
// Make newform 9065.2.a.t in Magma, downloaded from the LMFDB on 04 October 2025.
// To make the character of type GrpDrchElt, type "MakeCharacter_9065_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_9065_2_a_t();".
// 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_9065_2_a_t();".
// 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 := [18, -42, -746, 536, 5782, -5174, -12598, 12010, 12474, -12205, -6531, 6476, 1924, -1920, -320, 320, 28, -28, -1, 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, 1, 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, -5, 0, 1, 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], [-5962306659, -60991870882, 70069915789, 204853156523, -60283012228, -235805242958, -58954026739, 104465266815, 91576159963, -4566807072, -44257632029, -10453749268, 10672622154, 3379612730, -1397061875, -419944228, 95008225, 18948490, -2624248], [4755243851, 730650720, -71017658000, 36159587760, 149050114933, 58512860692, -189318880402, -203484731431, 158894866388, 167910075887, -78942991260, -62872645052, 22625667530, 12069896428, -3677289943, -1158331601, 314704415, 44078579, -11004863], [11088856365, -20447192477, -230158604893, 339047079583, 320174395333, -685345332529, 195211517614, 588473388369, -606282779128, -265907267496, 440108756123, 68695112872, -152294049393, -10230273038, 27840322631, 815634322, -2590969348, -26793352, 96730114], [-2505501323, 10371672294, 12535126762, -168408006171, 5121004606, 654826291707, -216711730085, -898930145580, 380586478407, 568425648228, -261584326210, -187770639086, 89884012777, 33577108008, -16457284397, -3081136661, 1536273262, 113680079, -57506159], [3557095491, -5629639817, -180302747584, -229052308283, 1547001890305, 313738242146, -3202866404813, -78526735947, 2955107751839, -54823685541, -1457782022221, 35879126830, 409833523263, -8153013050, -65700176287, 841303285, 5585357333, -33378319, -195223802], [-394600374, 94820373625, 66762703628, -975690717251, 250462644673, 2715847540547, -1392278434208, -3190109712528, 1911381574196, 1868747917206, -1177873128808, -593501858090, 380037822219, 104014853632, -66699305344, -9455352923, 6033515966, 347764181, -220285568], [1171342812, -2290622662, -50422198703, -25220929904, 299910571627, 178971312919, -715230405150, -286076180931, 785564990067, 190800416143, -443276778801, -64504226823, 137163240626, 11667941141, -23541543230, -1076186549, 2102523247, 39696959, -76200707], [-18377141415, 38466398137, 386376539129, -513118507301, -1406559844763, 2030360473190, 1192585212922, -2737134124719, 168495931271, 1688866464114, -589821445564, -547987304702, 277522089744, 97016816980, -58371791767, -8868930395, 5878930373, 327296369, -230500127], [-21557480895, 37506346631, 523681936069, -431915406580, -2409105879421, 1049255476045, 4341848717618, -1020986424948, -3860628083114, 504937594059, 1886277052879, -138079778830, -529429639266, 21114411377, 84924732355, -1693640542, -7227514151, 55775188, 252869075], [5062545609, -12619619918, -130499962246, -41602082267, 568953104614, 548742025181, -1582723562594, -903851923824, 2034649564574, 597548161170, -1273988888674, -200525842742, 421800845004, 36261659080, -75785692723, -3364760225, 6991001510, 125388053, -259442672], [8582927526, -16446464795, -215125227757, 104266135877, 1088317288855, -234190226398, -2105119026066, 236925093123, 1986302991978, -127716940949, -1018215569006, 38141758669, 296556242735, -6303759626, -48922781315, 542088930, 4253174725, -19110451, -151254431], [-3430367382, 3065765697, 169067596581, 41999396050, -1270691401705, 104010783621, 2612203101479, -291522296529, -2433601557689, 228307092066, 1214804306573, -82619656151, -344967294289, 15401258773, 55714786601, -1441064295, -4760605277, 53825972, 166930282], [-14815274583, 80693778581, 432444340942, -506343504661, -2646087788215, 633981258031, 5991885153383, -169070885889, -6293017706687, -89541975588, 3454650892519, 65102590961, -1051513785921, -15808567237, 178629734155, 1726565285, -15846903200, -70937051, 571727897], [-3101619378, 23067549022, -198607162336, -1127263570724, 2701661013811, 3425633855726, -7047834901418, -4005728029791, 7733276489414, 2292475383090, -4321934792962, -711414390440, 1327677669387, 122308178026, -226863179269, -10940834627, 20212437611, 396315491, -731738372]];
