
// Make newform 2116.4.a.h in Magma, downloaded from the LMFDB on 30 May 2026.
// To make the character of type GrpDrchElt, type "MakeCharacter_2116_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_2116_4_a_h();".
// 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_2116_4_a_h();".
// 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 := [540816101604, 0, -1555268628684, 0, 805244264149, 0, -183331346380, 0, 22485156097, 0, -1612065448, 0, 70316500, 0, -1885780, 0, 30325, 0, -268, 0, 1];
        Kf := NumberField(Polynomial([elt : elt in poly]));
        AssignNames(~Kf, ["nu"]);
    end if;
    Rf_num := [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1205226941410154146439577708179846100, 0, 6795775312284194634574637997515019438, 0, -4395542979329353583232927542208748295, 0, 850206870107424961445830100490127546, 0, -72101283539918087448541805405316540, 0, 3155301167892251047991088981221360, 0, -75897368184336229678969220724868, 0, 994278327364416437806697944566, 0, -6407683630266127617774618371, 0, 14538033778267359059300710, 0], [-8312999998288607167083750, 0, 20294910201571610238416913, 0, -8638432502880151244812678, 0, 1515068802915476421740001, 0, -135429077099839617818280, 0, 6835990074848305383808, 0, -203174665978854328494, 0, 3524449601279257329, 0, -33000566221068454, 0, 128821430608881, 0], [-75907337779106344979015826671657835678, 0, 515715185274715969457971579625738593989, 0, -164024395072032729875030709010701645534, 0, 17973211665785099365481113734431873981, 0, -745933091032863636417845887976281800, 0, -1871214949812695530806658573268448, 0, 1138581086094030842634996920901178, 0, -37121669663720008704116485506939, 0, 497917270504520701828374329922, 0, -2485386861805287506940041299, 0], [-276174563059258700291145754827750217206, 0, 676157843493776043832708649643623920089, 0, -258390204093947734780599906290416329998, 0, 41302353964882512853136625434910173085, 0, -3443485255554535502064403949681089992, 0, 164906465327238273318435958292941136, 0, -4707577635915919452016573266490782, 0, 79169298481877973172530550503177, 0, -723938058189770065595869309358, 0, 2775980111234908400987350125, 0], [-543381476236647531145014648219285464334, 0, 1409710827032387738455998293680392532317, 0, -565201893723093201000615576920701482598, 0, 94199159718291953765529902478119735869, 0, -8086473454573431718515204072370880360, 0, 394236950628594664882560192567319488, 0, -11361080144803840242476583112867062, 0, 191733102278791741556303975029117, 0, -1752069758082293289508618948838, 0, 6694522538740839431592042701, 0], [2363457791787103085570249578518981485718, 0, -6409439916659498661638556667769692742985, 0, 2735930367188517845989777976198001642662, 0, -477871397882999208545272358808260442481, 0, 42624832511671775949155449200959330856, 0, -2149011195206186200163647326928580192, 0, 63841158090837441028065090388941214, 0, -1107954654449263973710647037764105, 0, 10390634070875754533833996379462, 0, -40672792997334871068891368641, 0], [216987422338313749599849448484583050010, 0, -1148690281939793735351968217264582966991, 0, 467042157221824248119866338270488305942, 0, -77717398856468262838665236789843264347, 0, 6840180519269149531802331244259453832, 0, -349380727253269983171855486962997808, 0, 10655824696774903630028307093957058, 0, -190679495506388704858840784291679, 0, 1842718532555310670529454216646, 0, -7411496119648680687278354059, 0], [611537636534674607469804432732046187886, 0, -2009350403315677899064881392275769954109, 0, 850886371295011330952452696543057622470, 0, -146163401810011831748144044931863729501, 0, 12709019933161170598280582308911794344, 0, -621459054768421948135596413914666880, 0, 17882386760019128906082792900448262, 0, -300900298367126473248151757836733, 0, 2741957732935749255318664721478, 0, -10457029237790339069973513501, 0], [0, 13943491950093569074903126479055888343610, 0, -12262430528707011196476547934788686213311, 0, 3275471180207132895472052867634161038722, 0, -445645493556732041441746062970847678999, 0, 34822644660767212346701508582567573368, 0, -1628459557551797719591677026424395936, 0, 46142779825250227380173286677337490, 0, -775096865590405222738053716489535, 0, 7095856444859106085935080505538, 0, -27263277454994747020407330951], [-569566474473147339084023455630412485878, 0, 1625711771724851125622657809253391015021, 0, -680189463286449851987151666152960363332, 0, 116853976187040874537574701711264512587, 0, -10225021141539945225320814580905292512, 0, 504811272162362305464910501051386424, 0, -14677254199100550875567162103747446, 0, 249353156731068877351306175620821, 0, -2290642795509997084083295075468, 0, 8790516571340932892250777731, 0], [0, 11912161965975206414434366511362244837646, 0, 4920269417113461378964633557629353722395, 0, -3634052795361114807925185705499546553102, 0, 714210603105409271993833933374508148983, 0, -66349564434397957693897703184657873352, 0, 3398011412782735771215234188484252208, 0, -101501285396591892008616757408347066, 0, 1762451920723093403529060284074443, 0, -16490292467035402822423161193854, 0, 64282370956830282770815320311], [0, 11918783733728848828562571617302685715678, 0, -45926832393925257338201110814160596136325, 0, 19227247025901562577827147730660454378838, 0, -3254287034959433224512604215841659251837, 0, 280562189419981891395334043440397062504, 0, -13671459604479696280397349353785823008, 0, 393006123093907603123126863653409446, 0, -6611328490780880780985406630715653, 0, 60215992661369278865116529511958, 0, -229369397367230425709274826637], [0, 36515712390825503697820651360607364424062, 0, -35267535153514053731924427164283160239069, 0, 12148016313462517945767494519127505484298, 0, -1944247530626690128507256962522374754609, 0, 162747294554629440765925760179392479544, 0, -7723947691346146575644568525029987088, 0, 215997429452914365052114276426491862, 0, -3530148198221284848205838000616525, 0, 31216908397567250865187535900154, 0, -115451811949342810914559604593], [0, -2652510613709841307931597472088399265802, 0, 16239152637226445367798000435154275954751, 0, -6763390029219693249804882008440883870890, 0, 1124497364981790010269954299610427312507, 0, -95767508466017181756391324779295757128, 0, 4633848253537170307911407041674737584, 0, -132691588572817648472027044913143330, 0, 2227431965501602010739773178877279, 