// Make newform 825.6.a.v 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_v();". // 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_v();". // 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, 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-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_v();". // 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_v(: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_v();". // 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_v( : 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;