    Rf_basisdens := [1, 1, 1, 1, 1, 2229563793, 743187931, 2229563793, 743187931, 2229563793, 2229563793, 743187931, 2229563793, 2229563793, 2229563793, 743187931, 743187931, 2229563793, 2229563793];
    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_9065_a();"
function MakeCharacter_9065_a()
    N := 9065;
    order := 1;
    char_gens := [3627, 5736, 7106];
    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_9065_a_Hecke( : Kf := Kf)
    return MakeCharacter_9065_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, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0], [-1, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0], [1, 0, 1, -1, 1, 0, 0, -1, -1, -2, -1, 0, 0, -1, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, -1, 1, 0, 1, 1, 1, 0, 1, -1, 0, -1, 0, 0], [-1, 0, 1, -2, 1, 1, -1, 0, -1, -2, -1, 2, 1, -2, 0, 0, 0, 2, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, -1, 0, 1, -1, 0, 0, 1, 1, 0, 0, 1, -1, 0, -1, -2, 1, 0], [0, 0, -1, 0, -1, -1, 1, -1, 0, 1, 0, -1, -1, 1, 1, 1, 0, 0, 0], [-2, 0, -1, 0, -1, 0, 2, -1, 0, 1, -1, 0, 0, 0, 0, -1, 1, -2, -1], [1, 1, -1, 1, 0, -1, 0, 1, 0, -1, 0, 0, 0, 0, 0, 1, -1, 1, 1], [0, -1, 0, 0, -1, -1, 1, -1, 0, 1, 0, -1, 0, 0, 1, -1, 0, -1, 0], [-1, -1, 0, 1, 1, 1, 0, 0, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 2, -2, 1, 1, -1, 0, -1, -4, -1, 2, 0, -3, 0, 0, 0, 1, 1], [1, -1, 3, -1, 0, 1, 0, -1, -1, -2, 0, 0, -2, 0, 0, 1, 1, -1, 1], [-3, -1, -1, 1, -1, 1, 1, 0, 0, 1, 0, 0, -1, 2, 0, 0, 0, 0, 0], [1, -1, 0, 0, -1, -1, 0, 0, 0, 1, 1, -2, 0, 0, 0, 1, -1, 0, 0], [-4, 0, -2, 0, -1, 2, 1, 0, 0, 1, 1, -1, -1, 2, 1, 2, 1, 0, -1], [-1, -2, 0, 0, 0, 1, -2, 1, -1, -2, 1, 0, -1, 1, 0, 3, 1, 0, 0], [-5, 2, 0, -1, 0, 1, -1, 1, 1, 2, 1, 2, 1, 0, -2, 0, 1, -1, 0], [-1, 0, 3, -1, 2, 1, -2, 0, -1, -3, -1, 3, 0, -2, -1, 0, -1, 2, 0], [0, 1, -1, 1, 1, 0, 1, -1, 1, 0, 0, 0, 0, -1, 0, 0, 0, 2, 1], [-2, 0, 1, 0, 0, 3, -1, 1, -1, -2, -1, 0, 0, 0, 0, 2, 0, 1, -1], [0, -1, -2, 3, -3, 0, 1, 1, 1, 4, 1, -2, -1, 4, 0, 0, 1, -3, -1], [-5, 1, -5, 2, -4, 0, 2, 3, 1, 7, 0, -1, 1, 4, 1, 1, 1, -3, -3], [-1, 0, -1, 2, -1, 0, -2, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0], [2, -4, 1, -1, 0, -1, 0, -1, -1, -1, 0, -2, -2, -1, 2, 0, 1, 0, 0], [-1, -2, 0, -2, 1, 1, -3, 0, -1, -4, -1, 2, 0, -1, 0, 2, 0, 1, -1], [-1, 2, 2, -1, 2, -1, -2, -2, -1, -5, 0, 1, -1, -3, 1, 2, 0, 3, 2], [1, -2, 2, 1, 1, 1, 1, 0, 1, 1, 1, -2, 0, 1, 0, 1, -1, 0, 1], [0, -1, 1, 0, 1, 0, 1, -1, -1, 0, 2, 0, 0, -1, 0, -2, -1, 0, 1], [-2, 1, -2, 1, -1, -1, 2, 0, 1, 3, -2, -2, 2, -1, 0, -3, -1, 0, -1], [1, -2, -2, 2, 0, -2, 0, 0, 0, -1, 0, -2, -2, 3, 0, 1, 0, -1, 0], [-1, 2, 2, -1, 0, -1, 1, -1, -1, -2, -1, 0, -1, -2, 2, 0, 1, -1, 2], [-1, 1, -4, 1, -2, -2, 2, 1, 2, 5, -2, -1, 2, 1, -1, -2, -2, -2, -2], [3, 1, -2, 1, -2, -1, 0, -1, 1, 2, 0, -2, 1, 1, 0, 0, -1, 0, 0], [1, 1, -1, 2, -2, -2, 0, 3, 1, 3, -1, -3, 1, 2, 1, 0, 0, -1, -2], [0, 0, -4, 1, -1, 0, 0, 1, -1, 1, 1, 0, 1, 1, 0, -1, 0, 0, -2], [-6, 1, -3, 1, -1, 0, -1, 3, 1, 1, 0, -2, 0, 3, 0, 4, 0, 0, -1], [-1, -2, 5, 0, 3, 2, -2, -1, -2, -4, 0, 2, -2, -1, 0, 0, 2, 0, 2], [-4, -1, 4, -1, 3, 2, -3, 1, -1, -3, 1, 4, -1, -2, -2, 0, -1, 1, 1], [-1, 0, 1, -1, 2, 2, 0, 0, 1, 1, -2, 2, 1, -2, -2, 0, -1, 0, -1], [0, 2, 2, 1, 0, -3, 1, -2, 0, -1, 1, -3, -1, 1, -1, -1, -2, -1, 3], [0, -3, 7, -4, 1, 0, -1, -3, -2, -7, 0, 0, -2, -5, 0, -1, 3, 2, 3], [1, 0, -2, 1, 0, -3, 0, 0, 1, 3, 2, -1, 1, 1, -1, 0, -2, 1, 2], [3, -2, -2, 0, -2, -4, -1, 1, 0, -1, -1, -3, 0, 0, 1, 0, -3, -1, 0], [2, -2, -2, 1, -1, 0, 2, -1, -1, 3, -1, -2, -1, 3, 2, -1, 2, -2, -2], [-7, 2, -7, 3, -4, 0, 3, 2, 3, 11, 0, 0, 3, 3, 0, -4, 0, -3, -5], [-4, 0, 0, 1, 0, 1, 3, -1, -1, 2, -4, -2, 1, -1, 0, -2, 2, -2, -3], [1, 3, 1, -3, 1, 2, -1, 1, 1, -2, 0, 4, 2, -2, -2, 0, -2, 3, 1], [-4, 2, 4, -4, 5, 3, 0, -3, -3, -5, -2, 3, 0, -5, 1, -2, 1, 2, 1], [-3, 1, 0, 2, -2, -2, -2, 1, 1, 3, 0, 1, 0, 1, -1, -2, -1, -2, 0], [-8, -1, -6, 5, -2, -1, 2, 1, 2, 8, 0, -4, 1, 4, 0, 0, -1, -3, -2], [3, 2, -3, 0, 0, -3, 4, -1, 4, 5, -5, -2, 4, -2, 0, -4, -3, 1, -1], [4, -2, 1, -2, 1, 2, -3, 0, -2, -6, 0, 3, -2, 1, -1, 3, 0, 3, 1], [-9, -4, -2, 0, -2, 1, -1, 1, 0, 3, 1, 0, 1, 0, 0, 1, 2, -1, 0], [1, -3, 2, 1, -2, -1, 0, 1, -1, 2, 0, -2, -1, 1, -2, -2, 1, -3, 0], [-11, 4, -2, 0, -2, 0, 3, 1, 3, 9, -2, -1, 2, 2, -1, 2, -2, -1, -3], [-1, -2, -1, 5, 0, -3, 3, -1, 2, 5, 3, -4, 0, 3, 0, -1, -1, -1, 1], [1, -1, 3, -4, 3, 4, -3, -1, -3, -11, 0, 2, -2, -4, 2, 3, 3, 3, 