0, -20261810676934919633621368915402, 0, 77111451076449130171441425019], [0, -20067542356993529728363610213041300288074, 0, -42150208361927809303794174718187674138633, 0, 21752137477179040974098075000160316736766, 0, -4011194539406122814904223958998975506449, 0, 365290232798355501529920573289952291208, 0, -18565940494008044304600455043414703712, 0, 552779836187077910082815820387465310, 0, -9585047241585620155890529278905609, 0, 89643329967916339142687828540158, 0, -349503002610528644101035480609], [0, 1951122070796562967931633340425801977554, 0, -32231289385091980642111484179216706368763, 0, 14892348327404501087877982822789157062654, 0, -2635327724363879118312759959867273031767, 0, 233652262485524017901901148283788751016, 0, -11629260618990617450465006404103111792, 0, 340217444492238224079239467810175322, 0, -5810634059015276632321407877555531, 0, 53631913773359867079334820610414, 0, -206706764784578779352634493207], [0, -24548122361468220078016931061073926647556, 0, 53050268121282104764999704244685023684386, 0, -20272724736218578294315335246269117652121, 0, 3285958141786621672244990557582361145167, 0, -278601638579507002832905418872505638992, 0, 13565879239577675526550182246431252836, 0, -393218733525294315551636874890840720, 0, 6701938190415737375664633686400858, 0, -61982748166285988809258239239989, 0, 239915775183745880440895568371], [0, 74010506913002301728763241964459127551214, 0, -126406616853861788697774352415182612115933, 0, 50279894457151425933707108391546545168446, 0, -8568152275149531376204578667720341740901, 0, 751439322222882683226517017645675653576, 0, -37307844962427851162149955961355405216, 0, 1091945249484176725070586571883183766, 0, -18675402234246708809513063055767837, 0, 172633993804204161902795939007838, 0, -666231012462674605676919675381], [0, -513608643968424079088552578452116006143050, 0, 1198679718409760929252507943854855297955031, 0, -465549731568987254138234310730992540876866, 0, 76005650782977745540105016931313591835503, 0, -6451541473522835901394588498444630591032, 0, 313075364318034679877223990191189899808, 0, -9018397737904702692782338204714156066, 0, 152524130731875233581388554733673111, 0, -1398878730572798710480872792479042, 0, 5369100480362808381595287533023]];
    Rf_basisdens := [1, 94288605867981110157164945909488332, 557699844788193842867232, 5783034493236174756306116682448617696, 2891517246618087378153058341224308848, 5783034493236174756306116682448617696, 17349103479708524268918350047345853088, 2891517246618087378153058341224308848, 2891517246618087378153058341224308848, 844323036012481514420693035637498183616, 1445758623309043689076529170612154424, 422161518006240757210346517818749091808, 844323036012481514420693035637498183616, 422161518006240757210346517818749091808, 211080759003120378605173258909374545904, 844323036012481514420693035637498183616, 422161518006240757210346517818749091808, 158310569252340283953879944182030909428, 422161518006240757210346517818749091808, 2532969108037444543262079106912494550848];
    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_2116_a();"
function MakeCharacter_2116_a()
    N := 2116;
    order := 1;
    char_gens := [1059, 5];
    v := [1, 1];
    // chi(gens[i]) = zeta^v[i]
    assert UnitGenerators(DirichletGroup(N)) eq char_gens;
    F := CyclotomicField(order);
    chi := DirichletCharacterFromValuesOnUnitGenerators(DirichletGroup(N,F),[F|F.1^e:e in v]);
    return MinimalBaseRingCharacter(chi);
end function;

function MakeCharacter_2116_a_Hecke( : Kf := Kf)
    return MakeCharacter_2116_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 := 4;
    raw_aps := [[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, 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, 1, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, -1, 0, 0, 0, -1], [-4, 0, 2, -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, -1, -2, -1, 0, -1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, -1, 1, -2, 0, -1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-63, 0, -14, -1, -4, -5, -4, 1, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 2, 1, 1, 5, -3, -1, 1, -1, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -18, 0, 1, 6, 6, -4, -2, -5, 0, -1, 2], [-56, -4, 0, 2, 4, -15, -1, 3, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 0, -18, -7, 3, -4, -1, -8, 3, 2, -2], [50, 2, -46, 6, -5, -25, 5, -3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 31, 0, -11, -22, -17, -3, -11, 17, -2, 4, 2], [-75, -2, -51, -11, -4, -43, 1, -1, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, -30, 9, 22, -4, 48, 0, -8, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, -10, 30, 14, -1, -2, -7, 0, 1, 9], [23, -5, 34, -3, 38, -23, 10, 4, 0, 0, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-64, 5, 125, -6, -38, -29, 8, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -42, 0, -16, 37, -20, -37, -5, -92, 8, 1, -4], [0, 0, 0, 0, 0, 0, 0, 0, 0, -67, 0, 12, 32, 8, -20, -6, -7, 2, -5, -6], [0, 0, 0, 0, 0, 0, 0, 0, 0, 37, 0, -15, 32, 6, -20, 6, -46, -8, -16, 9], [0, 0, 0, 0, 0, 0, 0, 0, 0, -83, 0, -19, 10, 4, -26, 12, -16, -6, -14, -19], [-20, -8, -20, 9, -82, -45, -12, -4, 4, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 72, 0, 30, 39, 5, 33, 28, 27, -17, 0, 13], [0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, -10, -101, -9, 91, 1, 75, -5, 28, -14], [0, 0, 0, 0, 0, 0, 0, 0, 0, -37, 0, -28, 88, -17, -15, 7, -34, -18, -3, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 25, 0, 27, 98, -3, -11, 12, -34, 7, -11, -14], [115, -21, 416, 13, 95, 36, 11, 7, -10, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-448, 17, 84, 7, -18, -42, 23, -9, 8, 0, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 58, 0, 8, -40, -9, 125, 35, 81, 15, -1, 0], [99, 4, -189, -25, -21, -86, 16, 0, -7, 0, -33, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 83, 0, -87, -54, 10, 71, 19, 104, 18, 15, -2], [-339, -25, -709, 48, 3, -22, 17, 29, 7, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -54, 0, -71, -126, 50, 38, 44, -74, -32, 14, -18], [-47, 11, -212, -45, 60, -103, -6, -28, 6, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-785, -3, -120, -13, -35, -112, -23, -1, -22, 0, -21, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-277, 12, 690, -9, 24, -117, -20, -47, -6, 0, 19, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-778, -36, -169, -11, 60, 83, 22, 12, 9, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 67, 0, 96, 30, -1, 31, 15, -23, 22, -2, 12], [0, 0, 0, 0, 0, 0, 0, 0, 0, -77, 0, 36, -157, 72, -286, -85, 10, 4, 5, 21], [314, 28, 637, -12, -36, 12, 0, 42, 24, 0, -14, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-301, 18, -821, -7, 91, 96, 10, 1, -9, 0, -22, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -54, 0, 66, -263, -89, 20, 30, -65, -23, -29, 61], [-1542, -31, 481, 6, -45, -101, -70, -44, 5, 0, -11, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1910, -32, 80, 22, -129, 95, 5, 51, 16, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -130, 0, 122, 24, 9, 158, -20, 46, 11, -43, -37], [0, 0, 0, 0, 0, 0, 0, 0, 0, 120, 0, -55, -128, 6, 264, -38, 1, -12, -51, -52], [-1430, 2, 708, 38, 4, 82, 8, 29, -27, 0, 23, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2533, 13, 155, 88, 202, 171, -10, -32, -5, 0, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -216, 0, -94, -40, 88, 72, -3, -2, 19, -48, -12], [0, 0, 0, 0, 0, 0, 0, 0, 0, 267, 0, 100, 420, 34, 152, 67, 351, 48, -63, -23], [-648, -13, 1084, 36, 346, 177, 12, 39, -17, 0, 71, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 61, 0, -26, 154, -31, 298, -95, 347, 27, -46, -64], [-2671, -6, 835, -32, 109, 173, 40, -19, 8, 0, -52, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1376, 78, 144, -8, -115, 335, 11, 1, -12, 0, -61, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-91, -10, -1550, 28, 92, 694, 10, 41, 29, 0, -45, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -72, 0, -26, 41, -121, -253, 137, -112, 10, 89, 31], [0, 0, 0, 0, 0, 0, 0, 0, 0, -454, 0, 202, 62, -63, -503, 13, -162, -15, 20, 14], [0, 0, 0, 0, 0, 0, 0, 0, 0, 277, 0, -177, 24, 2, 129, -183, 384, -50, 73, -50], [-3667, -47, -459, 10, -92, 14, 20, 66, 25, 0, 79, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-282, 6, 2081, 127, -308, 476, -8, 92, 7, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 385, 0, -111, 104, 118, -492, 14, -183, 31, -36, 32], [-1248, 72, -379, 143, 1, 456, 82, -32, -18, 0, 67, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2425, -56, 541, -89, 299, 378, -134, -52, -21, 0, 34, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -41, 0, -323, -197, 93, 135, 147, -146, -16, -5, 28], [70, 78, -674, 34, 142, 167, 10, 28, -14, 0, -103, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1251, 30, 688, -62, 348, 272, 2, -99, 13, 0, -41, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3401, 42, -575, 80, -128, 142, 150, -21, 13, 0, -65, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 32, 488, 166, -39, -74, 254, -26, 95, 66], [0, 0, 0, 0, 0, 0, 0, 0, 0, 169, 0, -44, -446, -6, 196, 42, -138, 122, -117, -47], [0, 0, 0, 0, 0, 0, 0, 0, 0, -256, 0, -157, -330, 112, -588, -130, -213, -28, -81, 16], [0, 0, 0, 0, 0, 0, 0, 0, 0, -33, 0, 388, 62, 17, -103, 215, -114, 59, 35, 159], [0, 0, 0, 0, 0, 0, 0, 0, 0, 60, 0, 138, -969, -81, 21, -108, -107, 21, 106, 97], [0, 0, 0, 0, 0, 0, 0, 0, 0, -411, 0, 166, 744, 141, 203, -77, 213, 20, -156, 84], [-652, 88, -1926, 29, 26, 407, -28, -14, -32, 0, 140, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 304, 0, 114, 391, -75, 229, -20, 573, 46, 13, 150], [-3456, -37, 853, 26, -53, 507, 91, 102, -14, 0, -126, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 433, 0, 222, 249, -76, 178, 134, 345, -42, -131, 83], [0, 0, 0, 0, 0, 0, 0, 0, 0, -409, 0, 32, -320, -160, -599, 55, -442, -38, 93, 26], [0, 0, 0, 0, 0, 0, 0, 0, 0, -476, 0, 62, -224, 167, -731, -77, -727, 29, 26, 31], [0, 0, 0, 0, 0, 0, 0, 0, 0, -549, 0, -415, -141, 19, 181, 163, -251, -67, -31, 157], [1438, -22, -2337, -41, 361, 11, -85, -121, -11, 0, 128, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1462, -20, 651, 131, -130, -217, -44, 100, 5, 0, 61, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1084, -89, 1623, 138, 325, -172, -82, 41, -14, 0, 72, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 754, 0, -172, -3, 207, -302, 198, -332, 43, 9, -69], [-1654, 108, -544, -209, -54, 567, 88, 2, -7, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [628, 58, 1230, 16, -160, -654, 52, 22, 46, 0, -101, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -33, 0, -56, 457, 98, -259, -144, -102, -162, -118, -70], [0, 0, 0, 0, 0, 0, 0, 0, 0, -269, 0, -104, 330, -42, 213, 162, 248, -190, 46, -3], [-1198, -174, 2227, -171, -62, -312, 132, 78, 57, 0, 157, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4963, 13, -318, -245, -47, -256, -259, -133, -26, 0, -156, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-673, 1, -1671, 68, -675, -3, -13, 83, -1, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -68, 0, 610, -279, -229, -348, 156, -391, 249, -263, 55], [-4957, 44, 1171, -191, -289, 1156, 92, 117, -17, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 97, 0, 409, 1034, -8, 780, 373, 829, -120, 138, 24], [0, 0, 0, 0, 0, 0, 0, 0, 0, -798, 0, 56, 56, -491, -417, -118, -1263, -91, 132, 12], [-593, 76, -303, -13, 513, -340, -244, -223, -173, 0, 118, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1753, 25, -1620, 177, -287, -1062, -239, -77, -12, 0, 98, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1047, 0, 121, 202, -70, -219, -241, -218, -64, 139, -42], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1129, 0, -414, -381, 0, -515, -385, 175, -100, -64, 80], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1069, 0, 497, 752, 398, 89, 86, -199, -9, 124, -54], [0, 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, 70, -280, 43, -502, -141, 902, 181, -125, 74], [503, -8, 1180, 118, -164, 67, 69, -333, 64, 0, 90, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2071, -126, -1936, -320, 724, 277, -97, -123, 78, 0, -79, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3322, -139, -139, -102, -571, -923, -123, 16, -6, 0, 180, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-305, -55, 1444, -75, -714, -129, -50, -142, 38, 0, 94, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1273, -35, -1401, 450, -452, 924, 55, 123, 4, 0, 116, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1598, -96, 1669, 61, -138, 372, -26, 256, 67, 0, -147, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 129, 