
// Make newform 8001.2.a.v in Magma, downloaded from the LMFDB on 13 September 2025.
// To make the character of type GrpDrchElt, type "MakeCharacter_8001_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_8001_2_a_v();".
// 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_8001_2_a_v();".
// 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 := [210, 608, -2913, -5723, 13725, 14000, -28600, -13249, 29792, 4985, -17032, 21, 5572, -583, -1035, 178, 101, -22, -4, 1];
        Kf := NumberField(Polynomial([elt : elt in poly]));
        AssignNames(~Kf, ["nu"]);
    end if;
    Rf_num := [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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], [-9272820218, -9280440934, 124055335687, 26352010178, -394138444469, -42523921020, 560761757568, 32463907935, -419706704682, -8859733933, 177057585547, -1159028944, -43092462154, 1055361561, 5929350010, -185012986, -422890858, 10330919, 11967908], [-6128233325, -23752461453, 71510619076, 206901778527, -222447224597, -582478309828, 448072525313, 726626199106, -486402019943, -469100157707, 285664374904, 166375659285, -94107501027, -32561720490, 17368062950, 3285269092, -1671831523, -132926940, 65114179], [-133199717500, -242700042466, 1168583011302, 1473343414389, -2872131807524, -3225526895581, 3500770767616, 3295314382092, -2478737837371, -1803665054044, 1071360077368, 559933954855, -284325273789, -98469596705, 44954282930, 9112645479, -3866824621, -343698145, 138645363], [54702171430, -274887004146, -839166774003, 2961548762254, 2393312892281, -7808662348931, -2162801145399, 8851478759162, 375217402964, -5196857369249, 451103298313, 1696786234950, -281749529274, -309929331465, 67595392300, 29542139284, -7501449651, -1140866135, 318716503], [40044597930, 88500571266, -388056127817, -547670340074, 1292110192984, 1200884819526, -1887181446716, -1310268250057, 1466329373136, 781891378959, -664790856488, -263787283760, 181459391204, 49897035585, -29294218685, -4911478344, 2566480776, 195011795, -93609108], [-19775968325, -88500571266, 367787498212, 547670340074, -1289214674469, -1200884819526, 1887181446716, 1310268250057, -1466329373136, -781891378959, 664790856488, 263787283760, -181459391204, -49897035585, 29294218685, 4911478344, -2566480776, -195011795, 93609108], [2068831656, 15157612018, -44204269770, -194336671842, 230702575789, 548407227881, -439470286205, -638066586796, 404304603883, 381112300142, -206178478291, -126913768361, 61534319327, 23745817195, -10672704577, -2324375148, 991696752, 92196111, -37953488], [53652831630, 287009377064, -455951257588, -2201652718176, 906752365551, 5135218235504, -1060121848224, -5591713835683, 961255585349, 3307955295931, -605499617407, -1119608505200, 231300589556, 215066182570, -49786456290, -21651992771, 5495659804, 881338715, -240105167], [19309791560, -53779704136, 63474192337, 1145884621839, -1121219155374, -3584941413081, 2773105119646, 4389554678512, -2868279746356, -2705691492119, 1554464292428, 916160179920, -477184016914, -172281371545, 83341546495, 16815829469, -7697023186, -662122355, 290773938], [74147034150, 161926194492, -1176825672339, -2351933693773, 4085986343623, 6795149697847, -6493467022012, -8046688000049, 5615791269077, 4855571864208, -2816533502951, -1614947153800, 833859292088, 298637498085, -142770006155, -28691667118, 13007283232, 1113420900, -485961931], [28681664520, 88860693382, -255693379414, -1107518683308, 959561891823, 3182220496297, -1924408194587, -3854034717714, 1964936315422, 2402070934223, -1098123323401, -829200724505, 351910167043, 159447001730, -64356454145, -15917066553, 6214873087, 640007340, -244538816], [-23929479290, -709051042762, -102435732651, 6668255047918, -555145776623, -18219213168867, 3742541531697, 21361112833594, -5538919778952, -12928740475313, 3700939092301, 4348086495830, -1312960193338, -817470456425, 255548957080, 80069329128, -25673615907, -3169187735, 1036415051], [101431035930, 804092581722, -1017780451669, -6763494721768, 4616300955633, 17589452904587, -9698265109967, -20239239560654, 9922760972072, 12181293389813, -5505446366291, -4098812389930, 1747199273478, 773094156925, -316167323730, -76041669698, 30214864317, 3022806135, -1177420721], [-153741088340, -427993545432, 1709061696269, 3926288444198, -5626225717688, -10620725347607, 8959188531857, 12396449304189, -7810236222227, -7476870253978, 3952381907166, 2503001409990, -1184324624578, -467788147365, 205976043850, 45513393513, -19108483507, -1789420580, 727508506], [-509625256950, -1938290594534, 5559535596393, 18937119806716, -18711356928001, -50962697977249, 31177087450109, 59507326593548, -28613582641044, -36169011220831, 15248263236747, 12274426272960, -4806101920096, -2334094800655, 877139208820, 231373969696, -85049828069, -9263333215, 3366745827]];
