
// Make newform 1805.2.a.w in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_1805_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_1805_2_a_w();".
// 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_1805_2_a_w();".
// 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 := [256, 0, -2592, 0, 8701, 0, -11261, 0, 6639, 0, -2038, 0, 339, 0, -29, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [144, 0, -791, 0, 1190, 0, -687, 0, 181, 0, -22, 0, 1, 0, 0, 0], [-2448, 0, 13979, 0, -21999, 0, 14881, 0, -5070, 0, 913, 0, -83, 0, 3, 0], [-640, 0, 3869, 0, -6343, 0, 4433, 0, -1558, 0, 289, 0, -27, 0, 1, 0], [-3472, 0, 20999, 0, -31799, 0, 19613, 0, -6098, 0, 1017, 0, -87, 0, 3, 0], [-3728, 0, 21063, 0, -31799, 0, 19613, 0, -6098, 0, 1017, 0, -87, 0, 3, 0], [0, 10672, 0, -59269, 0, 90357, 0, -56855, 0, 17990, 0, -3035, 0, 261, 0, -9], [3376, 0, -20993, 0, 35097, 0, -24099, 0, 8254, 0, -1495, 0, 137, 0, -5, 0], [0, -3472, 0, 20999, 0, -31799, 0, 19613, 0, -6098, 0, 1017, 0, -87, 0, 3], [0, -3856, 0, 21063, 0, -31799, 0, 19613, 0, -6098, 0, 1017, 0, -87, 0, 3], [-9712, 0, 58693, 0, -90293, 0, 56855, 0, -17990, 0, 3035, 0, -261, 0, 9, 0], [0, -13328, 0, 83993, 0, -131433, 0, 82803, 0, -26110, 0, 4391, 0, -377, 0, 13], [0, 39184, 0, -237851, 0, 368251, 0, -233993, 0, 74858, 0, -12789, 0, 1115, 0, -39], [0, 40944, 0, -248885, 0, 387701, 0, -246727, 0, 78902, 0, -13467, 0, 1173, 0, -41], [0, 77296, 0, -462033, 0, 705921, 0, -441179, 0, 138734, 0, -23311, 0, 2001, 0, -69]];
    Rf_basisdens := [1, 1, 16, 64, 16, 64, 64, 256, 64, 64, 64, 64, 128, 256, 256, 256];
    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_1805_a();"
function MakeCharacter_1805_a()
    N := 1805;
    order := 1;
    char_gens := [362, 1446];
    v := [1, 1];
    // chi(gens[i]) = zeta^v[i]
    assert UnitGenerators(DirichletGroup(N)) eq char_gens;
    F := CyclotomicField(order);
    chi := DirichletCharacterFromValuesOnUnitGenerators(DirichletGroup(N,F),[F|F.1^e:e in v]);
    return MinimalBaseRingCharacter(chi);
end function;

function MakeCharacter_1805_a_Hecke(Kf)
    return MakeCharacter_1805_a();
end function;


function ExtendMultiplicatively(weight, aps, character)
    prec := NextPrime(NthPrime(#aps)) - 1; // we will able to figure out a_0 ... a_prec
    primes := PrimesUpTo(prec);
    prime_powers := primes;
    assert #primes eq #aps;
    log_prec := Floor(Log(prec)/Log(2)); // prec < 2^(log_prec+1)
    F := Universe(aps);
    FXY<X, Y> := PolynomialRing(F, 2);
    // 1/(1 - a_p T + p^(weight - 1) * char(p) T^2) = 1 + a_p T + a_{p^2} T^2 + ...
    R<T> := PowerSeriesRing(FXY : Precision := log_prec + 1);
    recursion := Coefficients(1/(1 - X*T + Y*T^2));
    coeffs := [F!0: i in [1..(prec+1)]];
    coeffs[1] := 1; //a_1
    for i := 1 to #primes do
        p := primes[i];
        coeffs[p] := aps[i];
        b := p^(weight - 1) * F!character(p);
        r := 2;
        p_power := p * p;
        //deals with powers of p
        while p_power le prec do
            Append(~prime_powers, p_power);
            coeffs[p_power] := Evaluate(recursion[r + 1], [aps[i], b]);
            p_power *:= p;
            r +:= 1;
        end while;    
    end for;
    Sort(~prime_powers);
    for pp in prime_powers do
        for k := 1 to Floor(prec/pp) do
            if GCD(k, pp) eq 1 then
                coeffs[pp*k] := coeffs[pp]*coeffs[k];
            end if;
        end for;
    end for;
    return coeffs;
end function;


function qexpCoeffs()
    // To make the coeffs of the qexp of the newform in the Hecke field type "qexpCoeffs();"
