
// Make newform 8034.2.a.bc in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_8034_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_8034_2_a_bc();".
// 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_8034_2_a_bc();".
// 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 := [2048, -17600, -11840, 65434, 21747, -71361, -16428, 33191, 5112, -7580, -707, 872, 44, -48, -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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [10315145682746966682944, -75481126501892671808752, 53532513774968079841586, 145425424067694665372939, -109525350370822082766017, -94142583432419588002804, 64612006487857426157383, 26184651556522014754456, -16731997871850458694196, -3389041191171673838947, 2065774167255360616712, 201894771958174626540, -118607585529944247160, -4451260489557971801, 2537687267978126305], [31232388687353964064640, 51082916732053674000704, -143327565524240360562922, -141476191243349227852339, 189558836334691265479921, 130523696906252529491036, -100220807092977766199447, -44104795536205132068824, 25017731332666579088492, 6347593527480726095411, -3040455429814694571304, -401147448883605874380, 173370522950640285632, 9148574385842311585, -3699895265701566353], [15999879528543583420672, -105730885302223976198336, 56590561866592878591298, 201052630181593672596943, -131442940707426684242005, -132396296199577483382588, 83503603148532481698995, 37839894450753416967704, -22880252731934338749548, -4977240979565848871999, 2937458974583126918344, 299029290976494333660, -173187246246377101328, -6621368153969086837, 3773756680062282389], [2332369560757484941472, -4580081011050082891228, -22217767129638255474988, 8259757592004157683545, 30948944380910040502771, -3172708855946150385058, -15679149848322058779965, 411319014825229416136, 3671032048907900349578, -14892506323265156095, -423613518372852698680, -740490576502024596, 23213090564296575506, 43110065350197505, -480421702545662123], [-17231425109937506795776, 85313542688545755485744, 86096965550968147850822, -329708970008761859686711, -17153063243581124000891, 263743776775326664831940, -35045824171083536765987, -80762745305159870682104, 16479152638452021523460, 10967030382881649513455, -2592166138155870798184, -668437526636551236252, 169062781332764512088, 14888092941463260925, -3904290949793122853], [4137311857191453969280, -36576815788443985896752, -26343781779899371656962, 96396192676307847030949, 668266301521186841729, -71147018611462724250524, 15463140566778105369785, 21396335118373983609512, -6497133196312926368636, -2894763636328689608669, 984697502339295110968, 176671191969983900820, -62994684520973032856, -3946760310112449751, 1437348996203833439], [-1099608980575046137664, 6876707545146179250864, 5767233907927992512410, -19543885760794156101025, -2596195015386327990477, 14947524072875232440620, -1259609430605682009317, -4539938442156400956040, 807482146801725193676, 615042765945550203385, -136909874293211051608, -37446683496667123780, 9225298037107150072, 833519197187931691, -216776146664850899], [5241129959594824984640, -5496566174053900711552, 22877990863326377997014, 60676860335814627002837, -62006168022988305824471, -59268935086500033928756, 44047896643808091309313, 19631778341601514731400, -12869509104005418846724, -2762375590140558319621, 1709275636723449924632, 172180740620193204084, -102677561674421271760, -3898546964586732887, 2262060993304819351], [-20760519604905515508992, -64975688162446145854064, 122418852737580306892054, 305614434437315646882457, -225796791826086771929275, -276567011587519356139052, 148333866313014220649117, 89945009312798312263112, -42434297297760917373068, -12587537843796393862097, 5596799573243534456152, 