
// Make newform 448.6.a.bd in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_448_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_448_6_a_bd();".
// 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_448_6_a_bd();".
// 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 := [5999, 43, -198, -1, 1];
        Kf := NumberField(Polynomial([elt : elt in poly]));
        AssignNames(~Kf, ["nu"]);
    end if;
    Rf_num := [[1, 0, 0, 0], [0, 2, 0, 0], [-959, -272, 8, 2], [-1820, 258, 20, -2]];
    Rf_basisdens := [1, 1, 21, 7];
    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_448_a();"
function MakeCharacter_448_a()
    N := 448;
    order := 1;
    char_gens := [127, 197, 129];
    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_448_a_Hecke(Kf)
    return MakeCharacter_448_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 := 6;
    raw_aps := [[0, 0, 0, 0], [4, 1, 0, 0], [7, 1, 1, 0], [-49, 0, 0, 0], [123, -2, -1, 2], [-161, -19, -3, 2], [-448, 44, -14, -2], [158, 7, 2, -4], [-57, 45, 25, -1], [-976, 22, -2, -24], [-3146, -88, -46, -6], [-274, 164, -48, 26], [5530, 140, 44, 30], [8189, 44, 69, -40], [692, 22, 148, 96], [-5992, 438, -414, -54], [27052, 47, -232, 72], [-1533, 897, -347, -40], [27177, 278, -383, -116], [-13930, 462, 98, -98], [-2702, -906, -212, -118], [-20168, 1258, -1036, 14], [30190, -2705, -726, -116], [-7504, -820, 14, -48], [10710, -418, -916, 468], [-15715, -3137, 1091, -154], [31102, -1240, 986, -306], [19777, -7032, -243, -102], [54122, -1432, -300, 362], [-41909, -1303, -257, -599], [129579, 2163, 505, -79], [12666, 5151, -3234, 0], [-55830, -10880, 1880, 188], [56790, -6011, 3674, 296], [-141582, -752, -2808, -572], [245269, 447, -637, 49], [5131, 13925, 25, -110], [57097, -13822, 4277, 462], [319588, 394, -2260, -184], [-63021, 11513, -3135, 794], [119449, 23598, -887, 1088], [133245, -5269, -5697, -1240], [108698, 21156, -5974, -1772], [-20615, 17619, -1351, 595], [-99748, -8422, 4118, 1242], [-30618, -25416, 698, -1886], [351625, -7574, 7305, 1168], [14322, 2362, 11838, 3274], [-90682, -3705, 1402, -4372], [129955, -5843, 3521, 278], [413302, -31560, -1028, 488], [-391547, -11031, 823, 167], [-583926, -26466, 1408, -5572], [195318, -12075, 13946, 3076], [197974, -40248, -12748, 1264], [-451738, 24930, -20838, -366], [608671, 10805, 4069, 166], [-997506, 56406, 15754, 1322], [348594, -22744, 4832, 1536], [373090, -57564, 8224, 212], [-42084, -61109, -1808, 2832], [1058169, -19305, -2425, -1670], [870682, -25937, 2990, 488], [-419420, -43064, -23300, 7008], [1514086, 28280, 13248, -5806], [-1128516, -77238, 8750, 9730], [288957, 111912, -9027, 3060], [589781, -39557, -36043, 539], [-804175, 66740, 7433, 6792], [1853257, -89701, -1413, 284], [-691628, 24786, -12170, -346], [776475, -85219, -7019, 4483], [-2175838, 45390, 1494, -930], [-2411934, -5512, -3480, -8692], [-1750759, 15264, 12321, -12000], [782544, 68834, -39080, 12892], [1279602, -44832, -47172, 8286], [119833, -107853, 5547, 5628], [219155, -130487, -2513, -9387], [-198856, 152458, -10322, 4884], [-1035380, -37571, -13448, -3288], [-1581386, 158500, -14852, 5484], [1435143, 173423, 34645, -13871], [-976780, -25232, 49462, 25638], [478238, 52510, -10990, -8302], [-2861709, 202490, -1173, 1268], [4565078, 42348, 10700, -9332], [1005053, 851, 11941, -8069], [4744901, 72055, 22551, -12740], [-1132110, -13724, 25866, 4912], [168066, -37113, -51090, 3984], [1984378, 