3], [-1, 1, -2, 1, 1, -3, -1, -1, 2, 2, 1, -1, 2, 1, -1, 1, -2, 2, 1], [4, 4, -3, -1, 0, -2, 1, 1, 3, 3, -1, 1, 1, -2, -1, -2, -2, 3, -1], [1, 2, 0, 2, -2, -2, 3, -1, 2, 5, 1, -3, 0, 0, 1, -4, 1, -3, -2], [-4, -6, -2, 2, -3, 1, 1, 4, 0, 2, 2, -2, -2, 2, 0, 3, 3, -4, -2], [-4, 5, -4, 5, -4, -1, 0, 3, 2, 8, 0, 0, 3, 4, -2, 0, -3, -1, -2], [-8, -4, 0, 3, -2, -1, 1, 3, 0, 6, -1, -4, 1, 3, 0, 0, -1, -4, -2], [4, 1, 11, -6, 6, 1, -5, -2, -4, -14, -1, 5, 0, -8, -1, -1, 1, 4, 3], [-9, -2, -2, -2, 2, 4, -1, -1, -2, -4, -1, 3, 2, 0, -1, -1, 1, 3, 0], [-2, -2, 0, 0, 2, 2, 0, 2, 0, 0, -2, 0, 2, 0, 0, -2, 2, -2, -2], [6, -7, 4, -2, 4, 1, -4, 1, 0, -4, 2, 0, -1, -6, -2, 0, 2, 5, 4], [3, 0, 0, 0, 0, -1, -1, 1, -1, 1, 1, -2, 1, 0, 0, 1, -2, 1, 2], [1, 6, -4, 1, 0, 1, 2, 0, 1, 4, -5, 3, 5, -1, -1, -3, -3, 1, -3], [-2, 0, 1, -2, -1, 1, 2, -1, -2, -3, -2, 1, -1, -2, 1, -2, 3, -1, -2], [3, 2, 3, -3, 3, 3, 0, -1, -1, -3, -2, 1, 1, -5, -1, -4, 0, 2, 2], [-2, 0, -2, -2, -1, -2, -1, -4, 0, 1, 1, -1, -3, 2, 1, 0, 1, 0, 1], [-3, 1, 2, -2, 2, 2, 0, -3, -1, -3, -2, 1, 2, 1, -1, 2, -1, 2, 0], [4, -5, -3, 3, -4, 0, 1, 0, -1, -1, 0, -4, -3, 4, 2, 1, 2, -2, -2], [-3, -4, -1, 3, -1, 3, 0, 1, 1, 3, 0, 1, -1, 3, 1, -2, 0, -2, -2], [-6, -1, 2, 2, -2, 1, 3, -2, -1, 3, 3, -1, -3, 5, 1, 1, 3, -3, -2], [-3, 0, 2, -1, -1, -2, 1, -2, -1, -1, -1, -3, -3, 3, 1, 4, 0, -1, 1], [-8, 1, -4, -1, -3, 1, 2, 2, 2, 1, -2, -2, 2, -1, 2, 1, 1, -3, -1], [-3, 5, -8, 5, -2, -3, 5, 2, 5, 9, -1, -3, 3, 4, -1, -2, -4, -4, -4], [1, -1, 4, 1, 3, -1, 0, 2, 0, -5, 2, -2, -2, 0, 2, 1, -1, 1, 1], [6, -4, 1, 0, -2, 0, 2, 2, 1, 3, -1, -2, -1, 1, 2, -1, -1, -1, -2], [3, -1, 4, -3, 2, 0, -1, 0, 0, -2, 0, -2, -2, -4, -2, 0, 0, 2, 1], [7, 6, 4, 0, 0, -2, -2, 2, 2, -4, -2, 2, 2, -1, -2, -2, -4, -1, 0], [-1, 0, 4, 1, 2, 2, 0, 3, 0, -2, -2, 1, 2, -1, -1, 4, -2, 4, -1], [5, -2, 7, -5, 3, -1, -2, -1, -3, -10, -2, 3, -1, -7, 1, -1, 2, 2, 4], [12, 0, -1, 2, 2, -2, 0, -4, 1, -1, 2, 0, -1, -3, 0, -3, -4, 4, 3], [2, 5, 6, -1, 1, 2, -1, -1, -1, -12, -3, 4, -1, -2, -2, -2, -1, 3, 1], [-1, 1, 5, -6, 5, 3, -4, -2, 1, -4, -1, 6, 1, -3, -4, -4, -1, 3, 1], [1, 5, 2, 2, -2, 0, 2, -1, -1, -1, -2, -3, -2, 5, 3, 4, -1, -2, 0], [-7, -2, -2, -1, -2, 3, 2, 0, 1, -1, -2, -1, 1, -3, 3, 0, 2, 1, 0], [-5, -3, 5, 3, 1, 2, -1, -1, -1, 2, 6, -2, -4, 2, 0, 2, 6, -1, 1], [6, 3, 4, -7, 1, 0, 1, -1, -3, -6, -7, 2, 1, -4, 0, -2, 1, 1, 1], [3, 1, 2, 2, 1, -1, 0, -2, 4, 4, 3, -2, -2, 0, 2, -1, -1, 2, 2], [3, -5, -3, 6, 0, -2, 2, -1, 3, 6, 0, -3, -1, 6, 1, 1, -1, -2, -1], [-7, -4, 0, 3, 0, 0, 2, -2, 2, 7, 2, -6, 0, 3, 2, 3, 3, -3, 0], [1, -2, 3, 2, 2, 1, -2, 0, 2, 0, 3, -1, 2, 0, -3, -1, 0, 0, 0], [1, 4, -6, 5, -1, -2, 1, 2, 3, 5, -2, 1, 1, 3, -1, -2, -5, 1, 0], [1, -2, -6, 5, -2, -4, 0, 4, 5, 7, 4, -6, 0, 3, 0, -3, -1, -3, 0], [1, -1, -5, -3, -3, -2, -1, 3, 1, 8, -2, 4, 4, -4, -2, -4, -2, 3, 1], [-1, 10, -5, 0, -5, 1, 3, 2, 1, 3, -2, 2, 3, 4, 0, -2, -3, -4, -5], [2, -2, -5, 8, -8, -3, 0, 2, 1, 3, 3, -7, -4, 13, 1, 8, 0, -9, 0], [10, 2, 0, -2, 2, -4, -2, -2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 6, 2], [-5, 5, -3, 3, 1, -4, 1, -1, 2, 2, 2, -2, 2, -2, 2, 0, 0, 1, 3], [-5, 10, 4, -4, 2, 4, -1, -3, -2, -5, -1, 3, -2, -2, 1, 2, 3, 1, 4], [-5, -2, 8, -4, 1, 3, -3, -2, -5, -12, -1, 0, -4, 5, 0, 4, 2, -3, 1], [-6, 7, -5, -1, 0, -1, 2, -1, 0, 2, 3, 2, 0, -1, 0, 0, 0, 0, 0], [3, 3, -2, 1, 0, -1, -3, 4, 1, -5, 1, 5, 1, -2, 1, 4, -4, 2, 0], [-1, -2, 7, -1, 1, 1, -2, -1, 0, -1, 1, 1, 1, -1, -1, 1, -1, 0, 5], [-6, 2, 10, -2, 2, 1, -1, -1, -1, -3, 5, 0, -1, -5, 0, -3, 4, -2, 0], [-10, -7, 1, 1, -1, -1, 0, 2, -2, -3, 5, -2, -3, 4, 2, 5, 4, -4, -1], [3, 0, -3, 1, 1, -2, -2, 5, 1, 0, -5, 4, 4, -3, -2, -4, -4, 3, -1], [3, 0, 4, -7, 4, 2, -1, -3, -3, -5, -3, 3, 2, -6, 3, -1, 2, 5, 0], [-3, -8, 2, -1, -1, 0, -4, 1, -1, 5, 4, 0, -1, 2, -4, -3, 1, -1, 1], [-5, 1, 1, -1, 0, 1, 0, -1, -2, -9, -4, 0, -2, 2, 2, 1, 1, -3, -1], [4, 7, -7, -1, -1, -2, 3, -3, 1, 5, -1, 2, 2, -1, 4, -5, -1, 5, -2], [1, 6, -9, 5, -4, -1, 4, 3, 2, 11, 2, -4, 2, 8, 2, 4, -1, -1, 0], [-11, -2, -8, 5, -2, -3, 0, 2, -1, 9, 4, -3, -1, 7, 3, 2, 0, -1, -2], [6, 2, 2, -4, 4, 4, -5, -1, -2, -13, 3, 5, 0, -5, 1, 6, 3, 6, 4], [-2, 0, 6, -5, 5, 4, -4, -3, -1, -11, 1, 6, 1, -1, -4, -1, 0, 4, 2], [-6, 5, 5, -3, 3, 4, -4, 0, 0, -2, 2, 3, -2, 0, -1, 3, 4, -2, 2], [-10, 2, 0, 3, 2, 4, 0, 2, -1, -1, -2, 4, 2, -2, 0, 3, -1, 6, -2], [-2, 4, 1, 2, -2, -1, 0, -1, 