# q-expansion of newform 20.11.f.a, downloaded from the LMFDB on 26 June 2026. # We generate the q-expansion using the Hecke eigenvalues a_p at the primes. # Each a_p is given as a linear combination # of the following basis for the coefficient ring. def make_data(): from sage.all import prod, floor, prime_powers, gcd, QQ, primes_first_n, next_prime, RR def discrete_log(elts, gens, mod): # algorithm 2.2, page 16 of https://arxiv.org/abs/0903.2785 def table_gens(gens, mod): T = [1] n = len(gens) r = [None]*n s = [None]*n for i in range(n): beta = gens[i] r[i] = 1 N = len(T) while beta not in T: for Tj in T[:N]: T.append((beta*Tj) % mod) beta = (beta*gens[i]) % mod r[i] += 1 s[i] = T.index(beta) return T, r, s T, r, s = table_gens(gens, mod) n = len(gens) N = [ prod(r[:j]) for j in range(n) ] Z = lambda s: [ (floor(s/N[j]) % r[j]) for j in range(n)] return [Z(T.index(elt % mod)) for elt in elts] def extend_multiplicatively(an): for pp in prime_powers(len(an)-1): for k in range(1, (len(an) - 1)//pp + 1): if gcd(k, pp) == 1: an[pp*k] = an[pp]*an[k] from sage.all import PolynomialRing, NumberField, ZZ R = PolynomialRing(QQ, "x") f = R(poly_data) K = NumberField(f, "a") betas = [K([c/ZZ(den) for c in num]) for num, den in basis_data] convert_elt_to_field = lambda elt: sum(c*beta for c, beta in zip(elt, betas)) # convert aps to K elements primes = primes_first_n(len(aps_data)) good_primes = [p for p in primes if not p.divides(level)] aps = map(convert_elt_to_field, aps_data) if not hecke_ring_character_values: # trivial character char_values = dict(zip(good_primes, [1]*len(good_primes))) else: gens = [elt[0] for elt in hecke_ring_character_values] gens_values = [convert_elt_to_field(elt[1]) for elt in hecke_ring_character_values] char_values = dict([( p,prod(g**k for g, k in zip(gens_values, elt))) for p, elt in zip(good_primes, discrete_log(good_primes, gens, level)) ]) an_list_bound = next_prime(primes[-1]) an = [0]*an_list_bound an[1] = 1 from sage.all import PowerSeriesRing PS = PowerSeriesRing(K, "q") for p, ap in zip(primes, aps): if p.divides(level): euler_factor = [1, -ap] else: euler_factor = [1, -ap, p**(weight - 1) * char_values[p]] k = RR(an_list_bound).log(p).floor() + 1 foo = (1/PS(euler_factor)).padded_list(k) for i in range(1, k): an[p**i] = foo[i] extend_multiplicatively(an) return PS(an) level = 20 weight = 11 poly_data = [130532036219814297600, 0, 87673968468747264, 0, 20025190470928, 0, 1918432665, 0, 75402, 0, 1] # The entries in the following list give a basis for the # coefficient ring in terms of a root of the defining polynomial above. # Each line consists of the coefficients of the numerator, and a denominator. basis_data = [[[1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 1], [[0, -25133664076757128794624, 0, -31903112343361645168, 0, -5722368475906305, 0, -296647947642, 0, -4541161], 1548528983441874649313280], [[52385259255902137290124920729600, 1805231517372463168818722956800, 22968475390724984057882264064, 930157843265327067522500816, 2260069007478252952167024, 132428737167523808186031, 78201849021081876576, 6227581417142813094, 904047821228016, 90309214939079], 104884448930157239789070643200], [[52385259255902137290124920729600, -1805231517372463168818722956800, 22968475390724984057882264064, -930157843265327067522500816, 2260069007478252952167024, -132428737167523808186031, 78201849021081876576, -6227581417142813094, 904047821228016, -90309214939079], 104884448930157239789070643200], [[3512747831129400612332645823283200, 