, -4, -4], [0, 17, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, -1, -2, -7, 0, 0, -2, 10, -6], [26, 0, 14, 0, 0, 0, 1, 0, -1, -5, 4, 1, 0, 0, 0, -1, 0, 0, 0, 0], [0, -26, 0, -10, 0, 4, 0, 4, 0, 0, 0, 0, -4, 6, -8, 0, 0, -2, 0, -4], [0, 3, 0, -16, 0, 1, 0, 4, 0, 0, 0, 0, -2, 0, -10, 0, 0, 9, -5, -4], [0, 6, 0, 14, 0, -8, 0, -10, 0, 0, 0, 0, 1, 0, 4, 0, 0, -5, -1, -3], [8, 0, -7, 0, -1, 0, 0, 0, -3, -1, -8, -8, 0, 0, 0, 5, 3, 0, 0, 0], [16, 0, -4, 0, 0, 0, 8, 0, 5, 10, -2, -8, 0, 0, 0, 3, -2, 0, 0, 0], [0, 22, 0, 4, 0, 4, 0, 4, 0, 0, 0, 0, -2, -2, -1, 0, 0, 8, -2, 8], [7, 0, 2, 0, -10, 0, -9, 0, -3, -11, 3, 11, 0, 0, 0, -6, -7, 0, 0, 0], [15, 0, 2, 0, 1, 0, 6, 0, 5, 2, -9, -2, 0, 0, 0, 2, -1, 0, 0, 0], [0, 0, 0, 4, 0, 2, 0, -6, 0, 0, 0, 0, 8, -10, 2, 0, 0, 2, 2, 6], [-2, 0, 6, 0, -1, 0, -2, 0, 0, 1, -8, -6, 0, 0, 0, 2, 1, 0, 0, 0], [0, 0, 0, 5, 0, -5, 0, -5, 0, 0, 0, 0, 1, -9, 9, 0, 0, -5, -4, -1], [0, -11, 0, -13, 0, 0, 0, 12, 0, 0, 0, 0, 0, 8, -8, 0, 0, 0, -1, -1], [-14, 0, -1, 0, 1, 0, -1, 0, -3, -10, -6, 5, 0, 0, 0, 1, -3, 0, 0, 0], [-22, 0, -4, 0, -8, 0, -10, 0, -3, -3, 1, 4, 0, 0, 0, -9, -5, 0, 0, 0], [0, -16, 0, -2, 0, 5, 0, 3, 0, 0, 0, 0, 2, 3, -9, 0, 0, -4, -3, -2], [0, -12, 0, -2, 0, -4, 0, 9, 0, 0, 0, 0, -10, 4, -1, 0, 0, 5, 1, -2], [-8, 0, 7, 0, 5, 0, 2, 0, -1, 3, -6, 2, 0, 0, 0, 5, 1, 0, 0, 0], [0, 3, 0, -9, 0, -1, 0, -5, 0, 0, 0, 0, -5, 9, 1, 0, 0, 1, -1, -6], [-15, 0, 4, 0, -1, 0, 4, 0, 5, 10, -4, -12, 0, 0, 0, 2, 1, 0, 0, 0], [0, 13, 0, 15, 0, 2, 0, 7, 0, 0, 0, 0, 3, -8, 7, 0, 0, 3, -2, 11], [0, 11, 0, -4, 0, 3, 0, 2, 0, 0, 0, 0, 9, 0, -10, 0, 0, 9, 0, 0], [37, 0, 11, 0, 11, 0, 5, 0, 4, 0, 7, -3, 0, 0, 0, 1, 8, 0, 0, 0], [0, -20, 0, -3, 0, -6, 0, 6, 0, 0, 0, 0, 0, 4, 1, 0, 0, 0, -14, 8], [-4, 0, -3, 0, 1, 0, 3, 0, 5, 12, -6, -7, 0, 0, 0, 7, 7, 0, 0, 0], [0, -11, 0, -10, 0, 1, 0, 3, 0, 0, 0, 0, -5, 10, 5, 0, 0, -2, 10, -2], [-3, 0, 8, 0, -7, 0, -4, 0, 2, -2, -5, -1, 0, 0, 0, 3, -3, 