781347790842433004388, -335494621667721213464, -17619842819561824147, 7389528242931052763], [54269842840724729422208, -114807959618689508407408, -156334774693565882680990, 392231796537565988390195, -22639092092040808747577, -345811571939604474832852, 99684232238791936686799, 113304212701430619470680, -39886372998134487110740, -15968681453075819058955, 6001036075358757513992, 995941970920453001676, -383811818206987097848, -22529199141324906641, 8766750062989708633], [-11807950134708017239328, 71793846729075368713576, 8344259772351224143546, -207964216939141801609367, 70235966360674007667737, 169932974581872220205488, -69555529379053943147695, -53545307775003849319096, 22849031189715444748168, 7398646108103984300491, -3196413318423942416024, -456611053302482919612, 197311809783773428132, 10268326608661339349, -4417538992890062809], [-2219445897514458889376, -62443733500550485578896, 69730647157650718059982, 258839300934634508381089, -190386748714222964816683, -228640259637922398414884, 141106197202116037886717, 74291750278280117421560, -42209961752351543724788, -10416374257422677241905, 5675871771319530293080, 648617517135946752852, -343394734237158555296, -14675949069150921499, 7599288743075757563], [9700285797997532462848, -79244364779543304621452, -19685540454780823356992, 256098528986214242270833, -62438278530719538088105, -212442650490802176795278, 72665931767149837846055, 67395099414387524537648, -25231217957008947225314, -9348618128120933493683, 3621424480522273550704, 578099458562396288700, -226696578225165112178, -13012426933683220879, 5118564908078654033]];
    Rf_basisdens := [1, 1, 4407137291368141811136, 4407137291368141811136, 4407137291368141811136, 550892161421017726392, 4407137291368141811136, 1469045763789380603712, 163227307087708955968, 1469045763789380603712, 4407137291368141811136, 4407137291368141811136, 2203568645684070905568, 2203568645684070905568, 1101784322842035452784];
    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_8034_a();"
function MakeCharacter_8034_a()
    N := 8034;
    order := 1;
    char_gens := [5357, 1237, 5773];
    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_8034_a_Hecke(Kf)
    return MakeCharacter_8034_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 := [[1, 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, -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, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 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, 1, 0, 0, 1, -1, 1], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, -1, 0, 1, 0, 0, 0, 0, -1, 1], [2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0], [2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0], [0, 0, 0, -1, 1, 0, -1, -1, 1, 1, -1, 0, 1, -1, 1], [0, -1, -1, 1, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, -1], [0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, -1, -1, 0, 0], [1, -2, 1, 0, 0, 0, -1, 0, 0, -1, 0, 0, -1, 1, -1], [2, -1, 1, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0], [2, 1, 0, -1, 0, 0, -1, -1, 1, 1, -2, 0, 0, 0, 1], [1, -1, 0, 1, 0, -1, 1, 0, 0, -1, 1, -1, -1, 0, 0], [0, 1, -1, 0, 1, -1, -1, -1, 1, 0, 0, -1, -1, -1, 0], [2, -1, 1, 1, -1, 0, 0, 0, 0, -1, 0, -1, 0, 1, 0], [2, -1, 2, 0, 0, 0, 1, 1, -1, -1, 1, 1, 0, 2, -1], [1, 1, 0, 0, 0, -1, 0, 0, 0, 1, -1, 0, 1, -1, 2], [2, -1, -2, 1, 0, 0, -1, -1, 1, 0, 0, 0, -1, 0, 0], [2, 1, 0, 0, 0, 0, -2, -1, 1, -1, 0, 1, 0, 0, 1], [2, 2, 0, -2, 0, 0, 0, 0, 1, 1, -2, 0, 1, 0, 1], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -1, -1, 1, 0, 1, 0, -1, -1, -2, 1, 0, -1, 0, -1], [3, -2, 0, 0, 0, 0, -2, -1, 0, -2, 0, 0, -2, 1, -2], [2, -2, -1, 2, -1, 1, 1, 0, -1, -1, 1, -1, -1, 0, -1], [0, -1, -1, 1, 1, -1, -1, 0, 2, 0, 1, -1, -1, -1, 1], [2, 0, -1, 0, 0, 1, 