20155810120283317413406538227200, 1654632245798721308199079119360, 7649837258133219253989741712, 225312408840219445590929360, 926283859724013800015867, 10492758055115205175840, 40402590323793675358, 152264363749954640, 564930968079603], 104884448930157239789070643200], [[695360187952896174027342207206400, -28439828591831587136855374356480, 232907169776827212260280212736, -12170753631420671839254010240, 23667049632778133149251876, -1488456653296048110752205, 868157502369340021224, -65259502203617343810, 10264353724844484, -914897678021365], 78663336697617929841802982400], [[-10763701260736589279793009312307200, -65704724596784247112617769697280, -4689003945240519268575872265600, -30080505844669410461372804704, -605011221932823664604849100, -3671916890550722016927429, -27198638407018194545400, -160836016495010223186, -385008305068617900, -2253724267404781], 78663336697617929841802982400], [[-845423982250231788778821364915200, -86305060834141789374336390789120, 615638286722972091755119844352, -29186967316632454181845341056, 161766785127981432763711332, -3695320236335913156752031, 8837159656564436548968, -170549183336661624054, 135178905838851588, -2481088965145559], 78663336697617929841802982400], [[1458368937525229995257761060454400, 132837375781014517934849148633600, 2164940401726914480858865294848, 47493790672604282107476060016, 409445389500490511743541968, 5985418659785267889989781, 21118094260708667212832, 274008990396578281794, 318817099901964112, 3963051222809629], 104884448930157239789070643200], [[5582232700423711503460798705459200, -98996508941602272269342548124160, 2820481676653063207819715549184, -40571339622373109254010004720, 401030649407404371931187944, -4961909763207647629722175, 19170999256470648432656, -217551766471964851430, 283095972228992296, -3049966507141015], 52442224465078619894535321600]] hecke_ring_character_values = [[11, [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]], [17, [0, -1, 0, 0, 0, 0, 0, 0, 0, 0]]] aps_data = [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [6, 6, -1, 0, 0, 0, 0, 0, 0, 0], [90, -174, 2, 0, 0, 1, 0, 0, 0, 0], [2227, -2227, 0, -7, 0, 1, 0, 0, 1, 0], [-20199, 3, -49, -61, 17, -17, -1, -6, -6, 5], [23905, 23860, -170, 0, -31, -60, 0, 14, 0, 15], [104076, -103836, 150, -2546, 205, 315, -5, 0, 0, 75], [387, -116801, -4256, 4484, -547, 313, -15, 14, -14, 129], [-408261, -408711, 7361, -100, -577, -950, -50, -177, 0, 200], [-1311, -645195, -58082, 57398, 1691, -589, 95, -342, 342, -437], [2307146, 180, -42535, -40735, -3485, 3295, -60, 175, 175, -960], [-8809329, 8800194, -4650, -127596, -4095, -10968, 720, 0, 492, -2325], [2971602, -3297, -26384, -21886, -10648, -3697, 1099, -2751, -2751, -1150], [15634784, 15641624, 37931, -4200, 7666, -5580, -2100, -1274, 0, -180], [-45025797, 45051447, 9300, 194517, -1650, 30993, -3900, 0, 693, 4650], [70025850, 69959655, -721400, 14350, -74252, -38035, 7175, -882, 0, 14890], [27279, -182124177, 1425148, -1440552, -80709, -45949, -16795, 6048, -6048, 9093], [299693575, -48636, 1350008, 1371182, -36524, -92111, 16212, -10388, -10388, 5625], [-698436064, 698442004, -79800, 2647539, -287220, 8082, -41880, 0, 42042, -39900], [991579746, 126804, -123487, -90023, -141989, 313279, -42268, -32793, -32793, -59000], [840296525, 840330905, 153460, 98100, 9284, 389190, 49050, 23954, 0, -60510], [-164196, -1169547184, -3722252, 3403988, -113404, -562664, -104400, -19132, 19132, -54732], [1701197646, 1701381756, 7538759, -141500, 231886, -249770, -70750, -22974, 0, 