0, -5, -3, -4, -4, 5, 0, 4, -1, -2, 1], [2, 7, -6, 2, -3, -2, 3, 1, 6, 10, 4, 0, 3, 0, 2, 2, 1, 0, -4], [-2, 2, -5, 4, -3, 0, 3, 2, 2, 9, -1, -7, 2, 3, -1, 0, -1, -3, -2], [3, -6, -2, -1, -2, 5, 4, 0, -1, 1, 2, -5, -1, 3, 1, 0, 4, -4, -2], [-6, 7, 2, -6, 2, 0, 1, -2, 0, 1, -1, 4, 4, -9, -4, -7, -2, 3, 2], [0, -1, -1, 5, -8, -3, 2, 3, 0, 12, 3, -6, -2, 5, 2, -2, 2, -4, -2], [4, -1, -2, 7, -2, -2, 1, 0, -1, 4, 3, -4, -2, 5, 0, 1, 3, -1, 0], [2, 4, 1, -1, 4, -2, 1, -3, 2, 7, -4, -1, 1, -2, -1, -7, -1, 1, 0], [-9, 4, -4, -2, -1, 0, 1, 3, 1, 5, -1, 0, 5, 3, 0, 0, -2, 2, -2], [12, -4, 2, -5, 2, 0, 2, -4, -2, -1, -2, 0, -2, -4, 2, -3, 3, 0, 0], [14, 5, 1, -6, 3, -2, 0, 0, 0, -3, -4, 5, 2, -10, 1, 0, -3, 6, 2], [-8, 0, -4, 8, -5, -1, 4, -1, 4, 16, 3, -5, 0, 7, 1, -5, 2, -8, -4], [2, 0, -1, -2, 2, 1, -4, 0, -1, 1, 1, 1, -2, 1, 3, 0, 0, -3, -2], [-7, 10, -1, 2, 0, -1, 2, 2, 1, 11, -2, 3, 2, 0, -3, -6, -1, -6, -5], [-1, 2, -3, 3, 3, -2, 2, 1, 5, 9, -3, 0, 4, -1, -2, -2, -8, 4, -3], [-7, -4, -3, 3, -2, 1, 5, -1, -2, 13, 3, -6, -2, 5, 2, 1, 5, -3, -1], [-7, -2, 1, -1, -1, 2, 0, -1, -3, 3, 4, 2, -2, 5, -2, -3, 3, -4, -2], [-1, 6, 0, 0, 0, 2, 2, -2, -3, -2, -4, 2, 0, -1, 2, -4, 0, 1, -4], [4, -2, -2, 5, 0, -3, -1, -1, 3, 6, 5, 2, -1, -1, 0, -6, -1, 2, -2], [-9, -4, -5, -1, -4, -2, 1, 0, -1, 15, 2, -4, -1, 5, -2, -8, -2, -5, -1], [-2, -5, 5, -5, 3, 4, -1, -5, -5, -17, 3, 2, -4, -9, 2, 5, 3, 6, 4], [-8, -3, -6, 3, -2, 4, 4, 1, 3, 8, 0, -1, 2, 10, 1, 1, 0, -3, -4], [4, 0, 5, 2, 6, 0, -6, 0, -2, -18, -1, 4, -3, -7, 0, 4, 1, 3, 6], [-4, 4, -7, 2, -4, -2, 3, 5, 5, 16, -7, -1, 7, 2, -1, -5, -5, -2, -7], [5, 8, 1, 4, 3, -5, 2, 0, 1, -3, -4, -4, -1, 1, 0, -2, -6, 3, 1], [16, 1, 3, -2, 4, -1, 2, -3, -5, -13, -5, 6, 2, -11, 2, -1, 1, 6, 2], [-4, -1, -5, 2, -5, 0, 3, 3, -2, 2, -1, 0, 2, 5, -2, 4, 0, -8, -2], [3, 1, -3, 3, -1, -7, 3, 3, 1, 8, -2, -5, 3, 2, 3, -3, -5, 1, -1], [-1, 6, -19, 9, -12, -11, 4, 8, 7, 23, 5, -9, 2, 10, 1, 0, -5, -8, -6], [4, 1, 9, -5, 3, -2, 1, -3, -2, -2, 2, 0, -2, -7, 2, -4, 6, 1, 1], [1, -2, 1, -3, 5, 0, -4, 1, -7, -17, -4, 6, -2, -5, 2, -1, -1, 8, 2], [-1, 3, -4, -1, -1, -5, 2, 0, 6, 0, -2, 2, 4, 0, -2, -3, -1, 0, -3], [1, -6, 0, 4, -4, -2, -1, -1, -2, 1, 5, -7, -8, 8, 1, 0, 3, -1, 2], [5, -3, 0, 0, -3, -1, 0, 2, -2, 3, 1, 0, 0, 2, 2, -1, 5, 1, 0], [0, 4, -3, -4, -1, -3, 2, 1, 2, 6, -6, -1, 5, -2, -1, -1, -3, 3, 2], [-5, 3, -3, -3, 2, 2, -2, -3, -1, -2, -3, 5, -1, -2, 1, 3, 1, 8, 0], [3, -3, -3, 0, -6, -2, 3, -2, 4, 13, 6, -6, 1, 5, 4, 1, 5, -3, -4], [4, 0, 2, -1, 3, 2, -1, 2, 1, -6, -4, 3, 1, -2, -1, -1, -1, 2, -2], [-2, 9, 11, -6, 3, 6, -1, -5, -4, -17, -2, 6, 0, -11, -2, -1, 3, 0, 1], [2, -8, 2, 2, -2, -2, -5, 3, 1, -9, 1, 1, -4, 1, 1, 2, 1, -1, 0], [-14, 9, 3, 3, 1, 3, 2, -2, 0, 3, 3, 0, -3, 6, 0, -3, 0, -6, -1], [7, 3, -7, 1, 1, 1, 0, 2, 1, -5, 1, 2, 3, -1, 0, 5, -2, 3, 1], [2, 4, 7, -5, 3, 6, -4, -3, 0, -4, 1, 4, 0, -4, 0, 2, 2, 6, 1], [4, 6, -2, 2, -4, -2, -1, 3, 0, -5, -3, -1, -2, 1, -3, 0, 1, -2, 0], [-9, 6, 0, 2, 0, 0, -3, 3, 0, 3, 1, 3, 0, -2, -7, -2, -3, -1, 0], [-9, 3, -10, 2, -3, -3, 0, 4, 1, -1, 1, 2, 2, 2, 2, 7, -3, -2, 0], [11, -2, -3, 2, 2, 3, -1, -1, 1, -9, -1, 0, -2, -3, 2, 5, 0, 4, 3], [2, 3, 4, -1, 7, 4, 1, -7, -1, -14, -3, 2, -1, -6, 2, 0, -1, 5, 5], [4, 3, 0, 2, -2, -1, 5, -1, 3, 7, -3, 0, 5, -7, 0, -8, 0, 0, -5], [-24, 2, -3, -5, -5, 1, 2, 3, 0, 9, 0, -1, 3, 0, -1, 0, 0, -4, -4], [-15, -4, 6, -7, 5, 8, -2, -7, -7, -17, 1, 4, -5, -4, 2, -1, 6, -1, 2], [6, -3, 7, -3, 4, -3, 1, -1, 0, -9, -1, -2, -2, -6, 2, -6, -1, 3, 2], [6, -2, 4, -2, -1, 3, -1, -2, -6, -15, 0, -2, -4, 0, 2, 7, 1, -3, 4], [-6, 1, -2, 3, -1, 2, 1, 0, -3, 2, 0, -3, -1, 6, 1, -2, -3, -6, -3], [7, 3, -7, 6, -3, -6, -1, 3, 4, 13, 8, -6, 0, 6, 0, -3, 1, -3, -3], [-2, 4, -7, -4, -3, -8, 1, 2, 6, 15, -3, 1, 6, -3, -3, -8, -1, -3, -2], [-10, -2, -2, 0, -3, 1, 0, 3, 2, 12, 1, 5, 2, 5, -1, -1, 0, -4, 0], [0, -6, 3, -4, 1, 2, -5, 0, -4, -7, 5, 3, -4, -5, 1, 6, 1, 5, 4], [6, 2, -4, 6, 4, -6, 2, -4, 3, 0, -2, -2, -2, 0, 2, -2, -4, 2, 0], [-10, -4, -7, 7, 0, -4, 2, 0, 3, 6, 2, -6, 1, 7, 0, 4, -1, 1, -5], [2, -8, -3, 6, -1, -1, -6, 5, 4, 0, 8, -1, -3, 6, -5, 3, 1, 1, 4], [-3, 1, 7, -3, 7, 0, -5, 5, 1, -10, -2, 8, 0, -6, -4, -2, -2, 7, 3], [0, 0, -1, 0, 5, 2, -5, 6, -2, 3, 3, 5, 2, -1, -3, -2, -3, 7, 0], [13, -1, 1, -3, 5, 1, 1, -1, -1, -12, -6, 5, 3, -6, 1, 1, -1, 5, 3], [-13, 8, 1, -5, 4, 3, 0, -2, -3, -5, -1, 3, -2, -4, -1, 