
// Make newform 208.10.a.j in Magma, downloaded from the LMFDB on 04 September 2025.
// To make the character of type GrpDrchElt, type "MakeCharacter_208_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_208_10_a_j();".
// 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_208_10_a_j();".
// 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 := [-2195812679340, 50183965132, 1089377733, -2752492, -69754, 0, 1];
        Kf := NumberField(Polynomial([elt : elt in poly]));
        AssignNames(~Kf, ["nu"]);
    end if;
    Rf_num := [[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [-1111353084345, 229184428576, 1079565658, -19288734, -45703, 368], [-23038541410395, -1418204636834, -12219130022, 199554531, 674552, -4837], [-930979994747460, 27441001372643, 282627831344, -3012685212, -10621154, 67849], [133358837451735, -3459009128638, -41746828279, 387694092, 1534489, -9059]];
    Rf_basisdens := [1, 1, 2334126375, 11670631875, 23341263750, 2334126375];
    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_208_a();"
function MakeCharacter_208_a()
    N := 208;
    order := 1;
    char_gens := [79, 53, 145];
    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_208_a_Hecke( : Kf := Kf)
    return MakeCharacter_208_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 := 10;
    raw_aps := [[0, 0, 0, 0, 0, 0], [-10, 1, 0, 0, 0, 0], [29, -2, 1, 0, 0, 0], [-570, -3, 0, 1, 1, 0], [16885, 54, 6, -4, -3, 4], [-28561, 0, 0, 0, 0, 0], [-28303, 502, -181, -14, -8, -40], [15308, -1820, 224, -95, 39, -50], [-394885, -6242, -286, 163, -208, 14], [-1503441, 595, -380, 530, -746, 217], [1649447, -3214, -1266, -368, -75, 562], [496290, 1547, -3535, 612, 1870, -629], [-496273, -9227, -3342, 1338, -446, 2435], [5264293, -8461, -2726, 1071, 2022, -576], [291009, -60803, 7978, 1826, 2761, -2248], [-22972897, -274175, 370, 1962, -1102, -761], [21428355, -100946, -10446, -182, -8695, -3756], [5613091, -65207, 43054, -3926, 25026, 7775], [103063918, 24416, 1796, -30917, 8359, -4254], [8772626, -758961, -34488, 26699, -37669, -5192], [-111279707, 167637, 60840, -3082, -26778, 14911], [66568376, -811376, 52672, -14142, -39226, 4316], [77858146, -455602, -77756, 71235, 14491, 20270], [-271595380, 1605754, -139836, -102192, -59816, -27650], [-544383751, 143885, -126952, 51874, 39494, -59257], [-193208196, 2032836, -381618, 101684, -10648, 136776], [-211266620, 1070956, 9768, -15208, -160272, -56020], [-337650397, 2553688, 18030, -184397, -115174, -142152], [-709515838, -4032853, 450273, 71340, -23898, -39373], [-640092246, -1924144, -284596, -112516, -190524, -169848], [-2001302803, -3811538, 1068886, 128049, 43156, -120318], [-1484642989, -1133237, 191878, -454905, -616216, -56124], [248810567, 13185141, -899842, 614230, 793754, 76731], [-3110991212, -8656357, 63708, 131246, -343992, -20544], [-265866494, -18662192, 46948, -895292, -183464, -614408], [-1330293267, 3980955, -909886, -329486, 980469, 147676], [1572758625, -14875695, 2463032, 371970, 432602, 447819], [-2546968437, 3522552, -6196278, -521014, 929273, -191392], [-7875537013, -29099070, 1052774, 1036058, 437743, -78746], [2112448684, -33975916, -8334690, 1236156, 215712, 769408], [-2839712442, 43495231, -520256, 1321354, 2038042, 1289636], [-2032918114, -28267486, -5714834, -1034708, -171700, -756350], [-3322901017, 62213040, 3349346, -2126003, -892386, -322606], [-1918633656, 40976380, -5116330, -922944, 1578892, -1218168], [-1162297048, -21456933, -9067465, -1708012, -2734410, 1952071], [-799210416, 101917746, -1581032, 1066360, 3743624, -1296076], [1456888343, 91825471, 9261598, 1645955, 599044, 1588528], [12337340815, 59656055, 11039302, 1298246, -2538389, 4549348], [2909191605, 95506856, 