9380], [382212, -2987348712, -11594956, 12091644, -211602, 930778, 120940, -64806, 64806, 127404], [-4897757035, 4898523745, 361200, -16960660, 241920, 1202068, -74970, 0, 254758, 180600], [5702910858, -373974, 9813152, 9650188, 269104, -1298534, 124658, -181482, -181482, 206140], [4868106707, 4868673437, 11908633, -507300, 995051, -1019910, -253650, 174671, 0, 64740], [-8900285406, 8899866486, 59000, 22896471, 765060, -720188, 169140, 0, -330768, 29500], [-457479, -3135484616, -4665048, 3667182, -72006, -2200581, -346440, 357342, -357342, -152493], [6403331970, 6404020080, -35642550, 339050, 847583, 2104155, 169525, 328998, 0, -398895], [-5932157855, 5931365855, -1286400, 89360885, -3446400, -1314377, -379200, 0, 120823, -643200], [1246356807, -3923259, -49405993, -47419717, -2578111, -6088169, 1307753, 86688, 86688, 314615], [4276399161, -4273192131, 1696700, -24109696, 1662410, 2708596, -220660, 0, -1346784, 848350], [4292379, 10032384975, 19610848, -18297412, -6781729, -67589, -774075, 1263668, -1263668, 1430793], [4313343, 3114034116, -122209884, 124574126, -8213158, 4985757, -255660, -1695054, 1695054, 1437781], [-22489642074, 5028228, -174484019, -179283011, 7467887, 4080023, -1676076, -454021, -454021, 723420], [49392979716, -49378061901, 402300, -111346326, -18482370, 14833701, -4771455, 0, -285264, 201150], [-47364008562, -47353293522, 180545407, -7101600, 11102552, -10568880, -3550800, -3163288, 0, -20880], [55651368837, -55671034767, -6688100, -66596127, 2812890, -22730365, 3211260, 0, 279615, -3344050], [-45581762694, -45579408549, 210953524, 5634450, -3016428, 22859435, 2817225, -2553348, 0, -3601940], [-3530391, 74157992421, 151369808, -149389852, 10895141, 5449081, 2166775, -312372, 312372, -1176797], [-83348950046, 12228552, -68076236, -66958124, -1719652, 34803212, -4076184, 4592756, 4592756, -4635240], [-93676213086, -1364112, 207504261, 215322469, -17207033, 6519063, 454704, -2025321, -2025321, -3454400], [-3830653772, -3827031632, -35879138, -5809350, 15236879, -15503205, -2904675, 8710064, 0, 1697295], [129372632367, -129385964412, 8046350, 429107768, 45938285, -1281680, 8467190, 0, 8027190, 4023175], [-5326506, 85257581066, 300132028, -330553372, -37299874, -54970814, -13435170, -4096372, 4096372, -1775502], [14047189785, 48812463, 137694971, 73032119, 105315157, 9161743, -16270821, -7739726, -7739726, 16060605], [-11506890947, -11435105507, 39682117, -20613000, 91801787, 23568420, -10306500, 9709847, 0, -13621980], [-204127250682, 204176542812, 20993100, -404312173, 7753010, 47251848, -5934160, 0, -12536832, 10496550], [-21936483, -274351848207, 99032454, -110516586, 18566013, -263187, 1570095, -15392916, 15392916, -7312161], [189157694802, 189173539992, 2174804078, 13094950, -10643429, 66959245, 6547475, -19941144, 0, -11829205], [-101299734, 135650334186, -1138447608, 1074015192, 150125964, -105506796, 1550370, 10408542, -10408542, -33766578], [110985460690, -7113537, -1812542544, -1778688606, -83291928, 16227423, 2371179, -17955231, -17955231, -14555790], [594207670035, 5627805, -911576165, -942898185, 54080445, -40539145, -1875935, -6687660, -6687660, 13785075], [-248699937504, 248701974114, -25706050, 850651834, -92686655, 41887495, -13531895, 0, 52703910, -12853025], [-78087302361, -78021774621, 885853441, 3889000, 35506705, 100981820, 1944500, -28076535, 0, -23787080], [47661543, -814130582772, 430309516, -470588514, -191394888, -76679053, -36026680, -19766124, 19766124, 15887181], [832261580244, -138037338, -429307851, -308907819, -179830977, -126530433, 