# Trace form for 354.6.a.e, downloaded from the LMFDB on 25 April 2024. [0, 5, 20, -45, 80, 166, -180, -198, 320, 405, 664, -516, -720, 1018, -792, -1494, 1280, 3004, 1620, -114, 2656, 1782, -2064, -1302, -2880, 8967, 4072, -3645, -3168, 16372, -5976, -4784, 5120, 4644, 12016, -9702, 6480, 5016, -456, -9162, 10624, 5440, 7128, 5494, -8256, 13446, -5208, 19470, -11520, 80323, 35868, -27036, 16288, 63310, -14580, 62324, -12672, 1026, 65488, -17405, -23904, 71776, -19136, -16038, 20480, -39492, 18576, 79962, 48064, 11718, -38808, 9928, 25920, 92772, 20064, -80703, -1824, 42750, -36648, -18444, 42496, 32805, 21760, 106030, 28512, 283366, 21976, -147348, -33024, 315950, 53784, 354078, -20832, 43056, 77880, 371662, -46080, 268078, 321292, -41796, 143472, 210784, -108144, 53522, 65152, 87318, 253240, 195470, -58320, 463084, 249296, -45144, -50688, 74896, 4104, -145886, 261952, 82458, -69620, 89856, -95616, -185243, 287104, -48960, -76544, 484332, -64152, -70004, 81920, -49446, -157968, -375724, 74304, -666108, 319848, -121014, 192256, 250810, 46872, -201648, -155232, -175230, 39712, -655688, 103680, 189334, 371088, -722907, 80256, -574954, -322812, -633876, -7296, 243324, 171000, -753814, -146592, 199298, -73776, -569790, 169984, -1307736, 131220, -509586, 87040, -560916, 424120, -888162, 114048, 712343, 1133464, -9234, 87904, -906178, -589392, -1010880, -132096, 156645, 1263800, -350824, 215136, -894224, 1416312, -645984, -83328, -606994, 172224, 603206, 311520, 144342, 1486648, -241560, -184320, 1723550, 1072312, 355428, 1285168, 826742, -167184, -446678, 573888, -719658, 843136, -544374, -432576, -1290350, 214088, -105462, 260608, 1313482, 349272, -1217628, 1012960, -89352, 781880, 1350600, -233280, -1839978, 1852336, -834948, 997184, -963570, -180576, 221932, -202752, 726327, 299584, 590042, 16416, -510172, -583544, -384750, 1047808, 108120, 329832, -2168306, -278480, 165996, 359424, -575320, -382464, -1334834, -740972, -295245, 1148416, 5425472, -195840, -3436834, -306176, -954270, 1937328, -3577160, -256608, -1116026, -280016, -2550294, 327680, 266950, -197784, -1396656, -631872, 1326132, -1502896, -887234, 297216, 1021896, -2664432, -2843550, 1279392, 2447192, -484056, -3493960, 769024, -3186702, 1003240, 4347500, 187488, -782050, -806592, -387504, -620928, 771878, -700920, -2165860, 158848, -3344958, -2622752, 24678, 414720, -486411, 757336, -2412702, 1484352, 3804376, -2891628, -577846, 321024, 376164, -2299816, 1454714, -1291248, -6704658, -2535504, -1897056, -29184, -1180286, 973296, -10871176, 684000, -481698, -3015256, 4875270, -586368, 1671964, 797192, -785862, -295104, 3459618, -2279160, -5625178, 679936, -1759230, -5230944, 3878638, 524880, -9083918, -2038344, -4167756, 348160, 120978, -2243664, -690388, 1696480, 406296, -3552648, 1862992, 456192, -5305000, 2849372, -674064, 4533856, -3198270, -36936, -6273000, 351616, 1312974, -3624712, -3379562, -2357568, 468442, -4043520, -742122, -528384, 3488714, 626580, -3355860, 5055200, -808704, -1403296, 108352, 860544, -1886361, -3576896, 1667187, 5665248, 9961882, -2583936, 432602, -333312, 440640, -2427976, 3817494, 688896, 1413692, 2412824, -4358988, 1246080, 3135402, 577368, 4973268, 5946592, 630036, -966240, 4840236, -737280, -9085770, 6894200, 445014, 4289248, 1894686, 1421712, -11996834, 5140672, 3381516, 3306968, 5039444, -668736, -932918, -1786712, 