// Make newform 825.6.a.y in Magma, downloaded from the LMFDB on 28 March 2024. // To make the character of type GrpDrchElt, type "MakeCharacter_825_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_825_6_a_y();". // 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_825_6_a_y();". // 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 := [522579400, 1518551280, -549984598, -448113518, 63733360, 42852537, -2591628, -1788312, 39928, 34574, -206, -306, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-47, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [47, -78, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-106897864882712539800, -402311074118157327640, 199509354313240171946, 70049303743635181112, -24351830189591083048, -4077078088562638155, 1094350658605128771, 99652279997334449, -22117609851884405, -1070733831520985, 204218759138159, 4192326267667, -700402408295], [42006278639656976040, 245880787163006069800, -159812706975579859334, -28691972747420774408, 22724782140307366552, 1313339364572873245, -1131487690678123109, -32986283289812231, 23986615688851235, 405732383014815, -224871623640281, -1865244494613, 766585621025], [108859082362413085240, 254514192787546459320, -204687179537376857474, -45006412620435468120, 27135033067925813384, 2719903982051047391, -1310417385514151927, -71978774652306477, 27550011911151841, 840913100582581, -258925322555763, -3560118843527, 891142389387], [109195940182617344040, 317895449303239080360, -198316404562741362214, -50250364922296724872, 27321713331404288280, 2888106974019675597, -1361970953807899797, -74940186253522199, 29178475899358323, 870845035605551, -277342519722953, -3695209656645, 960809696913], [-5838908631431567000, -18700122773955408200, 9882623374300818242, 3463407835467634840, -1233943843323193248, -208962596647831463, 57132039787794119, 5214046250333485, -1179797773473497, -56730273953229, 11044992841811, 223973388087, -38192377867], [63972700558511068520, 227639320701862380520, -143804124667129519446, -37738330064983749128, 20452604615297519128, 2241237579637481973, -1036751984703474717, -59055024989958863, 22380032040495979, 689953296380007, -213498624550193, -2928178310573, 741184491385], [445422533536363730120, 1279164570746265645640, -808000470358671430334, -210677016674580857256, 106889064036046920824, 12276652146072027649, -5147685024081143273, -314302653934271091, 108111535621357375, 3575445909121003, -1016300937086957, -14835282370393, 3500985580757], [-62886591661008471400, -136773333726102861800, 97140674013555388502, 21163941296672481160, -13050706684157641880, -1205156787836830453, 639286676939290845, 31485502355993423, -13533139426314155, -369800452473191, 127508098559345, 1585086479789, -438710012089], [-795789864248114939000, -2197360698914467879160, 1382211831635606493042, 373033830367176016024, -182209291250404738888, -21981184418647233255, 8777747840926557503, 561100881053427141, -184701905769257433, -6343052980971277, 1740222320821467, 26162256334671, -6007694208307]]; Rf_basisdens := [1, 1, 1, 1, 89091865697853440, 89091865697853440, 89091865697853440, 89091865697853440, 2784120803057920, 44545932848926720, 89091865697853440, 11136483212231680, 89091865697853440]; 