46012446, 14956641, 14956641, -14187570], [-441497012504, 441625882469, 97639800, 1864639714, 169912680, 91237493, 5863245, 0, -86452372, 48819900], [416855528784, 140577789, -385364032, -535678518, 253395216, 102168619, -46859263, -374493, -374493, 28297980], [-435601273128, -435998172498, 760182643, 96108300, -521545504, -192820110, 48054150, -76591984, 0, 84245640], [880540095429, 880692433164, 642552066, -115067700, 191633421, -199619970, -57533850, -18238164, 0, 6754605], [-344273569824, 344008994844, 37971600, 1518912699, 485667240, -135999798, 107177460, 0, 109589382, 18985800], [252209916480, 48186534, -1434596647, -1228965983, -498248549, 349956199, -16062178, -70925043, -70925043, -118877510], [796149182524, 796151210584, -1341121694, 84412950, -115947493, 298149405, 42206475, -75769078, 0, -42882495], [916450178628, -916534580163, -156693100, -1524269458, -435890470, -154381667, -50212705, 0, 8366418, -78346550], [-515264596243, -292275693, -8855179381, -8749448809, -142946027, -552290873, 97425231, -28910114, -28910114, 44559945], [2399843816017, -2400089390377, 75013800, -5814320072, 589980780, -264519304, 119365020, 0, -56451844, 37506900], [727244616516, -726399116346, 340291100, 1349640879, 63685290, 946189534, -111687840, 0, -69456186, 170145550], [386610471, -533123464357, -12040294998, 12590747802, 33330159, 862293399, 146356245, 109742052, -109742052, 128870157], [-21324303975, -21528021795, -5762950120, -25206200, -263653004, -359845460, -12603100, -72538284, 0, 80509040], [46863468, 3601574817816, -565142884, 387075876, -523250658, -224953118, -104654660, -146802054, 146802054, 15621156], [1263543473829, -1263546767469, -92612400, 2323101421, -319751880, -43195477, -45208320, 0, 6404363, -46306200], [1730908129444, 1729782653839, 1210491636, 445858950, -983641452, 59872185, 222929475, 364763628, 0, 152229060], [149687145, 3720251833841, 6995953140, -7050864480, -455568885, -135786525, -77351385, -23931870, 23931870, 49895715], [-5204157626283, -5203432517403, 9610614613, -279495400, 818640515, -11422060, -139747700, -46216065, 0, -101955260], [-370166463, -485309125452, -3597213756, 3594183234, 842387928, 134115813, 121873560, -16788036, 16788036, -123388821], [4376070974943, -4376422609218, -206295750, 4417423472, -253189425, -234983060, 14063550, 0, 219799090, -103147875], [-2781066404490, -743704680, 20262617740, 21249456660, -1588271820, -117548080, 247901560, 137504460, 137504460, -245517900], [-359051301, -5001036406870, 26482490038, -26981327452, -108180559, -680280254, -129734940, -197710807, 197710807, -119683767], [-21212625, 6345443739183, 7221951300, -6929841080, 772690465, 306262305, 153125985, 285029010, -285029010, -7070875], [-2785561720523, 512494398, -5994579164, -6457682726, 411886352, 157675613, -170831466, -343489306, -343489306, 60720315], [7634981379624, -414440406, 8218741053, 8066603597, 601777511, -1035878001, 138146802, 159355797, 159355797, 214215530], [6754100563875, 6754225741365, 3416020300, -631027800, 51421964, -2041693980, -315513900, -389269426, 0, 273788070], [115468092, -970542689160, -18235103396, 17634677684, -1479367222, -930037682, -338702220, -309303106, 309303106, 38489364], [-4827054639528, -4829407528938, -568312877, 905386700, -2701410040, 31667570, 452693350, 104172720, 0, 331603120], [747431685, -5840962818762, 14238024970, -13612311180, -913071435, 1109918540, 63713000, -107634855, 107634855, 249143895], [-2593853915544, 2597134540104, 1047773850, -1300467846, -706957605, 