5994972, 2295552, 7725050, -2878632, -6129346, 3372544, 1089126, -2177496, 779366, -1730304, -4184082, -5161400, -2257290, 856352, 689238, -421848, 2722922, 1042432, 1814832, 5253928, 10024184, 1397088, -12194634, -4870512, 1577070, 4051840, 18956426, -357408, -22603302, 3127520, 5901192, 5402400, 7504506, -933120, -3787628, -7359912, -1704006, 7409344, -293866, -3339792, 2466862, 3988736, 6506163, -3854280, 10301198, -722304, 14147982, 887728, 5174586, -811008, 15771122, 2905308, 2737946, 1198336, 5704884, 2360168, 39561462, 65664, 15460348, -2040688, -2189916, -2334176, 15460508, -1539000, 1215448, 4191232, 6784326, 432480, -6094976, 1319328, 13187934, -8673224, -1793682, -1113920, 5941276, 663984, 17744212, 1437696, 5128110, -2301280, 20389462, -1529856, 3608326, -5339336, 11769624, -2963888, 31346864, -1180980, -3468694, 4593664, 4586274, 21701888, 6002110, -783360, 16016920, -13747336, 5048244, -1224704, 11007558, -3817080, 3773832, 7749312, 7993458, -14308640, -236250, -1026432, -3428964, -4464104, -6411087, -1120064, -14005638, -10201176, 8130762, 1310720, 83106, 1067800, -10694704, -791136, -10920710, -5586624, 8155602, -2527488, 6859704, 5304528, -7699536, -6011584, 9097920, -3548936, -5571904, 1188864, 5716867, 4087584, -1409805, -10657728, 6200286, -11374200, 13462902, 5117568, 3157416, 9788768, -21671790, -1936224, 11362506, -13975840, 8048016, 3076096, 2419150, -12746808, -9791858, 4012960, 5813856, 17390000, -909320, 749952, -7139574, -3128200, 5462946, -3226368, 16243454, -1550016, -16024340, -2483712, -5428854, 3087512, 6054996, -2803680, 7745348, -8663440, -1299078, 635392, -3895162, -13379832, 22975466, -10491008, 2174040, 98712, -26646716, 1658880, -23252150, -1945644, -15511950, 3029344, -710550, -9650808, -14514884, 5937408, -3198852, 15217504, 2894296, -11566512, 398136, -2311384, -7440678, 1284096, -18729340, 1504656, -26517924, -9199264, 4020102, 5818856, -24304380, -5164992, 31695888, -26818632, 6476922, -10142016, -19610914, -7588224, 5815680, -116736, 4899366, -4721144, 2653778, 3893184, 13205158, -43484704, 11613150, 2736000, 9886368, -1926792, -571152, -12061024, 949158, 19501080, -21864078, -2345472, 10162449, 6687856, -11821338, 3188768, -24231814, -3143448, -9904752, -1180416, 10958652, 13838472, -10368476, -9116640, 6949580, -22500712, 804168, 2719744, -4874830, -7036920, -3536446, -20923776, -12155400, 15514552, 18550368, 2099520, 1796196, -36335672, 16559802, -8153376, -23720196, -16671024, 1435404, 1392640, 7514532, 483912, -29176762, -8974656, 37891776, -2761552, 8672130, 6785920, -60353352, 1625184, -28849220, -14210592, -1997388, 7451968, -5016022, 1824768, -7375630, -21220000, -6536943, 11397488, -4945650, -2696256, -31611906, 18135424, -5310378, -12793080, -8848668, -147744, 29331240, -25092000, 4591548, 1406464, 2311564, 5251896, 31811478, -14498848, 3462750, -13518248, -30083152, -9430272, -33342656, 1873768, -973080, -16174080, -17216262, -2968488, -22662050, -2113536, 19514754, 13954856, -10135080, 2506320, -11065030, -13423440, -1493964, 20220800, 5083860, -3234816, -26976564, -5613184, 5177880, 433408, 14640294, 3442176, 20468772, -7545444, 12013506, -14307584, 15814358, 6668748, -2928364, 22660992, 2657205, 39847528, -8322990, -10335744, 61460138, 1730408, -48829248, -1333248, 12028060, 1762560, -8340392, -9711904, 30931506, 15269976, -27658766, 2755584, -1403750, 5654768, 