
// Make newform 1045.4.a.c in Magma, downloaded from the LMFDB on 07 May 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_1045_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_1045_4_a_c();".
// 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_1045_4_a_c();".
// 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 := [150528, -4782848, -47350496, 411232, 122325928, 28436356, -102801526, -23777633, 42786958, 7570653, -9914845, -1160501, 1317797, 95592, -101844, -4345, 4500, 103, -105, -1, 1];
        Kf := NumberField(Polynomial([elt : elt in poly]));
        AssignNames(~Kf, ["nu"]);
    end if;
    Rf_num := [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-11, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -19, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-271872674486041609972254817820672, 164481970480440836310269763355569408, -481278885936654605567744173286774624, -291551522423973428517611638792957888, 1028773038660102731707656514910839368, 248526942059849040104304125651466348, -672509861488318377750729361599361242, -72890875254381189456812911755311727, 200124916623940026841788658288353935, 5800433014004594534132149968517088, -30464718601689822625420585322636713, 426940389563288603568803602199638, 2541869673398520220180787244457015, -96147049284979095898286939882697, -117560943520380650694457129847189, 6062448295157676956103617219910, 2823416111498113291504179810834, -169092526432807655970082784819, -27420983725696714946766147752, 1792075879159754310418474819], [-18812214678091796807951403920384, -238220892728105220172503260211328, 1259719997993320554070653527853696, -325380559375304446715237583099520, -2392539448265013436856652066188432, 977921122753378741469169149740504, 1594483459654753297184317812496724, -696480414057931788329299582665890, -486712848272390724253252217830115, 219326636183814541855510208459520, 74749759359042956588254217260760, -34616427907867739159642956461387, -6236884526103760675991260567067, 2959214882282807359801407261512, 287548439005208674696048645157, -139213682137955127172831878092, -6891590308358822970856076506, 3384583925496875436561193576, 67150080257411060458080215, -33161798078530033948132879], [899868432754282707683536727808, 24808062129177813806962059087360, 258349782856907039787633336395616, -181908170077250088141601729707232, -533023880675642690265945815412456, 207076964643402490687922854805644, 347308903517625226461527951747550, -115139199331908710069724740057331, -103201721076087639421148012789456, 33665197451967583879102599004304, 15638207383729796083566475175605, -5180779932444396237344580435483, -1297727159232129141014958155168, 438125989168702524403048913957, 59730754461000773944605381052, -20494346621999382455915897986, -1430629887918575084823725344, 496560729467175639171198567, 13914981821254018284679817, -4855468882697289501421048], [-22620524747788430661655486267026432, -384887057011932990442000487545817344, -688898463693991367317619931726004512, 1322390767222538086827039412990851968, 1577304101918122783658006476808598168, -1281576981451753668513341842047398764, -1052037803173919571490606919494175142, 607510476087914039320329596392954747, 312877516227577172259713582069915653, -156347999192322115680114048766243192, -47212924468062073290394668342730075, 22246535304188234755797155105816130, 3899851443011183969023975859891957, -1793792915852595131017156592253843, -178796740378284707931959581077703, 81410319439558952448550062458114, 4270794713626625547788730424206, -1933162516573638653311334012505, -41498658043315185550615372856, 18637278135300873993523712401], [1064656275509394714885242788200448, -371596507550888213540486537565325568, 1169474695665422913563590571905103264, 352736008070464788061810903649882624, -2269374101048798302059291047612708536, 111054161816037080113914594514844284, 1460641350282716200981138619228541822, -246694322311664327532866610161097407, -433116152824393010886597340149311761, 101411615937990258593232139712573768, 65608019714458432500154405648560975, -17819206009099246409092441803503626, -5444083799429536604425411913730769, 1606939334403664227475796199065239, 250561157459321508614810531965579, -77920815456853432795656119155770, -6000559254739860730971769616902, 1930345182879855243597409744437, 58352248074339773104434952616, -19154818243334479077103808141], [80305934574445165520007678561051648, 141041759297341830693694483020164352, -441559811638169365434974755713448352, 67101734219905188226625693364717568, 