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_825_a();" function MakeCharacter_825_a() N := 825; order := 1; char_gens := [551, 727, 376]; 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_825_a_Hecke(Kf) return MakeCharacter_825_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 := 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 := 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 := [[1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [9, 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], [23, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [121, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [76, -3, 1, 0, 0, 0, -1, 0, -1, 0, 0, -1, 0], [112, 4, 5, 2, 0, -1, 0, 1, 2, 1, 2, 0, 0], [19, -4, 6, 0, 0, 2, 0, 2, -1, 1, 1, -1, 1], [695, 19, 8, 5, 1, -1, -2, 0, -3, -1, 1, 1, 2], [913, -20, 13, -3, -7, 0, 0, 14, 2, -1, 0, 2, 3], [1474, 32, -1, -9, 7, -2, -2, -2, -1, 2, 1, 3, -2], [3076, 56, 88, 11, -7, 4, -3, -21, 7, 15, -2, 7, -1], [2707, -26, 45, 0, 6, -3, -5, -2, 3, 8, -4, -1, 6], [-13, -619, -69, -18, 5, 7, 15, 21, 4, -9, -1, 8, 11], [2673, -61, 92, -17, -1, 12, 20, 23, -1, -7, -5, 11, 4], [1760, 244, 126, 36, -3, 21, -14, -7, -20, -2, -24, -28, -10], [-720, -414, -91, 39, 15, 9, -22, 3, -19, 6, 25, 1, -4], [400, 124, -239, 48, 9, -39, 23, 46, 20, 5, 19, -8, -7], [5440, 284, 538, 73, -23, -52, 21, -13, 29, -1, 12, 11, -19], [7843, 1107, 5, 42, 0, 43, -18, -22, -8, -13, -34, -60, -38], [5977, 104, 275, -103, 55, 38, 47, -131, 4, -51, 49, 24, 4], [7257, -1778, 159, 24, -31, 9, 25, -86, 37, -32, -34, -63, -20], [14357, 2900, -441, 86, -30, -2, -22, -54, -27, 58, -53, 1, -11], [-1397, -4037, 30, -6, 77, -43, 49, -119, -78, -46, 9, -50, 1], [7393, 1543, 411, 0, -13, 51, 16, -314, -2, -29, -86, -90, -76], [17924, -3343, -154, 96, -11, 41, 7, 233, -1, -33, -30, 47, -60], [19747, -1183, -803, -183, 56, -4, -51, -352, -79, 100, -34, -51, 57], [18131, 7708, -899, 1, -57, 113, 69, 426, 140, -85, -67, 16, -10], [6325, -12433, -788, -141, -67, 30, 46, 231, 45, -161, -79, 13, 58], [24213, 8929, -1118, 49, -8, 55, 50, -272, -57, 91, -19, 11, -74], [51935, 11095, -844, 66, -80, 56, 22, -243, 84, -288, 18, 184, 52], [47260, -8498, 1058, -309, -103, -61, -153, 318, -169, -3, -38, -7, -21], [24121, 10227, 6, -383, 324, -34, -120, -429, 35, -125, -71, -145, -48], [-26506, -9279, -2113, 303, 60, -377, -53, 565, 308, 113, 91, -144, -150], [38229, -8840, -1475, 117, 463, 348, 40, 450, -46, 239, 176, 138, -53], [-48846, 3087, -2250, -177, -159, 40, 18, 769, 52, -224, 44, 56, -231], [-36905, -2773, -3977, 148, 195, -534, -160, 121, -178, -197, 328, 106, 128], [63482, -13164, -2884, 76, -296, 63, 128, 291, 380, -28, 6, 112, -260], [-67370, 5641, -1860, -123, -268, -553, -25, 451, 100, -4, -271, -372, -262], [105422, 7946, -5477, -235, -363, 208, 367, 501, -205, 220, 54, 455, 85], [129733, -14405, 4743, 945, -402, -279, 21, 1487, -85, 80, -558, 119, -65], [-64689, 30295, -2008, 1182, -325, -342, -325, 208, -344, -106, -413, -392, 165], [-94653, -10743, 2958, -1131, 45, 260, 812, 81, 341, 5, -133, -251, 86], [154685, -15458, -4893, 851, -419, 40, 427, -423, 356, 561, -539, -256, 74], [14558, 33822, -2625, -403, -203, 750, 91, 243, 43, 24, 82, 311, 549], [-18488, 