8588430, 9651296, -20130372, -17435952, -11415418, 4984320, 32194440, 12541608, -35059666, 2309472, -121682756, 19893072, 10044234, 23786368, -8845018, 2520144, -101418840, -3864960, 22952646, 19360944, -3543658, -2949120, 13473500, -36343080, -2402550, 27576800, 1688176, 1780056, -14637762, 17156992, 12569904, 7578744, -47358536, 5686848, 14316844, -47987336, -11935188, 20562688, -39557040, 13526064, -38325596, 13227872, 7985106, 20157776, -19299798, -2674944, -56024658, -3731672, -9197064, -7146848, 9593060, 23979888, 4842064, 9182208, 25591950, 30900200, 18959194, -11514528, 8052228, -24517384, -22024728, 13490176, 4026658, 4356504, 39913654, -8709984, 31445640, 3117464, -51578210, -6921216, 38525018, -16736328, 28680318, -20645600, -31008070, -9029160, 25945218, 3425408, -39127500, 2756952, -26601872, -1687392, -34726832, 10891688, 7038450, 4169728, 92825702, 7259328, -83536170, 21015712, 3487536, 40096736, -42902216, 5588352, 26606385, -48778536, -6946902, -19482048, 132190658, 6308280, -65556972, 16207360, 19492740, 75825704, 63040006, -1429632, 29848280, -90413208, 30104622, 12510080, -43289744, 23604768, 20934934, 21609600, -222102, 30018024, -56144882, -3732480, -107582294, -15150512, 4377699, -29439648, -41552500, -6816024, 50516708, 29637376, 21714318, -1175464, -173303298, -13359168, -23643570, 9867448, -34239384, 15954944, 22212376, 26024652, 7561912, -15417120, 5200614, 41204792, 9317904, -2889216, 84027150, 56591928, -3385476, 3550912, -49755820, 20698344, -34755400, -3244032, -13092426, 63084488, 29054990, 11621232, 108838626, 10951784, 60341922, 4793344, -7803142, 22819536, 6880540, 9440672, 17073504, 158245848, 40976606, 262656, 26871078, 61841392, 10622574, -8162752, 8825976, -8759664, 2829666, -9336704, 97840584, 61842032, -38049656, -6156000, -12465130, 4861792, 4335282, 16764928, 6129160, 27137304, 106967688, 1729920, -43877430, -24379904, 45551954, 5277312, 8894922, 52751736, -15047676, -34692896, 37007796, -7174728, 64440820, -4455680, 7072758, 23765104, -90960358, 2655936, 37829126, 70976848, -31136562, 5750784, -35317714, 20512440, -67549920, -9205120, 50626602, 81557848, 31744530, -6119424, -72188049, 14433304, 15833070, -21357344, 79015468, 47078496, -59207356, -11855552, -34907742, 125387456, 34839950, -4723920, -12628998, -13874776, 81755262, 18374656, -1901592, 18345096, -39291958, 86807552, 37509804, 24008440, -67668348, -3133440, 28220304, 64067680, -1088802, -54989344, 84422222, 20192976, 58761916, -4898816, 6213492, 44030232, -157014266, -15268320, 61702108, 15095328, -3656664, 30997248, 104271282, 31973832, -10456924, -57234560, -16766928, -945000, -7147006, -4105728, -14590890, -13715856, 47745000, -17856416, 37647660, -25644348, -4738698, -4480256, 6066576, -56022552, -145224556, -40804704, 94121034, 32523048, 28784430, 5242880, -8858170, 332424, 90400792, 4271200, 56457000, -42778816, 78260110, -3164544, -16835862, -43682840, -11816766, -22346496, -8009300, 32622408, -62678328, -10109952, 30416058, 27438816, -94932108, 21218112, 33731942, -30798144, -4215978, -24046336, 85263062, 36391680, -36705316, -14195744, 6679098, -22287616, -15324014, 4755456, -73703934, 22867468, -31398426, 16350336, 36795348, -5639220, -91500122, -42630912, 30202740, 24801144, 15907092, -45496800, 108879622, 53851608, 7278336, 20470272, -100921576, 12629664, 71706562, 