0, 0, 0, -1, 0, 0, 1, 1, 0], [2, -1, 0, 0, 0, 0, 0, 1, -2, 1, 0, 1, 1, 0, -1], [3, 3, 0, 0, 1, -1, -2, -2, 2, 0, 0, 0, 1, -1, 3], [4, 2, 3, -1, 0, 1, 3, 2, -2, 2, 0, 1, 4, 2, -1], [4, 2, 1, -2, 0, -1, -1, -1, 1, 0, -1, 1, 2, 0, 0], [-1, 0, 0, 0, -1, -1, 0, 1, 1, -1, 1, 0, -1, 1, 0], [2, 2, -1, 1, 2, -3, -5, -2, 3, 0, 0, -1, -2, -4, 3], [-2, 1, -1, 1, 0, 0, -2, 0, 2, -1, 0, 0, -4, 1, -1], [-1, 1, -2, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, -1, 0], [5, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, -1, -2, 0, -1], [1, 3, -1, 0, 0, 0, 3, 0, 0, 1, 0, -2, 0, 0, 2], [2, 0, 2, 0, 0, -1, -2, -1, -1, -2, -1, 0, 0, 0, -1], [2, 2, 0, 0, -2, 0, 2, 1, -1, 2, 0, -1, 1, 0, 1], [0, -1, 2, -1, -1, 5, 7, 3, -3, 0, 1, 0, 1, 4, -3], [-1, 0, 2, 0, 0, -1, -1, 0, 1, 0, 0, 2, 1, 0, -1], [3, 2, 0, 1, 0, -3, -4, -1, 1, 0, 0, 0, 0, -2, 2], [0, 0, -1, 0, 1, -2, -3, -4, 1, -2, 0, -2, -4, -1, 2], [-3, 3, -1, 1, 2, -2, -4, -1, 3, -1, 0, 0, -2, -1, 1], [2, 0, -3, 1, 1, -1, -1, 0, 0, 0, 1, -1, -2, -1, -2], [3, -2, 0, -1, -1, 1, 3, 2, -3, 0, 0, 1, 2, 2, -4], [5, 0, -2, 0, 0, 1, -1, -1, 1, -1, 2, 1, -1, 1, -1], [3, -1, 1, 0, 1, 1, 1, 1, -2, 0, 0, 0, 1, -2, -1], [-2, 1, 2, -2, 2, 0, -1, -2, 0, 0, -1, -2, 4, 0, 4], [1, 0, -3, 0, 2, -2, -2, -3, 2, -2, 1, -1, -3, -1, -1], [-1, -1, 2, 0, 0, 1, 2, 1, -1, 1, 1, -1, 4, -2, 0], [4, 1, -2, -1, 0, 1, 1, 0, -2, 1, 1, 0, 1, 0, -1], [-2, 1, -1, -1, 0, 0, -1, 0, 0, 2, -3, 0, 1, -2, 2], [3, -1, 3, 1, -2, 2, 1, 1, -2, -1, -3, 0, -1, 2, -3], [6, -1, 0, -1, 0, 1, 1, 1, -1, 0, 1, 1, 5, 0, 0], [6, 0, 3, -1, 0, 2, 5, 0, -4, 1, 1, 0, 5, 1, 0], [-2, 3, -5, 2, 1, -2, -4, -3, 3, 0, 0, -2, -5, -5, 4], [5, 3, 2, -1, 1, -1, -2, -1, -1, 0, -1, 0, 3, 0, 4], [2, 0, 1, -1, -2, 4, 9, 6, -5, 4, 1, 0, 5, 3, -4], [-1, 1, -3, 0, 2, -2, -2, -2, 1, 2, 1, -2, -2, -3, 3], [5, 0, -1, -1, 0, 3, 3, 3, 1, 5, -2, 1, 5, 0, 0], [3, 5, -3, 0, -1, 2, 0, -2, 0, -1, -1, 1, -2, -2, -1], [5, 0, 0, -1, 1, -1, 0, 0, 0, 0, -1, -1, 2, 0, 2], [2, 0, -1, -1, 0, -2, -1, 2, 1, 0, 1, 2, 0, 0, 1], [5, -1, 1, 2, 0, -1, -3, -1, 1, -1, 1, 0, -2, 0, -1], [-3, -2, 0, 0, -2, 2, -1, -1, 1, -1, -1, 2, -1, -1, -3], [-2, 0, 1, 0, 2, -2, -5, -3, 3, -1, -2, 0, -1, -3, 3], [-5, 1, 0, 1, 4, -3, -4, -4, 4, 0, 0, -1, -1, -4, 4], [7, 3, 1, 0, 0, 3, 3, 3, -1, 2, -1, 2, 1, 2, -2], [1, 1, 4, -2, 0, 2, 6, 3, -4, 4, 0, 0, 6, 2, 1], [-4, 4, 1, -1, 0, 2, 3, 2, -3, 4, -1, 2, 5, 1, -1], [8, 3, -3, -1, 0, 1, 0, -2, -1, -1, -3, 1, 0, 0, 1], [5, 1, 1, 0, -2, 1, -2, 0, 2, -4, -2, 1, -3, 1, -3], [0, 6, -3, 0, 0, -2, -1, -1, 2, 0, 0, 0, -3, -2, 2], [3, 0, -1, 0, -2, 0, 4, 4, -2, 0, 3, 0, 2, 0, -2], [1, 0, 0, 0, 2, 1, 4, 1, 0, 1, 3, -1, 3, 0, 1], [14, -3, 7, -3, -1, 4, 3, 5, -3, 0, -1, 4, 7, 6, -2], [-6, -1, -2, 3, 2, -1, -4, -2, 0, 1, 0, 0, 0, -3, 2], [-2, 4, -1, -4, 0, 1, 5, 1, -1, 2, -3, -1, 2, 0, 2], [4, -2, -3, 1, 0, -6, -4, 0, 1, -3, 4, 0, -4, 2, 0], [3, 3, -2, 1, -3, 1, -1, 0, 2, 0, -3, 2, -3, 2, -3], [9, 2, 2, -3, 0, -1, 1, 2, 0, 3, -1, 3, 7, 2, 2], [-7, 2, -5, 2, 1, -3, -3, -2, 5, 0, -1, -2, -4, -3, 3], [1, -1, 0, -1, 0, 2, 1, 2, 0, -1, 0, 0, 2, 2, 1], [4, 1, -3, 1, 0, 2, 0, 0, 2, 0, 0, 2, 1, -2, -2], [-7, 2, -2, 0, 4, -2, -6, -1, 6, 1, 0, 2, 1, -4, 3], [0, -2, 3, 2, 0, 1, 2, 0, -5, -3, 2, 0, -4, 3, -4], [7, -4, 6, -1, -4, 3, 7, 6, -4, 2, 1, 1, 8, 5, -5], [8, -1, 3, 1, -2, 0, 0, 1, -3, -4, 2, -1, -3, 4, -1], [5, -3, -1, 1, 1, -1, -2, -2, 0, -1, 2, 0, -2, -1, -1], [-5, -2, 0, 2, 0, 2, 2, -2, -3, -5, 0, -1, -6, 3, -5], [-2, -4, 4, -2, 0, 4, 3, 1, -3, 1, -1, 3, 3, 4, -4], [-4, -4, 2, 0, 0, -3, -2, -1, 1, 0, 3, 0, -1, -2, -1], [3, -1, 3, -3, -1, -1, 0, 0, 0, 0, -1, 1, -1, 2, 0], [3, 1, 2, 2, 0, 4, 4, 2, 0, 2, -2, -1, 4, 0, 1], [-1, -3, 1, -3, 0, 1, 5, 2, -2, 5, -2, 2, 3, -2, 1], [7, 2, 2, -3, 0, 2, 0, 1, -3, 1, -3, 3, 3, 2, 