4, 3, 0, -2], [5, -5, -1, -1, 5, 2, -4, -2, 1, -6, 4, 5, 0, -3, -3, 3, 2, 7, 2], [-9, 4, -1, 1, -5, -2, -1, 4, 0, 5, 0, -5, 0, 4, -3, 4, -3, -4, 1], [-3, -2, -3, -2, 0, -7, -1, 1, 0, 5, -4, 0, 2, -3, 2, 1, 1, -2, 0], [-7, 5, 6, -2, 3, 3, -2, 0, -2, 2, 3, 8, 0, 2, -2, -1, 3, -2, 0], [-1, 3, 2, 1, -1, 4, 0, -1, 0, -1, -5, -2, 3, 0, -2, 2, 0, -1, -3], [-2, -2, 12, -3, 8, 1, -3, -3, -4, -16, 1, 2, -5, -7, 0, -2, 1, -2, 6], [7, 11, 6, -4, 5, 3, -1, -3, 0, -16, -8, 3, 2, -9, -3, -1, -4, 4, 2], [1, 13, -3, -2, 4, -4, -4, 5, 1, -7, -3, 7, 1, -4, -1, -2, -6, 5, 2], [0, 2, 11, -9, 12, 0, -4, -5, -7, -20, -7, 3, 1, -17, -1, -2, -1, 10, 7], [-5, 3, 0, -2, -2, -2, 2, 3, 1, 5, -6, 3, 2, 5, -1, 0, -1, -6, -4], [12, 1, -17, 5, -7, -8, 4, 6, 6, 8, -6, -3, 2, 6, 3, -1, -6, -4, -4], [7, 2, -2, 2, 0, -7, 7, -3, 2, 1, -1, -8, 1, 0, 0, -1, -6, 3, 4], [-16, 0, 3, 4, -1, 1, 0, -1, 2, 4, -2, -1, 3, -2, -1, -1, 1, 3, 0], [-7, 5, 8, -3, 0, 0, 1, 0, 1, -5, -3, 4, 2, -2, -4, -5, -1, -4, 0], [-6, 0, 6, -1, 1, 2, 3, -4, -1, -2, 0, -3, 1, -4, 3, -3, 5, -4, -2], [-7, 4, -1, -5, 3, 6, -2, 3, -1, -5, 6, 0, -2, -1, -2, 3, 3, -2, 0], [-4, -3, 10, -9, 3, 4, 0, -4, -6, -12, -3, 7, -3, -7, -3, 1, 3, -1, 6], [10, 4, -6, -2, 1, 2, 5, -1, 1, 7, -13, 6, 5, -2, -2, -8, -4, 1, -4], [-7, 5, 0, 2, -4, -2, 6, -2, -1, 4, 0, -4, 0, 7, 0, 3, -2, -3, 3], [-26, 7, -4, 0, -4, 3, 5, 2, -1, 0, -7, -3, -1, 3, 3, 1, 7, -7, -4], [-3, -6, -3, 6, -1, 0, 1, 2, -1, 0, 4, 5, -2, -4, 3, 3, 4, 1, -1], [-4, 0, 1, -4, 1, -3, 0, 1, 0, 8, -8, 3, 5, -4, 3, -5, 1, -3, -4], [5, -4, -6, 1, 4, 1, -6, 2, 2, 1, 4, 5, 7, -1, -3, 0, 0, 6, -2], [8, -11, 11, 0, 4, 3, -4, -3, -3, -11, 2, 4, -2, -3, 0, -4, -2, 2, 1], [-11, -6, 2, -1, -5, 0, -1, 0, 0, 2, 4, 3, -1, -3, 1, 1, 1, 1, 2], [1, 11, -9, 3, -2, -5, -2, 5, 6, 3, 0, -2, 4, -2, 4, -3, -3, 5, 1], [7, -2, 1, -7, -1, -5, -2, -3, 0, 7, 3, -1, -1, -1, -3, -5, 1, -6, 3], [-16, 4, 11, 0, 0, 2, 0, -4, -4, -2, 3, -4, -5, -1, 0, 4, 5, -3, 4], [2, 3, 9, 2, 4, 1, 2, -2, -7, -15, 0, -7, -6, -5, 5, 3, 7, 5, 4], [-1, -3, 0, 8, -3, -3, 4, -2, 0, 6, 3, -8, -6, 6, 4, 5, 3, -4, 0], [-9, 8, -1, 1, 4, 3, 4, 0, -5, 1, -5, 1, 2, -2, -1, -6, 3, 1, -4], [-14, -6, -9, 10, -11, 4, 2, 9, 6, 21, 7, -2, 0, 16, 0, 5, 3, -13, -9], [-4, -6, -1, 0, 3, -4, 0, -3, 3, -2, 6, -4, -2, 2, 0, 2, 2, 4, 6], [-9, 6, -1, -7, -1, 5, -1, 6, 2, 0, -3, 6, 5, -4, -4, -2, 1, -2, -4], [-23, -12, 3, 3, -2, 4, 2, 0, -7, -9, -2, -8, -7, 8, 4, 7, 5, -4, 1], [13, 11, -6, 0, -1, -3, 3, -5, 4, 0, 2, 3, 2, -1, 1, 1, -2, 0, 2], [5, 6, 7, -2, 5, 0, -6, -3, 0, -10, 0, 2, -2, -1, -2, 0, -6, 8, 6], [-1, 12, -3, -5, 5, 6, 0, -5, -1, -11, -6, 6, 2, -1, -2, 5, -3, 10, 6], [-8, -9, 5, 4, 4, 3, -6, 1, -5, -6, 2, -2, -6, 7, -2, 6, 0, -5, 1], [-3, -1, 9, -1, 7, 1, -3, 1, -1, -8, -5, 3, 3, -12, -1, 0, -2, 13, 4], [-4, 2, -6, 5, -2, 1, 5, 4, 1, 0, -8, -1, 5, -1, -3, 0, -1, -1, -2], [-12, -2, 7, -4, 4, 7, 0, -1, -1, -2, -4, 8, 4, -9, -2, 3, 2, 2, 2], [-2, -5, 3, 3, 2, 3, -6, 5, 0, -12, 1, 2, -4, 7, -2, 10, -2, -2, 2], [4, -2, 9, -5, 2, 3, -9, 5, 1, -2, 1, 4, 0, -2, -6, 0, -3, 5, 3], [7, 6, 6, 1, 4, 3, 2, 2, -3, -4, -3, 1, 1, -5, -1, -3, -1, -1, -1], [-3, -14, 2, -2, 0, -3, 2, -3, -1, 8, -1, 0, 1, -3, -2, -9, 3, -6, 0], [6, 4, 11, 0, 2, 1, 1, -5, -3, -14, 0, 4, -2, -2, 2, -6, 5, -5, 0], [-10, -2, 8, 1, 6, -1, -3, -3, 1, 2, 2, 4, 1, -3, -2, -8, 4, -2, 3], [-1, -10, 3, -1, -1, 0, 2, -2, -1, -5, -7, -7, -6, 1, 1, 1, 3, -5, 0], [-17, -4, 0, -9, -2, 3, -1, -3, -7, -7, -4, 4, -3, -4, 4, 3, 2, -1, -1], [21, 3, -2, 10, 3, 1, 3, -1, 0, -5, -4, -1, 0, 3, -1, -3, -6, 2, -4], [3, 2, 5, -1, 2, -2, -1, -8, -3, -13, 6, 2, -5, -5, 0, 4, 2, 9, 7], [-6, -4, -10, -1, -8, 1, 5, 1, 1, 8, 3, -8, 1, 5, 6, 6, 1, 0, -2], [13, -10, -10, 4, -3, -7, 2, 6, 3, 19, 3, -2, 4, 0, 2, -12, 1, 0, -5], [10, -10, 0, 2, 2, 4, -5, 5, -2, -11, 8, 1, -4, 3, 1, 7, 4, 2, 1], [-6, 3, 0, -3, -2, -3, -1, 0, 2, 8, -7, 3, 1, -1, -5, -2, 0, -9, -2], [-12, 1, 5, -3, 3, 2, 1, -5, -1, 0, -4, 0, -4, 7, 0, 0, 4, -3, 1], [13, -4, -2, 7, -1, -2, -4, 3, 1, 7, 11, -2, 3, 0, 2, 7, 0, 3, 2], [-5, -6, 7, -4, 3, 2, 4, -7, 0, -2, 0, -2, -6, 3, 2, -4, 2, -8, 2], [11, 1, -2, 2, -2, -6, 6, -1, 0, 2, 0, -3, -2, 1, 3, 2, -1, -4, -2], [-6, -7, -9, 2, -5, -1, -4, 6, -3, 4, 3, -2, -1, 6, 0, 4, 3, 0, -1], [2, -1, -5, 6, -2, -2, 2, 3, 3, 1, 5, -13, 1, 1, 1, 0, 2, -2, 0], [-18, -3, -9, 8, -6, -1, 7, 4, 0, 8, 3, -3, -2, 8, 5, 3, 3, -2, -7], [12, -12, 4, -8, 5, -1, -3, -2, 