39155072, -975168, -86687160, -123472690, -7744896, -55157176, 45450024, 16977249, -55903360, -76157262, 32192064, -13951352, 12304384, -15004683, 9676600, -32002980, -50987232, -116203026, -39167432, -89656938, 16051840, 85582086, 23255424, -140094126, 69560000, -3893418, -3637280, -53654456, 2999808, -145830834, -28558296, -3965760, -12512800, 104635350, 21851784, -88057556, -12905472, -34357446, 64973816, 117587304, -6200064, -146505302, -64097360, -12723228, -9934848, 396834, -21715416, -69947910, 12350048, 39230892, 24219984, -41070396, -11214720, -139347274, 30981392, -28218618, -34653760, -21797060, -5196312, -53165278, 2541568, -44759412, -15580648, 32660362, -53519328, 208930626, 91901864, -5670324, -41964032, -76703182, 8696160, -27523440, 394848, -43562124, -106586864, 115377094, 6635520, 133107406, -93008600, 81771930, -7782576, 88843874, -62047800, -1537772, 12117376, -4005126, -2842200, 153584264, -38603232, 15991548, -58059536, -17052174, 23749632, 106033806, -12795408, 162245350, 60870016, 107971506, 11577184, 4748872, -46266048, -77419438, 1592544, -30433644, -9245536, 93963804, -29762712, -41830560, 5136384, -45354996, -74917360, 99239820, 6018624, -162503258, -106071696, 8396262, -36797056, 121916330, 16080408, 156387380, 23275424, -53954748, -97217520, -77494498, -20659968, -62678264, 126783552, -69525450, -107274528, 202621652, 25907688, 77804310, -40568064, 55164114, -78443656, -47772126, -30352896, 114014140, 23262720, -9802134, -466944, -34716650, 19597464, -275368738, -18884576, -7014294, 10615112, 142560442, 15572736, 105287991, 52820632, 37656738, -173938816, 114490494, 46452600, -95820344, 10944000, 20315610, 39545472, -287055558, -7707168, 158529956, -2284608, -6203142, -48244096, 122059492, 3796632, 131396916, 78004320, -24506298, -87456312, -96822606, -9381888, 9393128, 40649796, -16333488, 26751424, 305387118, -47285352, -296924720, 12755072, -90217656, -96927256, 17554808, -12573792, 66056396, -39619008, 109751706, -4721664, -9658918, 43834608, 75957354, 55353888, -14193630, -41473904, -55510390, -36466560, -111976198, 27798320, -170607834, -90002848, -35943866, 3216672, -65956582, 10878976, 203429718, -19499320, -39325750, -28147680, 31137444, -14145784, -53110728, -83695104, -115003842, -48621600, 162295470, 62058208, -67540554, 74201472, -27554292, 8398080, -56730048, 7184784, 34088652, -145342688, 31930722, 66239208, 137240626, -32613504, 15336054, -94880784, -34592380, -66684096, -275244948, 5741616, 2644794, 5570560, 276592108, 30058128, -258208074, 1935648, -22201758, -116707048, 79321676, -35898624, 240081044, 151567104, -58555467, -11046208, 184233970, 34688520, -201776484, 27143680, -92710782, -241413408, -41744592, 6500736, -1959154, -115396880, -127331838, -56842368, -294907266, -7989552, 187854456, 29807872, -46571274, -20064088, -69543934, 7299072, 10450436, -29502520, -141940098, -84880000, -90690166, -26147772, 149399784, 45589952, -24641514, -19782600, 39197408, -10785024, 4532262, -126447624, -51343956, 72541696, 117213288, -21241512, 160528030, -51172320, -356053158, -35394672, 120808982, -590976, -48945927, 117324960, -139143132, -100368000, 109267402, 18366192, 112836252, 5625856, 19709244, 9246256, 50374872, 21007584, -97700002, 127245912, -139144572, -57995392, -189273492, 13851000, 75237428, -54072992, -10939032, -120332608, 116030798, -37721088, -191294370, -133370624, -61058934, 