3741195963, -569654595, 0, -63315522, 523886925], [9058954711986, -99083142, -41517495144, -41739577996, 625417592, -416094102, 33027714, 148224174, 148224174, 144069140], [3604307217809, 3604216235279, -48696503019, -331716300, 89931669, -1282317090, -165858150, 15056049, 0, 196185660], [-11627370855894, 11626522074084, 251495500, -63129389461, 2011943330, -112396396, 408675020, 0, 610637664, 125747750], [1382986746, 5339408740686, -38731610948, 40544526252, 121334184, 2535904724, 445462070, 628930302, -628930302, 460995582], [-11051288662221, 11051417099241, -638500800, -71201659959, -2406002160, -756695655, -362062740, 0, -565882275, -319250400], [9865056668025, -2082582705, 45645518275, 48238792735, -4938694355, -1415787625, 694194235, -446339670, -446339670, -602442995], [-4664593197, -5807281666933, -11544672964, 8928657136, 6282893437, -3000033643, 246856485, -677133614, 677133614, -1554864399], [-5448170052825, -5451459957375, -97831467135, 1475318700, -3737869761, 777076050, 737659350, 289694139, 0, 358975500], [-2740007637, 3988072251207, -35354704694, 33010621866, 2590333647, -3487936513, -258705535, -286893264, 286893264, -913335879], [11280881579814, 671010330, 62961029960, 63465901740, -467863080, 3088549030, -223670110, 765550590, 765550590, -476106000], [4649793223184, 4656505015394, -49970274709, -1361751300, 6380313244, 4182926730, -680875650, -1012354616, 0, -1556388420], [-8340998493606, -1620987030, -6648232640, -8599787540, 4614569360, -6538504870, 540329010, 171130550, 171130550, 1516106460], [14753301316102, -14755544026732, -1929309300, 137338855603, -3762301710, -2915854408, -217084440, 0, 291510872, -964654650], [-3403137200157, 3406472882292, 1826107450, -122045409308, 1943799895, 1857147872, -198840320, 0, -2391587988, 913053725], [-17535413366358, -17531815324578, -167692550217, -2231196600, 6728337912, -3011799060, -1115598300, 2014697832, 0, -83748960], [62305365, 32222927261310, 30465293330, -27706201420, 3198580835, 6292093210, 1358777500, -794677845, 794677845, 20768455], [-32462594058107, 2042770815, 27089252215, 29534625595, -5599315975, 8406879695, -680923605, -27645610, -27645610, -1903610295], [27467664960496, -27466874254786, 2222717550, 76383127794, 6725237145, 3602608071, 847790205, 0, 1700543586, 1111358775], [20423366642820, -20425689274530, -2579612700, -217870308585, -5931802170, -3244964394, -515595780, 0, 367473666, -1289806350], [-52849709677707, -52846248933687, 33578962032, 316515400, 3694211248, 5722129260, 158257700, 391724928, 0, -1311839040], [193917918, 21586651792674, -68350608884, 63895269476, -8903363158, -7207439218, -2292309010, -1767878904, 1767878904, 64639306], [-36584262182212, -6500600271, 74531987448, 77745565602, -5497084824, -11584495341, 2166866757, -1236795273, -1236795273, 560077680], [36544153121703, -36547664088213, -2855690700, -107184882723, -5313628770, -6616397091, -257523180, 0, -1677585231, -1427845350], [-17894903535893, -17902141750208, -177682022162, 4079090700, -8837807503, 4625865030, 2039545350, 439952162, 0, 373192755], [-15143152003668, 15136989924558, -4366494950, -70302730082, -7066626845, -10915925281, -129221105, 0, -2570598696, -2183247475], [-12419171937, -13631456816361, -1412447244, -6416224704, 16612803807, -10895363793, 225388005, -622256124, 622256124, -4139723979], [-41218606750872, -7541906562, -104448915239, -97923424031, -9568862533, -6841394137, 2513968854, 968151029, 968151029, -748776750], [16768813737498, 4766412303, 141078564456, 