    Rf_basisdens := [1, 1, 1, 1, 579103703, 2895518515, 5791037030, 11582074060, 2895518515, 2895518515, 1158207406, 5791037030, 5791037030, 5791037030, 2895518515, 11582074060, 11582074060, 5791037030, 11582074060];
    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_8001_a();"
function MakeCharacter_8001_a()
    N := 8001;
    order := 1;
    char_gens := [3557, 1144, 7750];
    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_8001_a_Hecke( : Kf := Kf)
    return MakeCharacter_8001_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, 1, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0], [2, 0, -1, 0, -1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0], [1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1], [1, -1, 0, 0, 0, 0, 0, -1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, -1, 0], [3, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1], [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, -1, 0, 0, 0, 0], [1, -1, 0, -1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, -1, 0], [-1, 1, -1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1], [-2, 1, 0, 0, 0, 0, 1, 1, 0, 1, -2, -1, 0, 0, 0, -1, -1, 0, -1], [-1, -1, 0, 1, 0, 0, -1, 0, 0, 0, 2, 0, 2, 1, 1, 0, 1, 0, 1], [1, -1, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 1, 1, -1, 0, 1, 0, 0], [1, -1, -1, 1, 0, 1, 0, 0, 0, 1, 0, 1, -1, 1, 0, 0, 0, 0, 0], [2, 0, 1, 1, 0, 0, 0, 0, -1, -1, -1, 0, -1, -1, 0, 0, -1, 0, -1], [3, 0, 1, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 0, 0, -1, 0, 1, 0], [1, -1, -1, 1, 0, 2, -1, -1, 0, 0, 1, 1, -1, 0, 0, 1, 0, -1, 0], [0, 0, 1, -1, 0, 0, 1, 0, -1, 0, -2, -2, 1, 0, 0, -1, 0, 1, -1], [1, 1, -1, 0, -2, 1, 1, 2, 0, 0, -1, 1, -2, 0, -1, -1, -2, 1, -1], [-2, 0, -1, 1, 1, 1, -2, 0, 0, 0, 1, -1, 1, 1, 0, 1, 1, -1, 0], [0, 1, -1, 0, -1, -1, 2, 1, 0, -1, -2, -1, 1, -1, -1, 0, 0, 0, -1], [3, 0, 1, -1, 1, -1, 1, 0, -1, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0], [3, 0, 3, 0, 1, -1, 1, 0, 0, -1, -1, 0, 0, 0, 1, -1, -1, 0, 0], [5, -2, -1, -1, -1, -1, 1, 0, 0, 0, -1, 1, -2, -1, 0, 0, 0, 2, 0], [0, -1, -1, 1, 1, -1, 1, -1, 0, -1, 0, 0, 1, 0, 1, 1, 1, -1, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, -1, 0, -2, 0, 1, 0, 0, 0, -3, 1, -1, 0, -1, 0, -1, 1, -1], [3, 3, 2, -1, 2, -2, 1, 0, -1, 0, 0, -1, 1, 0, 0, -1, 0, 0, 1], [3, 0, 1, -1, 0, -1, 1, 1, 0, 0, -2, -2, 1, -1, 0, -1, -1, 2, -1], [-2, -2, 1, 0, 1, -1, 1, 0, 0, 0, -2, -1, 2, 0, 0, 1, 2, 0, -2], [3, -4, 2, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0], [0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, -1, 0, 1, 1, 1, 0, 0, 0], [0, 2, -1, -2, 1, -2, 0, 0, 0, 0, -1, -2, 1, -1, 0, 0, 1, 2, 1], [1, 1, 0, 0, 0, -2, 1, 0, 0, 1, -2, 0, 0, 0, -1, 0, -1, 1, -1], [-1, 2, -3, 1, -2, 1, 0, 1, -1, 0, 0, 2, -1, 1, 0, 2, 0, 1, -1], [1, 2, -1, -1, 0, 1, 0, -1, 0, -1, 0, 1, -1, -1, -2, 1, 2, 0, 0], [1, -1, -3, 2, -1, 0, 0, 1, 0, 2, -2, 0, -1, 0, 0, -1, -1, 1, -3], [2, 0, 4, -1, -1, 0, -1, 0, 0, 0, 2, 0, 1, 1, -1, -1, 2, 2, 1], [-1, -4, -1, 1, 0, 1, 0, 0, 1, 1, -3, 0, -2, 0, 0, 2, -1, -1, -1], [-1, 0, -2, 0, 0, 2, -2, 0, -1, -1, 3, 1, 0, 2, -1, 2, 3, 0, 0], [1, 1, -4, 4, -2, 2, 0, 1, -1, -1, 4, 3, -1, 2, 0, 0, 0, -1, 1], [-3, 0, 0, -1, -1, -1, 3, -1, 2, 0, -3, -1, 1, -1, 1, 0, -1, -2, 0], [1, 0, 1, -2, 0, 0, 0, 1, 0, 0, -1, -1, 0, -1, 1, -1, -3, -1, 1], [-3, -3, -1, 0, 1, 1, -2, -2, -2, 2, 2, 0, 2, 1, 0, 1, 2, -2, 1], [5, -2, 0, -1, -2, 0, 3, -1, 2, -2, 2, 0, 2, 0, 0, -1, 0, 0, 0], [0, 0, 1, 0, 1, -1, -3, -1, 0, 1, -1, -2, 0, 0, -1, -1, 0, 0, 2], [2, -2, 1, -2, 2, -2, 2, 1, 0, 0, -3, -4, 4, -2, 2, 0, -2, -1, -1], [3, 0, 0, 1, 1, 1, -3, -1, 0, -1, 2, 2, -1, 0, -2, 3, 4, 1, 0], [-6, -3, 0, 0, 1, 0, -1, -2, 1, 1, -1, -3, 3, 1, 0, 3, 2, -3, -1], [0, 4, -3, 1, 1, 0, -3, -1, 0, 1, 2, 2, -2, 1, -1, 3, 2, 0, 2], [-1, 2, -2, 1, 2, 2, -2, -2, 0, -1, 2, 0, 0, 2, 0, 0, 2, 0, 0], [-3, 0, 1, -1, 1, 1, 0, 0, 1, 1, -1, -1, 1, 0, 1, 1, 0, 