    weight := 2;
    raw_aps := [[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 1, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, -1, 0, 0, 1], [1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 0, -1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1, 0, -2, 1, 0, 1, -2, -1, 0], [0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, -1, 2, 0, 1], [0, -2, 0, 0, 0, 0, 0, 1, 0, -2, -1, 0, 1, 0, 0, 1], [0, -1, 0, 0, 0, 0, 0, -1, 0, 2, 1, 0, 1, 1, -1, -1], [6, 0, 1, 1, 1, 1, 1, 0, -1, 0, 0, 1, 0, 0, 0, 0], [2, 0, 0, 0, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, -1, 4, 3, -1], [0, -1, 0, 0, 0, 0, 0, 1, 0, 2, -1, 0, 1, 0, -1, 1], [2, 0, 0, 0, 1, -2, -1, 0, 3, 0, 0, -2, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 1, -2], [0, 1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, -1, 0, 2, 1], [2, 0, 2, 2, -1, 0, 0, 0, 1, 0, 0, -3, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 4, 0, -2, 1, 0, -1, 0, 2, 0], [8, 0, 1, 1, 1, -6, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 4, 1, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 1, -2, 2, -2], [3, 0, 0, 0, 4, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -3, 0, 0, 0, 0, 0, -4, 0, 1, 0, 0, -2, -2, -2, 0], [0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, -1, 0, -5, -2], [0, 1, 0, 0, 0, 0, 0, 3, 0, -1, 0, 0, -1, 0, 2, -1], [0, 2, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, -1, -2, -1, -1], [0, -3, 0, 0, 0, 0, 0, -1, 0, -2, -1, 0, 2, -2, 1, 1], [-1, 0, -2, 0, -1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0], [3, 0, -1, 1, -1, -4, -2, 0, -1, 0, 0, -1, 0, 0, 0, 0], [6, 0, 2, 0, 2, -5, 1, 0, 4, 0, 0, -3, 0, 0, 0, 0], [6, 0, -1, 1, -2, -7, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 3, 0, -2, -1, 0, 3, -4, 1, 1], [-6, 0, -2, -4, 0, 5, -1, 0, -2, 0, 0, 3, 0, 0, 0, 0], [7, 0, -1, 1, 3, -5, -1, 0, 2, 0, 0, -4, 0, 0, 0, 0], [0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -3, 0, 1, 2], [0, -1, 0, 0, 0, 0, 0, -1, 0, 3, 1, 0, -2, -4, 3, 1], [0, -5, 0, 0, 0, 0, 0, 1, 0, 1, 2, 0, -3, -2, 0, -3], [0, 0, 0, 0, 0, 0, 0, -2, 0, 4, 0, 0, 0, 2, -1, -1], [-7, 0, -1, 3, -3, 4, 2, 0, -1, 0, 0, -3, 0, 0, 0, 0], [0, -3, 0, 0, 0, 0, 0, -1, 0, -1, -1, 0, 2, 2, 1, 1], [2, 0, -3, 1, 0, 8, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0], [1, 0, -3, 1, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 0, -7, 0, 0, 0, 0, -2, 4, 1, 1], [0, -5, 0, 0, 0, 0, 0, -4, 0, 2, 1, 0, -2, -4, -1, 2], [0, 0, 0, 0, 0, 0, 0, 4, 0, 1, 2, 0, 0, 4, 0, -2], [-5, 0, -3, -1, -1, -1, 4, 0, 1, 0, 0, -2, 0, 0, 0, 0], [-8, 0, 1, 3, 2, 2, -2, 0, -2, 0, 0, -3, 0, 0, 0, 0], [1, 0, 3, -1, 2, -3, -3, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 0, -8, 0, 2, 3, 0, -1, -2, 0, 1], [-7, 0, 1, 3, -1, -2, 4, 0, 3, 0, 0, -1, 0, 0, 0, 0], [0, -4, 0, 0, 0, 0, 0, 7, 0, -5, -2, 0, 3, 0, -5, 1], [3, 0, 0, 1, -3, 0, 2, 0, -3, 0, 0, 1, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 1, 0, 0, -3, 0, -1, 2, -1, -1], [1, 0, -2, 2, 2, 5, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0], [8, 0, 1, -1, -1, -2, 2, 0, -1, 0, 0, 4, 0, 0, 0, 0], [0, -3, 0, 0, 0, 0, 0, -2, 0, 1, -2, 0, 3, -6, -1, -2], [5, 0, 0, 1, -3, 1, 1, 0, -1, 0, 0, 2, 0, 0, 0, 0], [0, -2, 0, 0, 0, 0, 0, -1, 0, 4, -2, 0, 0, 4, 1, 1], [0, -3, 0, 0, 0, 0, 0, -2, 0, -1, 3, 0, 1, 0, -1, 2], [1, 0, 0, -2, 3, 0, -2, 0, -5, 0, 0, 2, 0, 0, 0, 0], [-2, 0, 0, -4, 1, -1, 3, 0, 1, 0, 0, 2, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -3, 2, -2, 2], [0, 7, 0, 0, 0, 0, 0, 2, 0, -4, 3, 0, 1, 2, 2, -2], [0, -1, 0, 0, 0, 