0, -113, 156, -342, 303, -379, 1044, 176, -209, -248], [0, 0, 0, 0, 0, 0, 0, 0, 0, -439, 0, 841, 365, 85, 546, 220, 85, 130, -207, -115], [0, 0, 0, 0, 0, 0, 0, 0, 0, 710, 0, 822, -723, -669, -104, 335, 737, 105, -13, 184], [0, 0, 0, 0, 0, 0, 0, 0, 0, -620, 0, 118, -238, 213, -810, 401, -905, 175, -387, 67], [0, 0, 0, 0, 0, 0, 0, 0, 0, 347, 0, 475, -23, -149, -753, 53, -1134, -276, 45, 290], [0, 0, 0, 0, 0, 0, 0, 0, 0, -40, 0, 256, 758, 255, -80, 36, 305, -163, -129, 576], [2879, 7, 395, -36, -661, 100, 7, 111, -117, 0, -106, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-5059, -104, -3977, 167, -131, 296, 206, -41, -58, 0, 176, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 291, 0, 18, -639, 329, -327, -90, 964, 39, -271, -81], [0, 0, 0, 0, 0, 0, 0, 0, 0, 379, 0, 267, 268, -304, 619, -445, -290, 12, 11, -176], [1022, -187, -916, 8, -176, -24, 211, 134, 27, 0, -287, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -230, 0, 192, -1048, 60, -1594, 14, -1491, 140, -83, -54], [10221, 82, -286, 18, 186, -59, 347, -71, -116, 0, 131, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3084, 140, 1671, 511, -717, -113, -333, 19, -65, 0, 69, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1363, 0, 922, 432, -223, -135, 231, 739, 182, 28, 292], [0, 0, 0, 0, 0, 0, 0, 0, 0, 254, 0, -504, 446, 40, 1494, -254, 869, 126, 395, -364], [2053, -61, 4022, -57, -11, -868, -125, -213, -88, 0, 170, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -223, 0, -710, 375, 829, 65, 26, -499, -73, 9, -194], [0, 0, 0, 0, 0, 0, 0, 0, 0, -989, 0, -404, 454, 507, -1677, 59, -2356, -62, 175, -182], [4465, -41, -882, -179, -790, 927, -228, 154, 72, 0, -282, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -609, 0, -768, 1685, -130, 1067, 227, 62, 230, -48, -35], [0, 0, 0, 0, 0, 0, 0, 0, 0, -277, 0, -148, 1158, 366, 48, 386, 278, -258, 117, 203], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1053, 0, -825, -3086, 309, 417, -677, 1019, -234, -32, -646], [-6235, 40, 3871, -392, -366, 950, -78, 71, -9, 0, -263, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 312, 0, -848, -622, -505, -275, -194, 621, -30, 563, 36], [0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 1038, -1382, 200, 1683, 683, 184, -88, -67, 242], [0, 0, 0, 0, 0, 0, 0, 0, 0, -354, 0, 130, 150, 253, 1570, -45, -54, -93, -309, 36], [0, 0, 0, 0, 0, 0, 0, 0, 0, -421, 0, 546, 3184, -209, -725, -509, -473, 196, 70, 138], [3741, 13, -7491, 82, 215, -1213, -101, -31, -105, 0, 139, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4348, 105, 7631, -104, -695, 1491, -354, 280, 255, 0, -173, 0, 0, 0, 0, 0, 0, 0, 0, 0], [300, -32, 1570, 369, -750, 957, -262, -360, 150, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0], [14889, -321, 513, 118, -553, 1396, 169, 129, -147, 0, -100, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 871, 0, -800, -190, 185, -1128, -512, -180, -215, 42, -238], [-6868, 24, 6625, -459, -391, 2670, -34, 108, -82, 0, -133, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 587, 0, -238, 1035, -57, -1127, 434, 73, -31, 45, -250], [-2453, 96, 5383, -24, -829, -979, -736, -285, -260, 0, 104, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1873, 166, -2061, 94, -1239, -801, -258, 248, -51, 0, 413, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8766, -258, 3222, 234, -278, 2187, -282, 80, 174, 0, -193, 0, 0, 0, 0, 0, 0, 0, 0, 0], [18243, 337, -4591, 60, 145, -538, 305, 115, -207, 0, 37, 0, 0, 0, 0, 0, 0, 0, 0, 0], [479, -178, -1007, -530, -291, -1143, -274, 167, 48, 0, -100, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1871, 0, -163, 716, -639, 3046, 1050, 97, -94, 395, 107], [6626, 479, 616, -189, 512, 336, 133, -421, -112, 0, 128, 0, 0, 0, 0, 0, 0, 0, 0, 0], [63, -125, 4635, 114, 396, 1289, -548, -402, -69, 0, 375, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 605, 0, 40, -2418, -470, 1753, -296, 1575, -362, 336, 434], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2023, 0, -392, -587, 1166, 530, 453, -730, 34, -301, -241], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1116, 0, -2112, 395, 344, -1270, 29, -2248, -276, 494, -310], [-14017, 614, -6671, -200, 1529, -857, -110, -209, -168, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1410, 0, -290, 591, -111, 1347, -561, -984, 166, 155, -413], [0, 0, 0, 0, 0, 0, 0, 0, 0, 203, 0, -216, -384, 434, 1795, 1055, 3022, -40, 91, 64], [-340, -162, -2494, 128, 1237, 312, -441, -461, -148, 0, -204, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 146, 0, 364, -2187, -302, 738, 1104, 3323, -79, 162, -361], [4286, 284, 9659, -657, -18, 2136, -246, -260, 145, 0, -183, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -131, 0, 1132, 1952, 81, 2256, -62, -308, 245, -80, -20], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1018, 0, 468, 1149, -229, -134, 212, -434, 363, 529, -211], [0, 0, 0, 0, 0, 0, 0, 0, 0, 582, 0, -74, -2651, 133, -525, -202, 283, -489, -76, -261], [4924, 90, 2110, -980, -468, 2508, 478, 254, 30, 0, -162, 0, 0, 0, 0, 0, 0, 0, 0, 0], [7841, 66, 1029, -625, -2431, -648, -322, -189, 167, 0, -114, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1045, 0, -237, 334, 373, -466, 80, 2632, -297, -525, -2], [-11426, -90, 1652, 240, 1156, 2500, 50, -216, -50, 0, -22, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -2007, 0, 1084, 2894, 183, 988, 552, -2528, 339, -458, -54], [-17431, 54, -5859, 361, 1141, 2030, -138, -277, 179, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 293, 0, -858, 1568, 171, -904, -1075, -1133, 165, 474, -460], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2022, 0, 912, -3062, 444, 521, 1099, 2416, 33, -326, 198], [11090, -198, -389, 153, 1480, 2822, 144, 340, 249, 0, 356, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1400, 0, -546, -2369, 352, 2202, 458, -572, -194, -52, 380], [14752, 388, -11838, 104, -220, -752, -256, -286, 54, 0, -325, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-11833, 152, -7264, 547, -664, -3889, -146, -145, -77, 0, -143, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1250, 0, -1104, 1448, -396, 2392, 394, -358, 228, 198, -362], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1583, 0, -105, 750, 654, 665, -407, -828, -558, -95, 288], [15837, -107, 9830, 59, 368, 2745, 270, 110, -280, 