40320, -28922, 3650], [997151, -98987, -46735, 23351], [11963, 9946, 16627, 12708], [2115643, -136456, -69529, -22446], [6325562, 98598, 18774, -16674], [162981, -156505, 75407, -3456], [101948, -78270, 121674, 12456], [3356240, 43343, 35796, 9356], [-3187198, 11136, 97232, 10804], [10358797, -27314, 30713, 10310], [-1654148, -390150, 77710, 13154], [723468, 45293, -129056, -40592], [-18745, 139813, -121069, 5489], [3017557, -168912, -114003, 6624], [-3472392, 27978, -50758, 19054], [1864362, -53655, -41778, -25224], [4914406, -149372, -87980, -28992], [6171348, -327124, 106740, 1532], [-7080556, -4264, 77130, -8668], [-10204480, -140052, 17720, -15644], [-576952, 96334, 17710, -25032], [5001097, -145945, 160857, -21841], [2964736, -87885, -180972, -21432], [-6920568, 45928, -162488, 15492], [-8569213, -66559, 11535, 18293], [9371704, -187903, -924, 18116], [6154390, -117116, 60130, -2562], [-7239000, 449502, 12382, -9364], [8812793, -26966, 120605, 11042], [-4224591, 235707, -30681, -26106], [1729298, 306660, -128752, -26360], [8619849, -240061, 83547, 29720], [-363859, -51324, 91529, -8030], [4976598, 320223, -32326, -63728], [584056, 401998, -218642, 31788], [-4331718, 64904, 44660, 53886], [963304, -462194, -69392, -6060], [-3305628, 634490, -162940, 15612], [15024891, 306793, -21187, -42016], [5845033, 76738, 78293, 28046], [14511103, 410221, -35799, -13613], [-5385941, -49185, 193657, 73433], [1163060, -165822, 239202, -52356], [5025314, -155564, -313060, -35710], [6233122, 840270, -103712, -55192], [-302393, 76885, 165697, 13800], [-8139894, 159475, -316738, -16852], [2316139, 73, 113337, -50606], [-9607067, -450053, 51405, 78427], [3029972, 284951, -60984, 103544], [1449858, 296384, 67696, 21688], [-25326, -850526, 201022, -7986], [-2844195, 489100, 171009, 23326], [-1337749, 856765, 106901, 61268], [12484750, 559792, -89206, 60518], [-1341389, 181661, 102817, 49102], [-9913932, -408494, 163962, -14228], [-10585278, -439339, 10438, 82612], [11851582, -1102328, 62086, -888], [-7631534, 176240, -39244, -14682], [12737592, -968574, -422110, -28838], [-11982977, 163208, 301299, 32246], [2945844, -330786, 22412, -10328], [3818255, -181014, 198319, -18064], [-6790499, -519939, -354033, 59943], [-17840830, -182202, -36906, -47022], [18684204, 324844, 13182, 122086], [21789614, -470026, 345288, 26330], [-18401131, -110549, -230405, -55638], [7097513, -394158, -309587, 91346], [881270, 781740, 194724, -23796], [-12546229, 446365, 397309, -18801], [30557404, -443657, 249304, -24288], [771510, 92104, 406396, -136116], [475574, 577968, 144962, -166346], [-25134664, -249114, -131052, 16614], [-11927461, -341971, 23029, -8576], [-8893187, 480991, -233499, -115913], [19780215, 778917, 69797, -129842], [18443863, -159210, -29513, -43384], [-2457623, 890487, 318955, 69164], [-20934426, 5098, 58410, -51062], [7491398, 389904, -327076, 134080], [-142912, 2083018, 117040, -58464], [26189072, 1523460, -221130, -16500], [-6312947, -710180, -504831, -45602], [-29149192, 473030, -178930, -56064], [-8195948, -674088, -800172, 108588], [16696029, 60483, -533549, -217558], [-14851277, -1748877, 196953, -165027], [26977220, -1348899, -413224, 40096], [32606214, 752020, 19216, 166710], [16860130, -1226662, -144660, -100438], [32615033, 43389, -369013, -9665], [12091415, 1775469, 37373, 137554], [-15084412, 510410, 587598, 196622], [-11741962, 111899, 648146, -15432], [-27571006, 957664, 