0, 0, -2, 0, 6, 3, 0, -5, 0, -4, -2], [8, 0, -1, -1, 3, -11, 3, 0, 2, 0, 0, -3, 0, 0, 0, 0], [-1, 0, -2, -2, 1, -9, 2, 0, 3, 0, 0, 0, 0, 0, 0, 0], [4, 0, 2, 0, 1, -13, 1, 0, 3, 0, 0, 4, 0, 0, 0, 0], [-8, 0, -2, 0, -1, 7, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0], [10, 0, -2, -1, 1, -14, 2, 0, 9, 0, 0, -4, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 0, 5, 0, 1, -1, 0, 0, 2, 2, -3], [0, -4, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, -6, -4, -4, 2], [0, -2, 0, 0, 0, 0, 0, 7, 0, 6, 1, 0, -1, 0, -2, -5], [-16, 0, 1, -1, -3, 17, 0, 0, -5, 0, 0, 2, 0, 0, 0, 0], [0, 0, -1, -3, -2, 8, -6, 0, 2, 0, 0, 1, 0, 0, 0, 0], [0, 4, 0, 0, 0, 0, 0, 4, 0, 1, -1, 0, -2, -9, -5, -2], [0, 6, 0, 0, 0, 0, 0, 1, 0, 0, -3, 0, -1, 7, 0, -1], [-8, 0, -1, -5, -3, 6, 0, 0, -5, 0, 0, 6, 0, 0, 0, 0], [0, 6, 0, 0, 0, 0, 0, 5, 0, -3, 3, 0, 2, -4, 5, -2], [0, 1, 0, 0, 0, 0, 0, -3, 0, 3, -2, 0, -1, -2, 4, -3], [0, 7, 0, 0, 0, 0, 0, -8, 0, -1, 4, 0, -3, -2, -5, 2], [0, -5, 0, 0, 0, 0, 0, 1, 0, 1, -2, 0, -3, 8, 0, 1], [2, 0, 0, 3, -3, 4, 0, 0, 5, 0, 0, -2, 0, 0, 0, 0], [0, -3, 0, 0, 0, 0, 0, -9, 0, 8, 1, 0, -5, 1, 1, 3], [6, 0, 2, 0, 2, 4, -6, 0, -8, 0, 0, 0, 0, 0, 0, 0], [-2, 0, -4, 0, 2, -2, 5, 0, 2, 0, 0, -3, 0, 0, 0, 0], [5, 0, 2, -3, 0, 5, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0], [-12, 0, 1, 2, -4, 8, 6, 0, 0, 0, 0, -4, 0, 0, 0, 0], [-4, 0, 4, -4, 2, -1, 3, 0, -2, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 1, 0, -4, -2, -2, 0], [-2, 0, -2, -6, -3, -1, 1, 0, -3, 0, 0, 2, 0, 0, 0, 0], [6, 0, -3, -7, -5, 2, 4, 0, -1, 0, 0, 4, 0, 0, 0, 0], [9, 0, 7, 3, 3, -1, -5, 0, 2, 0, 0, -4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1, 0, 1, -3, 0, -4, 5, 8, 1], [0, -1, 0, 0, 0, 0, 0, 14, 0, 1, -4, 0, 1, -2, -1, 2], [0, -2, 0, 0, 0, 0, 0, 4, 0, -5, 4, 0, 0, -8, -2, -6], [14, 0, 3, -7, 4, -6, 2, 0, -4, 0, 0, 5, 0, 0, 0, 0], [0, 11, 0, 0, 0, 0, 0, 6, 0, -6, 1, 0, -2, 0, 4, -4], [-2, 0, -7, 3, 2, 6, 2, 0, 2, 0, 0, 1, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, -1, 0, 2, -4, 0, 11, 4, -2, 1], [0, -2, 0, 0, 0, 0, 0, -2, 0, 11, -4, 0, -1, 0, 1, -1], [5, 0, -1, 3, 3, 15, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0], [-10, 0, 2, 4, -1, 6, 2, 0, 7, 0, 0, -1, 0, 0, 0, 0], [-2, 0, -1, -2, -2, 12, 6, 0, -4, 0, 0, 0, 0, 0, 0, 0], [-7, 0, -6, -2, 2, 6, 2, 0, -6, 0, 0, 3, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, -4, 0, -4, 8, 0, -6, -6, -3, 0], [0, -4, 0, 0, 0, 0, 0, 10, 0, 2, -4, 0, 2, -8, 2, 2], [0, 1, 0, 0, 0, 0, 0, 8, 0, 4, -5, 0, -4, 4, -4, 2], [3, 0, 0, -2, 4, 14, 2, 0, 2, 0, 0, 3, 0, 0, 0, 0], [-7, 0, 3, 5, -4, -5, 3, 0, 0, 0, 0, 1, 0, 0, 0, 0], [7, 0, 2, 4, 0, 12, -2, 0, 2, 0, 0, -3, 0, 0, 0, 0], [14, 0, -1, -1, 4, -12, 2, 0, 2, 0, 0, -1, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 3, 0, 3, -1, 0, 0, 15, 1, -3], [14, 0, 6, 2, 2, -13, -1, 0, 1, 0, 0, 1, 0, 0, 0, 0], [6, 0, -4, -7, 1, -6, 2, 0, -1, 0, 0, -2, 0, 0, 0, 0], [-2, 0, 4, 2, 6, -5, -1, 0, 6, 0, 0, -9, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1, 0, 1, -1, 0, -6, -8, 3, 3], [0, 7, 0, 0, 0, 0, 0, -2, 0, -3, -2, 0, 7, 7, -1, 0], [0, 2, 0, 0, 0, 0, 0, -6, 0, -10, 1, 0, 1, -4, 1, 0], [0, -1, 0, 0, 0, 0, 0, -2, 0, -1, 4, 0, -1, -2, -3, -2], [0, 9, 0, 0, 0, 0, 0, -6, 0, 1, -3, 0, 1, 4, 2, 2], [-4, 0, -1, -1, -6, 14, -2, 0, -10, 0, 0, -3, 0, 0, 0, 0], [-3, 0, 2, 6, 3, 13, -4, 0, -7, 0, 0, 0, 0, 0, 0, 0], [3, 0, 5, 3, 6, 12, -5, 0, -6, 0, 0, 4, 0, 0, 0, 0], [-7, 0, -4, -2, 2, -5, 3, 0, -2, 0, 0, -4, 0, 0, 0, 0], [6, 0, 5, 0, -3, 8, -4, 0, 1, 0, 0, -3, 0, 0, 0, 0], [21, 0, -5, -5, -7, -10, 