29630, 1142, 6, 150, 304, 410, -1456, 208, -862, 738, 640, 148], [-234692, 10953, -6267, 1161, 388, -161, -41, 329, 588, 759, 295, 328, 36], [155105, 26157, -5217, 341, 430, 547, 245, -533, 381, 322, 588, 249, -23], [49572, 38377, 3030, 56, 507, -514, -54, 171, -265, 221, 603, -97, -157], [-48432, 27898, 5576, 618, -102, -506, -20, -3212, 466, 894, -314, -22, -248], [355252, 1872, 4295, -1831, 309, -574, -737, -1851, -393, -292, -62, -665, -331], [13378, 40844, -4242, -1566, 760, -1172, 344, -872, 680, -298, 1344, 596, 826], [-46951, 1685, 4189, -2991, 160, 1031, 133, -2489, 471, 558, 246, 543, -85], [28885, 21453, 10476, -522, -707, 116, -571, -2670, 882, 336, 563, 174, 669], [307107, 38669, -1978, -3161, 1122, -472, -30, -699, -1567, -759, -135, -231, 34], [180803, 26134, -7705, -2126, 1212, 340, 344, -800, 297, 770, -487, -291, -525], [38054, 57080, -1935, 798, -281, -527, -359, -2040, -340, 25, -437, -124, -765], [-148341, 654, -15223, -2622, 247, -827, -975, -1774, -2195, -414, 458, -1603, 394], [2071, -12302, -920, 1069, 1398, 671, 46, 1597, 690, 636, 2080, 1022, -83], [-139962, 53831, -11222, 168, -1885, 191, 81, 3103, -1009, 287, -56, 527, 582], [337625, 34921, -91, -940, -457, -1165, 499, -3795, 408, 869, 467, 332, 305], [214876, -10310, -6729, 1703, -371, 1850, -637, -497, 523, 2548, -10, -217, 759], [227871, 13231, -3427, 4312, -1157, -1607, -515, 2495, 116, -635, -1595, -108, -1025], [-95078, 78460, -5844, 621, -890, 312, 659, -1401, 685, 2073, 2302, -707, 5], [202129, 29731, -13445, -3665, -1158, 1084, 3631, -284, 2339, -1248, -58, 231, -637], [392986, 66218, 21562, -1172, -1327, -571, 2002, 79, 180, -1926, 1000, 1892, 454], [304406, 110444, -1025, 2682, 776, 883, -1993, -5918, -3524, 499, -2397, -1776, -181], [308400, -77231, 16422, 1416, 579, 555, -2176, -2854, -1915, -1189, -2807, -1543, 175], [254882, 67735, -23524, -1757, -2470, 893, -1035, -4071, -424, -216, -1221, -2400, -182], [-380028, -8740, 3091, -6336, 369, 485, 1925, 4504, 1404, 775, -1507, -1868, 351], [631491, 68551, 8326, 1157, 1886, -1905, -1426, -4570, 323, 1187, 573, 223, -326], [511709, -13555, -9751, 573, 1640, -967, -2819, -2367, -1327, -1332, 480, -611, 1257], [525633, -123871, -30209, -3415, 2586, -985, -1907, -8741, 669, 3370, 540, -199, -819], [59024, -96691, -30691, -902, -3340, -2586, 891, 1782, -507, -1794, 1326, 621, 2256], [-210524, 58514, 16546, 5499, -5017, 313, 453, -10454, 851, 213, 752, 1899, 1651], [295089, -134025, -7326, 4649, 2997, -2521, 650, 3388, -437, -2213, -1093, -49, -1656], [325664, 73964, -51319, -4746, -1123, 4529, 3069, 3156, 1726, -125, 721, 2530, 973], [-141128, -37906, -45614, 5427, -247, -212, 1723, -5873, 4493, 2015, -1818, -1611, -345], [-657189, 178405, -27632, 8628, 1775, -347, 2187, -7843, 2854, 3820, -2809, -1562, -1271], [-708491, 140265, -15427, 3465, -1748, -1589, 33, 21243, -3861, 2090, 2966, 779, 1011], [612149, 147535, -5289, 993, -674, -935, -187, -26501, -3817, -1844, -2010, -2121, -745], [289667, 218323, -9190, 6984, -3957, 4310, -913, 1156, 1038, 2326, -2755, 274, 1209], [265542, 209100, 9008, 468, 5504, -2828, -4376, -1760, 166, 2134, -962, -3482, -94], [-199157, 89675, -14991, -6891, 1600, 