4953686, -3149286, -3168497, -1400364], [-8981303201, -5061954, 15377379, -5278080, -3481144, 1619300], [-20889431008, 266174585, 5380499, 611974, -1234198, -127595], [16965208896, 77893169, -30507516, -2345935, 3960535, -1408340], [-14151721868, 275540002, 18101984, 573884, 3095320, 1095334], [6143123443, 218095984, 3861486, 5764149, -9040152, 4665556], [-21042099525, -120351200, 25943115, 6180178, 2866608, -2947234], [-7023864141, 145083662, -7563134, 4331569, 3832214, -9464426], [14140781007, -447650979, 11062154, -2853750, 6749298, -3175053], [37933179203, 24972825, -16760450, -15901564, -11480999, 6129604], [19712054275, -376719987, -72294030, 2919130, 7577954, 4897283], [2261045672, -293834778, -16342676, -6413648, -19550000, -5746830], [-2136161619, -101298212, -5704830, 1775511, -26561948, -9189412], [-13347847646, -140205565, 7724445, 9048680, -15131370, -7408285], [24216103423, 40139682, -18436670, -23779894, -2302719, -12136272], [-27377084198, -569900718, -43355300, 15568050, -7105464, 6672568], [73859126538, -156964599, -17281791, -2810334, -8328930, -2232679], [63357181276, 331223270, 83641524, 11202388, 11609792, 5219994], [75472058576, 1297762254, -5363360, -47651595, -18716361, 5132362], [5162121478, 1085259829, 92040641, 1479018, 79142, -21100811], [32594486014, 503961067, -8380528, -4929344, 56125796, -26860672], [2205481895, 1097515160, -154956095, 19141168, -41153564, -12079970], [54734791820, -100331836, 143791698, 38065276, -35300880, 16555608], [-81655889349, 626838398, -21632722, 60691154, 18420539, 11053762], [45126674020, 1526082842, 24052144, -5717402, -9461902, 27574460], [93355100360, -88741492, 62026970, -54611728, 60703184, -31256512], [64718852101, 926990168, -234538906, 18488666, -60010505, 11927428], [-192956536831, 1671242591, 3184402, -36288800, -53141393, -37410780], [25055516199, 3403353875, 14153076, 48165906, -28702994, 31635009], [-204465101546, 2896316244, 74357888, 3178324, -15797468, 8070956], [59509956559, -50281507, 45690378, -76338074, 67985310, -26151629], [-132778702199, -559944129, -218715698, 16587550, -49256082, 16942193], [133108081894, 933217017, -93075080, 34307996, -14234852, 4504568], [-164850442065, 2534470420, -165427051, -110229064, -77339044, -26623990], [-35964147428, -1364279, 235186164, -23324331, 94943879, 7624004], [-242870018108, -1175988821, 121856869, -5639034, 32564734, 49929191], [270737790751, -902542828, 162429546, 111864499, 139859216, 42855630], [75991849383, -3200775523, 451533510, 29958747, -38565836, 53343604], [-397469570723, 2284756657, 41938008, 19102130, 113320054, -28685965], [-508677151598, 453617380, 588499488, -123342452, -59640184, -44185556], [-259136159380, 1674103897, 44418841, 27639744, 74554658, 67370141], [134824590639, -362549402, 62278614, -14021650, 160841675, -38160262], [-37424720945, -3475488380, 89458454, 464489, 10071120, 9115500], [-450795252377, -6312461891, 37853166, -36617620, -20221655, 72676816], [-274768684527, 1676494298, -94844742, 146739834, -57085219, 110981454], [28699360611, -914720425, -41029738, 53552841, -138818158, -108100956], [45204134777, -2020568616, -37562338, -104572730, 76760039, -214298948], [-601936251172, 1729775642, -130954496, 34789742, 212332878, 67902072], [-414491404130, -1381023104, 758361248, 51510624, 115276572, -76817584], [211959612960, -6730650337, 146982145, -223221102, -255294246, -42821741], [710156129583, 5365287968, 566916438, 63770571, 156404294, 215450224], [-287361797902, 5321269605, 97855919, -33609764, 51359234, 71899077], [698254158316, -4234023359, 287074084, -2367494, 233213208, 68969696], [435815272884, -3927530621, -392807281, 141637712, -185281138, 81113863], [165122554626, -4153199649, 