1], [-10, -4, 0, -1, -2, 3, 1, 1, -1, -2, 3, 1, -1, 4, -4], [10, -1, 4, 1, -2, 1, 0, 2, -2, 2, -2, 2, 4, 2, 1], [7, 1, 2, 1, -1, -1, 4, 0, -2, 0, 2, -2, 3, 0, -3], [2, -4, -2, 0, 2, -1, -6, -2, 3, -1, 1, -1, 0, -1, 2], [-6, -1, 2, 0, 1, 0, 1, 1, 1, -3, 3, 2, 2, 2, -2], [-7, -2, 0, -1, 4, -3, -5, -3, 3, 0, 1, -2, -2, -1, 2], [2, -1, 0, 3, -2, 0, 2, 2, 2, -4, 1, 1, -3, 2, -1], [-1, 0, -6, 3, 2, -2, -4, -5, 1, -1, -1, -3, -9, -4, 3], [-1, 4, 0, 1, -4, 1, 4, 2, -2, -2, 2, -1, 0, 3, -3], [3, 0, 0, 0, 1, 0, 0, 1, 1, 3, -1, 2, 5, 1, 2], [-2, -1, -4, 3, 0, -4, -3, -2, 0, -3, 2, -1, -4, -1, 2], [2, 2, -1, -1, -2, 2, 1, -1, -1, -1, -1, -1, -1, 0, -3], [3, 1, -3, -1, 2, 3, 4, 1, 0, 1, 1, 1, 0, -2, -1], [-2, -1, -1, -2, 2, 1, -4, 0, 0, 0, 2, 2, 1, 1, 0], [2, 1, 3, -1, 2, 2, 3, 1, 0, 3, 1, -1, 6, 2, 4], [-2, 2, 0, -3, 0, 6, 8, 1, -5, 3, -3, 0, 2, 4, 0], [-1, -2, 2, -3, 2, 2, 4, 3, -2, 5, -1, 1, 5, -1, 1], [2, 4, -3, 1, -2, 2, 1, 0, 2, -3, 1, 0, -1, 0, -2], [3, -3, 4, -1, 0, -2, -4, 1, 1, -1, -1, 3, 2, 1, 0], [7, 2, 2, -1, 2, 1, -2, -1, 1, -1, 0, -2, -2, 2, 0], [1, 3, -2, 0, 2, -5, -10, -5, 2, 1, 1, -1, -5, -5, 4], [2, 1, 1, -1, -4, -1, 4, 0, 0, -1, 1, -1, -2, 1, 1], [0, -1, -1, 1, -2, 1, -2, 1, 1, -1, -3, 2, -3, 4, -5], [0, -5, 3, 4, 2, -5, -9, -4, 8, -5, 1, -2, -7, -1, 2], [6, 2, 2, -1, 2, -5, -1, -1, 1, 0, 1, -3, 3, -2, 6], [-7, -4, 1, 0, -2, 2, 6, 3, -3, 0, 1, 1, 4, 4, -1], [-11, -1, -4, 3, 0, 3, 3, -2, -1, -2, 3, -3, -2, -1, 0], [3, -5, -2, 1, 2, 1, -1, 0, -3, -2, 1, 3, -5, 1, -4], [4, -2, 2, 1, 0, -4, -2, 0, 1, 1, 1, 1, 1, -1, -1], [-7, -2, 0, 2, -2, -1, 0, 1, 2, -1, 3, -1, -2, 2, 1], [2, -2, -1, 2, -2, 1, -2, 0, 2, -3, 2, 0, -3, 1, -4], [4, 0, 0, 0, -4, 2, 2, 5, -1, 0, 2, 1, -4, 7, -5], [7, 0, 5, -2, -6, 4, 10, 3, -7, 1, 1, 3, 5, 7, -6], [-3, 6, -3, -2, -2, -2, 0, -2, 2, 2, -3, 2, 5, -4, 4], [-7, 3, -5, 3, 4, -5, -8, -6, 2, -1, -1, -4, -6, -6, 6], [3, 0, -2, 2, 4, -5, -9, -3, 6, 0, 6, -1, -2, -5, 6], [-17, 0, -3, 1, 2, -5, -5, -5, 3, 2, -2, -3, -7, -4, 2], [-1, -2, -2, 3, -4, 0, 5, 3, -1, -5, 6, -1, -6, -1, -4], [-1, -5, -1, 0, -2, -4, 0, 1, -1, 1, 1, -1, 3, 3, 2], [-2, 2, 0, 0, 2, -1, -2, 0, 2, 2, 1, -3, 4, -3, 4], [-18, 2, 2, -1, 4, -3, -3, -3, -1, 1, 1, -1, 6, -6, 7], [-10, -2, 3, 1, 0, -2, -5, 0, -2, -1, 1, 2, -1, -1, -2], [7, -1, 5, -1, -2, 3, 3, -1, -3, -6, 0, -1, 2, 7, -3], [-4, 3, 3, -1, -2, 1, -2, 1, 3, -1, -3, 4, 2, 5, -2], [9, 0, 2, -3, 0, -4, -4, 0, 2, 1, -3, 0, 4, 3, 5], [0, -4, 5, 0, 0, 6, 2, 1, -3, -7, 5, 0, -1, 5, -7], [-5, -2, -1, 2, -2, -2, -2, -2, 2, -5, 1, -2, -5, -2, 1], [-1, 1, 1, 0, 2, -7, -6, -2, 4, 1, -2, -1, 2, -3, 8], [-2, 3, -2, -1, 0, 1, 2, 1, 4, 2, -2, -1, 1, -1, 0], [11, 3, -4, 0, -1, 0, 1, 1, 1, 0, -2, 4, 1, -1, -2], [3, -3, -1, 2, -1, 0, 0, -1, 3, -2, 0, -3, -3, -1, 3], [-11, 5, 0, 0, -1, -6, -11, -6, 3, -5, 1, 0, -8, -3, 0], [-5, 1, -5, 1, -1, -1, 1, 3, 1, 3, -2, 4, 0, -1, 0], [3, 4, 6, -2, 2, 1, -1, 1, -3, 0, 0, -1, 4, 0, 0], [-3, 0, 3, -2, -2, 6, 5, 4, -6, 0, 0, 0, 5, 6, -3], [1, 3, 2, 0, -3, 1, 5, 3, -3, -3, 2, 4, 4, 7, -7], [-10, -4, 5, -3, 2, -1, 3, 1, -1, 5, 2, 2, 9, -4, 3], [-6, -6, 1, 5, -4, 2, 4, 0, -2, -5, 4, -4, -5, 0, -2], [-3, 4, -2, 1, 0, 3, 5, -1, -5, -2, 3, -2, -6, 0, -4], [-9, -4, 1, -1, -2, 1, -1, 0, 0, 2, 0, 0, -2, 1, -2], [8, -3, 3, -3, -2, 3, 7, 4, -6, 4, 2, 1, 11, 6, -4], [-6, 0, 2, 2, 0, -3, -3, -1, 0, 2, 2, 2, 7, -7, 3], [-6, 0, 3, 1, 1, -3, -3, -4, 4, 1, 1, -5, -3, -3, 5], [-8, 5, 2, -2, -4, 6, 12, 7, -5, 6, -2, 3, 9, 5, -6], [2, -9, 3, 2, -4, 3, -1, 0, -2, -7, -3, 2, -8, 8, -9], [-3, -2, 1, 1, -2, 0, -1, -2, 2, -1, 1, -3, 2, -1, 4], [-1, -2, 2, 1, -4, 3, 3, 0, 0, -4, 5, 1, 2, 5, -7], [-1, -1, -5, -1, -2, 3, 3, 2, -1, 2, -4, 2, -5, 1, -5], [-7, 9, -5, 3, 0, 0, 0, -4, 0, -1, 2, -3, -5, -6, -3], [10, -2, -2, 3, 2, -4, -7, -4, 3, -3, 