0, -1], [5, 5, 0, 1, 1, -2, -1, 1, -1, 0, -1, -1, -2, 1, -2, -1, 1, 3, -1], [2, -2, 4, -1, 2, -3, 1, 0, 0, 0, -5, -3, 1, -2, -1, -2, 0, 1, 0], [0, 2, 0, 0, 0, 1, 1, -1, 0, -1, -1, -1, -3, -2, 1, 0, -1, -3, 0], [-3, 0, 0, 2, 0, 3, -1, 0, 0, 1, 0, 1, -3, -1, 0, 2, -1, -3, -1], [1, 0, 0, 0, -1, 1, 1, 2, 1, 1, 1, 0, 1, 0, 1, -3, -2, -1, 1], [3, 1, -2, 2, 0, -1, -2, 0, 0, 0, 2, 2, -1, 2, 0, -1, -1, 2, 2], [-1, -3, -1, 2, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 0, -1, 2, 0, -2], [-1, -1, -1, -3, 2, -1, 0, -1, 1, -1, -1, -2, 2, 1, -3, 1, 4, 1, -2], [-4, 2, 0, 0, 0, -1, -1, -1, 0, 1, -4, 0, -1, -3, 1, 1, -1, 0, -1], [2, -2, -1, 1, 4, 0, -2, -3, -1, -2, 1, -2, 1, 0, -1, 3, 5, -1, -2], [3, 3, 0, 1, -3, 0, 0, 2, 1, 1, -2, 1, 0, 0, 1, 0, -2, 1, 2], [1, 1, -2, -2, 1, -2, -1, -1, 1, 1, -1, 0, 0, 1, 0, 0, 1, 3, 0], [2, 2, 2, -1, 0, 2, -2, -1, -1, 0, 2, 2, 0, 2, 1, 0, 2, 2, 1], [1, 0, 0, 1, 2, 1, -1, -2, 1, 0, 3, 0, -2, -2, 0, 1, 1, -4, 2], [2, 2, -4, 2, -3, 0, 0, 2, 0, 1, 1, 4, -3, -1, 0, 1, -2, 0, 0], [3, 1, 3, -1, 2, 1, 0, -1, -3, 0, 3, 1, -1, -1, 2, 0, 1, 1, 2], [3, 1, 0, 1, 0, -1, 2, -1, -1, 1, -4, 1, -2, 1, 1, 0, -1, 0, 0], [-6, 0, 0, 1, 2, -1, 1, -2, 0, 0, -3, -1, -1, -2, -1, 0, 0, -1, -2], [-2, -2, -3, 1, 1, 0, 0, -2, 1, -2, -3, -2, 1, 0, 1, 2, 2, -1, -2], [0, 3, 1, -4, 2, -1, 2, 0, 2, 1, -3, -3, 0, 1, -2, -3, 0, 3, -2], [5, 2, -2, -1, -2, -2, 0, 0, 1, 1, 2, 1, -1, 1, -1, -1, 1, 2, 0], [-1, 0, 1, 1, 2, 2, -4, -3, 1, -3, 5, 0, -1, 1, 0, 4, 4, -2, 1], [-6, -1, 3, 0, 0, 1, 3, -2, 0, 1, -8, -5, -1, -2, 0, -1, -3, -1, -2], [1, 0, -3, -1, 1, -1, 3, 1, 0, -2, -1, -1, 2, 1, -1, -2, 0, 1, 3], [5, -2, -2, 1, -4, 1, 3, 0, 2, 0, -3, 2, -1, -1, 0, 1, -1, -1, -2], [5, 2, 1, 1, -2, 0, 0, 1, -1, -1, -2, 0, -2, 1, -1, -4, -3, 1, 0], [-1, 2, -5, -2, -3, 3, -1, 1, 0, 1, 2, 1, -2, 2, -1, 0, 0, 2, -1], [6, 4, 2, -1, 2, 0, -1, 0, -2, -2, 0, -2, -4, -1, 1, 1, 2, 2, -1], [2, 3, -4, 1, -1, 0, -2, 3, 0, 1, 3, 3, -3, 2, 2, 2, 0, 4, 1], [10, -3, -4, -1, -3, 0, 2, -2, -2, -1, -2, 2, -2, 3, -2, -1, 1, 3, 0], [4, -2, 3, 0, 2, -2, 1, 0, 0, -1, -1, -1, 3, 0, -2, -2, 0, -1, 0], [5, -2, -1, 1, 0, 0, 1, -1, 1, -3, 1, 3, 2, 0, 1, 0, 2, 1, 1], [1, 4, 0, -2, -1, -1, -1, 1, -1, -1, 1, 0, -1, 2, -4, -1, 0, 2, 0], [2, 2, 4, -1, -1, -1, 2, -2, -1, -1, -1, 0, 5, 1, -1, 0, 1, 0, -1], [-1, 2, -5, 0, -2, -1, 0, 0, 1, 0, -3, 0, -1, -1, -3, 0, -2, -1, 0], [-1, -2, 0, 0, -3, 0, 3, 1, -1, -1, -1, -3, 4, 0, -1, 0, -3, 1, -2], [11, -3, -5, 0, -4, 0, 1, 1, -1, 0, -5, 2, -1, -1, -2, 1, -2, -1, -1], [5, 2, 2, -2, 1, 0, 2, 0, 0, -1, -2, -2, 1, 1, 1, -1, -1, 3, -1], [7, -1, -3, 1, 0, 1, -1, 2, -1, 0, -1, 3, -5, 3, -1, -1, 0, 3, 1], [0, 4, -1, 3, 0, 0, -2, 2, 1, 1, -2, -2, -1, 0, 1, -2, -2, -2, 0], [-1, 3, 2, -2, 4, 0, -3, 2, -1, -1, 0, -2, -3, -1, -3, -2, 1, 0, -1], [-2, 7, -4, 1, -2, 2, 0, 3, -3, 2, 2, 0, -1, 0, -1, -1, -3, 0, -1], [4, 7, -2, 1, 2, -1, -1, -1, 1, -2, 1, -1, 2, 1, 1, -1, 4, 2, 2], [3, -2, 6, -1, 2, -1, 1, -2, 1, -3, -4, -5, 2, -3, -1, -1, 0, -5, -2], [11, -2, -6, 0, -1, 1, 2, 2, 0, -2, -1, 0, 2, 0, -1, 0, 1, -1, -3], [-6, 1, -1, 3, 2, 0, -5, 1, 0, 2, 4, 0, 0, 1, 2, 2, 4, 4, -1], [5, -3, 1, -2, -1, -3, 3, -2, -1, -2, -3, -3, 0, -5, 1, -2, -2, 0, -3], [2, -1, -3, 1, -1, -1, 4, -3, -1, -1, 0, 1, -1, -2, 0, 0, 1, -1, -4], [-4, 0, 0, 0, 0, 1, -1, -2, -3, 1, -1, 1, -4, 2, -3, 0, 2, 1, 0], [0, -1, 0, 1, 0, -2, -2, 2, -1, 1, 1, -1, 1, 1, 1, -2, -2, -2, 2], [-4, -1, 5, -1, 2, 0, -4, -3, 1, 4, -1, -3, 0, 0, 2, 2, 3, 2, 0], [7, -2, 3, 0, 0, 0, -3, 0, 0, 4, -2, -1, -2, -3, 2, -1, -2, -1, 2], [9, 6, -1, 2, -2, -1, 1, 3, -1, -3, -1, 1, -4, -1, -1, 0, -4, -1, -1], [2, 2, 0, -3, 1, -3, 3, 1, -2, -2, -2, -4, 2, -3, -2, -1, -2, -1, -4], [2, -4, 2, -1, 1, 2, -4, -1, 2, 1, 4, 0, -1, 2, 0, -2, 1, 0, 0], [2, 5, 1, 1, 1, 2, -2, 0, -1, 1, 2, -1, 0, 3, 0, -2, 0, 0, 4], [-1, 4, 2, -2, 1, -2, 1, 0, 1, 1, -5, -5, 2, -1, -3, -2, -2, 2, -2], [-2, 10, -5, -1, -2, 0, 1, 5, 1, -1, 0, 3, -3, -1, -2, 1, -3, 1, 2], [7, -2, -2, 0, 2, 0, -2, -2, -3, 0, 3, -1, 3, -1, 2, 3, 4, 1, -3], [-3, 1, -5, 0, -1, 3, -1, 0, 3, -1, 7, 1, 2, 2, -1, 3, 2, -4, 1], [4, 1, 3, -5, 2, -1, 4, 1, 0, -3, -5, -3, 3, -2, 1, -2, 0, -2, 1], [2, -7, -1, 2, -3, 3, 1, 0, 1, -2, -1, 4, 0, -2, 2, 1, -5, -4, 1], [6, 0, -3, 1, 1, 3, -2, -2, 1, 1, 6, 0, 3, 2, 1, 0, 4, -4, 2], [3, 4, 2, -1, -2, 3, -2, 0, 0, 1, 0, 0, 0, 1, -2, 0, 0, -1, 2], [-2, 1, 3, -1, -1, -2, 3, 0, 0, 1, -4, -2, 3, 0, 