138826454314, 369163312, 5197210623, -1588804101, -2546252871, -2546252871, -462749030], [31406944385074, 31401134952484, 251920941151, 7651478700, -9622533706, 19034265330, 3825739350, 12638234, 0, -1889261820], [-15267923362365, 15288765005745, 7930402800, 451141087145, -32448040, 20859771993, -2982013060, 0, -3947072787, 3965201400], [-80265124436136, -80266825066701, -323264877704, 903418250, -2165223820, 894456455, 451709125, -12884130, 0, 115167730], [6604035039, 24034986009495, 231080841068, -226242815232, -7638494619, 6960824941, 217667905, 513881718, -513881718, 2201345013], [11140738075367, -611521848, 5596085604, -3109212174, 16975622808, -15123644343, 203840616, -638813364, -638813364, 4556489505], [-2305468875633, -2328173504223, -52712944732, 5402116200, -25836202904, -11365431420, 2701058100, -430516214, 0, 4867151430], [-75813564348573, 75822850182108, -1045394250, 402031117408, -16039991255, 12761768460, -3617974970, 0, 3998632050, -522697125], [-8649585544104, -8657507718024, 331957807579, -1745912200, -1838607790, -16673591260, -872956100, 5210610030, 0, 3513680740], [-38345837317211, -5147311437, 74151989291, 82249287719, -15428734763, -814354097, 1715770479, -949908386, -949908386, -2332878735], [142716017712081, 9118774398, -119913717664, -122376504226, 4544396852, 20241375613, -3039591466, 2658415194, 2658415194, -1808198185], [4010006367, -28433718500581, 93699395154, -77192572566, 16439631153, 30640897593, 6916742505, 1036078794, -1036078794, 1336668789], [-2335208886, -4274953779030, -45394939832, 40572983928, -951844524, -9697777444, -1632574990, 832268598, -832268598, -778402962], [-46052334197981, 46011441866381, -14498128200, 433127375521, 3779660100, -48693769543, 6381713100, 0, -552373843, -7249064100], [47292840119642, 47311739822147, 814152684028, -13272910950, 26206804964, -21255584985, -6636455475, 670646984, 0, 336554640], [-10763643591, -116279571922123, -87441430192, 78580073908, 11246747161, -13558444579, -842796945, -576386792, 576386792, -3587881197], [-296411212629, -294762131349, 693055204289, 6954509400, 55618881, 26539557940, 3477254700, 1883792301, 0, -4026948460], [8402073795210, -24470256888, 35445264789, 64481672181, -50769122217, -14395714713, 8156752296, -853059729, -853059729, -6361451400], [-60090834902544, 60095901392649, 9702301800, -319065660966, 27202736160, 6337411581, 3162320865, 0, -3580229424, 4851150900], [188770431038502, 20124193800, -441904117180, -449759506900, 6875623580, 33046276360, -6708064600, -2127091260, -2127091260, -2780369740], [18471153474, -81745938347822, -180190284612, 201453386868, -16315846044, 41480294676, 4474499970, -5111141322, 5111141322, 6157051158], [-148680359843877, -148694198209212, 536415470822, 223238500, -9557930723, -17669819030, 111619250, 4392053862, 0, 4501169195], [112063793292488, -112013103848528, 7643325600, -690406019813, -40834285680, 57078267146, -13074818520, 0, 2567160386, 3821662800], [-128747875998468, 128726103409953, -1337438300, 1077260620438, 24349083970, -18192433819, 6588810355, 0, 4248873846, -668719150], [11039816550, 213647257631022, 99222636500, -97955795020, -27980842690, 2975277070, -3046518110, -4121532960, 4121532960, 3679938850], [-106030476063885, 12691492893, 392580763451, 378413243159, 28832467357, 13090127383, -4230497631, 4727924404, 4727924404, 2853262515], [33914618893809, -75211691466, -53725565552, -2852939458, -78307091644, -100817410891, 25070563822, -1632403278, -1632403278, -365749225], [155192341856831, 