0, 0, -3, 0, 0, 3, 0, 0, 0, 0], [16, 0, 6, 8, 7, -6, -6, 0, 1, 0, 0, -3, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0, 4, 0, 2, -2, 0, 6, 6, -1, -2], [0, -4, 0, 0, 0, 0, 0, 13, 0, 2, 1, 0, 1, 2, 2, 3], [-9, 0, -8, -8, -4, 3, 1, 0, 4, 0, 0, 2, 0, 0, 0, 0], [-12, 0, -1, 1, -4, 4, -1, 0, 0, 0, 0, -2, 0, 0, 0, 0], [3, 0, -2, 2, 4, -7, 4, 0, 8, 0, 0, -1, 0, 0, 0, 0], [0, 13, 0, 0, 0, 0, 0, 12, 0, -7, -3, 0, 0, -6, 0, -2], [0, 4, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, -4, -2, 3], [0, 1, 0, 0, 0, 0, 0, -8, 0, 4, 5, 0, -3, 2, -2, 0], [-10, 0, 2, 2, -6, 5, -4, 0, -10, 0, 0, 3, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 0, -1, 0, -12, 2, 0, -6, 2, 3, 1], [-10, 0, -4, 0, 1, 15, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0], [8, 0, -3, -1, 3, -15, -1, 0, 0, 0, 0, 5, 0, 0, 0, 0], [0, 6, 0, 0, 0, 0, 0, -3, 0, 2, -2, 0, -3, 10, -1, -3], [0, -3, 0, 0, 0, 0, 0, 7, 0, -4, -6, 0, 2, 0, -11, 0], [0, 0, 0, 0, 0, 0, 0, -2, 0, -11, 4, 0, 5, -10, -4, 2], [-1, 0, -1, -5, -3, -12, -6, 0, -1, 0, 0, -3, 0, 0, 0, 0], [0, -4, 0, 0, 0, 0, 0, 9, 0, 4, -2, 0, 12, 6, -7, -1], [-2, 0, 0, -4, -8, -6, 0, 0, 4, 0, 0, -2, 0, 0, 0, 0], [0, 9, 0, 0, 0, 0, 0, -7, 0, -6, 6, 0, 5, -12, -6, -1], [0, 5, 0, 0, 0, 0, 0, 8, 0, 0, -7, 0, 1, -2, -4, 0], [-3, 0, 6, 2, 2, -5, -2, 0, 6, 0, 0, 3, 0, 0, 0, 0], [-6, 0, -3, -4, 4, 17, 1, 0, 2, 0, 0, -1, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 9, 0, -1, -4, 0, 2, 4, -1, 1], [0, -1, 0, 0, 0, 0, 0, 5, 0, -3, -7, 0, 2, 2, -5, -3], [0, 0, 0, 0, 0, 0, 0, 17, 0, 2, 0, 0, 6, 2, -1, -3], [2, 0, -1, 5, -4, 26, -4, 0, -6, 0, 0, -1, 0, 0, 0, 0], [0, 0, 1, -5, 6, -19, 10, 0, 6, 0, 0, -2, 0, 0, 0, 0], [-10, 0, 5, -3, 0, 13, -3, 0, -6, 0, 0, 2, 0, 0, 0, 0], [0, -3, 0, 0, 0, 0, 0, 6, 0, -8, 8, 0, 0, -9, -5, -8], [11, 0, 3, 4, 8, -10, -2, 0, 0, 0, 0, -5, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 0, 5, 0, 3, -1, 0, 6, 2, 6, 5], [-8, 0, -6, -4, -2, 19, -5, 0, -3, 0, 0, 5, 0, 0, 0, 0], [0, -2, 0, 0, 0, 0, 0, -12, 0, 3, 7, 0, 2, 2, 5, 0], [0, 3, 0, 0, 0, 0, 0, -10, 0, 2, -6, 0, -4, 10, 5, 0], [0, 7, 0, 0, 0, 0, 0, 0, 0, 1, 8, 0, 4, -2, 2, -4], [0, 3, 0, 0, 0, 0, 0, -5, 0, 0, -7, 0, -3, 4, 3, 1], [-20, 0, 0, -2, -4, 20, -10, 0, -4, 0, 0, -2, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 2, 0, 4, 5, 0, 11, -2, -1, -7], [-15, 0, 0, 6, -1, 27, 1, 0, 3, 0, 0, -5, 0, 0, 0, 0], [0, -7, 0, 0, 0, 0, 0, 4, 0, -8, 3, 0, 1, 0, 2, 4], [0, -3, 0, 0, 0, 0, 0, -4, 0, 6, -2, 0, -4, 4, 2, 5], [-11, 0, -4, 0, -2, 12, -4, 0, -2, 0, 0, 5, 0, 0, 0, 0], [-4, 0, -4, 2, 2, 2, 2, 0, 10, 0, 0, 0, 0, 0, 0, 0], [0, 11, 0, 0, 0, 0, 0, 10, 0, 2, 5, 0, -5, 16, 8, 0], [4, 0, 7, 1, 4, -7, -6, 0, 4, 0, 0, 1, 0, 0, 0, 0], [10, 0, -5, -3, -6, 2, -6, 0, -8, 0, 0, 7, 0, 0, 0, 0], [-1, 0, 1, -5, 2, -2, 5, 0, -6, 0, 0, 6, 0, 0, 0, 0], [0, -7, 0, 0, 0, 0, 0, 10, 0, -1, -2, 0, 8, 6, 2, -2], [-21, 0, 7, 5, -1, 10, 5, 0, 1, 0, 0, -1, 0, 0, 0, 0], [10, 0, 4, -2, -7, 1, -5, 0, -2, 0, 0, 6, 0, 0, 0, 0], [0, -14, 0, 0, 0, 0, 0, -9, 0, 11, -4, 0, 3, -12, -13, -1], [0, 9, 0, 0, 0, 0, 0, 1, 0, -9, -2, 0, -3, -14, 4, -1], [0, 1, 0, 0, 0, 0, 0, -10, 0, -5, -1, 0, 8, -8, -2, 0], [3, 0, -3, 1, -1, 10, -6, 0, -3, 0, 0, -1, 0, 0, 0, 0], [-9, 0, 1, -5, -1, -14, 7, 0, -3, 0, 0, 11, 0, 0, 0, 0], [0, 5, 0, 0, 0, 0, 0, 2, 0, -2, -2, 0, -4, 2, -3, 0], [0, 12, 0, 0, 0, 0, 0, 5, 0, 7, 1, 0, 4, 4, 0, -1], [0, 9, 0, 0, 0, 0, 0, 10, 0, 4, -2, 0, -6, 22, 5, -4], [-19, 0, 6, 4, 7, -3, 9, 0, 9, 0, 0, -3, 0, 0, 0, 0], [0, -9, 0, 0, 0, 0, 0, 2, 0, -3, 5, 0, 2, -6, 6, -2], [18, 0, -2, 0, 4, 20, 6, 0, -1, 0, 0, 4, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, -8, 0, 4, 6, 0, 6, -10, -9, 0], [0, -9, 0, 0, 0, 0, 0, -4, 0, 5, 0, 0, -11, 2, 2, -3], [23, 0, -1, 2, 0, -26, 10, 0, 4, 0, 0, -3, 0, 0, 0, 0], [0, -8, 0, 0, 0, 0, 0, 5, 0, 6, -6, 0, 4, 12, -1, 1], [3, 0, 4, 8, 3, -3, 0, 0, -7, 0, 0, 8, 0, 0, 0, 0], [-2, 0, 3, -5, -12, 4, -6, 0, -6, 0, 0, -5, 0, 0, 0, 0], [-12, 0, -6, 2, -3, -2, 2, 0, -11, 0, 0, 9, 0, 0, 0, 0], [5, 0, 5, -7, 6, 8, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 7, 0, 0, 0, 0, 0, 2, 0, -3, 3, 0, 6, 2, -1, 1], [0, 2, 0, 0, 0, 0, 0, -3, 0, -1, 4, 0, 3, -14, 7, -1], [0, 11, 0, 0, 0, 0, 0, 10, 0, -10, -6, 0, -2, 8, 5, 0], [0, 2, 0, 0, 0, 0, 0, 6, 0, 0, -9, 0, 5, -3, -7, 2], [16, 0, 0, 6, 0, -22, -4, 0, 2, 0, 0, 2, 0, 0, 0, 0], [-6, 0, -2, -2, -1, 9, 1, 0, -7, 0, 0, 4, 0, 0, 0, 0], [7, 0, 4, 4, -2, -18, 4, 0, 12, 0, 0, -1, 0, 0, 0, 0], [0, 5, 0, 0, 0, 0, 0, 3, 0, 3, 0, 0, -3, 4, 16, 3], [-17, 0, 4, 4, -8, 2, -1, 0, 8, 0, 0, -12, 0, 0, 0, 0], [0, 10, 0, 0, 0, 0, 0, -10, 0, -1, 1, 0, -6, 8, 11, 2], [-2, 0, -3, -1, 4, -15, -7, 0, -4, 0, 0, 4, 0, 0, 0, 0], [-21, 0, 3, -7, 0, 2, -3, 0, -4, 0, 0, 8, 0, 0, 0, 0], [-10, 0, -1, 1, -5, 21, -1, 0, -6, 0, 0, -7, 0, 0, 0, 0], [0, -6, 0, 0, 0, 0, 0, 18, 0, 0, 1, 0, 8, -10, 1, -6], [0, -6, 0, 0, 0, 0, 0, 9, 0, -6, -7, 0, 1, 0, 10, -1], [0, -3, 0, 0, 0, 0, 0, 9, 0, -4, 4, 0, -4, 3, 8, 1], [-5, 0, 1, -1, -2, 9, 3, 0, 11, 0, 0, -1, 0, 0, 0, 0], [0, 8, 0, 0, 0, 0, 0, -2, 0, -3, 1, 0, 4, -4, 10, 7], [0, -4, 0, 0, 0, 0, 0, 7, 0, -6, 2, 0, -1, 14, 10, -1], [-2, 0, -2, 0, -3, -10, -6, 0, 3, 0, 0, -3, 0, 0, 0, 0], [0, -3, 0, 0, 0, 0, 0, -2, 0, 12, -2, 0, -10, 1, -1, -2], [0, 7, 0, 0, 0, 0, 0, 4, 0, 5, -1, 0, -8, -4, 0, 0], [0, -6, 0, 0, 0, 0, 0, -5, 0, 5, 6, 0, -5, 16, 2, -6], [15, 0, -3, 9, 3, -5, 9, 0, 5, 0, 0, 2, 0, 0, 0, 0], [0, -6, 0, 0, 0, 0, 0, 3, 0, 9, -13, 0, 3, 16, 0, -3], [-16, 0, -8, -4, -4, -3, 4, 0, 0, 0, 0, -1, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, -10, 0, -10, 9, 0, -1, 6, 0, 0], [0, -3, 0, 0, 0, 0, 0, -7, 0, 0, 4, 0, -2, 4, -6, -3], [0, -4, 0, 0, 0, 0, 0, -2, 0, -6, 3, 0, 13, -10, 1, -2], [15, 0, 2, -10, 6, -17, 5, 0, 6, 0, 0, -2, 0, 0, 0, 0], [-12, 0, -1, -5, 5, -5, 3, 0, 11, 0, 0, -11, 0, 0, 0, 0], [0, 7, 0, 0, 0, 0, 0, 1, 0, -3, 0, 0, 11, 14, -2, 3], [0, 6, 0, 0, 0, 0, 0, 9, 0, -14, -2, 0, 14, -4, -1, 5], [0, -4, 0, 0, 0, 0, 0, 3, 0, -18, -3, 0, 9, -8, -7, 2], [7, 0, 4, 6, -8, -2, -4, 0, -8, 0, 0, -1, 0, 0, 0, 0], [3, 0, -4, -6, 2, 21, 11, 0, -1, 0, 0, 4, 0, 0, 0, 0], [3, 0, -2, -2, 7, 10, 6, 0, 1, 0, 0, 12, 0, 0, 0, 0], [5, 0, 3, 11, -7, 7, -1, 0, -7, 0, 0, 0, 0, 0, 0, 0], [-1, 0, -8, -6, 4, -3, -9, 0, -12, 0, 0, 6, 0, 0, 0, 0], [0, -8, 0, 0, 0, 0, 0, 2, 0, 3, -8, 0, -5, -4, -2, 0], [0, 2, 0, 0, 0, 0, 0, 9, 0, 5, -1, 0, 7, -16, 8, -1], [-6, 0, -5, -1, 4, 16, 2, 0, 10, 0, 0, 3, 0, 0, 0, 0], [15, 0, 2, 4, 8, -19, 1, 0, 16, 0, 0, -10, 0, 0, 0, 0], [0, 11, 0, 0, 0, 0, 0, 4, 0, -6, 7, 0, -5, 6, 15, 1], [0, 5, 0, 0, 0, 0, 0, 24, 0, -12, -1, 0, 1, -4, 4, 0], [1, 0, 2, -2, 0, -15, 7, 0, 0, 0, 0, 10, 0, 0, 0, 0], [7, 0, 11, 7, 6, 3, 7, 0, -2, 0, 0, 7, 0, 0, 0, 0], [0, -5, 0, 0, 0, 0, 0, -4, 0, 7, 1, 0, 0, -6, 0, 4], [0, 7, 0, 0, 0, 0, 0, 4, 0, 4, 3, 0, 3, 6, -8, -8], [-5, 0, -8, -6, 2, 12, -8, 0, -11, 0, 0, 9, 0, 0, 0, 0], [15, 0, 4, -2, -2, -15, 3, 0, 12, 0, 0, 4, 0, 0, 0, 0], [-5, 0, 5, 7, -2, -11, 12, 0, 2, 0, 0, -4, 0, 0, 0, 0], [9, 0, 9, 8, 4, 4, -4, 0, -4, 0, 0, 7, 0, 0, 0, 0], [0, 6, 0, 0, 0, 0, 0, 1, 0, -8, 6, 0, 18, -15, -1, 3], [14, 0, 5, 9, 2, -15, -7, 0, 10, 0, 0, -14, 0, 0, 0, 0], [-8, 0, 3, 3, 14, 13, 1, 0, 4, 0, 0, 