7495072, -86115412, -3892320, 85578146, -64696320, 54854784, -68865048, 115151392, -11873952, -67927936, -90648200, -118691406, -8454144, -87484716, 78059016, 272944652, 55819424, 16143138, -40540320, -453062578, 10025280, -196121274, -44260120, -53471484, -53693760, 612647780, -5975856, -38950506, 80883200, -159697908, 20335440, -3144372, -12939264, 181788824, -107906256, -46152990, -22452736, -30246972, 20711520, -1843974, 1733632, -183505158, 58561176, 116946960, 13768704, 155431508, 81875088, -32474934, -30181776, 303171968, 48054024, 116964390, -57230336, -105926616, 63257432, 165119642, 26674992, -132328992, -11713456, -282121776, 90643968, 100680042, 10628820, 98505298, 159390112, 31218246, -33291960, -133945920, -41342976, -26093906, 245840552, -41276466, 6921632, -106778344, -195316992, -109918320, -5332992, -54018990, 48112240, -31214127, 7050240, 184895424, -33361568, -144152280, -38847616, -8978748, 123726024, 96104862, 61079904, -45434196, -110635064, -114546600, 11022336, -175034606, -5615000, -99068022, 22619072, 188179042, 34353720, 131686254, 38605184, -33964488, -80521488, -257133696, -69743808, 136689166, -45661672, -71941122, 19937280, -389647242, 128777760, -23037596, 50166432, 2126250, -140238664, -29943226, 9237888, 141426408, -486731024, 30860676, 79572288, 462048368, 40176936, 86331800, 95145472, 57699783, -35380072, -49823696, 10080576, 316161350, -405675360, 126050742, -15459840, 49520960, 91810584, 260797518, 77443776, -73176858, -14174632, -252457208, -11796480, 577242594, 53894000, -747954, -145372320, -81754690, -9610200, -112876112, 110307200, 96252336, 6752704, 877519584, 7120224, -57283126, -58551048, 98286390, 68627968, -279636548, 50279616, 327058282, 30314976, -73400418, -189434144, -42956666, 22747392, -73138536, 57267376, -61737336, -191949344, -68351118, -47740752, 6993658, 82250752, 69295824, -158228160, -212955200, 54104256, -6814162, -153302384, -81881280, 52911488, 44393352, 31940424, -48666746, 80631104, 50147136, -77199192, -46209164, -10699776, 41732608, -224098632, -51451803, -14926688, 221687856, -36788256, 185251042, -28587392, 12688245, 38372240, 83253206, 95919552, -11796636, 19368256, -55802574, 36728832, -14477706, 102367800, 594508590, 123600800, -121166118, 75836776, 111675086, -46058112, -559522354, 32208912, -28416744, -98069536, -98590962, -88098912, 517237582, 53960704, 195046110, 16106632, -111416256, 17426016, -77528974, 159654616, -102262554, -34839936, -782105544, 125782560, 574037354, 12469856, -72432144, -206312840, -408144240, -27684864, -378555874, 154100072, -21772350, -66945312, 691019500, 114721272, 74976054, -82582400, 88126722, -124032280, 89464862, -36116640, -19586826, 103780872, -52324704, 13701632, 185235962, -156510000, 455971920, 11027808, 8183880, -106407488, 276602484, -6749568, 247632688, -138907328, 64256166, 43566752, 81475934, 28153800, -255017082, 16678912, -49166514, 371302808, 264065956, 29037312, -256628038, -334144680, -146191086, 84062848, 23459454, 13950144, 170474686, 160386944, 144219060, -171608864, -113065456, 22353408, 193396293, 106425540, 48859686, -195114144, -176378126, -27787608, -381646224, -77928192, -54494964, 528762632, 78806788, 25233120, 309839958, -262227888, -69708132, 64829440, 56195994, 77970960, 466544234, 303302816, 11691702, 252160024, -372286516, -5718528, -14580254, 119393120, 35056458, -361652832, 