0, -132, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 770, 0, 880, -6229, -132, 145, 561, 1303, 186, -621, 153], [-7280, -344, -2616, -101, -282, 3859, 780, 12, 127, 0, -340, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2354, -161, 14919, 360, -1732, 796, 429, 474, -109, 0, 39, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1750, 0, 560, -2858, -686, -1337, -926, 1768, 126, -213, 800], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3727, 0, -130, 1370, -221, -1241, -15, 998, -78, -85, 80], [11932, -330, 7095, -401, -581, -282, 42, 292, 15, 0, 215, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -113, 0, 1994, 1921, -154, -3064, -566, -1599, 32, 35, -333], [5330, 265, 8233, 296, 910, 2467, 342, -538, -40, 0, 94, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1318, -230, 696, 356, 77, 1647, -813, -753, -284, 0, 696, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2492, -347, 1793, 10, 743, -1936, 582, 583, -52, 0, -668, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-15203, 446, 7909, 29, 2623, -1418, 92, 130, 19, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -905, 0, 924, -1121, -1404, 155, 356, 628, -180, 234, -68], [-2674, -408, -5798, 395, -2116, 1473, -166, 238, -138, 0, 440, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 280, 0, -6, 2478, -1103, 2362, -1084, -1960, -325, 223, -115], [0, 0, 0, 0, 0, 0, 0, 0, 0, 778, 0, 1790, -2953, 22, -1377, 709, -2045, 296, 96, -445], [0, 0, 0, 0, 0, 0, 0, 0, 0, 197, 0, 209, -1719, -1110, -1185, 315, 1248, -279, 274, -9], [0, 0, 0, 0, 0, 0, 0, 0, 0, 106, 0, 1069, 4324, 539, 866, 436, -2684, -32, 12, 542], [0, 0, 0, 0, 0, 0, 0, 0, 0, 677, 0, 481, 2841, -1669, 1587, 57, 589, -249, 901, 783], [-2583, 667, 10451, 122, 696, -1539, 34, -120, 295, 0, 67, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -583, 0, 174, -1126, 270, -3029, 819, -3064, 142, 223, 716], [8150, -98, -5761, -343, 1542, -1108, -450, 190, -347, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-12114, 64, -3354, 1, 1072, -17, -684, -188, 75, 0, 290, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 957, 0, -1161, -3776, 882, -908, -43, -1643, 394, 228, -286], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1809, 0, 4, -1548, 174, -2526, 264, 1071, -316, 1, -182], [-321, -26, 6482, -304, 6, 3192, -230, -711, 1, 0, -299, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -4260, 0, 2464, 141, -240, -4069, -689, -1840, 864, 159, 298], [-1083, -283, 1935, -80, -1004, -991, 528, 710, 639, 0, -105, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-21177, -217, -181, 160, -1515, -1252, 342, 356, 191, 0, -199, 0, 0, 0, 0, 0, 0, 0, 0, 0], [10805, 205, 1164, -199, -1623, 1296, -283, -193, -72, 0, 156, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-12276, -19, 3806, -392, 1792, -2219, 328, 305, 305, 0, 47, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3555, -204, 9017, -205, -2259, -4016, 46, -73, -232, 0, -40, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -410, 0, 2762, -3835, 163, 1501, 634, 3513, 209, 0, -117], [0, 0, 0, 0, 0, 0, 0, 0, 0, 326, 0, 234, 365, -556, 178, -444, 188, -372, 1084, -41], [-18929, 137, -4660, -1057, 2017, 2128, -575, 103, 186, 0, 293, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -2989, 0, 29, 4441, 1033, -1063, -205, -1392, -162, -153, -850], [6099, -365, -7637, 156, 479, 1450, -467, 159, 131, 0, -285, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-25795, -690, 1068, -854, -1535, -5079, -438, 273, 402, 0, 68, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1275, 0, 392, -733, -1176, 749, -667, -3854, -576, 846, 525], [-20959, 52, 16491, 187, -503, 496, -646, -555, -222, 0, -210, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1768, -612, -1857, -483, 1289, 1982, 992, 416, 143, 0, 279, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -913, 0, 1824, 1101, -658, -1413, 1317, 264, -142, 104, 489], [-32099, -174, -4901, 326, -1534, -5528, -240, 583, -55, 0, -69, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1577, 0, -60, 2203, -1138, -497, -1057, -4746, 718, -18, -363], [-5281, 773, -11423, -96, -2647, -2125, -509, -201, -373, 0, -472, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8541, 982, 5188, 702, 110, -818, 942, -147, -357, 0, 317, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 4380, 0, 540, -4702, -295, 2113, -264, 4475, -1174, -169, -1074], [-5236, 294, -2389, 1233, 968, 3982, 684, -218, 213, 0, 251, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -861, 0, -252, 371, 1712, -3709, 1259, -300, 652, -662, -201], [-10217, -345, -19936, -197, 353, 989, 441, -85, -132, 0, -178, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3318, -892, -4392, 887, -1810, -33, -400, 1048, 17, 0, -164, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3004, 0, 1874, 2538, -248, 51, 1653, -3305, -10, -21, 358], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1522, 0, -1682, -606, 781, 4560, 1555, 3377, -677, -43, 137], [130, -571, -11536, 1010, 629, -1572, 482, 146, -183, 0, -73, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 454, 0, 1934, 265, -1314, -308, 2750, -538, 30, -52, -231], [0, 0, 0, 0, 0, 0, 0, 0, 0, 474, 0, -1728, -4351, -394, 657, -767, 3240, -458, -207, -1412], [0, 0, 0, 0, 0, 0, 0, 0, 0, -5765, 0, -639, 4120, -887, 1869, -1202, -448, 591, -191, 154], [0, 0, 0, 0, 0, 0, 0, 0, 0, 630, 0, 371, 5076, -842, 3466, -622, 2768, 146, -28, -354], [-19667, 211, 16928, 431, -2400, 1511, 866, -512, -318, 0, 248, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-5491, -449, 14898, 127, 2997, 1570, 469, 303, 88, 0, 885, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -5962, 0, -86, 2861, 983, 1527, -1295, -1245, -105, -780, -484], [-19826, 582, -23115, -891, -1201, -4192, -597, -691, -195, 0, 668, 0, 0, 0, 0, 0, 0, 0, 0, 0], [17313, 305, -3488, 737, 722, -3267, 850, 548, 110, 0, -287, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-5142, 526, 1859, 1391, 2133, 1958, 400, -220, -331, 0, -265, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1370, -366, 14645, 282, 3165, -6120, -487, -458, -226, 0, 114, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-5304, -178, -10437, -291, 148, 960, -1474, 362, -155, 0, -808, 0, 0, 0, 0, 0, 0, 0, 0, 0], [17829, -199, 12741, -990, -268, 3433, -132, -310, 165, 0, 213, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 597, 0, 1072, 356, -50, 189, 517, 613, 346, 1450, 71], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1111, 0, 1700, -6893, 1085, 3289, 601, 2339, -385, -343, 301], [0, 0, 0, 0, 0, 0, 0, 0, 0, -469, 0, 540, -2991, -1316, 566, 817, 1610, 712, -335, 853], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1969, 0, 166, 5062, -339, -1357, -857, -2761, 860, 834, -900], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1820, 0, 1940, -2621, 473, 1097, 891, 1494, 954, -619, -647], [0, 0, 0, 0, 0, 0, 0, 0, 0, -91, 0, -2548, -2901, 1124, 3639, 1479, -766, -128, -604, 239], [0, 0, 0, 0, 0, 0, 0, 0, 0, -3158, 0, -1302, -805, -1626, 90, -1580, -5289, 1003, 32, 13], [-62257, -466, -5164, -785, -1208, -3521, -556, 181, 79, 0, -135, 0, 0, 0, 0, 0, 0, 0, 0, 0], [17706, -642, -2956, -1972, 754, -555, 714, -532, 388, 0, -69, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3384, 0, 370, -2498, -1522, 826, -376, 665, 544, -557, 402], [0, 0, 0, 0, 0, 0, 0, 0, 0, -2097, 0, 1632, 5200, 587, -558, 2065, -1710, -153, 1000, 953], [-12520, 672, 9627, -603, 883, -1616, 950, -1440, -362, 0, 1117, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-7362, -831, -23497, -796, -1030, -2402, -681, 246, 613, 0, -85, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1761, 0, 1220, 1080, -546, -3596, 980, 4068, 530, 1365, 921], [0, 0, 0, 0, 0, 0, 0, 0, 0, -465, 0, -148, 3656, 1018, -2376, -1517, -2973, -1384, 313, -215], [2261, 210, -18892, -218, -2442, 3314, 210, -565, 19, 0, 647, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2667, 0, -2466, -2320, 1163, -2979, -1415, 1938, 254, 979, -772], [-24832, -484, 211, 374, 217, -1729, 1854, 105, -212, 0, 248, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2130, 0, 1174, 6344, -18, 2052, 1515, 4823, -618, -1134, -1002], [0, 0, 0, 0, 0, 0, 0, 0, 0, -4377, 0, 1840, -4200, -2241, -7381, -563, -10370, -240, 625, 1190], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2070, 0, -850, -6141, 901, 1818, -444, -2358, 265, -533, -1437], [0, 0, 0, 0, 0, 0, 0, 0, 0, 5271, 0, 522, 5048, 41, 3976, 724, 2173, -847, 666, -267], [-42164, -20, -11673, -35, -5443, -3462, 630, -150, -372, 0, 1233, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-15481, -120, -6384, -569, 2620, 3273, -230, -891, -556, 0, 493, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -765, 0, 738, -19, 587, 4191, -404, 912, 1261, -167, -281], [0, 0, 0, 0, 0, 0, 0, 0, 0, -2190, 0, 3074, -5284, -2323, -3567, -1825, -894, 74, 1217, -221], [0, 0, 0, 0, 0, 0, 0, 0, 0, -3263, 0, -914, -2213, -1869, 2403, -2004, -1329, -123, 1433, 1200], [1808, 1267, -16942, 216, -4524, -724, -111, -104, 101, 0, -975, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-24175, -1495, 2824, 57, -912, -333, -806, 202, 694, 0, -566, 0, 0, 0, 0, 0, 0, 0, 0, 0], [6026, 786, 10791, -1075, 159, -1479, -69, -925, -649, 0, 1185, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3469, 792, 3322, 767, 5776, 4621, 656, -89, 39, 0, 87, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 755, 0, -2709, -5917, -787, -2619, -2683, 3364, -438, 781, 448], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3543, 0, 1490, -3039, -1695, -8282, -1432, 1394, 53, -124, -993], [-38455, 955, 2569, -8, 352, 1571, 1010, -32, 33, 0, 233, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 7203, 0, 2902, -202, -709, -4315, 231, 4275, 33, 473, -250], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1400, 0, -734, 803, 115, -6194, -648, 1837, 9, -361, -651], [0, 0, 0, 0, 0, 0, 0, 0, 0, -5537, 0, 874, 3376, 638, 2019, 1749, 609, 296, 34, -760], [-6330, 428, 9008, 806, 3443, 4894, 145, 667, 450, 0, 469, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-41433, 947, -16079, 836, -3048, -1235, 394, 486, 9, 0, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1806, 0, 188, 9739, 2193, 4094, 672, 9140, -331, -1163, 995], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3270, 0, 1277, 280, 34, 3460, -1160, -970, -38, -664, 1016], [-26648, -44, 34, 506, -2048, -2038, 1470, 732, -94, 0, -843, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-66320, 378, -3858, -444, 1066, 4573, -961, 308, -535, 0, -143, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -916, 0, 2441, -1640, -342, -2628, 98, -6031, 416, 141, -2188], [0, 0, 0, 0, 0, 0, 0, 0, 0, 402, 0, 2308, 12239, 503, 1251, 508, 2518, 131, -538, 1316], [-28164, -475, 11003, -146, 5948, -3753, 58, -706, -134, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -2175, 0, -4036, 2888, 385, 4084, -237, -3634, -459, 1846, 167], [16700, 648, -11447, -361, 6743, 3172, -796, -646, 228, 0, -535, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 4176, 0, 4887, -2580, -2861, -1118, -1798, 8909, 120, 1777, 764], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3322, 0, 2836, -6489, -1588, -623, 45, 990, -160, 699, 962], [-11855, 1164, -10472, 764, -3106, -524, -2148, -713, -419, 0, 2205, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-25497, 1299, -10044, -1689, -3687, -491, 1081, -833, -16, 0, -224, 0, 0, 0, 0, 0, 0, 0, 0, 0], [32803, 803, 7357, 1018, 2476, -643, -520, -488, -71, 0, -752, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1017, 0, 4051, -2745, -1584, 572, -442, -3766, -1404, -1196, 1037], [0, 0, 0, 0, 0, 0, 0, 0, 0, -749, 0, 2626, -1762, 1756, 851, 1169, -2615, -1876, -1442, 788], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2949, 0, 3316, -1697, -688, -1133, -499, -2432, 356, 212, 31], [-29848, -453, -25606, -2109, 1399, -3903, 402, -278, -4, 0, -27, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -4354, 0, 3160, 3947, 253, 6643, -1025, 2786, -847, 742, -467], [14895, -1074, -19220, 1066, -614, -4338, -1316, -942, -38, 0, 1632, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-55187, 579, 24124, 777, 2638, -6384, 464, 956, -450, 0, -21, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 8268, 0, 1737, -4702, -1083, -7012, 398, 65, -472, -1527, 948], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2542, 0, -694, -7059, -1511, -5351, -262, -3883, 127, -30, 593], [-9865, -174, 4264, -1043, -16, 11915, 874, 769, -209, 0, -2317, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-33740, 378, 34221, 631, 2158, 2300, 26, -128, 155, 0, -1751, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1804, 0, 