5, 1, -4, -3, 2], [-8, 1, 1, 1, 1, 5, 1, -4, 0, 0, 1, 1, 0, 1, 0, 5, 1, -2, -2], [3, -6, -3, 3, 5, 0, -3, -4, 0, 0, 1, 1, 1, 1, 0, 4, 2, -4, 2], [-1, 2, 1, 1, -1, 3, -1, -2, 0, 0, 2, 0, 0, 2, 4, -1, 2, 3, 1], [-7, -1, 2, 0, 1, -1, 1, 0, 2, 5, -9, -3, 0, -3, 1, 1, -1, -2, -2], [2, -1, 1, -2, -3, 1, 4, 2, -1, 2, -2, 0, 0, -1, -1, -1, -3, -1, -2], [-2, 1, 1, -5, 1, -4, 1, 1, -2, 0, -3, -3, 1, -3, 1, 1, 3, 3, -3], [7, 0, -1, 0, -2, -2, -2, 1, 0, 0, 5, 1, -2, 1, -1, 1, 3, 3, 3], [5, 4, -4, 1, 0, -4, 3, 1, 1, 0, -4, -2, 3, 2, 1, -1, -1, -1, 1], [5, 1, 6, 0, 1, -1, 0, -1, 2, 2, 0, -3, 1, -2, 3, -4, -7, -1, 4], [-2, 0, -6, 2, 0, -2, -1, 0, 3, -1, 0, -1, 1, 3, -2, 4, 3, -1, -1], [4, 0, -3, 3, -1, 4, -1, -1, 0, -3, 5, 7, -1, 1, -1, 3, 4, -2, -1], [2, -7, 6, 0, 4, 1, -5, -5, -1, 3, 10, 1, 0, 1, 0, 3, 5, -1, 1], [1, -2, 2, -1, -2, 1, 3, 1, -1, -4, -1, 0, 2, -2, 1, 1, 1, 1, -1], [1, 3, 4, 0, 3, 1, -2, -1, -5, 0, 1, 1, -3, -2, 1, -2, 1, 1, 0], [-1, -6, 6, -2, -1, 0, 5, -1, -1, 1, -6, -5, 0, -3, 0, -6, -6, -1, -1], [-1, 0, 1, 0, 2, 0, 2, 0, 1, -1, -1, 2, 1, -1, 3, 0, 2, 0, 0], [-5, -4, -1, 5, 4, 3, -6, 1, 0, 1, 8, 4, 1, 1, 1, 2, 3, -7, 2], [14, 0, 0, 6, -1, 0, -1, 1, 0, -1, -1, 0, -3, -2, 0, -1, -4, -2, -2], [-1, 3, -1, -2, 1, 2, 0, -3, 2, 4, -1, 0, -2, 2, -3, -1, 2, 2, 0], [2, 0, 2, 2, 4, 1, -3, -1, -2, -3, 3, 1, -1, 0, -1, 0, 1, -3, 2], [4, -2, 2, -1, -2, -4, 0, 5, -2, 1, -6, -1, 2, -2, -1, -3, -4, 5, -2], [5, 5, 5, -2, 2, -1, 1, 1, -4, -1, -1, -4, 3, -2, -1, -4, 1, 2, -2], [-13, 0, -7, 2, 5, -1, 0, 0, 0, 1, -4, -3, 1, 0, 1, 3, 6, -1, -3], [0, -1, -4, 1, -1, -2, 6, 1, 0, 1, -9, 2, -3, -4, -1, 1, -5, -1, -3], [6, 9, 1, -2, 0, -1, 1, 1, 2, -2, -5, -2, 0, -2, -2, 0, 0, 0, 1], [4, 6, -3, 0, -4, -2, 2, 2, 1, 0, 2, 1, 3, 2, -1, -3, -2, 4, 1], [-1, 6, 2, -5, -2, 1, 1, 2, 0, 2, 0, 1, 3, 0, -2, 0, 1, 2, -1], [-3, -6, -1, 1, -4, 3, 2, -2, -2, 4, 1, 2, -3, 1, -1, -1, -2, -2, 0], [-1, 3, -1, 4, -1, 0, -1, -1, 1, 0, 1, 3, -2, -1, 1, 4, 1, -2, 1], [-8, -6, 0, -3, 1, -1, 3, 1, -1, 1, -1, -3, 2, -3, 0, 0, -2, -6, -1], [-5, 1, 5, 0, 6, 1, -9, -6, 2, -1, 5, -3, 3, 3, 0, 3, 7, 2, 4], [0, 5, 4, -4, 5, -3, -3, 0, 1, -1, 1, -5, 3, 1, -3, -1, 7, 2, -2], [-7, -1, 3, 2, 1, -3, -5, -1, -1, 1, 10, -1, 2, 5, 1, -3, 5, 5, 3], [12, 2, 1, 1, -5, 2, 3, 4, -3, -2, -3, 3, 0, -1, 0, 0, -8, 0, -4], [7, 9, 0, 1, 0, -1, 1, 1, 0, -4, -4, 1, -1, 0, -4, -1, -5, 0, 1], [0, 5, -2, -2, -1, 4, 2, -1, 0, -2, 0, 0, -1, 3, 1, 1, -1, -2, -1], [13, 1, -1, 3, 1, -4, -1, 1, -1, 1, -5, -4, 1, 1, 0, -2, 2, 3, -1], [-17, -1, 4, 2, 4, 0, 0, 2, -4, -2, -4, -3, 3, 1, 1, 0, 2, 0, -2], [-5, 6, -3, 2, -1, 2, 2, 2, 1, 1, -6, -4, 2, 4, -6, -5, -1, 0, -1], [-2, 5, 2, -2, 4, -6, 3, 0, -2, -3, -8, -6, 1, -2, 1, 0, 1, 1, -3], [4, -9, 10, -4, 6, 2, 0, -3, 0, -5, -1, -5, 4, -1, 1, 1, 3, -5, -2], [6, 0, 3, 0, 2, 2, -3, -4, -4, 0, 4, 1, -4, 2, -2, 0, 0, 4, 0], [9, -2, -5, 1, -1, -1, 0, 2, -1, -2, 3, 4, 2, -1, 1, -1, -2, -2, 0], [-1, 3, 9, -7, 1, -4, 5, 2, 0, 0, -8, -3, 6, -1, 0, -3, -1, 4, 0], [-4, 6, -2, 1, 2, 3, -3, -2, 3, 3, 0, 0, -2, 2, 2, 2, 1, -1, 4], [3, -9, 1, 4, -3, 1, -3, 2, -1, 1, -3, 2, -3, -3, 0, 2, -3, -2, -1], [0, 0, 2, 0, 3, -2, -1, -4, -1, -2, 0, -1, 8, 3, 1, 1, 6, 1, 2], [-11, -4, 5, -2, -1, -3, 6, -1, 1, 0, -11, 1, 2, -5, -1, -1, -1, -1, -3], [7, 8, -6, 2, -3, 4, 1, 2, 2, 2, 5, 1, 1, 6, 0, -1, -1, 1, 1], [4, 2, 3, -6, 5, -1, -1, -3, -1, -2, -1, -2, -2, -4, -2, -1, 1, -4, -1], [5, 1, 4, -2, 0, -4, 1, 2, 2, 1, 0, 1, -2, -4, 4, 1, -2, -2, 1], [0, 1, -10, 3, -5, 0, -2, 1, 0, -1, -1, 5, -4, -3, 0, 4, 0, 1, 3], [0, 0, -6, 4, -7, 1, 3, 2, -1, -1, -1, 2, -1, 0, 0, 3, 3, 0, -2], [-8, -7, -2, -3, 2, 0, -3, -1, 1, 2, 8, 3, 3, 1, 3, 5, 6, 2, 4], [-3, 9, -5, -3, 1, 1, -3, 1, 2, -2, -4, -2, -2, -2, -2, 6, 4, 1, -5], [1, 5, -2, -1, 3, -1, -2, -1, 1, -5, -3, -2, -1, 2, -1, 1, 3, 1, 1], [2, 4, -6, 0, -2, -4, 4, 7, 0, -1, -1, -3, 3, 1, 1, -1, -2, 1, -4], [3, 10, -1, 0, -2, -1, 2, 2, 5, -1, -4, 2, -3, 1, -2, 0, -3, 5, -1], [1, 4, 3, 3, 3, -1, -6, 3, -3, 1, 0, -2, -4, 1, -3, 0, 1, 1, 0], [-8, -3, 4, 0, 0, 2, 0, 0, 4, 4, -5, -4, 0, 0, 7, 1, -2, -1, -3], [14, -2, -2, -3, -2, 1, 4, -2, 0, 1, 8, 6, -3, 5, 0, -6, -2, 3, 4], [-9, 7, 0, 3, 0, -1, -3, -1, 0, 0, -5, 0, -3, -1, 0, 0, -1, 1, -4], [0, 1, -8, 5, -2, 5, -3, 0, 0, 0, -2, 2, -7, 4, 1, 2, 1, 5, -5], [-5, -3, 0, -2, -2, 1, 2, 0, 3, 1, -3, 1, 1, -3, -1, 2, -4, -5, -4], [0, -8, -1, 2, 0, 2, 2, 2, -1, -2, -5, -3, 