2, -1, -9, 1, -1], [-6, -6, 5, -1, 0, 4, 7, 3, -8, 0, 1, 3, 5, 4, -8], [-1, 0, -2, 2, -3, -3, 0, 1, 4, -1, 0, -1, -5, 2, 0], [0, 0, 3, -4, 2, 0, -4, -1, 3, 4, -3, -2, 4, 2, 4], [0, -5, 3, 0, -4, -4, 0, 4, -2, -2, 3, 3, 3, 3, -2], [-11, 2, -7, 1, 3, -2, -7, -7, 7, -4, -4, -2, -10, -7, 2], [-3, 6, -1, -1, 5, -2, -3, -3, 1, 4, 2, 0, 6, -3, 6], [0, -9, 3, 1, 2, 3, -1, 2, 0, -2, 2, 3, 5, 4, -2], [0, -3, 2, 2, -6, 3, 7, 5, -4, -3, 0, 0, -7, 5, -7], [-8, -2, 3, -3, 2, 1, 6, 3, -5, 7, -3, -2, 11, -4, 1], [2, 3, -1, -1, 6, -6, -5, 0, 5, 5, -3, 0, 4, -4, 7], [-1, -2, -4, 1, 4, -3, -9, -5, 3, 0, -1, 0, -6, -6, 6], [17, -3, -1, 1, -6, 3, 4, 2, -4, -5, 5, 0, -2, 5, -6], [-11, 6, -1, 0, 4, 4, 2, -2, -5, 5, -5, 0, 4, -2, -1], [-11, -4, 1, 1, 1, -2, -1, 2, -2, -1, 1, -4, -3, 2, 4], [2, 5, 0, 0, 0, -4, -6, -7, 5, 4, -4, -1, 4, -10, 11], [-3, -10, 1, 1, -2, 1, 5, 5, -4, -2, 4, 1, -2, 8, -9], [4, 9, 4, -1, 2, 1, -2, 3, -4, 2, -2, 3, 10, 1, 0], [3, -3, -2, 2, -2, 9, 9, 8, -2, 0, 2, 0, 5, 3, -6], [0, 1, -6, -2, 2, -8, -9, -7, 7, -1, -1, -5, -6, -6, 9], [-4, 6, -6, 2, 2, -2, -3, -6, 3, -1, 1, -4, -4, -4, 1], [-4, -4, 4, -2, 3, -4, -9, -3, 5, -1, -2, -3, -3, 1, 3], [-8, -3, 1, 2, -2, 3, 2, 5, 1, -6, 6, 1, -1, 3, -3], [-12, -3, 6, -1, -2, 2, -3, 1, 0, -1, 2, 2, 11, 2, 1], [-3, 4, -4, -2, 0, 1, 1, 0, 0, 2, 0, 4, 0, -6, 1], [7, -2, -1, 0, 2, 1, -3, -4, 0, -2, -3, -5, 0, 0, 0], [1, 3, -5, 1, 0, -3, -6, 2, 4, 2, -1, 2, -6, 1, -2], [-11, 6, -6, 2, -2, -1, 3, -1, -1, -6, 6, -1, -6, -2, -4], [-13, 3, 4, -5, -2, 1, 3, -1, -3, -2, -3, 2, 3, 8, -5], [3, -3, 2, 1, -3, 1, 6, 6, -6, 4, 0, 0, 9, 2, -1], [-2, 2, 2, 2, -2, -2, 6, 4, -4, 0, 6, 0, 2, 6, 0], [7, 1, 0, -2, -2, -1, 1, 1, -4, 0, -6, 1, 2, 0, -1], [-6, -9, -3, 1, -4, 2, 2, 3, 0, -1, 0, 3, -5, 0, -6], [3, 0, 0, 0, -2, 3, 2, -3, 1, -8, 1, 1, -3, 5, -5], [-4, 4, 4, -1, 2, -3, -8, 0, 4, -3, -4, 0, 0, -1, 2], [-12, -7, 3, -2, 0, 5, 3, 2, 0, -1, 1, 2, 8, 2, -3], [-5, -6, 0, 5, 4, -3, -4, -3, 2, -2, 0, -6, -3, -2, 4], [1, 0, 1, 2, -4, 1, 5, 4, -4, -6, 3, 1, -4, 10, -6], [-11, 1, -2, 0, 0, -3, -2, 4, 2, -3, 1, 0, -5, -1, 0], [5, 7, -3, 1, -1, -2, -5, -8, -2, -1, -3, 0, 2, -4, -1], [10, -2, 0, 1, 0, 0, -4, 1, -2, 0, 1, 0, 4, -2, 5], [-14, 0, -7, 0, 1, -1, -3, -5, 3, 1, -1, -2, -9, -4, 2], [-11, 8, 1, 2, 0, 1, 4, 4, 0, 2, -2, 1, 4, 0, 2], [-17, 8, 0, -5, 2, -4, -2, 0, 0, 1, -5, 0, -1, 0, 4], [3, -2, 10, 0, -1, 10, 10, 10, -6, 3, 1, 5, 9, 9, -7], [-9, 3, -8, 3, 2, 0, -2, -7, 7, -1, -3, -3, -10, -1, 0], [-7, -5, 3, 3, 3, 0, -3, 0, -1, -3, 0, 3, 4, -4, -1], [0, -3, 4, 0, -6, 1, -4, 1, -3, -5, -5, 2, -2, 10, -7], [-9, -1, -7, 3, -4, -1, -1, -3, -1, -5, 2, -3, -10, 0, -5], [6, 1, 1, 0, 4, -3, -2, 3, -3, 3, 4, -3, -1, 1, 1], [1, -1, 3, 1, 3, -3, -5, 3, 2, 6, -2, 2, 5, -3, 3], [16, 4, 3, -6, -4, 3, 4, 1, -1, -1, -4, 5, 9, 3, -5], [9, -4, 3, -2, 0, 3, 1, 3, 5, -1, -1, 2, -3, 5, -6], [-11, 0, 4, 3, 2, -1, -2, 3, 5, -1, 0, -2, -4, -1, 2], [7, -6, 0, 1, 0, 0, 2, 1, -8, -1, 3, -1, -2, 1, -5], [-1, 4, 3, -1, -2, 3, 6, 7, -6, 6, -3, 3, 5, 3, 4], [14, 8, -2, -2, 1, 2, -7, -3, 2, 5, -4, 1, 5, 0, 5], [-18, 1, -4, 2, -1, -4, -4, -6, 0, -7, 3, 0, -6, -2, -3], [11, 9, -4, 2, 1, -1, -4, -5, 1, 0, -1, -2, -1, -1, 2], [5, 3, -2, 1, 3, -4, -4, -2, 6, 0, 2, -2, -5, -12, 3], [-7, 3, -1, -3, 0, 1, 6, 6, -1, 3, 1, 2, 1, 4, 0], [8, -6, 1, 1, 3, -3, -3, 1, -1, -4, 4, -3, -2, 3, -1], [10, 6, -1, -3, 1, 7, 4, -2, 1, 4, -5, 2, 2, -4, 2], [-8, 2, 1, 1, 2, 8, 9, 4, -8, 5, 1, -2, 0, 3, -3], [-10, -3, -1, 4, -3, 3, -1, 4, 0, -2, 6, 6, -5, 0, -9], [5, 5, -5, 4, 0, -2, 5, 2, 3, 1, 2, -8, -4, -3, 4], [-6, 0, 3, 1, 5, -1, -6, -3, 3, 3, -2, 0, 11, -2, 6], [-7, -3, -5, 5, -2, 0, -4, -5, 5, -6, 0, 4, -8, -1, -5], [-5, -5, -1, -1, -4, -1, 3, 1, -1, 3, 0, 1, 0, 3, -5], [0, 3, 3, 2, -3, 7, 9, 13, -1, 2, 7, 