281104, 65580], [15510706, 1359384, 249670, -20218], [-16577848, -460714, -242142, -150958], [31867329, -1110900, -230403, -65454], [-7550917, 650768, 918495, -124930], [36384915, -658315, 596545, 2770], [23435495, 2366852, -462413, -254702], [-31341324, -699640, -478110, -112720], [9879105, 227655, -520935, -106305], [3027716, 1273202, 530698, -88340], [25398632, -2761914, -376534, -76226], [25960634, -891510, 40006, -177130], [-21671384, 1219110, 282442, -138094], [13923866, -182296, 470718, -120490], [14198247, -2043955, -613295, -43904], [-2670612, 834630, -210002, -360634], [50191740, -1236269, -273000, -103544], [10428453, -816653, 594955, 91338], [49596806, 555424, -96086, 45270], [5861915, -670108, 1046795, 170700], [27230287, 2180817, 197515, 135353], [14142958, -2414075, -150598, 170072], [-15751653, 1021577, 906695, 85773], [-27409417, -3380803, 233113, -157628], [38862981, -352337, -500525, -77391], [37546316, 1343771, 79808, -131784], [25357750, -2039190, 66210, 173046], [-17223570, 1570236, -657784, -40142], [28167778, -421584, -500334, -156516], [9758938, 1840914, -8768, 235268], [17942028, 4192164, -662436, 205908], [15316668, 1108290, -246710, 117464], [7390412, -519958, 1353586, -183560], [-981666, 2003510, -184558, -351870], [-36698546, -35964, -757964, 20756], [57867417, 17301, -239517, -62661], [8869250, -3059749, 857422, -32576], [18496216, 141766, 481190, -28300], [11701396, -968940, 1030514, -240560], [-18643495, -773143, -636053, -510857], [-1577074, 218230, 1128746, -173914], [98663967, 536534, -414685, -76542], [-40439856, -360346, -1562442, 176204], [-54451368, 348517, 78612, -61184], [4571674, -668896, 877802, 558372], [-8161090, 1983364, 944220, 102052], [-48493768, -907217, -68276, -312288], [-10473542, -1590606, -473874, 130134], [5597032, 2119388, -8006, 141334], [1069334, -854644, -52108, -153048], [30208583, -2876846, 600015, 203428], [-79830740, 2239804, -134076, 176032], [-8629197, 3875388, -24069, 198960], [-20319848, 3399055, 1125724, 66252], [10267030, -1109774, 478090, -34686], [-2843708, 5404698, 322830, -121458], [44304568, 4078810, 472178, 38618], [-86507606, -2602820, -498490, 51182], [-4117104, 2083008, -257152, 118384], [48502822, 1358807, 813034, -148424], [-25116837, -293730, -1718937, -590514], [29821304, 2286338, 697436, -216030], [1868874, 423768, 453736, -215788], [-6780732, 2065466, -371194, -210450], [-2171656, -1811048, 1373400, 662620], [-38353672, 809780, -119802, 340568], [-2637033, 1884429, 424033, -142828], [14486669, 606918, 1387389, -319584], [24598856, -4493218, 630102, 65204], [-57930282, -2640311, -208486, 33008], [39345579, -1462107, -1039283, 507356], [-37017484, -6509362, 235970, 34824], [4975141, -4333591, -1518905, 256423], [74693795, -864716, -917117, 18588], [15874999, -1161387, -258151, -282284], [51709623, 292765, 1480609, -193620], [-18315402, -901902, 1548692, -182624], [28068584, 2990137, -468356, 459648], [-91113218, 415884, 421428, -424368], [-78865080, -6811036, 340950, 414416], [-129883191, -994012, 736989, 189278], [28137286, -2972460, 1013728, -464314], [49842695, 2139057, -429595, 427306], [-26580997, -366800, -328917, 142060], [-20740888, -4098024, 1329094, -155200], [-11999789, -5961509, -14623, 92897], [-28952462, 2774256, 1478304, 96264], [47400812, -2526612, -2224044, -24240], [-73788977, 2960558, -1463381, -445418], [-24251620, 2153322, -1697730, -65382], [134407063, -1995295, 1795635, 