5, -4, 1, 3, -2, -8, -1], [2, 6, 6, -6, 1, 1, 1, 2, -4, -3, -3, -3, 1, -1, -2, -2, -1, 5, -3], [1, -1, 5, 1, 0, 3, -4, -6, -1, -1, 11, 2, 4, 5, 0, 3, 6, -2, 5], [3, 6, -4, 5, -5, 4, -4, 0, -1, 1, 9, 10, -4, 7, 0, 2, 2, 1, 6], [-1, 5, -4, -4, 1, -1, 2, -1, 3, 2, 3, 1, 5, 2, 1, -4, 1, -1, 2], [8, 8, 5, -5, 1, -1, -2, 2, 3, 3, -1, -1, -3, -3, -1, 1, -4, 1, 1], [-11, 4, -6, 2, -3, -2, 5, 4, -1, 5, -6, 0, 2, 2, 1, -3, -4, 1, -3], [-10, -1, 5, -1, -3, 2, -1, 0, 0, 2, 3, 2, -2, 0, 3, 2, -2, -4, 0], [17, 7, 0, 2, -5, 3, 1, 0, 0, 1, 5, 6, -7, 0, 0, 0, -2, 2, -2], [-15, -8, 2, -1, 1, -1, 1, 4, -1, -2, 1, 0, 2, -1, 2, 3, 1, -3, -2], [-4, -2, -3, -1, 1, 1, -4, 0, 2, 3, -2, 1, -2, 3, 2, -1, 3, 2, 2], [2, -2, 2, 2, 2, -2, -1, -2, -1, 5, -2, -2, -1, -1, 1, 1, 0, -2, -3], [-5, 2, 12, -8, 4, -3, 5, -1, 0, 1, -5, -5, 5, -7, 1, 0, 1, -2, -2], [3, 1, 6, 6, -2, 0, -1, 0, -2, -1, 2, 0, 2, 0, 1, -8, -5, -3, 5], [5, -9, 0, 1, 0, 3, 1, -1, -2, 0, 3, 3, 5, -1, 1, 5, 2, -6, 2], [15, 0, 6, -2, -5, -1, 6, 0, 3, 1, -1, 1, -7, -3, -1, -5, -7, 3, -2], [0, 5, -7, 3, 1, 1, -3, 1, 3, 2, -1, 2, -5, 3, -3, 2, -3, 1, 0], [-10, -1, 4, 5, 3, 1, -5, -1, -2, -1, 1, 1, -3, 1, 0, 5, 1, -4, -1], [11, -6, 5, -2, -1, 0, 4, 0, -2, -4, -2, 4, -1, -3, 1, 0, -2, -1, 0], [-13, 3, -4, -2, 2, -1, 0, -3, 2, -1, -2, -3, 4, 2, -6, 4, 8, -3, -3], [-2, -5, 9, 1, 5, 0, 1, -4, -1, 2, -5, -8, 5, -2, 2, 0, 3, -5, -3], [-4, -12, 0, 0, 0, 0, 2, 1, -2, 2, 3, 1, 4, -2, 4, -3, -3, -4, -3], [5, 2, 4, 0, 2, 1, 1, -1, -2, 1, -6, 0, -5, 4, -3, -1, 1, 5, -1], [-1, -11, -1, 0, 2, 0, -3, -3, -1, 2, 0, 0, 2, 3, 3, 4, 9, 0, 0], [14, 2, 7, -3, 3, 2, -6, -1, -3, -1, 11, -1, -4, 4, -3, -7, 1, 4, 7], [-1, -2, 8, -1, -3, 0, 3, 1, -1, -2, 0, -3, 2, 2, 2, -8, -2, 4, 1], [0, 8, -3, 0, 3, -2, -1, 4, -1, 2, -8, 1, -4, -5, 0, -1, -4, -1, -2], [-12, 1, 4, 2, 0, 0, 2, 0, -2, 1, -2, -5, 1, -2, 2, 2, -1, -3, -3], [3, -1, 6, -2, 4, -1, -2, -5, 0, 2, 5, -3, -1, 1, -3, 0, 7, -2, 2], [7, 1, 4, -5, 2, 0, -2, 0, -4, 2, 3, -2, 3, 5, 4, -3, 1, 6, 2], [-2, -2, 4, -7, -1, -4, 1, -2, 0, 0, -8, 4, -5, -7, -3, 3, 0, 2, -1], [3, 4, 3, 1, -2, 1, -3, 4, 3, 0, 3, 1, -6, 1, -3, -2, -1, 5, 1], [-5, -12, 6, 0, 1, 2, 1, -2, 2, 0, 0, -4, 1, -3, 2, 2, -3, -2, -2], [-8, -4, -1, -3, 1, -2, -5, 1, 0, 2, 2, 4, -1, 2, 2, -1, -1, 3, 3], [15, 1, -3, 2, -7, -1, 2, 2, 0, -4, 7, 4, -2, 3, -4, -5, -4, 0, 3], [-2, 1, 0, 4, -2, 0, -1, 1, 1, 2, -5, 2, 4, -1, 1, -2, -4, -1, 3], [-6, -10, 5, 3, -1, 4, 2, 5, -2, -1, -6, 1, 1, -2, -2, -5, -6, -5, 0], [0, 3, 7, 0, 6, -1, 1, -2, 1, -3, -6, -7, 4, -2, -1, 1, 0, -2, -3], [-4, -1, 2, -1, 3, 1, -3, -5, -2, 2, 4, -7, 3, 1, 1, 5, 2, -4, -4], [-9, 9, -5, 2, -1, 1, 2, 5, 2, 1, -8, -5, -3, 0, -1, 1, -2, 3, -7], [-5, 2, 0, 0, -2, 3, -5, 6, 0, 3, 1, 3, -2, 3, 3, -2, -4, 0, 2], [17, -4, 5, 1, 3, 1, -2, -5, 3, 1, 1, -7, 3, -3, 3, 3, 3, -3, 1], [-11, 5, -7, 3, -4, 2, 3, 5, -2, 2, -7, 0, -4, -2, -2, 4, -4, -3, -5], [-2, -2, 8, -8, 2, -6, 5, 0, 3, 2, -1, -5, 9, 0, 2, -3, 5, 3, 1], [1, 2, 1, 4, 1, 1, -3, -3, 5, 1, 0, 3, -5, -1, 5, 4, 0, -1, 3], [1, -4, -2, -1, -2, 1, 6, 5, -2, 1, -10, 3, -2, -3, 0, -3, -9, -3, -3], [1, 2, -6, 2, 5, -3, -4, -2, -3, 2, 3, 2, 0, 2, -1, 0, 5, -1, 3], [1, -8, 10, -3, 7, -2, -3, -4, -3, 1, 3, -3, 2, 0, 4, -3, 3, -3, -1], [-4, 5, -4, 4, -3, 2, -3, 4, 1, -3, 8, 4, 0, -4, 3, 2, -5, -1, 3], [2, 2, 1, -3, 0, -1, -1, 0, -1, -4, -6, 2, 0, -6, 2, 3, -4, -1, -1], [10, -4, 3, 7, 2, 1, -4, -3, 0, -2, 7, 1, 4, 4, 2, -3, 0, -4, 4], [-18, 6, 1, 3, 3, 0, 2, 1, 2, -1, -2, -1, 1, 0, 4, 1, 2, 1, -2], [21, -5, 2, 3, 2, 1, -7, -2, 0, 2, 1, 3, -7, 0, -5, 3, 5, 3, 0], [5, -5, 9, -1, 1, 4, -3, -5, -1, -2, 11, 3, -4, 0, -2, 3, 2, -3, 6], [4, 9, -1, 3, -1, -1, 0, 3, 2, 0, -4, 3, -10, -3, 1, 1, -2, -2, 1], [2, -6, 2, 4, -2, 1, 3, 0, 0, -3, -1, 3, -3, -3, -1, 4, -4, -2, -4], [4, 3, 6, -2, 5, -1, -2, -2, 1, 3, 2, -3, 6, 5, 0, -2, 3, 2, 7], [4, 8, -1, -1, -2, 3, 4, 2, -4, -1, -4, 0, -6, -4, -1, 0, 0, 0, -8], [-6, -5, -3, -2, 0, -1, 4, 2, -6, -1, -8, -3, 4, 2, -1, -2, 3, 3, -3], [4, -2, -1, -2, -1, 0, 2, -1, 0, -3, 0, -5, 3, -5, 3, -3, 1, -6, 1], [-1, -8, 0, 3, 0, 5, 0, -3, 5, 3, -6, -2, -8, 2, -2, -2, -5, -2, 2], [1, -4, 0, -5, -7, -3, 10, 5, -3, 2, -13, 0, -4, -4, 0, -4, -9, 5, -4], [9, -8, 13, -6, 6, -4, 4, 0, -2, 1, 0, -7, 4, -1, -3, -4, 0, -4, -1], [4, -8, -7, 3, -5, 1, 6, 4, 3, 3, -1, -3, 7, 1, -3, -5, -4, -5, -3], [2, 6, -4, 1, -1, -3, -5, 2, -2, 1, 6, 1, 0, 7, -1, -1, 