4, 11, 7, -6], [-1, -4, -2, 6, 0, -1, 2, -3, -3, -6, -1, -5, -12, 2, -4], [-3, 5, -4, 1, -4, 3, 4, 0, -2, -8, 2, -3, -12, 6, -3], [4, 1, -3, 3, -2, 3, 0, -1, 2, 2, 5, 0, -4, -5, -5], [-10, -8, -4, 4, 2, -1, -7, 0, 7, -1, 0, 1, -6, 2, 1], [-5, 1, 0, 1, 1, 5, 0, -1, -3, -1, 3, -4, -4, 5, -1], [1, -1, -1, -2, 2, -1, 2, 6, -6, 6, 4, 1, 5, 5, 1], [0, 12, -6, 1, -2, -1, -5, -5, 3, 2, -1, 3, -1, -8, 0], [-1, 5, -1, -3, 6, -3, -14, -8, 5, -1, -7, 0, 0, -6, 6], [1, -5, 2, -3, 2, 1, 12, 7, -6, 7, 2, 0, 6, 0, 0], [-7, 11, -5, 0, -1, -7, -6, -4, 0, -3, 3, -5, -10, -4, 5], [-4, -5, 3, 0, 3, 2, 0, 6, -2, 0, 3, 2, 5, 4, -3], [-8, -5, 2, 3, 2, -4, 2, 0, -4, -5, 1, -3, -7, 2, 1], [5, 2, 0, -2, 3, -4, -11, -1, 5, 2, -2, 2, 8, -6, 11], [-17, 7, -1, 0, 3, -5, -11, -6, 6, 0, -1, -6, 1, -5, 8], [-15, 5, -1, 4, 6, -5, -4, -1, 1, 1, 6, -6, 2, -5, 5], [9, 4, -1, -2, 4, 0, -5, -2, 6, 1, 0, 0, -1, 0, 7], [3, 1, 5, -2, 0, 2, 4, 4, -6, -2, 9, 4, 9, 9, -3], [9, 13, -3, -4, -4, -2, 3, 1, 4, 2, -2, 1, -2, 2, 0], [-5, 3, -3, 3, 4, -6, -12, -8, 10, -3, -4, -3, -12, -3, 4], [7, -10, 9, 0, 0, 1, -3, 0, -8, -4, 1, -1, 2, 4, -4], [-14, -2, 2, -4, -2, 5, 13, 8, -9, 5, 2, 1, 5, 10, -5], [15, 2, 4, -1, -2, 0, 0, 6, -3, 2, -1, 4, 2, 2, -5], [-7, -1, 2, -2, -3, 2, 8, 1, -3, -5, -1, 0, -4, 10, -7], [-17, 2, -6, 2, 5, -7, -16, -8, 6, -2, -1, -5, -4, -7, 6], [-5, 1, 8, -2, -4, 4, 3, 6, -4, 4, -1, 3, 17, 4, 4], [1, -2, 1, 4, 2, 1, -2, -4, -6, -7, 0, -5, -5, 3, -3], [11, 1, 1, -4, 4, -3, -2, 1, 1, 8, -4, 0, 17, -7, 6], [25, 0, 1, -3, -2, 1, 7, 5, -5, 0, 0, 3, 4, 5, -7], [-9, 5, 3, -3, -6, 4, 11, 7, -5, -1, 3, 4, 2, 7, -1], [14, 2, -2, 0, 0, -4, 0, 1, 1, -2, 6, 1, -8, 1, -1], [-10, 7, -4, -4, 5, -3, 2, -1, 5, 4, -1, -1, 3, -3, 5], [3, 7, -3, 1, -4, 3, -2, 0, 2, -3, -3, 4, -6, 5, -2], [-15, 0, 2, -2, 4, 0, 2, 3, 3, -2, 6, 2, 0, -2, 2], [2, 4, 4, -3, 0, 5, 8, 3, -6, 5, 2, 1, 12, 2, -2], [-5, 1, -6, 5, 7, -10, -16, -9, 10, -2, 4, -1, -11, -9, 8], [1, 8, 4, -6, -3, 7, 12, 3, -7, 6, -2, 1, 10, 2, -3], [2, 4, -5, -1, 2, -3, -6, -8, 5, -4, 3, -7, -5, -6, 9], [13, 9, -2, -2, -2, -2, 5, 2, -2, 3, -3, 3, -2, 0, -1], [-6, 0, -5, 2, 2, -7, -11, -9, 6, -4, 1, -7, -12, -1, 4], [-8, -3, -1, 2, 6, -9, -12, -8, 9, 1, -6, -2, -1, -8, 8], [8, 7, 6, -2, -6, 7, 9, 5, -3, 1, -2, -2, 4, 10, -5], [-15, 7, -4, 2, -2, 6, 5, 1, 3, -1, 3, 0, -2, 2, 2], [1, 1, -4, 2, -4, 1, 1, -3, -3, 2, -2, -5, -6, -2, 4], [17, -3, 0, 3, -2, 2, 2, 0, 1, -6, -1, 0, -3, -1, -8], [21, -6, 1, 0, 1, 0, -1, 3, 1, 1, 2, 4, 3, 1, 1], [-5, -8, 1, 1, -4, 1, 10, 7, -4, -2, -1, 1, -7, 8, -11], [3, -5, 3, -3, 4, 4, 0, 6, 2, 9, -6, 5, 8, 2, -2], [-15, 5, -8, 1, 9, -7, -11, -7, 11, 4, -2, -2, -5, -10, 14], [8, -1, 7, -6, 2, 5, -2, 1, -2, 5, -8, 3, 5, 3, 4], [-5, 1, -4, 3, 2, -7, -17, -9, 7, 1, -1, -2, -2, -9, 6], [-6, 5, 1, 1, -1, -6, -8, -1, 3, 3, 2, 2, 4, -3, 1], [3, 1, -1, -3, 3, 0, -4, 1, -5, 7, -2, -1, 2, -8, 6], [-7, -3, -2, 1, 0, 2, 2, 5, -1, 0, 5, -1, -3, 0, 5], [9, 3, -2, -1, 0, 2, -1, -2, 2, 3, -4, 2, 0, -2, -5], [-3, 0, -7, 2, 8, -13, -13, -9, 6, -3, 1, -4, -15, -4, 8], [1, -4, 0, 0, 0, -1, -6, -5, 1, -2, -5, -5, 2, -6, 2], [10, -3, 4, 0, -2, 2, -3, 2, -4, 6, -3, 2, -1, -1, -5], [8, -2, 4, 1, 3, 0, -5, -3, 3, 0, 4, -1, 4, -1, 2], [4, -7, 0, -2, -4, 4, 0, -2, -6, -4, 4, 0, 5, 9, -11], [-1, 5, -4, 1, 3, -4, 4, 2, -2, 2, 3, -5, 1, -3, 5], [-3, 0, -6, 4, -4, 1, 0, 3, 2, -1, 1, 3, -10, 2, -3], [5, 1, -5, -3, 3, 0, 1, -8, 2, -6, -3, -2, -3, 0, 4], [-12, 3, -7, 2, 2, -3, 2, -3, 0, 0, 0, -3, -7, -4, -3], [5, 9, -4, -4, 4, -3, -9, -4, 4, 4, -8, 4, 7, -4, 2], [8, -7, 4, 1, -2, 4, 9, 4, 0, -7, 4, -1, 4, 3, -6], [9, -8, 0, -3, 3, -1, 7, 0, -6, 6, -2, -3, 12, -3, 2], [7, -11, 0, 6, -4, 3, 1, -1, 1, -9, 6, -1, -12, 3, -4], [-10, -2, 4, -2, -8, 12, 18, 12, -10, 3, 4, 6, 7, 13, -15], [16, -3, 