0, 0, 0], [-20, 0, -7, 0, -3, 0, -2, 0, 2, -9, -5, -5, 0, 0, 0, -4, -5, 0, 0, 0], [-3, 0, -6, 0, 10, 0, 5, 0, 3, 5, -5, 5, 0, 0, 0, 0, 1, 0, 0, 0], [0, 20, 0, -2, 0, -13, 0, -1, 0, 0, 0, 0, -9, -6, 3, 0, 0, 2, -1, -5], [0, 0, -1, 0, -6, 0, 0, 0, 2, 4, 4, 2, 0, 0, 0, -10, 2, 0, 0, 0], [0, -2, 0, 0, 0, -4, 0, -2, 0, 0, 0, 0, -2, 2, 2, 0, 0, 2, -12, -4], [0, -11, 0, -7, 0, 3, 0, 5, 0, 0, 0, 0, 4, -3, -5, 0, 0, 8, -5, 1], [-6, 0, 1, 0, -3, 0, 0, 0, 11, -1, 2, 4, 0, 0, 0, -1, 1, 0, 0, 0], [0, -2, 0, -6, 0, -7, 0, -7, 0, 0, 0, 0, -6, 1, -3, 0, 0, -8, 7, -12], [0, 0, 10, 0, -4, 0, -2, 0, 1, -4, -5, 1, 0, 0, 0, -3, -6, 0, 0, 0], [-6, 0, -3, 0, -8, 0, 2, 0, -6, 6, -8, -4, 0, 0, 0, 4, 0, 0, 0, 0], [0, -6, 0, 14, 0, 2, 0, 0, 0, 0, 0, 0, 5, -2, 8, 0, 0, 1, -3, 7], [3, 0, -6, 0, 1, 0, 0, 0, -1, -5, -5, -3, 0, 0, 0, 2, -4, 0, 0, 0], [0, -15, 0, 7, 0, -4, 0, -4, 0, 0, 0, 0, -2, 8, -4, 0, 0, -4, -13, 1], [0, 0, 17, 0, -8, 0, -6, 0, -5, 0, -14, 6, 0, 0, 0, -3, -5, 0, 0, 0], [0, -17, 0, 0, 0, -6, 0, 3, 0, 0, 0, 0, -2, 2, -11, 0, 0, 1, -1, -11], [-8, 0, -7, 0, 1, 0, -4, 0, 9, -3, 4, 4, 0, 0, 0, 7, -5, 0, 0, 0], [0, -3, 0, 4, 0, -6, 0, -9, 0, 0, 0, 0, -4, 2, 9, 0, 0, -7, -1, -1], [0, 2, 0, 10, 0, 9, 0, 3, 0, 0, 0, 0, 10, -1, 17, 0, 0, -14, 0, 8], [-16, 0, 4, 0, 9, 0, 7, 0, 3, -4, 7, 10, 0, 0, 0, -1, -5, 0, 0, 0], [-27, 0, -20, 0, -9, 0, -8, 0, -1, -2, 0, 12, 0, 0, 0, -12, -7, 0, 0, 0], [0, 7, 0, -1, 0, 0, 0, -3, 0, 0, 0, 0, -1, 3, 1, 0, 0, -6, 5, -11], [5, 0, -6, 0, -3, 0, -5, 0, 0, 9, 4, -7, 0, 0, 0, -5, 7, 0, 0, 0], [0, 9, 0, 6, 0, -13, 0, -5, 0, 0, 0, 0, -9, 1, 1, 0, 0, 4, 2, -5], [-6, 0, -6, 0, -2, 0, -2, 0, -8, 4, 4, -2, 0, 0, 0, -2, 0, 0, 0, 0], [0, -3, 0, 3, 0, -7, 0, 0, 0, 0, 0, 0, -2, -2, 1, 0, 0, 3, 3, 0], [0, -16, 0, -10, 0, 6, 0, 3, 0, 0, 0, 0, 3, 7, -17, 0, 0, -2, 3, -4], [-22, 0, 9, 0, 8, 0, 0, 0, 4, -8, 4, 10, 0, 0, 0, -10, 0, 0, 0, 0], [-18, 0, -2, 0, 2, 0, -6, 0, 1, -3, 1, 6, 0, 0, 0, 3, 3, 0, 0, 0], [0, -3, 