8, 7, 2], [-8, -1, 4, -1, -3, 1, 4, 4, 1, 3, 3, 0, 11, 3, 2, -1, -3, -1, 2], [17, -4, 13, 2, 6, 1, -5, -3, -1, 1, 4, 3, -4, 1, 1, 0, 0, 1, 5], [-2, -1, 4, -3, -1, -3, 6, 2, -2, 3, -8, 0, 4, -1, 1, 3, -4, 0, -3], [0, -2, 6, 2, 1, -5, -3, 0, -1, -3, -5, -3, 1, -1, 0, -4, -3, 3, 5], [0, 2, -4, 5, 0, 0, 0, -3, -2, 1, 3, 3, -4, 1, 0, -3, -3, 3, 5], [10, 3, -1, -8, 0, -3, 4, 0, 5, 2, -4, -3, 10, 0, 2, 0, -2, -3, 0], [7, -13, 2, 5, -1, 0, 2, -5, 5, -1, -2, 2, 0, -2, 3, 5, 1, -5, 1], [3, 2, 1, 0, 7, 2, -5, -4, 1, -1, 8, 2, -2, 0, -2, -1, 6, -3, 9], [-14, 1, -4, 0, 2, 2, 2, 3, 4, -2, -7, -3, 2, -6, -1, 4, -3, -7, -2], [1, 1, -10, 5, 2, 2, 0, 0, -7, -2, -6, 0, -3, 2, -3, 2, 4, 2, -3], [-5, 4, -2, 0, 4, -1, 2, 3, 0, 2, -3, -3, 6, 4, 2, -1, 7, 2, -3], [1, -4, 12, -1, 1, -1, 0, -2, 2, 1, 7, -5, 6, 1, -2, -1, 6, 1, 3], [4, -11, 5, 0, 2, 3, -5, 3, -8, 5, 8, 1, 4, 5, 5, -1, 1, 3, 3], [4, -9, 7, -8, 4, -3, -3, -5, 0, -3, 1, -4, 9, 4, 0, -2, 4, -1, 5], [9, 4, -5, 3, 0, 1, -8, -9, 0, -5, 18, 8, -1, 3, -1, 6, 11, -3, 6], [0, -4, -4, 2, -3, 3, -2, 3, -1, 0, 3, 0, 1, 3, 5, -4, -4, -2, 5], [-8, 5, 6, 4, 2, 1, -3, -7, -2, 1, 4, 0, 3, -2, 1, -2, 4, -5, 1], [-9, 2, 6, 0, 3, -1, -3, -5, -3, 3, 4, -3, 3, 1, 0, 0, 8, 1, -1], [2, -4, -6, 4, -2, 3, -6, 2, -3, 1, 5, 5, -6, 2, -3, -2, -3, 2, 4], [-12, 2, 10, -1, 3, 0, 0, 0, 1, 0, 2, 0, 1, 3, 1, 4, 1, 3, -3], [-2, 1, -9, 0, -1, -1, -1, 4, 1, 0, -5, 5, -3, -3, -3, 4, 0, 0, 1], [-2, 7, 2, 0, -1, 4, -1, -3, 0, 0, 4, 8, -10, -1, 0, 0, -3, 2, 4], [-7, -7, 2, -5, -1, 1, -1, 0, 4, 0, -7, -1, 4, 0, -1, -1, -3, 1, 0], [-5, -14, 4, 0, 1, 0, -2, -5, 1, 6, -4, -7, 10, 2, 4, 1, 3, 2, 3], [-5, 2, -3, -6, 1, -2, -1, -1, -1, -3, 3, 2, 2, 4, -1, -3, 2, -4, 4], [-1, 1, -4, 1, -2, -5, -3, 1, 2, 0, 1, 2, 0, -2, -2, 4, 3, 4, -2], [0, 4, -1, -1, 1, -3, -1, 1, 1, 0, 3, 4, 0, 1, 1, -5, -2, 1, 2], [8, -2, 8, 1, 3, 3, -6, -4, -3, 5, 13, 0, 3, 5, 3, 0, 5, -2, 1], [2, 3, -6, 0, -1, 2, -5, -4, -3, -1, 9, 3, 2, 3, 1, 1, 7, 4, 2], [7, -1, -10, 4, -8, 4, 6, 4, 0, 0, 3, 5, 0, 3, -2, -6, -7, -1, 1], [-18, 1, 6, 0, -1, -2, -3, -1, 3, 2, -5, -6, 0, -4, 3, 5, 0, 0, -5], [20, -5, -3, 3, 1, 3, 2, 1, 6, -1, -2, 2, 2, -2, 0, 3, -3, -7, -1], [17, -1, 3, -1, 1, 1, -1, -4, 6, -3, 2, 4, -1, -2, -3, 0, -4, -3, 2], [-16, 5, -7, 2, -3, 0, -1, 2, 0, 1, 2, 4, -5, 1, 6, 2, -5, 2, 3], [2, 5, -8, -4, -2, 0, -1, 1, 2, -1, -3, 2, -6, -3, -4, 6, 3, 3, -6], [7, 6, -8, -4, -1, 0, 3, 2, 1, -3, -12, -2, 0, 2, -1, -1, -2, 1, -1], [-19, -6, 7, -3, 0, -4, 0, -6, 0, -2, -2, -1, 6, -8, 1, 2, 0, -5, 1], [4, -7, 2, 1, -1, -1, -1, 5, 6, 0, 1, 6, 2, 2, 0, 0, -3, 2, 6], [-12, -9, -7, 5, 1, 6, -6, -3, 1, 3, 15, 1, 4, 4, 4, 2, 1, -1, 2], [11, -5, 0, 0, 0, 4, -6, 1, -4, 0, 7, 3, 2, 2, 2, 2, -2, -4, 5], [-10, -3, -2, -3, 0, -6, 5, -2, 4, 5, -14, -3, -1, -7, 3, 3, -3, -3, -6], [-10, 1, 2, -7, 0, -3, 6, 1, -2, 3, -12, -6, 3, -1, -2, -3, -4, 3, 0], [1, -8, 2, 1, 1, 1, -2, -3, 3, 5, 1, -3, 1, 2, -1, -3, 0, -1, 4], [-3, 1, -6, 2, 4, 7, -6, -6, -4, 0, 15, 1, 1, 7, 2, 4, 5, 3, 1], [6, 6, 2, 5, 2, -2, -5, -4, 3, -6, 3, 1, 1, 1, 1, 0, 4, 0, 6], [-7, -1, 1, -3, 5, -1, -5, -5, -1, 0, -2, 0, -5, -3, 0, 0, 6, 0, -3], [-6, 13, -10, -4, -3, -1, 3, 2, -4, -3, -6, 2, -4, -1, -7, 0, 3, 6, -3], [-7, 0, -5, 4, 1, 4, -3, 1, -4, 0, 11, -1, 3, 3, -1, 4, 0, -8, -1], [-10, -8, 3, 0, -8, 3, 1, 5, -1, -2, -1, 3, -1, 0, 3, -2, -6, 3, -3], [-9, -1, -6, -4, -2, 0, 1, -3, 4, 1, 3, -2, -2, -2, -2, -2, 1, -2, -2], [-20, 14, 6, 2, 3, -2, 2, 6, 0, 6, -9, -5, -5, -3, 0, -7, -4, 1, 1], [3, -5, -1, -2, 1, 2, -4, -3, 2, 0, 7, -1, -5, 2, 3, 0, 2, 2, -1], [16, -10, -2, -9, -2, -2, 10, 4, 4, -5, -8, -1, 2, -7, 1, 1, -5, -2, -6], [-4, 6, 11, -7, 2, -10, 2, 0, -2, 3, -1, -2, 2, -2, 2, -2, 3, 5, -1], [-5, 0, 1, 1, 5, -3, -5, -8, -2, -2, -7, -7, 2, -1, 0, 6, 10, 2, -6], [20, 1, -6, 4, -7, 3, 2, 9, 0, 0, 1, 7, -2, 1, 2, 0, -4, 3, 1], [13, 9, 4, -4, 3, -2, 3, 3, 0, -1, 6, 0, -1, 3, 3, -6, 0, 4, 5], [11, -2, -7, 7, -1, 3, -1, 1, 1, 2, 8, 7, -1, 2, 5, 0, 2, -2, 3], [10, -3, 3, -1, 2, -1, -4, 1, -2, -6, 2, -2, 1, -5, -2, 0, -1, 3, -1], [0, -2, 1, 3, 8, -3, -1, 2, 1, 2, 3, -4, 2, -4, 2, 1, 0, -5, 3], [17, -7, 4, 4, 0, -2, -1, -1, 0, -1, 1, 4, -1, -1, -2, -4, -1, 7, 6], [7, -3, 5, 3, 1, 7, -2, -2, -5, 4, 6, 1, -1, 2, -1, 1, 7, -5, -3], [-2, -2, 4, -1, -1, -1, 2, -4, 1, -3, 1, 0, 3, -1, -7, 0, 3, 0, -1], [-3, 6, 6, 0, 2, -6, 4, 8, 1, 1, -5, -6, 1, -3, 4, -5, -12, -2, 2], [0, -12, 