536910050864295427334680299415104888, -621712609855560436913938800078033372, -347556793862218221766215115525850750, 462377989284860096171609614799379327, 107550118727814825864094034901472725, -140857507685617878180899233759112360, -16269504067829577222190015594007623, 21593758611977362245179212904005078, 1316264988956193932244973901802453, -1810513571378641384539445094166031, -58584459640273411283984481465191, 84121603138394081391619144280154, 1362366675836381450076081055646, -2028545068380558903928206909469, -13086147915833226818965480436, 19758477371528064228704499457], [-1411440533044883904539854870528, 51245418826744070222772805107712, 139084144161479572977633688625120, -163514599357849991562329261589888, -293944521456982425764405605625768, 141652555220586796023302738114356, 191695881311338815054762152744610, -65794051682294441058898314385829, -56819063938461296442720838027335, 17482867210147834703272240025232, 8608414145343594918422354561413, -2564414374941391832954933061938, -715274854232661547276622843807, 211096913521421422955789857317, 32980723232827475053516083453, -9708214497676132214301321326, -791166828677976629154119538, 232518179348748555386995943, 7700077704922051464715772, -2255232375229393285453835], [62256610406659067324182521247606784, 389832849138410304565230288683726080, -175954501610790635017002896556175008, -426017508918493869965071921491348608, -134333284283188535533634176793839240, -458885420884519916701799690903225660, 20114761869516934643528997360754162, 502287686983352882255928246684238119, 20736463654310580116789251577485253, -172433833238607727592113333479522760, -4811603327193286242469616510580127, 28008056022161672323015221826944494, 419580422578816520583955030012613, -2427528369791763940860475866128743, -17873969268576749162843968223799, 115177377823479149689527498099658, 385294068310659215091418494078, -2816644487911163655978649627525, -3631568734237926329838070012, 27699944044106316829727935889], [4812212399666762645774171136343936, 56425725089876509294815237761061120, 148037227094332906647146222057228320, -252369184509833187894845511001868064, -316841959748796708412477646659397416, 291113100930430579022545792322443272, 210800181814691277330652103681837538, -152049739955215635551710663202325382, -62849934618637493232946917522828383, 41016143724131165042266919622048874, 9456331151142143952574903982122466, -5978859982369438559479195210434163, -776683169211004382408798548122053, 489008708419262244156526717038676, 35387347367158973488903994323913, -22403510789995170359831139144184, -841028360365200758761921721324, 535539697783034272470890257426, 8156293209533537694908895307, -5187332255414398193826921607], [-20469439300481379236607276747101696, 73720920295144943856735433587629568, 931961903485208275810634275830831264, -566277732371025492412811320418824288, -1849771416129262788928238206039850616, 650683068435180317198479920189438380, 1196954661339078250116496120590465846, -365155661909307398886758438178977139, -355052921771099332139121579029464030, 107411511639260094582670275818123344, 53817830168403487056993862222575193, -16565268137642532748475980195671965, -4470591590171749718058951956470726, 1401286143921024046268714637336625, 206011509808856897765686437578598, -65516619847552081868606887486178, -4939242591498220018215647571468, 1586243405145251378339830322411, 48067420355832495870830648403, -15499680269117815944930532486], [-87670004747503005404920980197076992, -1046099396799597840778963122541869824, -541890962433968000374421062756310240, 3795978142545526658290576228254974976, 1190972778545719975277895421874222696, -4420324627836807101072708639827253812, -884626118506968940047328434143853226, 2250042332792836402918520715304228957, 280267374005828490580887778804928771, -585911943589733000964332311449763304, -42072061844246065685857991279248221, 83294660889544335407922419064065518, 3349015163827843443823401440440883, -6706363006706829244484671912444293, -146439585604072225373576199310545, 304279999664396233928143851753934, 3357053990935446893969271493698, -7228889302019211770841439234063, -32094468751495991555116376616, 69715835015382015616750989463], [-2508174532479839702362946051390464, 411982462622920323584683944594681088, 1824863343331637425810000820129324256, -3104827263325897521921854214084648192, -4126041195533470013072359327797279720, 4182666747740418337262880322476153908, 2955641976654476832118982353782434138, -2357552086926890001698936385463817973, -928277624124467712776273902706603443, 