0, -9, -4, -4, 0, -10, 0, 1, -3, 3, 4], [9, 9, -15, 8, -6, 4, 11, 2, 5, 14, -5, -2, 3, 11, 2, -6, -2, -11, -9], [-11, -1, 5, -1, -5, 2, -5, -3, -4, 0, 0, 0, -2, 0, 0, 8, 6, -1, 1], [2, -4, -10, 11, -9, -5, 3, 6, 4, 12, 5, -12, -4, 10, 6, 5, -3, -6, -5], [-13, -1, -1, 5, -2, -3, 2, -1, -1, 8, 12, 0, -2, 6, 0, 2, 1, 1, 3], [1, -3, -3, -6, 2, 2, -6, 3, -3, 1, 1, 11, 3, -2, -1, 0, -4, 9, -4], [-7, -6, -2, 4, -1, -2, -4, 3, 0, -1, 8, 0, 1, 4, -2, 5, -2, -1, 1], [-4, -11, -3, 6, -5, 5, 2, 8, 5, 14, 1, -4, 3, 8, -4, -4, -3, -2, -5], [-15, -2, 7, -3, 5, -6, 4, -7, -3, -5, 0, 2, -4, -9, 0, -3, 1, 4, 4], [-2, -6, 1, 2, -4, -4, 9, -5, 8, 11, 1, -7, -3, 6, 1, -6, -1, -11, 1], [1, 12, -6, 4, -4, -2, 0, 2, 4, 6, 0, 0, 2, 1, -4, 2, -4, 2, -2], [-13, 5, -4, -7, -3, 7, 3, -1, -2, -4, -7, 7, 0, -5, 1, 5, 8, 4, -1], [-12, 1, -2, 4, -2, -2, 3, -2, 2, 1, 9, -6, -6, 7, 2, 3, 6, -9, 2], [-6, -2, -10, 8, -6, 0, 7, 2, 1, 10, 3, -4, 2, 11, 2, 3, -4, -1, -1], [-8, -7, -1, 0, -1, 0, 7, -3, -1, 1, -5, -2, 0, -7, 2, -4, 4, 8, 0], [6, -7, -1, -5, 1, 1, -6, 4, -1, -11, -3, -2, 1, -2, -2, 3, 0, -2, 3], [-9, 5, 3, -1, 1, -1, -4, 2, -1, -11, -9, 4, 1, -5, -4, -5, -4, 1, 1], [11, 3, 2, -4, 7, -1, 1, -9, -4, -14, -2, -1, -2, -1, 3, 1, 4, 6, 4], [-15, 0, -14, 7, -5, -7, 6, -1, 8, 14, 3, -7, 4, 2, 3, 2, -1, -3, -10], [-3, -11, -2, 5, -2, -2, 1, -6, 1, 3, 1, -2, -2, 8, 0, -7, -3, -4, -2], [9, 14, -2, 1, 4, 1, -5, 3, 1, -3, 0, 6, 3, -2, -2, 3, -2, 5, -3], [7, -6, 14, -7, 12, 8, -5, -9, -6, -21, 2, 7, -2, -12, 3, -2, 3, 8, 7], [-8, 6, 0, -6, -1, -5, 1, -4, 2, 5, -8, 4, 4, 0, 0, -3, -3, 3, -2], [-11, -6, 12, -5, 1, 5, -6, -1, -1, -1, 10, -3, -4, -2, -5, 5, 2, -3, 7], [2, 4, -3, -4, 1, -4, 3, 0, 8, 0, -2, -3, 8, -3, -1, -7, -4, -1, -1], [5, -6, 6, -2, 3, -4, -4, -3, -3, 1, -7, 2, 7, -4, -4, -2, -5, 7, 2], [0, 1, 11, -7, 2, 1, -4, 1, -2, -6, 5, 4, -2, -1, 0, -2, -4, -4, 4], [-5, 10, 0, -9, 6, 0, 2, -2, 1, 1, 0, 8, 2, -7, -2, -7, -7, 5, 4], [-1, -7, -9, 9, -8, 2, 8, 5, -2, 19, 4, -7, -3, 10, 3, -2, 4, -3, -5], [-13, -4, 4, 9, -4, -4, 6, 2, 8, 19, 1, -14, 0, 11, -4, 3, -4, -11, -1], [-19, 14, -3, -2, -2, 1, 0, -2, 5, 9, -4, 13, 6, -6, -5, -4, -3, 0, -1], [-2, -4, -11, 4, -7, -4, 5, 0, 3, 16, -4, 1, 4, 5, 3, -5, -2, -3, -9], [2, 4, -1, -3, -1, 2, 0, 5, 0, 12, -5, 4, 8, -4, -8, -6, -6, 0, -5], [-2, -7, 13, 1, 2, 0, -3, 2, -1, 1, 8, 4, -1, 0, -2, -5, 0, -2, 2], [5, -2, 0, -1, 2, 1, 3, -7, -1, 0, 1, -4, -7, -6, 0, 2, 5, 1, 6], [18, 4, 5, -6, 2, -5, 7, -7, 3, 2, 1, 0, 0, -14, 0, -14, -8, 3, 5], [8, -3, 0, -3, 3, 0, 0, -2, -4, -10, -5, 5, 3, -7, 1, 5, 3, 3, 0], [-5, -5, -7, -1, 1, 2, 2, -4, 3, 6, -4, -3, 2, -3, -1, -11, -4, 5, -4], [7, 9, -4, -6, 5, -3, -2, 0, 1, 1, -5, 8, 8, -10, -2, -9, -1, 4, 4], [-14, -20, -8, 2, -4, -2, 0, 2, 6, 18, 8, -2, 0, 8, 0, 0, 2, 2, -2], [21, 0, -7, 8, -11, -11, 1, 4, 3, 3, -2, -6, -1, 4, 4, 4, -5, -2, 1], [14, 4, 0, -3, 6, 1, 3, -3, -1, -12, -10, -2, 3, -13, 8, -4, 4, 8, 1], [-14, -1, 7, 5, 1, 2, -3, 7, 2, 0, 4, 0, -4, 5, -2, 2, -6, -3, -1], [-3, 3, 5, -1, -5, 2, -1, 3, 2, -4, 0, 0, 4, 6, 0, 6, -2, -3, -5], [-8, -1, 3, -3, 0, 3, -1, -2, 2, 10, -3, 5, -2, 0, -1, 3, 4, 4, -3], [3, 7, -6, -7, 1, 1, 2, -2, 3, 2, 0, 10, 10, -12, 2, -11, 3, 10, -1], [5, 3, 20, -10, 14, 6, -10, -6, -7, -38, 2, 10, -6, -11, -2, 7, -2, 7, 11], [13, -16, 4, -4, 9, 3, -1, -4, -2, -6, 5, 2, -2, -7, 0, -2, 6, 9, 3], [8, 6, -4, 7, -4, -4, -1, 0, 5, -2, 8, -4, -2, 5, 2, 5, 0, 3, 4], [10, -7, -2, -1, 0, -1, 1, -2, -2, -3, 5, -5, 3, -5, 1, -2, 4, 4, -2], [-1, -4, 4, 1, -2, -1, 2, 4, -1, -10, -1, -3, -1, -5, -3, 3, -3, 4, 7], [-4, 4, -3, -4, 3, 3, -2, -3, 2, -5, 3, -1, -5, 6, -3, 6, 0, 2, 5], [15, -3, -9, 3, -8, -5, 2, 1, 3, 18, 8, -2, 6, 0, 2, -6, 1, 1, -3], [-4, 6, 1, 5, -5, 0, 0, 1, 2, -7, -1, -4, -2, 2, -2, 5, 4, 1, -1], [9, -4, -12, 1, 0, 2, -3, 3, -2, -5, -6, 1, -2, 10, 1, 4, -5, 2, -1], [-10, 2, -5, 2, -6, -2, 4, 5, 3, 12, 4, -11, 1, 1, 1, 4, 3, -12, -4], [-4, 10, 4, -10, 0, 8, -6, 2, -2, -4, -4, 16, 4, -2, -2, 4, 0, 8, -6], [-11, 9, -7, 7, 0, -3, 10, -1, 3, 2, -2, -2, 2, 4, 2, -2, 3, -5, -3], [-6, -2, 4, 2, 4, 4, -3, 0, -7, -20, -7, 4, -2, -3, 2, -5, 2, -5, 1], [1, 1, -4, 12, -7, -5, 8, 0, 9, 15, 3, -10, -2, 10, 2, -1, -5, -6, -4], [-13, -1, 9, -5, -5, 3, 1, -3, -3, 4, -2, 5, 1, 0, -1, -1, 3, -3, -7], [7, -8, 2, 2, -1, 0, 0, -3, -1, -4, 1, -10, -1, 2, 0, 6, -5, -1, 0], [0, -2, -3, 8, -3, 0, -5, 10, 4, -4, 4, -5, 2, 5, -3, 3, -8, 5, 1], [2, -1, 6, -10, 