193612552, 120418488, -56990932, 50040320, -206779194, -173158976, -55896948, 94419072, -328232964, 83739736, -19566360, 86438400, 360428352, -888408, -86455768, 120072096, 239820444, -224579528, -36605908, -14929920, 527004756, -430329176, 209269350, -60602048, -138804834, 17510796, 148658270, -117758592, 139607550, -166210000, 48943096, -27264096, -145840070, 202066832, 6394950, 118549504, -91147952, 86857272, 208122678, -4701856, 130633956, -693213192, -291324124, -53436672, 168248296, -94574280, 28789668, 39469792, 102509694, -136957536, 384013776, 63819776, -26048664, 88849504, 187895766, 104098608, -510854210, 30247648, -3583224, -61668480, 79484074, 20802456, 815656932, 164819168, 66966102, 37271616, 346475848, -11556864, -133873930, 336108600, 168564060, 226367712, 124289956, -13541904, 801200472, 14203648, 238661316, -199023280, 361753902, 82793376, -341406482, -139021600, -36180918, -12976128, 58322506, -52369704, 229598736, 252337952, 218739420, 116219960, 36452880, 46484928, 64667538, 435354504, -285262992, 43807136, -34148964, 241367688, -231303356, 19173376, -58292298, -31212568, 344032188, 91278144, -754574574, 27522160, 176498226, 37762688, 407725090, 68294016, 115500702, 632983392, -52341120, 163906424, -240908696, 1050624, 296944594, 107484312, -44094294, 247365568, 16653104, 42490296, 139195230, -32651008, -23884002, 35303904, 174008356, -35038656, -511381326, 11318664, -118846422, -37346816, -67818294, 391362336, 454982826, 247368128, -104518350, -152198624, 136173404, -24624000, -282337135, -49860520, -88977312, 19447168, 176831074, 17341128, -92126754, 67059712, 5140368, 24516640, 319988548, 108549216, -570959286, 427870752, -8542422, 6919680, -260091350, -175509720, -215499530, -97519616, 196776702, 182207816, -52214118, 21109248, -90039646, 35579688, -91462041, 211006944, 311666820, -60190704, 162284870, -138771584, 106392042, 148031184, 9984114, -28698912, -318316338, 257763280, 218086326, -17822720, 210222074, 28291032, 262807886, 95060416, 89142768, -363841432, -300942916, 10623744, -136065258, 151316504, -98627868, 283907392, 390457036, -124546248, -311577642, 23003136, 93316284, -141270856, -5371728, 82049760, -728628420, -270199680, -62546220, -36820480, -562558112, 202506408, 879381200, 326231392, -7237512, 126978120, -354332860, -24477696, -102107206, -288752196, 43873470, 57733216, -1003268736, 63332280, 165822802, -85429376, 31828014, 316061872, -360580192, 188313984, -297797766, -236829424, 109398600, -47422208, -564060974, -139630968, 439713018, 501549824, -166953312, 139359800, -97906070, -18895680, -175632988, -50515992, -16165764, -55499104, 199950112, 327021048, 320287258, 73498624, -149038218, -7606368, -681986402, 73380384, -467537968, -157167832, 213481764, 347230208, -601530278, 150039216, -540631046, 96033760, -12918636, -270673392, 527899068, -12533760, 23912104, 112881216, -67630788, 256270720, -462830770, -4355208, -693479764, -219957376, 262590858, 337688888, -307344870, 80771904, 23394060, 235047664, -341025984, -19595264, -577345568, 24853968, -175227878, 176120928, -78049170, -628057064, 117420114, -61073280, -453156656, 246808432, 543180168, 60381312, -174990316, -14626656, -208931402, 123988992, 259642980, 417085128, 379399600, 127895328, -249832674, -41827696, 17976492, -228938240, -1466894608, -67067712, 58556724, -3780000, 45144198, -28588024, -577653390, -16422912, -602479618, -58363560, 