216905], [-46107042, -2615633, -1268662, -153364], [134799006, 4193062, -369854, 129462], [-12154098, -1180986, 1944290, -488078], [-2219376, 4227226, -1381840, -392116], [118933745, 207535, -314913, -231878], [67158764, -1273237, 1971064, -372380], [-46754615, -4989843, 1648315, -140785], [130080390, -112644, -804692, 669788], [-103271128, 440614, 1498618, 339510], [72390992, 3466410, -588432, -142020], [-66615108, -2758826, 549030, 580810], [38312988, 1121274, -814058, 110726], [45312714, 228387, 524286, 504336], [123708957, -3879349, -1883739, 69371], [53624508, 4243299, -818392, -35684], [-50568282, 4138996, -1077260, 360420], [96024453, -1762413, 1422295, -139060], [-38109690, 3544242, -105254, 27542], [103457319, -15287, -1732731, -790658], [-11146250, 2058629, 1753098, 337364], [97693700, 854289, -450864, -699984], [-136552752, 1336070, -3374530, 155184], [26492318, 259284, -1108528, -653042], [45461806, 93728, 2562990, 138188], [-95340533, 1173824, 2611043, -473496], [-58569981, 5245410, 237719, 140002], [-138920842, 2553200, -1624628, -566612], [130513757, -6602328, -2314899, 97788], [39946907, -2962835, 3044973, 231856], [116698849, -3487841, 1626279, -422171], [-160577498, -676652, 477436, 200100], [61334142, -4456046, 651498, 153970], [133540930, -4774296, -77108, -261682], [103886210, -1649084, -469904, 195792], [84581947, -4889424, 1125603, -350496], [-19550256, -7447504, -1264400, -253028], [16318260, 8139700, -1897598, 630576], [13855800, 2194117, -3551300, -184680], [-75663654, -7028604, 601026, 208560], [-44420460, 2969914, 1104190, -552342], [-5626946, 1076028, -2121228, 360732], [143113480, -531567, 1498348, -196444], [239332582, -4476, -828836, -93616], [-92762719, -6923833, -1476305, 96070], [67369688, 17218, 2516340, 376822], [-11025391, -4763393, 2247857, -249073], [-140053676, -8082848, 1678710, 834766], [190904233, -938866, -1599979, -797658], [45414028, 2833011, 748520, 1329868], [-70484523, 2730097, -4926257, 506499], [-21811808, 3333758, 3640110, 1197284], [43944792, -4330962, 4160770, 93734], [101013964, -2653382, -1798502, -371016], [-128311212, 6294458, -371988, 227516], [23586852, -5119195, -2644304, -45140], [126856001, -857432, 608125, -546126], [96761240, 793011, 3797364, 857184], [47216298, -10183040, 37604, -11998], [15460676, 3472986, 4542710, -429410], [-187366074, -973418, 1923896, 1024982], [-118458802, 9040, 2879122, -604914], [214068812, 2279818, -70970, 1182714], [95815751, 2910261, -3760093, 224905], [88855417, -10503741, -246837, -592704], [-101874116, 6340136, 3646636, -595364], [75232984, -9841562, -1401618, 162220], [3788087, -10103420, 1447919, -1112728], [135181641, 8796167, 288931, 524332], [164434801, -12852868, -317615, -288812], [-187903830, 1998766, -195714, 908182], [-239042209, 531117, -312551, -360808], [42159840, -4186939, -5163596, -1207604], [114069074, 16511848, -2217816, 154096], [-108583048, 4340478, 256490, -12494], [-206821462, -8106284, -1197850, -547534], [-180783452, -17830830, 1203726, 391050], [-62001184, 11837676, 389414, 362068], [72600110, -171204, 816722, 349390], [-23317876, 1940819, 842000, 389484], [18734898, 1536400, 961104, 1783648], [-66860569, -8150895, -3420559, 729691], [-143041906, -4462116, -1541076, 508224], [45441298, 6853614, 1663900, -321046], [51970055, -4459953, 124877, 875629], [-124275913, -6624438, 3442055, 392488], [150519858, 2404311, -3779402, -675940], [66094589, -12322877, -1070027, -708981], [-124607889, -1022891, 