75130040, -44796942, 240549202, -26543008], [-93275054019, 5751462320, 140614233, -115165594, 27914832, -107862982], [114546614212, 17738410861, 950326436, 92219072, -57595922, 54810736], [-13666889835, 10429814925, 399585076, 293017526, 140448258, -212564793], [301795273455, -1645914968, 760222626, 154439028, 191615, -34042184], [-1012704349521, 7754032643, 1286192172, 39841450, -370245130, -232456671], [-1785325808915, -3560824636, -474778650, 123456715, 269046106, 261971090], [-272891473583, 6784600474, -280277621, -532163250, -112709208, -274332596], [135774726039, -18542216968, 348361162, -380608191, 107985382, -180179418], [-630922768146, -812893148, -1149901552, 231991016, 347108208, -55016020], [511859296650, 24443983318, 1118837974, 39902288, 24161168, 96168646], [3493185098277, 7715219796, -521322842, 114292868, 274050145, -217794156], [350094204505, 21087604715, 203304874, 88360778, -314430931, -130884696], [1184259967058, 2868258816, -917612184, 143369176, -521747668, 281687696], [1627747549704, -18989198556, 890435856, 561424073, -315197197, -230586770], [700302701109, -10675820832, 494507854, -353607295, -636744544, -126071742], [-595723959720, -9048330852, 856965438, 229517268, -463123512, 125250208], [1871513255133, -17858090336, 189398194, -689922171, -511362202, 250505568], [656219211480, -44206304934, 71192572, -226078524, 113051176, 96788214], [-1394711537569, 1737821680, -616463437, 210957486, 726116140, 507305934], [4010565605300, -5125078248, 177576966, -590755504, 1007595304, 123272516], [2094438815994, 23129359906, -625822188, 521589897, 753369521, -472726866], [6433598942038, 8777482754, -1706540092, 380651311, 336266583, -139711934], [1286731152891, -38530839755, -450064322, 157996282, -441877462, -249630485], [-4516319367624, -22961657382, -335325692, 201102140, -1024692432, 257443734], [-1405948396366, -40237542906, 192288988, 1126194638, 704511192, 19473020], [-1521335675225, 35513839120, 2643104066, 196506271, 421102360, -308362966], [2609152276849, 11739475400, 955946311, -162512140, -171297252, 178593178], [5961510293511, -29450828868, 2080650458, -270400710, -198920535, 264724636], [-839673211915, 15008241837, -1067556182, -522367112, -144602809, -264673988], [7343576931181, -5891971190, -2835886018, 817448385, 167201112, 485879278], [-4699963059003, 17478918735, 542451970, -99704318, 204070078, -866056695], [-2011555347053, -8827417841, -1086974168, -7924378, 1548352902, -205072451], [-4172674731146, -5015058618, -454423762, -1462742724, -1542303512, -243824898], [-772909297997, 40534609580, -2600654307, 1428205236, -93878268, -28804438], [9944286033265, 16634768388, -1437958330, -150490956, -193873431, 593989560], [414416011516, 26344327374, -2603903116, 1385565544, 864473044, -464916894], [5072414934570, 12795437353, -659784735, -1678818966, -1037029714, 1121735841], [-2847986766726, 57994266814, 2012141492, 1527280907, 343173679, -49831950], [-2233712491837, -24085981252, 5209025617, -291951424, 1140473316, -658674702], [110673756979, 39796476808, 4740537826, -2284334549, 1644505676, -312726826], [-1336893210932, 34260401432, 7272314896, 1134123495, 12055465, 25002186], [-7514421726790, 22119146900, -3109174524, 565735916, 665835776, 798819340], [-7235448736657, 1260553842, 6239647454, -12456594, -693012721, -24637442], [-7462376564585, 20793439510, -2578983501, -1038432072, -934790032, -284726028], [674507692064, -10047562174, 4744988932, 1553556952, -1270906796, -510934818], [-3185768436625, -5028213832, -10569678506, -364395293, -2796295282, 765091344], [-14534095701416, -19582659695, 843600148, 308351765, 1216770047, 490057904], [-5398293066141, 39503888238, 