2, 0, 0, 0, 0], [-2, 0, 0, 0, -2, 4, -13, 0, -6, 0, 0, -5, 0, 0, 0, 0], [0, 16, 0, 0, 0, 0, 0, 15, 0, -9, 1, 0, 4, 8, 6, -3], [0, -4, 0, 0, 0, 0, 0, 3, 0, -1, 5, 0, -6, -10, -2, 5], [-26, 0, -4, 2, 1, -3, 7, 0, -1, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, 0, 0, 0, 0, 0, 0, 7, 4, 0, -7, -4, 14, 2], [0, -12, 0, 0, 0, 0, 0, -7, 0, 1, -4, 0, 16, 2, -12, -5], [17, 0, 4, 4, 1, 3, 10, 0, -1, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -6, 0, -4, 5, 0, -13, -2, 3, 0], [-33, 0, -5, -1, 1, 0, 6, 0, 3, 0, 0, 1, 0, 0, 0, 0], [0, 4, 0, 0, 0, 0, 0, 0, 0, 10, -1, 0, 7, 8, 9, -8], [0, -14, 0, 0, 0, 0, 0, 3, 0, 10, 1, 0, 5, 17, 0, 3], [-11, 0, 5, -1, -1, -8, -11, 0, -7, 0, 0, -1, 0, 0, 0, 0], [0, 4, 0, 0, 0, 0, 0, -3, 0, 15, -8, 0, -6, 6, 1, 3], [3, 0, -1, -5, -3, -2, -6, 0, 5, 0, 0, 5, 0, 0, 0, 0], [0, -8, 0, 0, 0, 0, 0, 16, 0, -2, 7, 0, -5, -20, -8, -1], [0, 4, 0, 0, 0, 0, 0, -9, 0, -1, 2, 0, -5, -14, 5, 1], [0, 0, 12, 8, 5, 2, 0, 0, 9, 0, 0, -5, 0, 0, 0, 0], [3, 0, 5, -9, 5, 1, 9, 0, 3, 0, 0, 2, 0, 0, 0, 0], [0, -3, 0, 0, 0, 0, 0, 9, 0, -3, -3, 0, 8, 2, -5, 1], [-10, 0, -6, 4, -5, -18, 6, 0, 4, 0, 0, -3, 0, 0, 0, 0], [-14, 0, 7, 7, 0, -6, 2, 0, 8, 0, 0, -11, 0, 0, 0, 0], [0, 5, 0, 0, 0, 0, 0, 5, 0, 1, 4, 0, 1, 1, -8, 1], [0, -3, 0, 0, 0, 0, 0, 9, 0, -5, 3, 0, -12, -14, -12, -8], [-5, 0, 5, 3, 6, -25, -1, 0, 2, 0, 0, -5, 0, 0, 0, 0], [0, -4, 0, 0, 0, 0, 0, 4, 0, 5, 2, 0, -2, -4, -5, 6], [-2, 0, 5, 13, -6, 10, 4, 0, -8, 0, 0, 9, 0, 0, 0, 0], [13, 0, 4, 13, -2, 1, 15, 0, -2, 0, 0, -1, 0, 0, 0, 0], [0, -8, 0, 0, 0, 0, 0, -7, 0, 9, -3, 0, -12, -4, -6, -9], [10, 0, -5, 1, -2, 6, -4, 0, -9, 0, 0, 7, 0, 0, 0, 0], [-25, 0, 2, 0, -5, -14, 2, 0, -7, 0, 0, 8, 0, 0, 0, 0], [8, 0, 1, -7, 3, -6, 12, 0, -9, 0, 0, 10, 0, 0, 0, 0], [0, -7, 0, 0, 0, 0, 0, -7, 0, -3, 0, 0, -21, -2, -2, -3], [-1, 0, 6, 8, 8, -4, -14, 0, -4, 0, 0, -3, 0, 0, 0, 0], [0, -17, 0, 0, 0, 0, 0, 13, 0, 8, -8, 0, -4, -4, 5, 12], [3, 0, 3, 5, 0, -13, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -3, -1, -13, -2, -8, 0, -8, 0, 0, 5, 0, 0, 0, 0], [0, -15, 0, 0, 0, 0, 0, 3, 0, 6, -8, 0, -2, -4, -6, -7], [0, -6, 0, 0, 0, 0, 0, 5, 0, -1, -9, 0, -8, 18, -2, 1], [0, -6, 0, 0, 0, 0, 0, -5, 0, -7, 13, 0, -2, -6, 6, 7], [-5, 0, -3, 7, 3, -3, -1, 0, -7, 0, 0, -4, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 8, 0, 7, -2, 0, -5, 20, 13, -8], [10, 0, 4, -10, 4, -20, -2, 0, -10, 0, 0, 10, 0, 0, 0, 0], [0, -25, 0, 0, 0, 0, 0, -2, 0, -2, -10, 0, 6, -16, -13, 4], [37, 0, 6, 0, 11, -21, 3, 0, -4, 0, 0, 3, 0, 0, 0, 0], [10, 0, -3, 9, -7, -28, 2, 0, 1, 0, 0, -2, 0, 0, 0, 0], [0, -17, 0, 0, 0, 0, 0, 13, 0, -5, 0, 0, 3, 12, -4, 1], [13, 0, -12, -2, -6, -3, -3, 0, -6, 0, 0, 6, 0, 0, 0, 0], [0, -7, 0, 0, 0, 0, 0, -23, 0, 8, 4, 0, 6, 8, 0, -5], [4, 0, 8, 2, 9, -10, -4, 0, 13, 0, 0, -11, 0, 0, 0, 0], [0, -9, 0, 0, 0, 0, 0, -11, 0, -6, -5, 0, 3, -14, -3, 3], [0, -1, 0, 0, 0, 0, 0, -27, 0, 3, 7, 0, -9, -2, 2, 1], [0, -1, 0, 0, 0, 0, 0, -10, 0, 11, 4, 0, -13, -7, -1, 2], [-1, 0, -4, 6, -1, -9, -9, 0, 9, 0, 0, -7, 0, 0, 0, 0], [12, 0, -5, -13, -8, 10, 4, 0, 2, 0, 0, 9, 0, 0, 0, 0], [15, 0, -2, -11, 4, 18, -2, 0, 6, 0, 0, 2, 0, 0, 0, 0], [-7, 0, 3, 9, -1, 23, -6, 0, -3, 0, 0, 5, 0, 0, 0, 0], [0, 16, 0, 0, 0, 0, 0, 2, 0, -10, -1, 0, -9, -2, 7, -6], [0, 0, 0, 0, 0, 0, 0, -9, 0, -3, -1, 0, 11, -4, -4, 5], [-5, 0, -7, 5, -1, 17, 3, 0, 9, 0, 0, 4, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 0, -3, 0, -10, 2, 0, 4, 4, 0, -4], [21, 0, 2, 2, -1, -3, 7, 0, 1, 0, 0, -1, 0, 0, 0, 0], [0, 6, 0, 0, 0, 0, 0, -6, 0, -1, 5, 0, -2, 4, 15, -8], [8, 0, 