2, 3, -3, -2, -4, -10, -2, -3, -1, -7, 1, 2, 8, 1, 5], [2, -10, 4, 0, -1, -5, -2, 3, 1, -1, -4, -5, 2, -5, -3, -6, -3, -4, 1], [-8, -12, 1, -1, -4, 5, -6, 2, -2, -3, 2, 1, -6, 7, -3, 12, 2, -9, -1], [-1, -3, -5, -3, 6, -1, -2, -3, -2, -19, -4, 6, 0, -2, 6, 7, -3, 3, -1], [-14, 13, -14, -1, -7, -3, 6, 0, 4, 21, -2, 6, 2, 7, 0, -5, -9, -3, -5], [-1, -8, 14, -2, 4, 3, 5, -9, -4, -2, 8, -4, -7, -2, 2, -2, 3, -3, 7], [-9, 5, 3, -7, 8, 3, 0, -2, 2, 1, -3, 5, 4, -14, -5, -7, -9, 8, 5], [2, -16, -2, -2, 4, 1, 1, -1, -2, -3, -1, 2, 3, -1, 0, -5, -6, 10, 2], [-16, -9, -3, 7, -2, 1, 4, -1, 1, 7, 2, -8, 2, 9, 0, 11, 3, -4, -3], [-9, -4, 10, -2, 1, -5, -1, -6, -7, -18, -1, 0, -6, -11, 8, 2, 10, -1, 9], [5, 2, -4, -3, 3, 2, -2, -1, -3, -11, -6, 6, 5, -4, 2, 0, -1, 9, -3], [4, 1, -12, 3, 2, 4, -1, 6, 6, 13, 0, 4, 0, 3, -4, 3, 0, -1, -7], [-15, 9, 4, 1, 0, 5, 0, -3, -5, -2, -5, 2, 1, 3, 4, -1, -2, 0, -3], [13, 6, -4, 8, 0, 4, 0, 4, -2, 6, -6, 4, 6, 9, -2, 0, -6, 7, -6], [10, -1, 18, -3, 3, 2, -4, -4, -3, -5, 2, 3, -3, -3, -5, -4, 0, -1, 7], [15, 1, 16, -15, 18, 4, -10, -7, -12, -29, -2, 17, -4, -19, -1, 0, 0, 12, 10], [1, 3, -6, -3, -5, 0, -5, 7, 3, -4, 3, 12, 3, 5, -2, 6, -1, 1, -1], [-11, 9, -10, 6, 0, -2, 4, 1, -4, -7, -4, -5, 0, 3, 3, 6, 3, 1, -6], [2, -2, 6, 3, 1, 2, -1, 0, -5, -11, -5, 1, -3, 4, 1, 6, 6, -3, -5], [-20, 11, -6, 13, -8, -4, 5, 4, 4, 20, -3, 0, 6, 7, -2, -5, -9, -3, -10], [9, 5, 2, 5, 1, 1, -1, 1, -6, -4, -3, 5, 6, 3, -1, -1, -2, 6, -1], [-18, -4, -12, 10, -3, -3, -8, 11, 5, 3, 4, -1, 0, 1, -1, 2, 1, 2, -3], [5, 10, -8, 8, -4, -1, 0, 6, 4, 10, -7, 1, 3, 5, -1, 7, -8, -1, -5], [3, -12, -4, -7, -2, -5, 0, -2, -5, -2, -5, -1, -1, -1, 3, -3, 1, -5, -1], [12, -4, 9, 3, -3, -1, -9, 3, 2, 15, 11, -3, -3, 5, -5, 1, 6, -8, 1], [2, 7, 15, -14, 3, 4, -1, -9, -6, -14, -1, 8, -6, -5, 2, 2, 4, 0, 6], [14, 7, 3, 5, 3, -6, -4, -4, 8, 0, 2, -3, 0, 8, -1, -5, -6, -2, 0], [-26, -4, 7, -8, -2, 3, -5, 3, -9, -6, -1, 0, 0, -8, 0, 6, 4, 1, 3], [7, -8, -3, 0, -1, 1, -4, -1, 1, 6, 10, -3, -5, 5, -3, 1, -1, 0, 2], [10, -6, 8, -6, 0, 2, -4, -2, -4, -1, 4, 2, -6, 2, -2, 0, -4, -2, 6], [-20, -3, -6, 5, -2, -3, 0, 11, 2, 14, -10, 0, 5, 4, -2, -4, -5, -9, -6], [-6, -4, -13, 6, -13, -2, 5, 0, 2, 23, -3, -3, -2, 17, 1, 2, -3, -11, -6], [23, -6, 3, 1, 3, -9, -6, -3, 3, -3, -2, 9, 3, -5, -1, -6, -6, 4, 0], [-2, -7, 7, -9, 7, 0, -7, -3, -3, -12, 0, 2, -2, -13, -2, 4, -2, 10, 5], [-14, -1, 20, -16, 9, 5, -8, -4, -5, -14, -2, 2, -2, -9, 2, 4, 2, 2, 9], [-3, -6, -7, 16, -11, -5, 6, 10, 7, 27, 4, -12, -3, 15, -2, 0, 4, -11, -7], [-13, 8, 4, 4, 2, -2, -2, 8, 8, 18, 0, 0, 8, 3, -8, -2, -10, -2, 0], [3, 0, -11, 5, -1, 6, 0, -3, -6, -8, -5, 4, 0, 7, 0, 2, 2, 2, -5], [7, -9, -8, 13, -8, -2, 7, 4, 3, 15, -1, -6, 2, 10, 0, -7, -3, -8, -10], [-13, 5, -4, -6, 1, 1, -4, -6, 0, 4, 7, 8, 2, -2, 0, -5, 5, 0, 0], [9, -4, 9, 5, 1, -2, 10, -7, -7, -2, 5, -12, -8, -1, 6, -2, 10, -5, 1], [-1, 3, -6, -4, 5, 7, -6, 0, -1, 7, -3, 14, 4, -4, -2, -9, -1, 6, -6], [3, -13, 9, -2, 10, 3, -2, -5, -7, -8, 9, 10, -4, -6, 2, -6, 3, 5, 4], [7, 2, 0, 0, -1, 3, -5, 6, -2, -2, 3, -2, -8, 13, 4, 6, 4, -7, -3], [-5, 14, -3, 0, 0, 9, -8, 8, -4, 6, 0, 3, -2, 8, -1, 5, 1, -2, -7], [18, 11, 9, -1, 2, 3, -3, -3, -4, -11, -11, 0, 0, -6, 4, 2, 3, 5, -4], [8, -1, -3, 0, -1, -1, -4, 0, -2, -16, -3, 2, -3, 0, 0, 2, -7, 4, 1], [-10, -6, 10, 1, -2, 4, -1, 0, 3, 0, 8, -2, -2, -1, 0, 1, 2, -7, 8], [-2, 1, -6, 4, 4, 8, -2, 1, -2, -6, 3, 5, 4, 2, -3, -3, 2, -1, -5], [3, 6, 11, -5, 1, -1, -10, 5, -3, -17, -2, 5, -3, 1, 1, 6, -2, 6, 8], [-8, -4, 7, 5, -7, 3, -10, 8, 1, -10, 4, 8, -1, 8, 2, 7, 1, -4, -3], [-2, 7, -6, -3, -10, -2, 2, 7, 3, 8, -2, 5, 4, 4, -3, -5, 0, -5, -4], [-10, -2, 6, -6, 7, 5, -3, -3, 0, -8, -2, -1, 0, -2, -3, 0, -2, 5, -3], [0, -12, -2, 17, -11, -2, 1, 2, -1, -1, 13, -9, -5, 14, 3, 10, 2, -9, 3], [12, 4, 13, -4, 4, -3, -5, 1, -1, -14, -5, -2, -4, -6, -2, 6, -4, 3, 9], [12, -13, 0, -5, 2, -1, -4, 3, -6, -12, -2, 0, -1, -8, 0, 0, -1, 11, 2], [8, 7, 1, 2, 2, -5, 1, 0, 0, -5, 1, 5, 4, -4, -3, -4, -7, 2, 7], [-16, -5, -10, 4, 2, 7, 0, 0, -1, -1, -1, 5, 3, -6, 3, -1, 8, 2, -6], [-4, -8, 0, 0, 0, 0, -5, 1, 0, 0, 5, 7, 0, -3, -5, 3, -3, 2, -2], [-7, 9, 9, -4, 2, -6, -5, -2, -2, -17, 0, 6, -3, -1, -10, 1, -9, 1, 10], [13, 4, -11, 10, -8, -8, 3, 5, 9, 15, 0, -7, 7, 3, 1, -2, -4, 1, -8], [4, 4, 0, -4, -7, 4, 3, 0, 4, 7, 3, 5, -1, 8, -1, -4, -3, 0, -1], [1, 10, 0, 4, 4, 4, 