6903643203, -2526395884, -880750744, -65920540], [-13210837822793, -78899321972, -6731691713, -2032032154, -1399898520, -1520893870], [-10253197962399, -23883278411, -6332041230, -1129511249, -1191719374, 429805420], [-12265699116797, 15989579870, -6457767086, -949992363, -581265562, 213812906], [13602371539647, -29939523893, 3183937622, -611385655, -784290130, -483309724], [-10131439875479, -62421772636, 4733645246, -2275494381, 3739527594, -1296394050], [-715906225494, -17314711908, 2696417308, 158181720, 1154196230, 2559002092], [4423337638694, 7521983518, 1666030778, -3149144928, 2860559688, 433607110], [7102655271078, 18014953200, -7839991236, -3866395584, 4342339792, -1535547944], [-256473482909, 70622972998, -11232164437, 2449099660, -378313800, -1409648980], [4900289764069, -86831758578, 5322296734, 1363900532, 1788794221, 3073870012], [-974389301057, -117019532638, 11318973801, 372264278, 335416020, 1788576840], [-1497390518482, 71634016151, -9452653272, -371003457, 2770876911, -1698550020], [-13839933711091, 30542443165, -7763250870, 3085711585, 458782968, 265613028], [-14209741330786, -40073213536, 9128716168, -1698394008, -1183879676, -33042120], [24385246187154, 44911301845, -2393635016, -2689204523, -2329642695, 1760914008], [-293046094902, -22281491338, 3364159020, -723124880, -1993896102, -1835018260], [4614918086467, 37804244919, -2509234764, 3975262270, 2340560854, 1560431405], [-23515111603757, -98575998985, 1380709708, 1103909086, 1809462490, -359784267], [15568977800224, 111228352370, 7390169524, 1801413268, 6274232132, -1380919794], [-16220208705212, -12423964792, 16627463760, -1683500663, -3991911573, 1637756282], [-22094583554754, 101278288209, -3223374189, -2415385976, -1321926654, 198739521], [-5493932439867, 60477407726, 5896551654, 4670593205, -2800430464, 2608142810], [-10120645672702, -178290635094, -5735431586, 2858414980, -4328678424, -469865270], [10101823477516, -164777659850, 12419351800, 2884925868, 6789696616, 4329738908], [-3285879239802, -151082452887, 4202326421, 2632789746, -3310879790, -1297576383], [18245338578500, 42155154770, -7944427272, 1083243619, -726283587, 1067675542], 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-7762513954810, -920100192266, 128984573398, -600309379933, -111083748970], [1404224509791731, -9711305425129, 601993531444, -171547837102, 7034591134, 140118501405], [-527616337812562, -1727732070942, 1152608034516, -186863459499, 326046739749, 126458024922], [490237286927534, 13318640484957, 788621651600, 45245224881, -166603293867, 253766953060], [1532790913377916, -1517260796027, -416969617732, -95599244611, 26607604199, 244531245532], [919258575473505, -9154188628937, -486791631082, -413796436854, 241395138798, -186346905351], [-932193089661970, 7959842958108, 97228944132, -94886412501, 212734814327, -199765190606], [407869536429578, -736247333308, -982902236756, 374366333268, 338671510934, -104909526304], [200007208541994, 9624560373820, 692110440024, -519807418436, -468673759768, -142949091148], [1094877978834328, 2075948290311, -914176873477, -135420541012, -155832132378, -30258779301], [646866135529780, -428919470168, -829459477792, 455078509547, 415826664061, -40085346846], [-2082400492287813, -6272529962641, 486405540038, -470794863189, -389243997080, 42054072808], [937531816667848, 2639240678077, -1408359026908, 214291089675, -384388496123, -36066155528], [-1159231805265355, 12380765671906, -451656886453, 126751286618, 58941817972, -166549656700], [-262262313441267, -2786609735237, -94274993558, 430914215596, -77621244469, 176005781384], [-502439901996144, -116961502627, -367030156129, -129933781914, 478967009294, -236998345111], [-1259876650998467, 2079484518208, 221474250322, 277756190037, -79284388298, 