1, 2, -6, -1, 13, 8, -4, -1, 7, 0, 0, 8, -11], [-20, 0, 2, 2, -6, 0, 5, -4, -2, -8, 3, -2, -4, 0, -8], [13, -1, 1, -1, 4, -7, -8, 0, 2, 2, 5, 2, 9, -2, 7], [13, 2, -11, 5, 0, -2, -2, -6, -1, 2, -2, -3, -7, 0, 2], [-4, 7, -4, -2, 2, -11, -10, -8, 7, 3, -7, -1, -5, -9, 12], [-1, -3, 13, -6, -2, 2, 2, -4, -2, -5, -3, 2, 1, 12, -1], [-11, -2, -4, 2, 0, 5, 10, 8, -4, 1, 1, 2, 4, 1, -7], [5, 0, 1, -2, 2, 3, 0, 4, 2, 4, 2, 7, 6, 7, -2], [9, -2, -2, -1, 1, 0, -12, -3, 3, -3, -5, 0, -3, 0, 0], [5, 4, -1, 1, 1, -3, -10, -5, 1, 7, -6, -1, -3, -4, -1], [-6, -5, -4, -2, 0, 5, 5, 4, -6, 9, -2, 5, 9, -4, 2], [10, 8, -2, -2, 0, -3, -3, -3, 1, 2, 0, -2, -2, -3, 3], [9, 2, 0, -1, -3, -4, -5, -7, 4, -2, -3, -1, 0, -2, 7], [-7, -2, -1, 0, 3, -2, 6, 7, -7, 5, 2, -5, 5, 1, 3], [-20, 3, -5, 2, 2, -5, 0, -3, 5, 1, -4, -3, -5, -3, -3], [0, 0, 6, -3, -7, 6, 8, 4, -4, 3, 5, 4, 7, 10, -10], [-3, -4, 8, -7, 4, -4, 2, 1, -1, 7, 3, 1, 11, 0, 3], [-1, 7, -8, -2, 12, -8, -13, -6, 9, 7, -3, -1, 0, -15, 13], [12, -1, -1, -2, 4, -6, -5, -3, -3, 3, 2, 0, -4, -8, 4], [-7, -8, -1, 3, -6, -4, 0, -1, 3, -7, 2, -2, -13, 6, -2], [-1, -14, -6, 3, -1, 3, -3, -3, 1, -5, -1, 3, -9, 0, -4], [25, -2, 3, -3, -6, 6, -2, 0, -4, 2, -2, 5, 7, 4, 1], [-13, 2, 1, 0, -2, 7, 13, 9, -7, 3, -3, 2, 3, 5, -8], [5, -13, 10, 2, 0, -2, -9, -3, 3, -8, 7, -2, -7, 5, -3], [-3, 0, -2, -1, 2, -12, -11, -6, 8, -2, -2, -4, -4, -7, 13], [17, 8, 1, -4, -2, 8, 5, 9, -6, 2, 2, 3, 13, 7, -1], [13, 7, -7, 5, 2, -10, -19, -14, 10, -1, -3, -3, -7, -12, 11], [-6, -1, 2, -3, 0, 5, 13, 0, -4, -1, -3, -2, -2, 7, -4], [5, 11, -2, -7, 4, -7, -13, -8, 6, 6, -11, 1, 10, -7, 15], [8, 4, -5, 0, 2, -6, -9, 0, 6, 9, -6, -3, -1, -7, 14], [20, -2, 6, 1, -3, 5, 9, 7, -5, 0, 0, 3, 4, 8, -2], [2, 4, -8, 8, -2, -1, 2, -3, 3, 1, 5, -8, -5, -7, 2], [-12, -2, -4, 5, -5, 5, 6, 2, 0, -1, 5, 2, -7, -2, 0], [-13, -9, -1, 1, -3, 5, 10, 12, 0, 1, 5, -1, -2, 11, -7], [-2, -4, -1, 4, -1, 2, 7, 3, -3, 3, 2, -3, 1, -1, 0], [4, 7, -6, 2, -3, -8, -2, -7, 3, -1, 1, -1, -4, -6, 4], [20, -9, -1, 0, 3, -4, 3, 0, 2, 3, -3, -5, 4, 2, 6], [3, -12, -1, -1, -4, 11, 6, 7, -7, 0, -1, 3, 5, 4, -12], [8, -6, 3, -1, 0, 15, 17, 5, -6, 1, 0, 0, 5, 9, -11], [16, -7, 4, 3, -2, 6, 0, -2, 2, -8, 1, 7, -4, 2, -10], [-8, -4, -4, 3, -2, -3, -9, -3, -2, -3, 1, 5, -8, -1, -4], [18, -4, 3, -3, 4, 9, 6, 7, -6, 3, 1, -2, 5, 3, 1], [1, -6, 7, 0, 0, 12, 13, 9, -9, 1, 6, 1, 13, 13, -8], [-11, -16, 1, 1, -7, 6, 6, 3, -5, 0, 2, 1, 0, 5, -12], [-7, 3, 3, 0, 2, 5, -5, -5, -3, -3, -3, -4, -2, 0, 3], [1, 2, -8, 3, 5, -3, -2, -5, 5, 5, -6, -7, -3, -10, 14], [-9, -6, 0, 1, 3, 0, 9, 3, -4, 3, 3, -5, 7, -3, -2], [20, 8, 10, -7, -2, -1, 9, 8, -8, 9, 1, 6, 23, 0, 3], [12, 7, 0, 1, -4, 5, 8, 8, -8, -2, 4, 0, 1, 0, -11], [-6, -3, 5, 0, 0, -5, 4, 3, -2, -4, 2, -5, -2, 1, 2], [1, -1, 5, 0, -4, 5, -4, 7, 2, -1, 4, 2, 9, 6, -3], [11, -1, -6, 4, 0, -4, -1, -2, 5, -2, 1, -5, -10, 4, 6], [20, 7, 2, -3, 0, 8, 2, 2, 0, 4, -1, 1, 7, 2, 1], [-8, -9, 6, -6, 0, 12, 15, 2, -10, 6, -3, -2, 9, 5, -7], [2, -1, 2, 1, -8, 3, 5, 2, -2, -7, 1, 4, 0, 4, -8], [-9, 3, -8, 1, 1, 0, 6, 1, 1, 5, -2, 5, 10, -3, -7], [5, 8, 0, 1, 7, -3, -5, -4, 8, -4, -2, -5, -6, -6, 10], [-23, 3, 2, -1, 2, -2, 1, 4, 1, 1, 2, 2, 1, 2, -1], [19, 1, -2, -2, 6, -9, -15, -7, 5, 0, -4, 1, -11, -3, 3], [20, 4, -12, 5, 6, -10, -18, -16, 7, -3, -3, -7, -10, -18, 13], [-10, 15, 0, -3, 10, -13, -13, -6, 10, 8, -5, -2, 5, -16, 23], [1, 7, 0, -5, -6, 3, 10, 8, -2, 2, 0, 5, 9, 2, -4], [-4, 4, 3, 2, 0, 3, 3, 5, -2, -3, 1, 3, -2, 6, -9], [-1, -12, 7, -1, 0, 4, 2, 1, 0, 6, -4, -4, 8, 0, 3], [0, 2, -3, 1, 4, -4, -3, 0, 8, 2, -1, -2, 0, -3, 7], [7, 4, -3, -4, -1, 5, 6, 8, -4, 4, 0, 2, 10, 6, -5], [11, 5, 0, -1, -3, 9, 7, 8, -10, 2, 1, 6, 7, 2, -7], [11, -8, -3, -2, 6, -2, -3, -5, 