3029, -3460, 256, 1290, -296, 1887, 316, 1453, -1378], [0, 0, 0, 0, 0, 0, 0, 0, 0, -7113, 0, -3159, 2646, -1297, -110, -865, -2783, -21, 1979, -2029], [-15643, -970, -33805, 519, 1546, -5089, 419, -259, -449, 0, 132, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1364, 0, -2536, -7470, -98, -7680, -1338, -2536, -54, 1490, -446], [0, 0, 0, 0, 0, 0, 0, 0, 0, -4636, 0, 4624, 230, -1706, -1581, -435, -188, 661, -560, 834], [-20993, 367, 1189, 1284, 1950, -2993, -1074, -904, -827, 0, 379, 0, 0, 0, 0, 0, 0, 0, 0, 0], [17070, -690, -29091, 1061, -2537, 2559, 333, -839, 99, 0, 782, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -756, 0, -536, 8999, 813, -2463, 647, -4610, -622, -255, 1165], [-29618, 411, 2020, 326, 3196, 8920, -1021, 424, -377, 0, 1191, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1086, 0, 3820, -4309, 1147, -935, 723, -2294, 151, -446, 63], [0, 0, 0, 0, 0, 0, 0, 0, 0, -3155, 0, 31, -2735, -2277, -6962, -1092, -4241, 864, -179, -905], [-31711, -484, -31776, -1576, -5108, -4990, -1376, -159, 539, 0, 361, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4143, 401, 8705, -2760, -2677, -4580, -1155, -425, -143, 0, -279, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 6889, 0, 1155, 2281, -784, 4519, 349, -114, -1407, 1026, 1497], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1049, 0, 4401, 5765, -1618, 512, 2880, -4314, -54, -976, 1927], [0, 0, 0, 0, 0, 0, 0, 0, 0, 531, 0, 3378, 2790, 2935, 1815, -1484, 4765, 73, -3479, -715], [-20659, -850, 12470, 218, -2967, 3650, 86, -312, -410, 0, -71, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -2694, 0, -1712, -3778, 1806, -3425, 1638, -4080, 62, 1019, 692], [0, 0, 0, 0, 0, 0, 0, 0, 0, -7179, 0, 584, 14756, 1897, -1421, 4029, -5552, 932, -49, 736], [1044, -124, -2847, 1083, -233, -1458, 1882, 1640, 1362, 0, -15, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-13411, 1094, 2757, 1658, -123, 5247, 472, 55, 156, 0, 38, 0, 0, 0, 0, 0, 0, 0, 0, 0], [22518, -30, -3956, 590, 5722, -242, -34, -286, -1008, 0, -84, 0, 0, 0, 0, 0, 0, 0, 0, 0], [609, -526, 23352, -1580, -3347, -3814, 342, 776, -612, 0, 489, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -3637, 0, -142, 5218, -257, -4843, 2204, -1199, 477, 1839, -895], [-53175, -425, 14804, 1259, -6388, 1400, -570, 64, 326, 0, -1496, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -9055, 0, 1560, -6684, -3386, -351, -1555, -4647, 596, 1226, 86], [0, 0, 0, 0, 0, 0, 0, 0, 0, 840, 0, -1574, 6339, -677, -1935, 2958, -5303, -14, -793, 196], [31282, 230, 2947, -8, 5535, -1441, 768, 437, -514, 0, -632, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -3856, 0, -1586, 12128, 1149, 24, 1387, -3455, 287, 199, -2775], [18475, 1042, -10197, -366, 7705, 2859, 116, 331, -134, 0, 514, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 6371, 0, -1997, -14889, 720, 551, -1595, 2137, -542, -392, -676], [-15281, -2050, -28526, 851, -1260, -1787, 918, -97, 333, 0, -795, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 819, 0, 560, 6925, -522, 4455, 4487, -2420, -1230, -404, 155], [0, 0, 0, 0, 0, 0, 0, 0, 0, -6083, 0, 4951, -10702, -3457, 145, 1851, -2321, 560, 778, 1440], [-32048, -1056, 18897, -527, -1265, -9999, 1855, 751, 1033, 0, 111, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1664, -618, 6302, -1704, 4846, -6228, 580, 1162, -56, 0, -1092, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-24910, -676, -28187, -1923, 1072, -2763, -186, 1346, 1143, 0, -691, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1004, 0, -674, 10603, -2237, 60, -2782, 1839, 1377, -495, -907], [0, 0, 0, 0, 0, 0, 0, 0, 0, -4846, 0, 7843, 7388, -2850, -1684, 1196, 3369, -1194, -963, 3330], [-24946, 12, 16342, 1106, 825, -7629, -1941, 167, 816, 0, -664, 0, 0, 0, 0, 0, 0, 0, 0, 0], [35198, -1092, 5413, -708, 3527, -474, 481, 1512, 730, 0, 514, 0, 0, 0, 0, 0, 0, 0, 0, 0], [22933, -204, -2594, 666, -2364, -6328, 876, 511, 655, 0, -1297, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3317, 0, 2822, -7204, 1149, -3436, -973, 2315, -2181, -1888, -836], [0, 0, 0, 0, 0, 0, 0, 0, 0, 9898, 0, -7777, 906, 1236, 4584, -1284, 8852, -104, 160, -1830], [-47439, -46, 9730, -416, 14, -9222, -1904, 387, 247, 0, 539, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3124, 0, -1312, -5420, 1254, 2684, -2802, 1590, -1190, 1182, 1050], [0, 0, 0, 0, 0, 0, 0, 0, 0, 971, 0, -1466, 7876, -4348, 5088, -565, 3614, 674, 1811, 1410], [-15546, -167, -9541, -142, -4594, -1814, 1261, 196, -689, 0, -1465, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-15265, -2733, -30953, 1240, -171, -4776, -609, 649, 703, 0, -991, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 261, 0, -2232, 7314, 617, 7699, 827, 14118, -1280, 19, 1378], [-16095, 906, 1260, -1598, 4922, 3575, 2717, 571, -448, 0, 1980, 0, 0, 0, 0, 0, 0, 0, 0, 0], [12747, -933, -44059, 498, -5055, -128, -367, -1043, 681, 0, 516, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 792, 0, -5688, 6141, 252, 1424, 1366, -8207, -484, -2724, -88], [30019, -1686, 4056, -4090, 4157, -4066, -204, 548, 1064, 0, -1328, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-6342, 207, -14932, 1190, 5403, -10162, -216, 1328, -107, 0, -1199, 0, 0, 0, 0, 0, 0, 0, 0, 0], [46891, 1008, 41888, -1524, 4172, 1770, -620, -1269, -411, 0, -381, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 4555, 0, -1904, -4823, -4112, -1171, -5851, -2888, 336, -752, -385], [0, 0, 0, 0, 0, 0, 0, 0, 0, -422, 0, -5328, -1178, 2326, -4045, -2227, -7964, -885, 2566, 414], [-52446, -1052, -17470, -1586, 1133, -13721, 595, -797, 980, 0, -208, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-66049, 291, 13536, -237, -5335, -2726, -187, 403, -976, 0, -1398, 0, 0, 0, 0, 0, 0, 0, 0, 0], [10139, -363, 46711, 384, -8000, -13331, -1890, -1484, -133, 0, 1003, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -8927, 0, -4048, 8558, -2042, 2931, -3353, -830, 1326, 845, -1976], [0, 0, 0, 0, 0, 0, 0, 0, 0, 6681, 0, 2062, -15668, 1007, -6543, -1107, 3569, 321, -165, -50], [58547, -682, -2735, 496, -1647, 3089, 612, -593, -1402, 0, -78, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-72125, 619, -48450, 1411, -3449, 3516, -589, -465, -914, 0, 2091, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -9284, 0, -1774, 10891, 5825, -1545, 674, 7117, 487, -1058, 105], [0, 