9, -1, -1, -7, -11, 0, -9, 0, 0, 11, 0, 0, 0, 0], [4, 0, 10, -2, 7, -4, -6, 0, 1, 0, 0, -9, 0, 0, 0, 0], [0, 6, 0, 0, 0, 0, 0, -1, 0, -7, 3, 0, 0, -20, 10, 5], [14, 0, 3, 7, -3, 2, 16, 0, 11, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 1, 0, -2, 4, 0, -6, 9, 6, 1], [0, -7, 0, 0, 0, 0, 0, -2, 0, -5, 1, 0, 11, -4, 2, 10], [-9, 0, -2, -6, 0, 29, 9, 0, 0, 0, 0, 14, 0, 0, 0, 0], [0, -4, 0, 0, 0, 0, 0, 9, 0, -5, 1, 0, -10, -4, -2, -1], [0, -17, 0, 0, 0, 0, 0, 5, 0, -11, -11, 0, 4, 8, -3, 9], [0, -12, 0, 0, 0, 0, 0, -14, 0, -1, 7, 0, 10, -18, -5, 4], [0, -4, 0, 0, 0, 0, 0, 15, 0, 9, -14, 0, 16, 6, 1, 1], [6, 0, -4, -2, -14, 12, -16, 0, -8, 0, 0, 4, 0, 0, 0, 0], [5, 0, -11, -13, 0, 3, 0, 0, 8, 0, 0, -5, 0, 0, 0, 0], [0, -2, 0, 0, 0, 0, 0, -20, 0, 7, 4, 0, -15, -16, 14, 4], [16, 0, 10, 8, -2, -52, -4, 0, -2, 0, 0, -4, 0, 0, 0, 0], [1, 0, 1, 5, -7, 11, -13, 0, -8, 0, 0, -8, 0, 0, 0, 0], [38, 0, -6, 4, 7, 1, -5, 0, 3, 0, 0, 0, 0, 0, 0, 0], [2, 0, -5, -6, 1, -2, 2, 0, 11, 0, 0, -11, 0, 0, 0, 0], [0, 6, 0, 0, 0, 0, 0, 10, 0, -1, -3, 0, -10, 11, -5, -6], [0, -1, 0, 0, 0, 0, 0, -11, 0, -10, -8, 0, -10, 8, 12, 5], [18, 0, -4, 4, 12, 0, 11, 0, -4, 0, 0, 3, 0, 0, 0, 0], [5, 0, -14, 0, 2, 4, 0, 0, 5, 0, 0, -3, 0, 0, 0, 0], [0, 4, 0, 0, 0, 0, 0, 19, 0, -5, 6, 0, 1, -10, 7, -1], [-20, 0, -7, -23, -3, 3, -7, 0, -7, 0, 0, 11, 0, 0, 0, 0], [0, -11, 0, 0, 0, 0, 0, -13, 0, -1, -8, 0, -9, 8, 6, 3], [0, 5, 0, 0, 0, 0, 0, 2, 0, -14, -9, 0, 7, -4, -4, 4], [0, -8, 0, 0, 0, 0, 0, -5, 0, 6, -12, 0, -2, -2, -11, -3], [0, -1, 0, 0, 0, 0, 0, 9, 0, 4, -6, 0, -16, 10, -8, -9], [0, 0, 1, -1, -3, -1, 2, 0, -9, 0, 0, 19, 0, 0, 0, 0], [0, -7, 0, 0, 0, 0, 0, 4, 0, -1, -3, 0, 0, 20, -12, -4], [0, 11, 0, 0, 0, 0, 0, -4, 0, -8, -8, 0, -2, 8, -9, -6], [4, 0, 3, -5, 6, -4, 6, 0, -2, 0, 0, 5, 0, 0, 0, 0], [0, -11, 0, 0, 0, 0, 0, 21, 0, 9, -4, 0, 11, -10, 6, -5], [0, 12, 0, 0, 0, 0, 0, 7, 0, 12, 7, 0, -7, 8, 0, -5], [9, 0, -5, 5, 1, -11, 3, 0, -5, 0, 0, 6, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 0, -13, 0, 10, -8, 0, -11, 10, -2, 3], [0, -1, 0, 0, 0, 0, 0, 9, 0, 4, -5, 0, -11, 8, 14, 0], [0, 8, 0, 0, 0, 0, 0, 1, 0, -5, 17, 0, -2, 10, 6, 5], [-4, 0, 10, 8, 7, -7, 5, 0, -5, 0, 0, -4, 0, 0, 0, 0], [16, 0, -10, 0, -2, 0, 2, 0, 2, 0, 0, -8, 0, 0, 0, 0], [2, 0, -3, 3, -4, 24, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0], [0, -11, 0, 0, 0, 0, 0, -23, 0, -9, 2, 0, 4, -16, -10, 1], [43, 0, 5, 13, 7, -31, 7, 0, 13, 0, 0, -10, 0, 0, 0, 0], [-30, 0, 0, 8, -4, 8, 3, 0, 0, 0, 0, -16, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, -18, 0, -13, 0, 0, 12, -2, 1, 6], [0, 10, 0, 0, 0, 0, 0, -10, 0, -9, -8, 0, -9, -2, 14, 6], [28, 0, 0, 1, -7, -30, 6, 0, -3, 0, 0, -12, 0, 0, 0, 0], [0, 16, 0, 0, 0, 0, 0, -10, 0, -6, 3, 0, -7, 12, 11, -4], [-17, 0, -1, -3, 2, 5, -9, 0, -4, 0, 0, -3, 0, 0, 0, 0], [0, -11, 0, 0, 0, 0, 0, -2, 0, 9, -4, 0, -16, 10, 13, -6], [0, -5, 0, 0, 0, 0, 0, -7, 0, -1, -5, 0, 12, -14, -2, 4], [-26, 0, -5, -3, -7, 20, -18, 0, -13, 0, 0, 2, 0, 0, 0, 0], [0, -12, 0, 0, 0, 0, 0, -14, 0, 18, -4, 0, -28, -2, 2, 2], [27, 0, -1, -8, 8, -2, -14, 0, -10, 0, 0, 3, 0, 0, 0, 0], [0, -3, 0, 0, 0, 0, 0, 2, 0, 3, -3, 0, 14, -7, -10, 8], [-12, 0, -1, -13, 15, -25, 3, 0, 1, 0, 0, -7, 0, 0, 0, 0], [-15, 0, 9, 5, 3, 25, -11, 0, 5, 0, 0, -6, 0, 0, 0, 0], [0, -4, 0, 0, 0, 0, 0, -1, 0, 14, 0, 0, 6, 0, -3, 3], [2, 0, -3, -9, -1, 14, 0, 0, 11, 0, 0, 6, 0, 0, 0, 0], [25, 0, 16, 12, 7, 10, 0, 0, 3, 0, 0, -6, 0, 0, 0, 0], [-28, 0, 2, -10, -16, 14, -3, 0, -8, 0, 0, 4, 0, 0, 0, 0], [0, 20, 0, 0, 0, 0, 0, -19, 0, -1, -9, 0, -2, 26, 10, 9], [0, 14, 