665181777246593806094343268214374312, 143458563828784934667024886248170181, -99476659783940104617404862355574262, -11942607488586701188640043680243523, 8260984499466044431054778237674029, 547842887684811517917676645578433, -382116217424735475088081244182654, -13068193803270481334335458542658, 9192272969665003297526050690919, 127088030406980145865731572064, -89422663409658714611445742599], [10413162258406957659639975852127872, 151236861739304494040450909846827136, 206441689219613519582183448640676608, -551862455680805158349623058198585840, -510866858475825971318591039677214568, 608536531150901117421044118888756472, 373520085683188873836433041884982464, -316198959155134868597789192388044899, -118873700205861801325992595981828965, 86362054097314850301009447505732050, 18558589519191212514964979306709389, -12747996394350383982882543269028762, -1557833563218973669003219413926707, 1052700137937707858774398635980347, 71954633771245316705039190966419, -48566139547281503360129564238490, -1725943445264190627311485249168, 1166843642253135685077583000699, 16854199349582415670675149488, -11344345310434784725047094393], [43027358791221476646056541338779648, -78605889794215852249807143130786560, -5351410059091882428073959554201832288, 3300676713034585301200310805189917056, 10634951345173642692271663961329527816, -4784570370118512630169406567391995236, -7021667886188735095651663262672359474, 2875001355615260716061199396774927177, 2114716788222236498838741249067066307, -852747105529050021985745910301513272, -322531454561737428003037673245504257, 131227121226497584981287045938632410, 26832224683764917332904558447026051, -11072569082274221848606414479826905, -1235852714603023718491663886383905, 516846600367527093172426597959478, 29606514493484479627570661383922, -12501469410383785088674047773275, -288196165972624734605362735500, 122064073083224968976112986871], [-8196731865205067949570366490680576, 281214632475051208728310311959031552, 1657817618956155754917598407960965408, -1586505001184143388172659442188742432, -3439849658794753338283928819765974184, 1809422490508501051099393714332406380, 2273939711741516531400393707753032562, -974497242028909250980593800141317849, -681709356870164310873409284792056147, 274734453407329984744849282788213824, 103689849935077572521182812242502017, -41278590128183541594939026845038282, -8616359083209848911486154500487883, 3439054409083960533607127184417945, 396739250061724351446248092987017, -159327985485308994383211957553230, -9504564301689095641445294184698, 3835317758611079402810427893131, 92510047901626771291058008612, -37327104831218602532821657279], [13597285350107932784635950653773312, -169586823739864306261728700133200768, -1735135764138789488208820745121611936, 1649700237279243532006461352492903616, 3505357781124740285039797062556538296, -2224875629524536104218953415333418404, -2353604450831243077836574991768502170, 1278812482477732634072256609079591013, 716082983076467989907781435958352775, -368498743132678746864115393572925496, -109526489086147320552572656985592333, 55852984681057220422694063801946946, 9106808293465389136948531481744119, -4675462535313471765450496762032645, -418708024458066975413838537871517, 217310249030532884458911055708062, 10014448398997898838236289416074, -5243598618514244729974460695727, -97452850610481933134047676892, 51119164122276371974782875403]];
    Rf_basisdens := [1, 1, 1, 1, 549488430961654131324559417765376, 3763619390148315967976434368256, 537659912878330852568062052608, 1098976861923308262649118835530752, 1098976861923308262649118835530752, 1098976861923308262649118835530752, 97756347796060155012374918656, 1098976861923308262649118835530752, 137372107740413532831139854441344, 274744215480827065662279708882688, 1098976861923308262649118835530752, 1098976861923308262649118835530752, 137372107740413532831139854441344, 1098976861923308262649118835530752, 274744215480827065662279708882688, 274744215480827065662279708882688];
    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_1045_a();"
function MakeCharacter_1045_a()
    N := 1045;
    order := 1;
    char_gens := [837, 761, 496];
    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_1045_a_Hecke(Kf)
    return MakeCharacter_1045_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 := 4;