0, 0, 0, 0, 0, 0, 0, 0, 9334, 0, -2050, -6438, -2757, 4301, -4799, 92, 1384, -577, -1437], [0, 0, 0, 0, 0, 0, 0, 0, 0, 4352, 0, 1260, -22644, 659, -6149, 497, -8405, -409, -1485, -2128], [3162, -2208, -19787, 1792, 1859, -481, 470, 1449, 1116, 0, -1702, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 6513, 0, 2157, -14820, -971, -1841, -4387, 13527, -170, 378, 672], [0, 0, 0, 0, 0, 0, 0, 0, 0, -2920, 0, 1872, 794, -493, -5195, -2148, 8113, 1098, -143, 1214], [10603, 199, 26875, 1092, 1105, -13132, -3827, 293, 467, 0, -400, 0, 0, 0, 0, 0, 0, 0, 0, 0], [57432, -481, -4483, -964, 5163, -3576, 534, 1429, 600, 0, -1450, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -6800, 0, -4760, -3914, 2978, -134, -3581, 6166, 66, -790, -1415], [38555, 533, -14697, 1780, -3366, -15361, 530, 1954, -893, 0, -588, 0, 0, 0, 0, 0, 0, 0, 0, 0], [59573, -1701, 2649, -1860, 4306, 6371, 1246, 2062, 117, 0, -344, 0, 0, 0, 0, 0, 0, 0, 0, 0], [22104, 1028, 25802, 1943, -5232, -5375, 1528, 1534, 811, 0, -376, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 722, 0, -4818, 3647, 1569, 8172, -3781, 4751, -1433, 1945, -2430], [0, 0, 0, 0, 0, 0, 0, 0, 0, 11384, 0, 1612, -1372, 3304, 9439, -354, 5424, -1076, -1673, -710], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1753, 0, -1693, -8767, -72, 452, 2960, -9476, 168, 2684, 1529], [11641, 552, -39197, 1740, -3711, -14267, 1014, 1373, -834, 0, 1262, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-9199, 1322, 42832, -878, 8549, -6460, -2746, 158, 48, 0, -60, 0, 0, 0, 0, 0, 0, 0, 0, 0], [44853, 191, -21544, -2067, 1906, -5497, -1764, 868, 922, 0, -1741, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 386, 0, -696, -14075, 3440, 2068, 2857, -266, 2184, -2026, 124], [0, 0, 0, 0, 0, 0, 0, 0, 0, 6103, 0, -3749, 3942, -1030, 2367, 1402, 5897, -1805, 620, -1790], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3772, 0, 1004, 3717, 2682, -6897, -383, 1924, 1894, 553, 894], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2916, 0, 4026, 497, -1497, -3769, -4318, -2875, -1244, 213, -1098], [0, 0, 0, 0, 0, 0, 0, 0, 0, 5613, 0, 1840, 4066, 199, -1677, -1583, -11140, 333, 869, 911], [-32491, -130, -2836, -856, -2654, -5406, -768, 295, -311, 0, 1801, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1579, -256, -39957, -461, 7417, 5152, -698, 725, -4, 0, -638, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-7608, 1719, 15455, -1374, 5714, 2529, -2108, 230, 1324, 0, 1788, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 8036, 0, 3406, 3108, -4589, 8426, -81, 16419, 1149, 1811, 993], [0, 0, 0, 0, 0, 0, 0, 0, 0, 5300, 0, 4912, -16968, 191, -12115, 1807, 650, -122, -619, -2103], [-66290, -344, 33203, -1013, 269, -10354, -1098, -1042, 705, 0, -113, 0, 0, 0, 0, 0, 0, 0, 0, 0], [72991, 1975, -18175, -1328, -1606, 6399, -986, -1480, 25, 0, 341, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2804, 0, -1461, 824, 1015, 128, 2994, -1747, 1972, -2431, -2396], [32098, -578, -911, 472, 1473, -16746, -463, -866, 1208, 0, -798, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -8072, 0, 2454, 2738, -3092, -11207, -3660, -4081, -498, -481, 2413], [-58066, 486, 68748, -72, -3772, 7431, 3112, -270, -144, 0, 887, 0, 0, 0, 0, 0, 0, 0, 0, 0], [14501, -420, -24371, -1266, 1551, -3437, -1768, -679, 834, 0, -460, 0, 0, 0, 0, 0, 0, 0, 0, 0], [14425, -1528, -27905, -1497, -2531, 1948, -930, -237, -888, 0, -1864, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 7104, 0, -4482, -11174, -1800, 12740, -114, 5061, 1276, 836, 465], [0, 0, 0, 0, 0, 0, 0, 0, 0, -9208, 0, -2634, 10216, 449, -4425, -6865, -1160, -567, -664, 2094], [0, 0, 0, 0, 0, 0, 0, 0, 0, -5087, 0, 2661, -8060, 879, 7184, 2873, -3397, 1807, -925, 355], [-23591, -122, -18037, -4216, 157, -10407, 1384, 1445, 364, 0, -1200, 0, 0, 0, 0, 0, 0, 0, 0, 0], [53358, -376, -7239, -163, -2180, 13570, 1088, -1850, -1641, 0, 455, 0, 0, 0, 0, 0, 0, 0, 0, 0], [7853, 459, -1105, -3566, -6202, -4785, -598, -434, -957, 0, 428, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -904, 0, 4284, 6058, -1214, -10927, 2016, -3279, -2627, 512, 449], [0, 0, 0, 0, 0, 0, 0, 0, 0, -7691, 0, 1742, 26468, -1601, -1572, 685, 523, -167, -726, 1216], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1812, 0, -2652, 14272, 5909, -3702, 3722, 4548, -2406, -1612, -1136], [0, 0, 0, 0, 0, 0, 0, 0, 0, 8101, 0, -3479, -2574, -1087, -9295, -2923, -1107, 90, -1640, -1708], [-25345, -711, -42615, 2652, -1683, -12616, -2341, -89, -647, 0, -1048, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-12338, -1179, 25635, -4886, 3144, 14008, -1557, -21, 469, 0, 1200, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-22924, -999, 13826, -2104, -1315, -7005, -1147, 158, 608, 0, 786, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4651, 270, 49844, -158, 576, -5514, 1308, -2695, 477, 0, 145, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 11615, 0, 2408, 11460, 2442, 0, -3843, -5259, 884, -1511, -831], [-33602, 328, -74088, -1614, -1510, 4896, -2046, 369, 1851, 0, -1797, 0, 0, 0, 0, 0, 0, 0, 0, 0], [22870, 37, -52989, 2, -5023, 8339, 464, 1544, 727, 0, 1838, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-50929, 1293, -19304, 4107, 3177, 2044, 3477, 1635, 146, 0, 767, 0, 0, 0, 0, 0, 0, 0, 0, 0]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_2116_a_Hecke( : Kf := Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_2116_4_a_h();".
// 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_2116_4_a_h(:prec:=20)
    chi := MakeCharacter_2116_a();
    f_vec := qexpCoeffs();
    Kf := Universe(f_vec);
    // SetVerbose("ModularForms", true);
    // SetVerbose("ModularSymbols", true);
    S := CuspidalSubspace(ModularForms(chi, 4));
    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_2116_4_a_h();".
// 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_2116_4_a_h( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_2116_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,4,sign)));
    Vf := Kernel([<3,R![-3250544, -184800, 1469776, 78896, -189560, -5464, 9016, 92, -167, 0, 1]>,<5,R![746637281052043536, 0, -330014408537802096, 0, 48961962020347209, 0, -3382347850082856, 0, 124313836152828, 0, -2580872908536, 0, 30826147294, 0, -208727480, 0, 764700, 0, -1400, 0, 1]>],Snew);
    return Vf;
end function;