9, -1, 2, 3, -7, -3, 1, 0, 2, -1, -4, -2, 6, 0, 1, -3, 2], [15, -12, 15, -1, 5, 2, -5, -8, -4, 0, 3, -5, 3, 5, 4, -2, 8, 0, -2], [13, 5, -12, 3, -3, 0, -2, 3, -2, 3, 3, 8, -3, 5, -3, 3, 3, 2, 3], [9, -4, -6, 2, -7, 0, 6, 4, 1, -6, -9, 1, -4, -3, -2, -1, -2, 1, -3], [-5, -11, 2, -1, 1, -2, 6, 4, -4, -1, -4, -6, 5, -1, 0, -5, -1, -5, -2], [0, -5, 2, 2, 1, -4, -1, -4, 1, 1, -14, -6, -2, -9, 2, 0, -2, -1, -8], [2, 5, -2, 2, -2, 1, -2, 0, 6, 4, -3, 6, -9, 0, 1, 5, -2, 1, 1], [-3, 2, 3, -2, -2, -3, 2, 0, 3, -4, 0, -4, -2, -5, 4, 0, -5, -2, -1], [3, 4, -2, 5, 0, -6, 4, 3, 0, -2, -4, 4, 6, -1, 1, 5, -4, -1, 1], [-15, -3, -1, 3, 2, 6, -3, -3, -3, -1, 17, 6, -1, 4, -2, 3, 2, -10, 7], [-28, 2, 5, 0, 4, -2, 0, -5, 5, 0, -8, -5, 3, -2, -2, 3, 0, 1, -4], [-28, -1, -9, 0, -2, 5, -1, 3, 5, 1, 2, 3, -6, 5, 1, 5, -1, 3, -1], [-9, -6, 5, 10, -1, 1, -3, -6, -2, 2, 3, -1, 0, 2, -1, 0, 3, -1, 1], [16, 0, 6, 0, -4, -1, -5, -2, 2, -3, 6, 6, -1, 2, 1, -1, 2, 1, 9], [-3, -5, 9, 0, 1, 2, 4, -5, 2, 0, 2, 5, -1, -3, -2, 2, -1, -8, 0], [7, -2, -8, 2, -12, 2, 9, 2, 2, 0, -4, 1, 2, -1, 1, 1, -6, -3, -2], [16, -4, -1, -3, 1, -5, 8, 0, -3, -1, -17, -3, -1, -5, 3, -3, -4, 1, -3], [-15, 2, 4, 2, 3, -3, -6, 0, -3, -4, 8, -2, 5, 8, -6, 0, 6, 2, 4], [-8, 2, 3, 0, 1, 5, 0, 0, 6, 2, -5, -3, 0, 6, -4, 1, -1, -1, -2], [10, 0, 10, -2, -1, -3, 3, 2, -2, -1, 6, -4, 2, -2, 3, -3, -4, 3, -1], [2, -1, 7, -5, 1, -2, 4, 3, -1, 1, -14, -7, -2, -4, 4, -6, -3, 5, -2], [4, 6, -6, 2, -3, -2, -6, -2, -1, 4, -1, 2, -6, -4, 3, -2, -1, 3, 3], [5, -3, -7, 7, -1, 0, -3, -1, 3, 0, 0, 5, -8, -4, 2, 5, -4, -1, 0], [1, -1, 1, 5, 3, 2, -4, -1, 1, 3, 12, 1, -1, -2, 2, -4, 1, -3, 2], [0, -12, 6, 2, 3, -5, 5, -1, -2, -2, -7, -1, 0, 2, 2, -4, 0, 3, 1], [21, -1, 1, 1, -5, 4, 1, 4, 0, 2, 6, 1, -1, 5, -1, -7, -6, 3, 9], [-2, 6, 1, 1, -1, 0, -4, 3, 2, 2, 8, -3, 0, 3, -1, -2, 5, 4, 1], [-7, -6, 7, 1, -6, -4, 3, 0, 6, 3, -8, -5, 7, -5, -2, 0, -6, -1, -4], [2, 2, -6, -1, -3, 3, -6, 1, 6, 1, -3, 2, -1, 8, -1, 2, 2, 3, 5], [-12, 1, -8, 2, -1, 0, -5, 4, -1, 1, 5, 8, -5, 2, 4, 8, 4, 4, -2], [24, -9, -7, -2, -6, 2, 0, -1, 3, 3, 15, 9, -5, 2, 2, -1, -3, -2, 8], [-6, -4, -1, -1, 2, 2, -2, 9, 1, -1, 7, 0, 3, 5, 1, 4, -1, -7, 2], [-5, -14, 3, 0, 5, 1, 1, -6, 2, 1, 2, -1, -1, 2, 1, 0, 1, 2, 1], [8, 10, -8, 10, -1, 2, -1, 3, -4, -3, -5, 3, -3, 4, 1, 6, 1, 1, -4], [-5, 15, -7, 2, -8, 3, -1, 2, -1, 1, 2, 4, -8, 5, 2, -2, -3, 10, -1], [1, 4, 5, 1, 1, -2, 8, 1, 3, -5, -9, -2, 0, -5, -4, -2, -8, -8, 3], [5, 0, -3, -3, -1, 6, -1, 7, -1, 4, -2, 5, -4, -2, -1, 0, -4, -2, -1], [-15, 6, -2, 2, 2, 4, -4, 2, 5, 4, 3, 5, -11, -3, 0, 5, -2, 1, -1], [5, 0, -2, 2, -1, -2, 3, -2, -7, 1, -3, 3, 0, 5, -1, -2, 4, 2, -4], [7, 2, -2, 2, -3, -5, 1, -2, -2, -2, -2, -1, 3, -2, -1, -3, -2, 0, 4], [-6, -17, 3, 2, 1, 0, -5, -2, -2, 3, 12, -2, 7, 3, 4, 2, 3, -2, 3], [9, -11, 0, -1, 0, 0, -3, -2, 3, -1, 13, -2, 1, 1, 1, -6, 1, -5, 7], [3, 7, 14, -5, 6, 0, 1, 1, 3, -2, 1, -4, 1, 2, -6, -4, -3, 0, 0], [5, 7, 5, -1, 0, 1, -7, -10, -3, 3, 6, 2, -2, 0, -1, -3, 6, 5, 6], [-11, 8, -4, 0, -5, 1, -7, -1, 1, 7, 4, 6, -5, 5, -3, 7, 3, 2, -1], [11, -1, 4, 2, -3, 2, 5, 9, 0, -1, -4, 8, 1, -1, 1, 0, -12, -2, -1], [0, 5, 4, -6, 6, -3, 2, 4, -4, -4, -6, -4, 1, 0, -3, -5, 2, 1, -5], [4, -13, 12, 1, 10, 2, -11, -6, 3, 4, 14, -5, 6, 2, 2, 3, 12, -2, 3], [19, 0, 4, 0, 0, -3, -6, -1, 0, 1, 1, 1, -1, 1, 3, 4, 4, 1, 4], [3, -10, 2, 4, -3, 4, -6, -1, 2, -2, 7, 6, -9, -5, 3, 4, -2, -6, 7], [-21, 10, -3, 1, 0, 0, 4, 1, 1, 2, -4, -4, -5, -4, 4, 5, -6, -4, -5], [2, -3, 8, 1, -6, 3, -2, -5, -2, -3, 8, 6, -1, 3, 2, 1, 8, 1, 6], [2, 6, 4, 3, -1, -3, -3, 8, -2, 3, 5, -4, -2, 2, 5, -6, -2, 10, -1], [8, -2, -2, 0, 0, -2, 5, 4, -4, -3, 1, 3, -4, -3, 5, -2, -8, 4, 2], [4, 3, 5, -7, 6, -8, 1, 1, -2, 0, 3, -1, 4, 0, 6, -1, 6, 7, 4], [12, -10, -3, -1, -6, 1, 5, 4, 1, -4, -3, 7, -2, -3, -2, -2, -6, 0, 4], [10, 12, 4, -4, 1, -4, 0, 0, 2, -1, -1, -8, 3, 1, 2, -1, 0, 0, 2], [9, 16, 7, -4, -1, -3, 1, 3, -2, -4, 3, 1, 1, -2, 3, -9, -4, 5, 3], [13, -4, 4, -8, 3, 0, -4, -2, 0, -1, 11, 4, 0, 5, 0, -2, 4, 2, 8], [-5, -1, -7, -2, 2, 0, -10, -3, -1, 6, 9, -4, 2, 0, 2, 5, 5, 3, -1], [-3, 11, 0, 0, -5, 1, 9, 3, 4, -5, -4, 0, 0, -3, -3, -2, -10, -4, 3], [-2, 12, 4, 4, 3, 4, -4, -8, -4, 1, 5, 0, -3, 1, 2, 1, 2, 4, 4], [4, 4, -8, 2, -1, -2, -1, 3, -5, -3, 11, 5, -2, 4, -2, -2, 8, 2, 3], [18, 0, 6, -6, 5, 0, -3, -2, 5, 3, 7, -5, 1, -3, 1, -4, -2, 2, 