66380670, -54863424, -233250190, 190980000, -88562952, -71425664, 58832487, 150590640, 238406628, -102577392, -484242356, -18954792, 44510850, -17921024, 213552958, 24266304, 300535690, -224090208, 284507154, -580898224, -547843734, -163218816, -615400300, 376484136, 47793402, 130092192, -1033475660, 115137720, 205789360, 20971520, 79638012, -35432680, 9182160, 1329696, -523357530, 361603168, -263981160, 17084800, -505156246, 225828000, 114166806, -171115264, -41323932, 313040440, -756772120, -12658176, 33772662, -67343448, -20804076, -174731360, -426127640, -47267064, 111410302, -89385984, -286303302, -32037200, 1072121172, 130489632, -439130538, -250713312, -31164750, -40439808, -771828182, 121664232, -358081896, 109755264, 270748368, -379728432, -802900122, 84872448, 149799030, 134927768, 300083904, -123192576, -1628941032, -16863912, 190547976, -96185344, 8757720, 341052248, -754011846, 145566720, -275785296, -146821264, 154946358, -56782976, -524191832, 26716392, -21790492, -89150464, 203958450, -61296056, 45435556, 19021824, 488200570, -294815736, -175632786, 91469872, 139131346, -125593704, 35197466, 65401344, 91215720, 147181392, 251792592, -22556880, 864913974, -366000488, 99585270, -170523648, -176493962, 120810960, -57756788, 99204576, 13445676, 63628368, -1532942730, -181987200, -403878914, 435518488, -45754740, 215406432, -744367348, 29113344, -627678052, 81881088, 242789076, -403686304, -15387690, 50518656, 362983392, 286826248, -46600920, 156620288, -317549030, -3900672, -511027518, -346748640, -131762646, -493890760, -288972002, -30979584, -207232434, -220628704, -184218948, 181800096, -384940178, 67908996, -298011628, -223613440, -108121554, -304629048, 800707986, 128768256, -787605114, -55805408, -142329222, 49217536, -685436364, -60018732, 339139710, 38706400, 26355276, -128011920, -17460696, -203948928, -731838098, -464812104, -23914845, -156669728, -887936422, -358627752, -555855264, 64207360, 74906910, 342328344, -879957118, 93021696, -995179864, -560376504, -553141242, 278240000, 65127290, -15573672, 108277304, -14549120, 439463232, -214617824, -941353984, 11999232, -493083653, -583323336, -108252540, -114233184, -693154542, -15863040, 96776922, -50051200, 75063528, 418541400, 675634590, 87407136, 7721512, -352230224, -278383554, -51621888, 362285072, -137429784, 219609852, 259895264, 248928894, 470349216, 504139926, -24800256, 242911674, -586021208, 12633750, -256389440, -89360148, -50892912, 359065254, -39739392, -77295870, 1587336, 1151847332, -86861664, -197159620, -279791640, 181173348, 49400192, 192550606, 156923568, 367445334, 96879936, 102738762, -164281584, 457552634, -44858880, 811425236, -557389096, -289749960, 123925568, -1184229666, -112874472, -515994762, -138615040, 315536994, -87188240, 338191050, -20785248, 436553968, -212661112, 1095144804, 10166272, -445873896, -179037648, 2494802304, -62322592, -90398106, 130641448, -716243264, -214077312, 713932, 835722504, 79605162, 367607456, 515165954, -22681296, 797243988, -167856128, 912769560, -306812728, 241479914, 34784640, -256935914, -110093760, -206573814, 1579392, 650383972, -174248496, 11082480, -426347456, 31892922, 461508376, -132212982, 26542080, 60966486, 532429624, -121261500, -372034400, 770809960, 327087720, 1199026026, -31130304, 21622950, 355375496, -437505090, -248191200, -1897823736, -6151088, -15193584, 