12328678008], [1074000373642380, 16191379737, -191544208343, 572777178552, 421920907130, 252221536597], [44109427982858, -9710612322225, -951825817695, 197998812104, 290905783470, 235076533007], [-890592627036306, -7277555891472, 1307549245404, 54680604816, 110591764876, 115694513848], [508680355604166, 9260949339683, 595149013392, -634948306871, -698001615999, -271410101316], [-974570109026990, -4027033910022, 638545438950, -214595665336, 448674155036, 64872590754], [-353487012366781, -5867592865610, 298319456143, -356552364224, -239763779896, 153263068020], [-169221517924594, 8021300394618, 1315284871548, 5980094640, 191013672026, 104032802744], [-1376040221689581, -8440161486726, -1076030418565, -222736762600, 434307660840, -361272072096], [241660599120902, 16239690505446, -748644882706, 543712990828, -130205930688, 100918769070], [-44721866734287, 5085500751630, 719323727510, -319187895024, 271324375637, -70998865508], [-818959539229928, 20793626049630, -547115352152, 178328702139, -102430648471, -164749687266], [1010304027810251, 3781989327040, 433510634203, 380025935258, -91749031520, 344577010758], [-915934723383517, -3970297386945, -91090487100, 40005847974, -363628277874, 342643034429], [-194507288644997, 12982149851817, -80244033754, 80137442019, -318880111572, 39556357848], [-893020868724468, 10791707576243, 966667656756, 374589248896, 460016117262, -149039075332], [-2349982630549670, 5013708275583, -1751250917153, 73226004422, -448879229450, 66886302207], [-851338403987258, 9971898445230, 645266478998, 31593769940, -150067671556, -286653217914], [706018494991891, -2662593236593, 388694382030, 709522760126, -361616274517, 32980679424], [-1682077025353474, 9526002013012, 64848345524, -276789712500, 433952478566, -96586455292], [-141924095624310, 7707329767696, 1121492049088, 535156491476, 576872391364, -76976013472], [-705366899529414, 21085124023118, -1098396371604, 608765597166, -95054463260, 255507663424], [-2587079146381022, 9805232778634, 1082151477910, 188086814324, 21789873148, -172631793542], [170153138985912, -800716886650, 902078298660, 505907057796, -741599229972, 43820890826], [1080292894579033, -7825565759710, -116123961590, -493331927326, -48765250291, -235851817258], [945358361176273, 8207839804241, -917693491694, 41589216077, 494420470064, 38634633812], [-180820644865060, -1375240766088, 484168001890, -308575082104, 460335736688, -317557950148], [852047614117430, -30625975724440, -364007750148, 35963093024, 116974158176, 126216425392], [190017098046942, -16223813445469, -344772527984, 7629865586, 451702849534, 187173988936], [803667841404674, -17415568381430, -438550735314, -19169661468, -286125493048, -22686620774], [-885970332592321, -7778288068256, -620171603214, 436867704058, 171980848673, -52351026636], [219058527745059, 21839372560052, -919372798814, -1017838682883, -266048623998, 106656222210]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_208_a_Hecke( : Kf := Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_208_10_a_j();".
// 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_208_10_a_j(:prec:=6)
    chi := MakeCharacter_208_a();
    f_vec := qexpCoeffs();
    Kf := Universe(f_vec);
    // SetVerbose("ModularForms", true);
    // SetVerbose("ModularSymbols", true);
    S := CuspidalSubspace(ModularForms(chi, 10));
    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_208_10_a_j();".
// 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_208_10_a_j( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_208_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,10,sign)));
    Vf := Kernel([<3,R![-1588484286720, 70867356192, 965100573, -5522652, -68254, 60, 1]>],Snew);
    return Vf;
end function;