2628, -483, -4886, -4017, -3834, -428, -869, -2133], [-1251725, -177152, 7793, -5490, -4691, 3875, 1135, -21384, 2123, 2668, -1026, 99, -362], [-253558, 280916, 10942, -5918, 3500, -43, -332, -1771, 690, -1644, 1832, -3858, 1876], [1278585, 104481, 39028, -3594, 581, -4347, -4403, -11385, -5918, -6772, 101, -3318, 1165], [-195089, -351112, -42897, -6649, 3647, -2022, -1077, -71, -1524, -4051, 4449, 2252, 1402], [-311758, -153027, -2442, -13164, 5203, -975, -1021, -12035, -455, 841, 2404, 3545, 666], [-94795, 190841, -22135, 9633, -3260, 2185, -3125, -4889, -1147, -4044, -754, 3177, 2219], [713222, 48318, -3888, -8026, -888, 29, 1618, -2891, 936, 11988, 4336, 1856, -92], [331003, 3569, -29807, 9519, -7692, 4609, 1771, 8299, 5089, 1692, -4286, 1253, -2183], [1122799, 117641, 79545, 2413, -3724, -452, -1637, -30206, 425, 740, -3072, -4143, 1395], [976376, 12894, -8356, -7140, 5574, 9324, 4182, -1968, -1534, -2638, -108, 7690, 2232], [-1169408, -423204, 90318, -7479, -4709, -2373, -1571, -10478, -2705, 1793, 4664, 1703, 569], [-349861, 111152, 104465, -7848, 3610, 254, 1556, 15212, 2305, 1300, 2881, 1669, 129], [808694, -98532, -84151, 3924, -659, 623, 4715, 41824, 7270, -1325, -697, 490, -247], [300261, 312671, 7694, 7020, -2603, -471, 171, -589, 6626, 5490, -2193, -4838, -3023], [-748381, -327097, 45871, 5808, -7059, 1897, 2861, -4393, 1968, -1449, -4795, 1156, -637], [-811716, -6, 30307, -1002, 2325, -151, 4921, 30586, 7016, 1455, 6573, 1740, 1317], [2626235, -39069, 148637, -3394, -651, 1067, 1121, 3177, -5882, -5205, -2125, -1454, 1735], [476446, -202588, 62799, -13021, 1379, 4328, 6907, -1061, 5043, -8268, -2342, -4201, -2765], [-1333766, -287691, -23192, -16390, -9135, -3070, 3386, 17751, 6583, -13681, 4559, 3039, 1325], [721777, 176282, -19843, 8493, 9767, 2550, 4330, 18884, 6040, -2175, -2020, 3576, -2573], [-3166766, 254703, 18803, 11169, -224, 6755, -709, -1133, -3284, -143, -10909, 1756, -268], [993758, 25646, 120444, 10433, 6967, -1339, -797, -17108, -5277, 579, 2458, 3695, -2669], [-487372, -21272, 49596, 8770, -8280, 6073, 5400, 17869, 14548, 9256, -1682, 4676, -794], [27764, 13450, 17139, -1464, 12720, 2663, -1778, 2465, 138, 6475, 4060, 11232, -732], [34232, -562680, 16655, 2736, -5337, 7049, 4041, -15704, -4366, -1423, -305, 7742, 1309], [1389452, 200118, 36894, 29208, -9330, -3544, -8296, -6514, -6076, 8670, -280, -644, -2464], [-409477, -156333, -66036, -4818, 8224, 476, -1866, -27787, -9832, 9972, -2666, -11708, -2276], [-2782431, 381868, 32730, 39341, -9318, 2247, 3460, -4811, 7234, 19758, -2722, 1878, 171], [-87971, -129171, -54336, -20231, -6460, -9533, -3228, -8270, -6761, -15359, -53, -1081, 4048], [-3430656, 133980, 34801, 12855, 9263, -1990, 236, -27204, -1127, -6466, -3403, -443, 2658], [-1555352, 276170, 15428, 20556, 2530, -16964, -3518, 19504, 5474, -4222, -2516, -654, -8552], [3424421, -37031, -6650, 5124, -4669, -14481, 421, 19125, -8000, 3612, 6359, 5240, 1677], [-306952, 333840, 97462, -369, -6549, 7696, -4147, -5877, -2001, -12759, -3078, -2731, 3893], [4745293, -550877, 182390, -15391, 2557, 2421, 10794, -29442, -297, -3653, -301, 1131, 4868], [-2355218, -198428, 118174, -2142, 6011, 2792, -6024, -49842, 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[79213187, -21939777, -1406344, 