2495957, 843686], [14552995, 8205101, 2518149, -569017], [-91197435, 6335891, 424637, 708891], [-158171717, 2297640, 1613375, -31754], [72528270, 12976529, -3588998, -2660], [90835000, 10791294, -3051948, -1257570], [-211597722, 3538652, 196004, -889008], [-111242004, -10334588, 194796, 373828], [69658974, 12706884, -53804, -176704], [-354686278, -3018297, 774574, 1097636], [-42705323, -9090023, 3857943, 1058887], [76793276, -510954, -733250, 196430], [-129232614, 9220742, -1384960, 312492], [1998976, 13525386, -1942442, 825932], [85264949, 19618039, -1222913, -1102968], [-131171091, -7441821, -514139, -38557], [39482070, -23659738, 4846730, 288330], [103602730, 13380328, -1678872, -1210400], [356362000, 7589041, -120196, 1816820], [-134794930, -8635322, -1223134, -917974], [-206861300, 1860734, -4708336, 869994], [-94025001, 16220605, -4988791, 323444], [-188060833, -3790966, -1657929, 869876], [177528450, 17703532, 1625726, -1086142], [-280023327, -120025, -381431, 748015], [-381601745, 8134121, -4016119, -630648], [-48769731, 2747564, -771519, 543830], [68054352, -8970327, -776540, -354196], [-389039743, -463657, -738865, -1010343], [343675890, 296016, 719600, 999628], [-100948734, -9311840, -1976066, -682974], [-97436556, 1003626, 4104450, -1187376], [-6043275, -5219736, 4043761, -1613446], [85869516, -1766726, -1739830, 677420], [322073913, -783729, 1078071, 1896534], [-288155126, -96224, -5711576, -613656], [77932830, 5769968, -5494290, 1546868], [89932388, -3064774, -2225670, 1642676], [38492279, -17933223, -2314227, 1310394], [-147968578, 16358860, 896706, -463454], [-326556574, 394072, 777112, -203280], [-327094383, -5097389, 2371137, -1076045], [139670644, -18183191, 5042184, 58828], [120243292, 6908413, -548112, 1764976], [-297200792, 12102902, 5967274, 1002286], [382112004, -10794118, 5910602, 593184], [-384487, -5603772, 7857625, 798044], [38858899, 16867624, -5833233, 452914], [59720126, 2466744, 8596308, 512400], [40450921, -11392665, 5454235, -1351924], [55685552, 4528398, 3181076, 1764106], [217932476, -4640410, 371636, 1695360], [514628002, 8821290, 127600, -1299856], [-40362922, 22208734, 4109186, 16862], [-266306546, -28197660, 122880, 1515510], [180469191, 1867881, -7437079, -107324], [33120780, -10003858, 3746184, -232234], [-95534414, 12121545, -512570, -21892], [-69362818, -24463912, 4693544, 1175418], [219356095, 26048233, 397161, 215356], [37258907, 28546648, -3593157, 171964], [179350202, 13457684, 5437960, -552740], [-125872454, -12344955, -6352826, 727112], [-168404368, 19564914, 3067352, 316048]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_448_a_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_448_6_a_bd();".
// 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_448_6_a_bd(:prec:=4)
    chi := MakeCharacter_448_a();
    f_vec := qexpCoeffs();
    Kf := Universe(f_vec);
    // SetVerbose("ModularForms", true);
    // SetVerbose("ModularSymbols", true);
    S := CuspidalSubspace(ModularForms(chi, 6));
    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_448_6_a_bd();".
// 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_448_6_a_bd( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_448_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,6,sign)));
    Vf := Kernel([<3,R![82320, 6328, -672, -18, 1]>,<5,R![3096576, 7680, -7452, -30, 1]>],Snew);
    return Vf;
end function;