0, 0, 0, 0, 0, 19, 0, 9, -3, 0, -4, 18, 3, 2], [16, 0, 4, -12, 11, -36, 0, 0, 11, 0, 0, -3, 0, 0, 0, 0], [18, 0, 7, 3, -12, 0, -8, 0, 4, 0, 0, -1, 0, 0, 0, 0], [-40, 0, 1, 1, -9, -2, -6, 0, 7, 0, 0, -10, 0, 0, 0, 0], [0, 17, 0, 0, 0, 0, 0, -16, 0, -8, -1, 0, -9, -4, 2, -6], [0, 19, 0, 0, 0, 0, 0, -31, 0, 10, 4, 0, -5, 4, -3, 3], [28, 0, -3, 3, -2, -31, 1, 0, 8, 0, 0, 2, 0, 0, 0, 0], [-20, 0, -1, -5, 4, -10, 4, 0, -10, 0, 0, 3, 0, 0, 0, 0], [7, 0, -9, -6, 3, -2, 12, 0, 15, 0, 0, -8, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 0, 9, 0, 12, 1, 0, -4, -4, -6, -11], [0, 5, 0, 0, 0, 0, 0, 2, 0, 5, -13, 0, 2, -4, 5, -3], [0, 7, 0, 0, 0, 0, 0, 15, 0, 5, -12, 0, 3, 0, -4, 5], [-1, 0, -4, -12, -4, 15, -5, 0, -6, 0, 0, 4, 0, 0, 0, 0], [16, 0, 2, 3, 1, 28, -8, 0, -7, 0, 0, 0, 0, 0, 0, 0], [0, 12, 0, 0, 0, 0, 0, 2, 0, -9, 3, 0, 8, 6, -11, 8], [0, 7, 0, 0, 0, 0, 0, 11, 0, 9, -9, 0, 4, 14, -13, -5], [0, 6, 0, 0, 0, 0, 0, 9, 0, -2, 4, 0, -4, -10, -1, -3], [0, 0, 0, 0, 0, 0, 0, -14, 0, -1, 5, 0, 6, 4, 2, -9], [0, -2, 0, 0, 0, 0, 0, 7, 0, -2, -2, 0, -6, 18, 11, 11], [-12, 0, 8, 8, 8, 16, -7, 0, 4, 0, 0, -1, 0, 0, 0, 0], [0, 4, 0, 0, 0, 0, 0, -23, 0, 15, -1, 0, -8, 0, 13, -12], [-18, 0, -2, -16, 3, 25, -17, 0, -9, 0, 0, 0, 0, 0, 0, 0], [0, -12, 0, 0, 0, 0, 0, -6, 0, 10, 1, 0, 10, 10, 2, -10], [0, -4, 0, 0, 0, 0, 0, -10, 0, 10, 9, 0, 13, -2, -1, 0], [0, -4, 0, 0, 0, 0, 0, -8, 0, -6, 12, 0, -14, -16, -1, 7], [-20, 0, -1, -11, -1, 2, -4, 0, -9, 0, 0, 8, 0, 0, 0, 0], [-12, 0, -2, -4, -2, -16, 16, 0, 4, 0, 0, -6, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0, 9, 0, 2, 3, 0, -5, -5, 1, -13], [0, -5, 0, 0, 0, 0, 0, -1, 0, 7, -3, 0, 13, -10, 0, 7], [-27, 0, 7, 7, -4, -8, 0, 0, -14, 0, 0, -4, 0, 0, 0, 0], [0, -13, 0, 0, 0, 0, 0, -3, 0, -9, -4, 0, 5, -26, -20, -1], [-21, 0, -6, -20, -5, 3, -5, 0, -9, 0, 0, 5, 0, 0, 0, 0], [0, 5, 0, 0, 0, 0, 0, 5, 0, 2, 1, 0, 4, -14, -21, -5], [21, 0, 6, 10, 4, 29, -11, 0, 2, 0, 0, -12, 0, 0, 0, 0], [-7, 0, -5, -5, 7, -12, 2, 0, 5, 0, 0, -3, 0, 0, 0, 0], [-14, 0, 13, -1, -2, -6, 1, 0, 2, 0, 0, 17, 0, 0, 0, 0], [0, 5, 0, 0, 0, 0, 0, 25, 0, -15, -3, 0, 12, -8, -3, -5], [0, 0, 0, 0, 0, 0, 0, -3, 0, 21, 3, 0, -12, 0, 14, 3], [-23, 0, 1, -7, 4, -1, -1, 0, 4, 0, 0, 7, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 14, 0, 5, -4, 0, 3, 28, 10, 4], [0, 30, 0, 0, 0, 0, 0, 1, 0, 8, -2, 0, -10, 17, 15, 3], [0, -29, 0, 0, 0, 0, 0, -2, 0, -2, -1, 0, -3, 10, 8, 6], [12, 0, 6, 4, 10, -30, 4, 0, 7, 0, 0, -2, 0, 0, 0, 0], [0, 15, 0, 0, 0, 0, 0, -8, 0, -10, 14, 0, -8, -12, 7, -2], [0, -14, 0, 0, 0, 0, 0, 3, 0, 13, 2, 0, 7, -18, 3, -7], [0, 7, 0, 0, 0, 0, 0, 5, 0, -12, -2, 0, 0, -26, -6, 3], [0, 9, 0, 0, 0, 0, 0, -9, 0, -1, 1, 0, 5, -14, 0, -13], [-7, 0, -15, -13, -1, 13, 2, 0, 1, 0, 0, -3, 0, 0, 0, 0], [4, 0, -4, -18, -3, -29, 1, 0, 3, 0, 0, -2, 0, 0, 0, 0], [-26, 0, -2, 0, 5, 0, 14, 0, 3, 0, 0, 3, 0, 0, 0, 0]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_1805_a_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_1805_2_a_w();".
// 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_1805_2_a_w(:prec:=16)
    chi := MakeCharacter_1805_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_1805_2_a_w();".
// 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_1805_2_a_w( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_1805_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![256, 0, -2592, 0, 8701, 0, -11261, 0, 6639, 0, -2038, 0, 339, 0, -29, 0, 1]>,<3,R![841, 0, -11321, 0, 27709, 0, -25742, 0, 11974, 0, -3074, 0, 441, 0, -33, 0, 1]>],Snew);
    return Vf;
end function;