12, -4, -6, -1, -6, -4, 2, -3, 6, -5, 2, 1, -4], [16, 1, 12, -3, 11, 1, 0, -6, -4, -21, -6, -4, -6, -5, -2, 3, -9, 1, 9], [-16, -3, -13, 4, 0, 1, 2, 7, 11, 25, 6, 2, 4, 7, -2, -12, 2, -8, -7], [23, 4, 8, -7, 13, -1, 0, -9, -4, -24, -9, 13, -2, -14, -1, -8, -1, 13, 4], [-17, 7, 11, -15, 5, 15, -9, -5, -9, -22, -3, 15, -3, -6, -1, 16, 8, 9, 4], [-21, -14, 14, -15, 10, 11, -7, -7, -7, -18, -1, 6, -3, -12, -2, 0, 13, 7, 6], [2, 3, 1, 4, -4, 3, -2, 7, 3, -5, -3, -4, 4, 1, -4, 1, -5, 4, -6], [-8, -1, 5, -9, 7, 4, -3, -3, -5, -2, 4, 8, -2, -3, 4, 2, 8, 0, -3], [13, -13, -3, 9, -1, -4, -5, 1, 0, 0, 9, -2, 0, 2, 0, 4, 3, 1, -2], [20, 0, 16, 0, 8, -3, -7, 3, -7, -27, -1, -2, -7, -7, -2, 7, -6, 6, 12], [17, -11, 0, -1, 4, 1, -9, -4, -9, -7, 9, -3, -3, -4, -3, 6, 2, 2, 2], [1, -12, 2, 3, -8, -5, -1, 3, 4, 14, 13, -4, -3, 6, 4, 0, 1, -5, 0], [19, -6, 18, -7, 12, 10, -12, -4, -9, -35, -5, 12, -6, -3, -2, 3, 4, 5, 3], [-13, 0, -3, 6, 2, -1, 8, 0, -1, 9, -8, 1, -2, 2, 3, -10, -1, -12, -7], [0, 8, 10, -3, 9, -2, -7, -2, 1, -31, 3, 3, -1, -10, -5, 0, -8, 7, 13], [13, -12, -18, 11, -5, 0, 2, 11, 9, 31, 7, 2, 9, 6, 0, -5, -2, 1, -12], [-2, 6, 0, -10, 0, 4, -3, 1, 1, 3, 1, -1, 4, -1, -1, -4, 5, -1, 0], [-9, 10, 0, -1, -10, 2, -3, 10, 4, 10, 8, 6, 4, 0, -2, -3, 0, -4, -4], [-2, 0, 8, -10, -4, 0, 4, -6, 2, 2, -4, 2, -2, 0, 2, -4, 2, -4, 4], [-8, -10, -7, -1, -14, 4, 5, 1, -3, 19, 2, -5, -3, 14, 7, 1, 13, -13, -8], [-18, 3, -2, -5, -5, 2, 7, -8, 1, -2, -4, 5, -1, 0, 1, -4, 9, -4, -3], [-4, -3, 9, -3, 9, 1, -6, 0, -5, -1, -5, 6, 5, -8, 0, 5, 4, 4, 1], [-2, -12, 1, 1, 7, 1, -6, 2, 1, -6, 12, 2, -7, 2, -2, 7, -3, 2, 9], [-15, -13, 6, -2, 7, 7, -8, -6, -7, -21, 1, -2, -10, -10, 0, 7, 1, 8, 8], [0, -1, 9, -4, 8, 11, -1, -5, -6, -27, -2, 0, 0, -2, 0, 2, 1, 7, 5], [6, 14, 5, -4, 8, 0, -1, 1, 6, -9, -5, 15, 5, -8, -9, -8, -5, 1, 1], [18, -4, 3, -3, 5, 0, 0, 1, 4, 1, 3, 2, 2, -12, -4, -9, -6, 11, 3], [-12, -1, -10, 1, -1, -2, 2, 2, 0, 4, -1, -5, 1, 3, 5, 1, -1, -1, -2], [1, -12, 4, 8, -2, 1, -5, 7, 7, 7, 1, 2, 7, -2, -4, -5, -4, 4, -8], [9, -9, 13, -1, 7, -2, -2, -2, -5, -6, 16, 1, -4, -7, 1, -9, 2, 3, 6], [-16, -5, -4, -3, 6, -1, -5, 4, 0, -9, 3, -1, -1, -1, 1, 8, 2, 0, -2], [6, -7, -2, 3, -7, -4, -4, -2, -7, -21, 2, -5, -9, 5, 5, 14, 8, -9, -1], [11, 21, 4, -1, 0, -8, -2, 0, -1, -10, 3, 0, 0, 3, 0, -1, -2, -1, 4], [-5, -10, -12, 11, -5, -4, 0, -1, 1, 3, 11, -18, -5, 12, 6, 7, 2, -9, 0], [6, 14, 12, 0, 14, 0, -5, -11, -7, -21, -3, 5, -6, -9, -3, -6, -1, 5, 8], [-15, 6, 3, -5, 1, -2, -3, -4, -3, 3, -3, 7, -2, 2, -7, -5, -2, 0, 6], [0, 8, -3, -10, 4, -1, -5, 5, 2, -13, -9, 10, 6, -6, 2, -4, -6, 3, -1], [2, 10, -16, 0, 2, -7, 7, 3, 3, -9, -11, 2, 3, -1, 2, -7, -12, 0, -2], [-12, 5, -5, -9, 2, 8, -3, 4, 1, -9, -6, 2, 5, 8, -2, 5, -4, -6, -4], [-18, -5, -15, 14, -13, 1, 6, 4, 3, 42, 5, -10, 5, 16, 2, 0, -1, -2, -11], [-18, 0, 3, 4, -1, 0, 1, 0, 0, -7, 3, -5, -2, 5, -1, 4, 9, -3, -2], [3, 0, -9, -1, 0, -1, 2, -4, 1, 17, 5, 5, 4, -4, 1, -4, 5, 6, -4], [-5, 0, -9, 3, 0, -4, 6, 2, 0, 4, -7, -2, 7, -4, 4, -6, 2, 4, 0], [2, -16, 12, -3, 4, -1, -5, -10, -9, -32, -6, -3, -13, 3, 5, 8, 3, -1, 6], [10, -6, 15, -10, 6, -1, 9, -13, -1, -18, -5, -4, -6, -8, 6, -6, 12, -3, 3], [-5, 4, -5, -5, -3, 5, 2, -1, 3, -15, -8, 7, 5, -3, 5, -10, 0, -1, -4], [12, -12, 13, -6, -2, -2, -6, 2, -8, -8, 5, 0, -1, -3, -2, 0, 5, -9, 2], [-2, 9, -15, 13, -10, -4, 4, 9, 8, 11, 7, -3, 3, 5, 5, 1, -1, 2, -8]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_9065_a_Hecke( : Kf := Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_9065_2_a_t();".
// 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_9065_2_a_t(:prec:=19)
    chi := MakeCharacter_9065_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_9065_2_a_t();".
// 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_9065_2_a_t( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_9065_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![18, -42, -746, 536, 5782, -5174, -12598, 12010, 12474, -12205, -6531, 6476, 1924, -1920, -320, 320, 28, -28, -1, 1]>,<3,R![-2672, 8072, 13593, -45833, -33846, 98884, 55831, -102449, -56489, 54811, 32320, -15450, -10466, 2098, 1903, -65, -181, -13, 7, 1]>,<11,R![209498112, 367090176, -421019008, -814512632, 320816837, 603570063, -162141999, -203926793, 53515229, 33970399, -9811223, -2821201, 963055, 105657, -50125, -671, 1295, -55, -13, 1]>],Snew);
    return Vf;
end function;