0, -11, 0, -6, 0, 5, 0, 0, 0, 0, 3, 6, -23, 0, 0, 5, -10, -7], [0, 5, 0, 4, 0, 0, 0, -5, 0, 0, 0, 0, 11, 1, 8, 0, 0, -1, 1, -2], [44, 0, 8, 0, 3, 0, 6, 0, -10, -5, -7, -10, 0, 0, 0, 6, -1, 0, 0, 0], [0, 3, 0, 1, 0, -1, 0, 16, 0, 0, 0, 0, 5, 3, -12, 0, 0, 4, -7, -2], [0, -2, 0, 0, 0, 0, 0, -11, 0, 0, 0, 0, -7, 3, -5, 0, 0, -6, 9, 0], [0, -17, 0, 1, 0, 1, 0, -3, 0, 0, 0, 0, -2, 5, -5, 0, 0, 6, 2, -7], [-12, 0, -6, 0, -7, 0, 6, 0, -12, -3, -7, -2, 0, 0, 0, 4, -7, 0, 0, 0], [0, 5, 0, -1, 0, 11, 0, -1, 0, 0, 0, 0, 7, 5, 9, 0, 0, -7, 6, 0], [0, -2, 0, -15, 0, -1, 0, -4, 0, 0, 0, 0, 0, 8, -8, 0, 0, 10, -3, -14], [-1, 0, 0, 0, 1, 0, 1, 0, 9, -6, -1, -9, 0, 0, 0, 6, 0, 0, 0, 0], [0, 1, 0, 6, 0, 5, 0, 3, 0, 0, 0, 0, 9, -1, 2, 0, 0, 3, -4, 8], [0, 6, 0, 7, 0, 6, 0, -3, 0, 0, 0, 0, 15, -9, 7, 0, 0, 4, -5, 0], [0, 0, 0, -4, 0, 0, 0, 12, 0, 0, 0, 0, 0, -4, -10, 0, 0, 6, -11, 0], [2, 0, -1, 0, 2, 0, -7, 0, 1, -6, 6, 5, 0, 0, 0, -9, -5, 0, 0, 0], [0, 6, 0, 4, 0, -15, 0, -11, 0, 0, 0, 0, 0, -5, -7, 0, 0, 0, 3, 2]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_9675_a_Hecke( : Kf := Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_9675_2_a_da();".
// 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_9675_2_a_da(:prec:=20)
    chi := MakeCharacter_9675_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_9675_2_a_da();".
// 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_9675_2_a_da( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_9675_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![100, 0, -1388, 0, 7084, 0, -17428, 0, 22796, 0, -17056, 0, 7613, 0, -2052, 0, 326, 0, -28, 0, 1]>,<7,R![176, 1304, 1738, -2570, -1772, 890, 426, -110, -35, 4, 1]>,<11,R![33477796, 0, -2208526992, 0, 2681308277, 0, -1225856692, 0, 294290156, 0, -41906460, 0, 3712786, 0, -205848, 0, 6912, 0, -128, 0, 1]>,<13,R![-20240, -54848, -16013, 28308, 15770, -1818, -2584, -390, 50, 16, 1]>],Snew);
    return Vf;
end function;