2, -3, -6, -1, 0, -11, 7], [28, 2, -1, 3, -6, 8, 5, 1, -1, 3, -1, 3, 5, 0, -1], [7, 0, 8, -4, -2, -6, -11, -1, 9, -3, -1, 10, 11, 1, 3], [-2, 5, 6, -2, -6, 5, 16, 13, -3, 3, 5, 8, 12, 10, -7], [7, 5, 9, -7, -4, 9, 7, 7, -1, 1, -6, 7, 6, 9, -9], [1, -11, -7, 6, 4, -5, -16, -12, 4, -7, 0, -7, -7, -8, 5], [24, 5, 1, 0, 4, -4, -4, -3, -1, -1, -1, -2, 5, -5, 1], [-15, 8, -9, 0, 8, -10, -2, -5, 5, -2, 3, -3, -5, -4, 6], [33, -8, 2, 4, -11, 7, 11, 10, -6, -3, 4, 3, -5, 9, -11], [1, -1, 1, -2, -3, -5, 1, -3, -5, -4, 1, -5, -3, 0, -1], [19, -6, 10, -2, -8, 5, 4, 9, -3, -2, 3, 9, 6, 12, -6], [16, -4, 3, -1, -3, -1, 10, 7, -9, 5, 6, -4, -1, 8, -4], [12, 6, -2, 1, -2, 9, 6, 2, -1, 1, -8, 0, 0, 9, -7], [-2, 4, 4, -3, -6, 9, 18, 5, -6, -1, 0, -3, -2, 11, -2], [-8, 10, -6, -3, 0, -3, 10, 2, 1, 4, 0, 2, 4, -2, -2], [1, -13, -2, 6, 0, 0, 3, -4, 4, -10, 3, -3, -11, -3, -2], [2, 5, -2, 0, 8, -9, -13, -7, 7, 4, -2, 2, 7, -11, 12], [-7, 0, 5, -5, 2, 4, -2, -6, 4, 8, -8, -5, 3, 0, 3], [7, 4, 3, -6, 4, -5, 0, -3, 5, 7, -6, 0, 7, -7, 10], [8, -1, 1, 3, 8, -9, -10, 0, 4, -6, 5, -1, -5, 0, 0], [-5, -3, 8, 0, 0, -1, -6, -1, 0, 0, -3, 1, -6, -5, 4], [-5, 1, 4, 4, -4, 4, 15, 11, -3, 4, 3, -4, 2, 2, -2], [12, -5, 6, 1, -2, -2, -9, -6, 4, -11, 0, -3, -2, -3, -2], [-1, 9, 5, -11, 4, 0, 6, 2, -4, 10, -6, -3, 17, 1, 11], [20, 7, 4, -5, -2, 5, 0, 1, 3, 6, -10, 3, 5, 0, -4], [9, 1, 0, -3, 2, -2, 4, 6, -3, 6, 1, 0, 13, 1, -2], [-5, -7, -2, 2, 2, 0, 7, 7, 1, 2, 3, -4, -3, 5, -5], [-8, 6, 2, 6, -10, 7, 10, 4, -8, -7, 1, 5, -9, 13, -13], [-10, -3, -4, 5, -2, -3, -5, -7, 3, -4, -5, -1, -9, -1, 0], [0, -6, 6, 2, -5, 3, -10, -1, -1, -11, 5, -5, -3, 3, -1], [20, -1, 0, 4, -2, 2, 12, 4, -10, 1, 4, -2, 0, 4, -2], [-4, -4, 3, 5, 0, 2, 5, 4, -2, 1, 5, 8, 5, -6, -2], [1, -5, -4, 5, -1, 0, 6, -5, -3, -5, 0, -7, -16, 3, -1], [-2, -13, 0, 3, 5, -4, -2, 1, -1, 4, 3, 1, -1, -4, -3], [23, -5, 0, 1, -1, -1, -8, 2, 2, -5, -1, 3, -6, 1, -4], [-13, -5, 7, -3, -4, 6, 12, 8, -7, 0, -2, -3, 6, 5, -9], [15, 4, -11, -2, 5, -3, -3, -8, 10, 0, -1, -4, -2, -6, 7], [12, -13, 3, 1, 0, 3, 11, 0, -2, -5, 6, 1, -2, 8, -11], [36, 10, 0, -4, -4, 1, 0, -1, -3, 2, -7, 2, 11, -1, 4], [25, 9, 0, -3, -10, 0, 6, 1, -4, 2, -5, 5, 9, 1, -3], [12, 7, -3, 2, -4, 4, 3, -1, -3, -7, 0, -4, -4, 8, 0], [-29, 1, -2, -1, -4, 2, 10, 8, -2, 6, -1, 4, 9, 5, -2], [-1, -6, -8, 5, 6, -2, -16, -7, 9, -4, 1, -3, -13, -7, 1], [-11, -2, -5, 6, -5, 3, 7, 5, -8, 1, 3, 3, -9, 2, -11], [-7, 2, 2, 2, 2, -2, -9, -3, 7, 2, 7, -6, 6, -8, 16], [25, -4, -4, 4, 0, -1, -3, -2, -2, 0, -6, -2, -3, 1, -4], [-3, -2, -1, -4, -3, -5, -10, -3, 5, 2, -4, -1, -6, 7, 2], [-9, -2, -1, 4, 8, -7, -11, -3, 6, -6, 1, -6, -10, -5, 3], [-2, -1, 2, -1, -3, 3, -1, 6, -9, 1, 7, 5, 4, 0, -5], [-22, 9, 1, -2, 7, -10, -12, -9, 3, 2, 0, -6, 3, -17, 22], [10, 14, -4, -2, 6, -3, 0, -6, 7, 1, 1, -7, -1, -14, 13], [12, 1, -4, 1, 2, -9, -13, -8, 10, -10, -5, -6, -19, 4, 5], [14, 0, 2, 3, 1, 2, 4, -1, -5, 2, 5, -5, -6, -3, 4], [-30, -5, -7, 8, 4, 1, -2, -1, -1, 1, -2, -5, -8, -6, -2]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_8034_a_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_8034_2_a_bc();".
// 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_8034_2_a_bc(:prec:=15)
    chi := MakeCharacter_8034_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_8034_2_a_bc();".
// 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_8034_2_a_bc( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_8034_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<5,R![-2048, -17600, 11840, 65434, -21747, -71361, 16428, 33191, -5112, -7580, 707, 872, -44, -48, 1, 1]>,<7,R![211634, -81965, -603653, 198660, 590741, -164378, -255993, 63048, 53846, -12093, -5625, 1187, 275, -56, -5, 1]>],Snew);
    return Vf;
end function;