4], [13, -22, 3, -2, 3, 0, -6, -7, -1, 3, 11, 5, 1, 3, 0, -1, 8, 1, 4], [-23, 10, -1, -1, -1, -3, 0, -2, 4, -1, -9, -6, 3, -2, -2, 4, -3, -3, -1], [-18, 9, -5, -1, 3, 2, -4, 0, -1, 1, 2, 1, 0, 1, 2, 6, 0, 2, 4], [8, -1, -4, 4, 1, -1, 1, -7, -2, -3, 3, 5, 1, 6, 1, 5, 6, 1, 2], [8, -4, 6, -10, 3, -2, 9, -3, 3, 0, -2, -6, 10, -2, 0, -2, -2, -1, 0], [-11, 5, 11, -1, 2, 2, -8, 0, -7, -1, 11, -3, 3, 9, -5, -2, 7, 9, -1], [-9, 4, -19, 4, -2, 5, -2, 0, 3, -2, -9, 0, 2, 7, -4, 4, 3, 0, -3], [-2, 4, 3, 0, 0, -1, 7, 2, -1, 1, -2, -3, 3, 0, -5, -12, -5, -4, 1], [-14, -10, -2, 6, 5, 0, 1, -1, 4, 0, 0, -5, 12, 4, 5, 4, 3, -2, -2], [2, 6, 3, 0, 8, -1, -8, -5, -1, -4, 16, 1, 0, -2, 8, -1, 8, 3, 6], [17, 6, 0, 4, 0, 5, -7, 2, -2, 3, 5, -2, -9, 6, 0, 1, 7, 6, -2], [17, 3, -11, -3, -4, 1, 10, 8, -7, -5, -5, 6, -6, 1, -6, -7, -8, 2, -1], [-19, -5, -6, 8, -1, 4, -2, 2, -2, 6, 0, 3, 1, 2, -1, 2, -4, -5, -4], [12, -5, 11, -4, 8, 4, -2, -2, -3, -2, 0, 6, -5, 0, -3, 1, -1, -2, 2], [-16, -10, 5, -3, 5, -1, -7, -2, 0, -4, 7, -2, 6, -2, -1, 1, 7, -6, 2], [8, 9, 3, -6, 2, -5, 4, 3, -6, 4, -13, -8, -3, -1, -2, -3, -3, 6, -9], [0, 7, -9, 0, 1, -2, 8, 3, -5, -4, -4, 1, 0, -1, 0, 4, -1, 0, -8], [14, -12, -11, -1, 4, 2, -5, -5, -1, 1, 3, 3, -2, 3, -1, 10, 10, 0, -3], [-15, 2, -12, 5, 4, 5, -7, 1, -1, 0, -3, -2, -1, 0, 2, 5, 2, -4, -4], [3, -6, -1, -2, -4, 4, 9, 4, 0, -1, -4, -1, 0, 5, -3, -8, -5, 1, 1], [-9, 0, 2, -2, 3, -1, 6, -4, -5, -3, -16, -6, -1, 2, -5, 1, 3, -2, -7], [-18, -1, 18, 2, 6, -1, -3, -2, -1, 1, -2, -3, -6, -4, 4, -5, 2, -6, 3], [-4, 3, 0, 4, 0, -2, 7, 3, -4, -1, -10, -1, 6, -4, -2, 5, -7, -4, -9], [-1, -3, 0, -5, -1, 1, 1, 2, 5, 4, 3, -1, 2, 4, 9, -1, -3, 1, 2], [11, -1, 4, 2, -5, 1, 1, 1, -4, -1, 3, 4, 10, -1, 3, 4, -4, -4, 7], [-16, -3, 1, -5, 5, 6, -8, -6, -4, -3, 13, -2, 6, 6, -2, 3, 16, 1, 3], [-10, 8, 1, 1, 5, 0, -7, -6, -3, 5, 5, 1, 5, 2, 1, 6, 9, 1, 3], [3, -10, 5, 1, 0, 3, -7, -4, 3, -6, 10, 9, 0, 1, -1, 0, 1, -1, 9], [0, 22, 5, -8, 3, -4, 3, 0, -3, -5, 0, -6, 6, 1, -4, -5, 0, -2, -1], [2, 1, 13, -2, 7, 1, -3, -7, -7, -1, -2, -1, 1, 2, -2, 5, 8, 1, 0], [-6, 3, -9, 5, 6, 0, -6, -8, 1, 2, 6, 3, 0, 2, -3, 2, 5, -1, 1], [-18, -16, 2, -3, 5, -1, 0, 3, 1, 5, -10, -6, 1, -6, 3, 4, 0, -7, -3], [-4, 0, 4, -5, -2, 3, 2, 0, 3, 3, -1, -4, -4, 3, 1, -4, 7, 4, -3], [8, -2, -2, 0, 1, -5, 3, -5, -1, 1, -7, -1, 4, -6, 3, 4, 1, -3, 0], [-17, 2, -4, -5, 0, 0, 0, 0, -1, -3, -4, 0, -5, 1, -8, -6, 0, 3, 0], [26, 4, 2, -1, -1, -1, -1, -8, 7, -2, -4, -1, -9, -2, -2, -2, -1, 2, 1], [15, 3, 7, -2, 5, 0, -6, 1, -3, -6, 19, -2, 8, 4, -3, -3, 8, 4, 6], [7, 2, -16, 5, -7, -2, 6, 4, -5, -1, -2, 6, 0, -1, -2, 2, -4, 5, -2], [6, -25, -7, -1, -2, 1, -2, -6, 3, -1, 3, 2, -2, 0, -2, 5, 8, 1, -5], [6, 7, -10, 5, -5, 0, -8, 1, 0, -3, 17, 13, -8, 1, -8, 0, 4, 5, -1], [-4, -8, 7, -6, 1, -2, -3, -6, 0, 5, 5, -8, 5, 1, 9, -3, 5, 3, 0], [18, 12, -1, -5, -2, -4, 7, 6, -4, 3, -13, -1, -2, -6, 3, -3, -9, 3, -7], [10, -9, 10, 2, -5, 5, 4, 3, 1, -4, -2, -5, 5, 6, -4, -8, -2, 0, -3], [12, 2, 1, 6, -6, 3, -2, 6, -3, 4, 1, 5, -12, -4, -3, -1, -14, -2, 1], [3, -14, 0, 4, 2, 3, -4, -7, -2, 0, -1, -2, -9, -4, -4, 4, 5, 0, -2], [13, 2, 0, -4, -8, -2, 5, 7, 0, 7, -10, 2, -8, -2, -9, -5, -13, 5, -5], [-9, -4, -10, 1, 2, 0, -2, -1, -1, 5, 0, 5, 0, -3, 7, 11, 6, -4, 0], [13, 0, -4, 0, 5, 1, -8, -1, 3, 0, 8, -3, 6, 0, 1, 1, 0, 1, 4], [10, -4, 6, 6, 1, -5, -6, -3, -3, -4, -1, 0, -1, -7, 1, 4, 6, 0, 1], [16, 3, -1, -5, -5, -5, 4, 3, -4, -7, -7, 1, -1, -4, -2, 2, -3, 3, -6], [3, -5, 14, -3, 3, 1, 1, 0, -7, 2, -9, -6, 3, 5, 4, -8, -4, 5, 0]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_8001_a_Hecke( : Kf := Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_8001_2_a_v();".
// 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_8001_2_a_v(:prec:=19)
    chi := MakeCharacter_8001_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_8001_2_a_v();".
// 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_8001_2_a_v( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_8001_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![-210, 608, 2913, -5723, -13725, 14000, 28600, -13249, -29792, 4985, 17032, 21, -5572, -583, 1035, 178, -101, -22, 4, 1]>,<5,R![-45312, 196352, 422528, -1545280, -2252672, 1896320, 3153420, -635484, -1786966, -34796, 500048, 56012, -76184, -11859, 6431, 1147, -282, -54, 5, 1]>],Snew);
    return Vf;
end function;