501156, 240019, -46708, 399017, -415224, 447136, -409954, 295841, 379588, -161947], [-68418464, 9126045, 784296, -404428, -343869, 80987, 141916, 1352862, 11553, -562707, -56667, 724861, 128191], [-91402114, -20169272, -2717903, 265971, 132451, 214524, -334741, -1435577, -309829, 407130, 29106, 128171, -223233], [-88467030, -6520122, 3867866, -238858, -68400, 325936, 45010, -787812, -121654, 198008, -471332, -491678, -271026], [-85892921, 10823052, -1004032, -495120, 268520, -45096, 342242, -399598, 441139, -186729, 144535, 298439, 27751], [-7720190, 17944799, 4484396, -536988, 382993, -61901, 289448, 913080, 10689, -189071, 253225, 320725, 321163], [-33273673, -26714131, -1126069, -63396, 201382, 245386, 39364, -937927, -93076, 464449, -219944, 89256, 148708], [61188837, -4582381, 838601, 143193, -756094, 312737, 26027, 17517, -905, -330826, -758452, -349877, -171783], [-30391135, -53003357, 1124275, 131995, -197736, 396106, 83027, 207858, 419583, 475372, 78966, -81165, 22051], [-95298355, -387827, -3350920, 772483, 162864, -475261, 235420, -612962, -114795, -416717, 186229, 209637, 148704], [174477298, -1703727, -2726428, 437727, 354926, 173339, 507173, 1302065, 668842, -472502, -186631, 226298, -40128], [-8883007, -2377703, -866813, -603420, 68510, -170790, 418196, 804693, 332114, 26207, -46286, 95606, -24778], [-111369889, -24112708, 109698, 62563, -127234, -302375, -366540, 1022195, -432002, -162938, -266294, -627238, 60637], [9533751, 1602751, 25562, -222145, 153523, -104996, -704064, -1003053, -453539, 504697, 83709, -137543, -43130], [79054912, -26650870, -4572508, 210912, -22430, 453744, -113626, -803744, 182666, 109898, -257636, 178450, 132324], [-127330220, -50717138, -1322526, 676887, -143955, 255755, -157031, 1032336, -95625, 484585, 30708, 238979, 102123], [39512470, -2384120, -521864, -1470902, -124833, 310508, 277494, 1765188, -144130, -410122, -53720, 460494, 385166], [6121924, -8709856, 5060584, -196644, 391040, -33706, 28932, -1044998, 377432, 305512, 218072, 137928, 75288], [48878944, -18549275, 4803688, 709179, -52320, -42330, -67370, -1866833, 335796, 263106, 47294, 143056, -247969], [-59971182, -33638456, 116724, 604407, -13223, 183797, -26591, -1623696, -283005, -115525, -590232, -747613, -400841], [99729947, 9255213, -4421453, -498411, -412414, 372747, -72281, 572473, 76395, 147040, 155276, 149223, 262545]]; aps := ConvertToHeckeField(raw_aps); chi := MakeCharacter_825_a_Hecke(Universe(aps)); return ExtendMultiplicatively(weight, aps, chi); end function; // To make the newform (type ModFrm), type "MakeNewformModFrm_825_6_a_y();". // 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_825_6_a_y(:prec:=13) chi := MakeCharacter_825_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_825_6_a_y();". // 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_825_6_a_y( : sign := -1) R := PolynomialRing(Rationals()); chi := MakeCharacter_825_a(); // SetVerbose("ModularSymbols", true); Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,6,sign))); Vf := Kernel([<2,R![-1145312512, -484005120, 1157491968, 125987072, -183538464, -3851488, 11270528, -348208, -292621, 16399, 3286, -228, -13, 1]>],Snew); return Vf; end function;