155273511636701, -30506270271, -25714100700, 99966648075, 18227020710, -12857050350, 5939817855, 0, -14199542940], [8674003430484, -8639873614434, 26466496300, 1421924372671, 47126315650, 31631566286, 1856642800, 0, -15731497914, 13233248150], [-3664858041, -68483045351052, 734770048708, -772534942522, -57464095324, -64940078249, -17660827560, -9368090032, 9368090032, -1221619347], [-41017962078, 214986985160922, 646049843264, -660441968616, 67731031878, -8722238402, 6476591350, -6389358276, 6389358276, -13672654026], [66326704897047, 66296559284772, -1069332449482, 24970633500, -15490605227, 47203067550, 12485316750, 27140323798, 0, -2436779325], [20809314841773, -20825366087463, -26661418900, -369160078168, -71913305230, -16585831016, -7980294220, 0, 12796124124, -13330709450], [-14399892441, 58560052998815, 27893150708, -81403413872, -50736450749, -98149757149, -21955167435, -4070805032, 4070805032, -4799964147], [-289576466983143, -289616695838493, -1310809860147, 32964142900, -62060511695, 61736026350, 16482071450, -5349584895, 0, -3072453000], [240641343637808, -240643932774593, 6576716700, 1231357343042, 26470690830, -1404349199, 4151403945, 0, -2103570764, 3288358350], [-119869298601552, -62929156587, -519819808504, -497459284606, -30297012568, -119846263157, 20976385529, -6552350301, -6552350301, 9796123580], [-92831487300918, -92816403220458, 1949729051303, -15506970600, 13266512896, -34162289820, -7753485300, -9571052864, 0, 2725458480], [-152125014916401, 152121895394301, -15414782000, -1006073919599, -49792374200, -35103425227, -6667550300, 0, -24276512127, -7707391000], [353001123806230, -352923792735790, 22934569200, -527944721145, -22837101720, 96579513456, -14309738880, 0, 7781158416, 11467284600], [285436844587746, -35043832548, -1033238101431, -1011608525999, -21253282157, -38999988273, 11681277516, 10324591191, 10324591191, 866489800], [3205498842, -156415267531562, 190134872004, -145801177956, 45132039498, 101487892758, 21098347410, -13889004276, 13889004276, 1068499614], [15755443563, 202977600072018, -2222264241794, 2223209080436, -40854183613, 2146602692, -4779395200, -5508739929, 5508739929, 5251814521], [218206926790668, -218141890927398, 19999487850, -3447184841338, -16716276885, 55121844319, -11678877165, 0, -19913762876, 9999743925], [-6866089999446, 101409654216, 373821807212, 327381870108, 47537134884, 155423099596, -33803218072, -11539521252, -11539521252, -10583249520], [-66281148569568, 66195702233868, 11395706000, 799103876203, 153813418600, -71540544710, 34179964900, 0, 8207937990, 5697853000], [-86868233235816, -86877168040056, -456850742534, -26505924250, 33199820939, -104683807195, -13252962125, 28881663054, 0, 16231230205], [-290497449009227, 290393868314237, -24549228900, 906274581057, 52185292170, -106807382181, 22252283880, 0, 9047927259, -12274614450], [167446173136959, 23749357269, 924763049543, 899800613947, 25675083121, 1638177919, -7916452423, -16333335648, -16333335648, 4564765375], [-271474043521791, 271399373567061, -58866927200, 251114184916, -106474305560, -106555192672, -4543478690, 0, -2451774342, -29433463600], [-270632382243789, -270548582791029, 1875510012489, -21820988800, 90866982713, 35359142880, -10910494400, -3842964447, 0, -17022656520], [368530088717668, -36786640374, 557196443217, 604368981513, -69383543661, -2377367289, 12262213458, 12699319473, 12699319473, -11324055690], [10444429008060, -10495086087705, -24965539200, 2011438074230, -19836614340, -47840352431, 4402923615, 0, 15299496814, -12482769600]]