    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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [-9, 4, -2, 0, 0, -2, 0, -1, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0], [19, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-9, 2, -1, 2, 1, -2, -1, -2, 0, 0, 0, 0, 0, 1, -1, 0, 0, -1, -1, 0], [-12, 7, 2, 2, 0, 2, -6, -2, 2, 1, 4, -1, 2, 2, 1, 0, 1, 0, -3, 0], [-41, -8, -8, -2, 1, 0, 2, 0, -2, 0, 0, 1, -3, -1, -1, 0, -2, 1, 3, 1], [28, 15, -1, -1, -3, -10, -4, 3, -4, 1, -1, 2, -2, -1, 1, -1, 2, 0, -1, 0], [30, 8, 2, 4, 4, -4, -6, -5, 1, -1, 0, -2, 1, 4, 2, 2, 1, 0, -3, 2], [-47, 5, -2, -2, -1, 1, 2, 0, 1, 5, 2, 2, 2, -1, 0, 1, -1, 0, -1, -2], [-38, 2, -1, -2, 2, -10, 7, -4, -1, -2, -3, -1, 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103, 4585, -997, -4300, 1823, 642, 1618, -945, 369, 865, -174, 1538, -48, -1329, -1686, 1610], [-5080, 6829, 2422, -2029, -197, 5261, -26, 1890, -264, 992, 257, -307, -1323, 552, -304, 1873, -699, 284, 200, 604], [24382, 727, -956, 52, -69, -5743, -3713, -737, -328, -92, 1314, -199, -1231, 858, 595, 145, -131, 800, -699, -183], [26187, 10354, -3918, 1584, -92, 1833, -890, 2361, -153, -791, 1280, 743, -1243, 1148, 132, -509, 1082, 1101, 29, -103], [59514, 19818, 2996, 775, 222, -10456, -765, 1041, 558, -1423, -306, -168, 812, 134, 77, -1165, 289, 193, 85, -222], [-24415, -9376, -6510, -2387, 202, -8560, -1630, -892, -1417, 241, 308, 343, 467, 491, -417, -84, -325, -6, -25, 350], [-50329, 15313, -2003, -3259, -16, -6972, 614, -753, -877, 476, -1266, 159, -2466, -214, -157, 377, -988, 1265, 1199, 621], [-14291, 1792, -4966, 701, -318, -1900, 7532, -526, -2250, -1436, -3326, 389, -1642, -2065, -1659, -68, -458, 1332, 2278, -256], [-9787, 2185, -515, 11, 134, 5962, -1585, 2554, 1468, 461, 1195, -1891, 1427, -353, -262, 1022, 925, 444, -1337, -319], [-32249, 6584, 697, 3434, 212, 4615, -4634, 228, 1491, 1700, 3639, 732, -490, 2303, -895, 689, 39, 393, -1668, -231], [18483, 2872, -6234, 970, 12, 7201, -4543, -2508, 1732, 873, -494, 123, 252, 1647, 252, 335, 861, -169, -1613, 528], [56651, 7229, 3451, 1561, -10, 453, 2326, -1247, 1654, 178, 3446, 189, 1009, 1048, -731, 144, -180, 938, 34, -332], [37464, 6093, -1920, -2126, -380, 8498, -1247, -15, 21, 348, 2577, 997, 301, 253, -537, 115, 47, -1133, -1129, -796], [-26122, -2630, -196, -599, -1452, 4344, -300, 3564, -1434, 1598, 1808, 1348, -1182, -1125, 228, -3, -1132, -901, -768, 815], [-9969, -20155, -1402, -1307, -1163, 2052, -1962, 1426, -879, 1233, 3828, 112, -1166, -1598, 681, -544, 84, 179, -1493, -215], [-6498, -3500, 3591, -1328, -335, 5497, 1147, -2348, -806, 406, -392, 503, -2064, 851, 121, -349, -333, 610, 1685, 1457], [-3876, 14569, -2600, 647, 1607, -2243, -1521, -5532, -268, -740, 733, -953, 829, 931, 813, -100, 851, -801, -137, 1350], [10548, 5833, -4581, -643, 479, -8123, -579, -543, -710, 671, -182, 922, -1132, 1982, -107, -522, 739, 1843, 788, 94], [62884, -10557, 1911, -1012, 438, 6176, -5514, 297, -1000, -598, 825, -854, -263, -775, 755, -796, -131, -1096, -872, 1568], [13346, 9283, 977, 1424, 848, -1035, -1797, -676, -825, -650, -551, 444, 20, 26, 2094, -132, 367, 160, 78, 1073], [22251, -10891, 885, -1619, -242, -3118, 3300, -1560, -1034, 170, -4609, 1465, -799, 684, 1641, -1422, -1710, -812, 970, -1094], [8953, -5676, 1200, -888, -955, -1635, -1220, -2937, 1575, 298, 523, -385, 1340, 1837, 573, -383, 1520, 14, -2002, 486], [12407, 3356, 2122, -2636, -706, -4614, -2966, -1871, 704, 422, 936, -227, 530, 2230, 347, -869, -390, -173, -86, 509], [11238, -19197, 2940, -53, 138, 2191, 7441, -1717, -389, -1182, -1647, -185, 43, -2788, 1039, -342, -603, -546, -535, -943], [-15000, 7472, -95, 3452, 2911, -4913, 1555, -1498, 412, 1520, 1950, -469, 794, -203, 25, 721, 781, -2336, -1823, 2281], [-14873, 2294, 1410, -859, 121, 1418, 1476, 947, -1352, 274, -3060, 477, -531, -756, -398, -85, 587, 198, 279, 1162], [-22370, 15822, -1108, 1632, 906, -2169, 706, -820, 827, 1329, 421, -90, 193, 784, 333, 448, -570, -3710, -2073, 1706]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_1045_a_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_1045_4_a_c();".
// 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_1045_4_a_c(:prec:=20)
    chi := MakeCharacter_1045_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_1045_4_a_c();".
// 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_1045_4_a_c( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_1045_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,4,sign)));
    Vf := Kernel([<2,R![150528, 4782848, -47350496, -411232, 122325928, -28436356, -102801526, 23777633, 42786958, -7570653, -9914845, 1160501, 1317797, -95592, -101844, 4345, 4500, -103, -105, 1, 1]>],Snew);
    return Vf;
end function;