48469504, 88903666, -16020504, 1101655796, -11368800, 131739858, 614337056, 1130089740, -154412928, 572416518, 63966192, -113129136, -232238144, -105149536, -68208696, -173493320, 94998528, 426226824, 424135224, -387847908, -51181632, 886814454, 648981400, -128851596, 243480064, 400710006, 431886024, 756138872, 46308736, 107416692, 18995488, 507297288, -185064192, 83916086, -309677752, 356013360, 6370176, 1022883668, -121734576, 952979112, -36982144, 344930364, 375855216, -272475418, -119050848, 500781216, -167322240, -71865954, 20545536, 545689784, -181419984, -148872980, -299669440, 173698182, 396959280, 1228665930, 24074496, -579538576, -650013032, 504221922, -424286784, 249206712, 33585048, 647049516, -147188224, 82773576, 487665320, 497740878, 64321632, 206317832, 625549520, -86337540, 93101696, 343137024, -215818992, 1817981434, -388870080, -43578576, -309977992, 99794560, -82639872, 2098833317, -250713056, -230327550, 507134208, 348413094, -278101800, 705405062, -429098112, -170632746, 810486608, 268324466, 103630752, -556268222, 311217240, -72470052, -162272256, -400360352, 220656456, -18936640, -313774624, 198222552, -191088504, -390781972, -121411584, 508939002, 456056560, -36239922, 93050880, -269185590, -39208536, -663570102, -1867776, -359222886, -138866600, -256084058, 78389856, 224962846, -1101474952, -283010760, -75538304, 65630792, -28057176, 450913770, 42460448, 464203890, 570241768, -168149456, 62290944, -41452122, 421151964, -346725162, 211282528, 291036976, 150626952, 549200386, -695755264, -258122862, 457961976, 813298816, 185810400, 249997654, -383281376, 279072630, 43776000, 1409140744, 81262440, -262390390, 158181888, -233506962, -1148222232, 271424700, -30828672, 458086604, 634119824, 352147500, -9138432, 677609272, -24812568, 701705530, -192976384, 239416848, 488237968, -977275308, 15186528, -542726874, 525587664, 312541488, 312017280, 410921308, -98025192, 881384642, -349825248, -63346050, -387290424, 901547292, -37527552, -708814682, 37572512, -835431318, 162599184, 1203383758, -65333952, 111516832, 107005696, 751825530, 1221548472, 195817942, -189141408, -499623524, -1187698880, -31387824, 51020288, 1077858072, -360870624, -1176959286, -387709024, 386119944, 70219232, 314114674, -50295168, -508510558, 264225584, -239457465, -158476032, -1083654404, 439006824, -748192356, -18886656, 62522118, -38635672, 731745238, 175338432, -75691934, 303829416, -1189715922, 221415552, -19124614, -56774520, 938132862, -165895616, 590012748, -222041560, -197736524, -145866240, -418231842, -447904792, -175434660, 111193280, -264374520, -682431336, -164169914, -360011392, -567360054, -143775464, 185102406, 12866688, 188199008, -263826328, -268634520, 43515904, 985594256, 813718872, -752773572, -77997280, -270941598, -157303000, -478674976, -112590720, -1748294514, 124549776, 389607696, -56583136, 235482578, -212442912, -721174502, -334780416, -188414406, -460015368, 1116506130, -194486400, 932471190, 649181880, 1998918, 248232832, 318495242, -270162216, -70813398, 296805888, 505303938, -110217168, 109005842, 33592320, -146353728, -226920192, 968240646, 28739136, 2162240228, 136354608, 490008354, -581370752, -39399291, 127722888, 377792246, 264956832, -1795265342, 548962504, 373972500, -130454016, 217281284, 61344216, 874347012, -379523136, -454650372, -138369520, -849235892, -266736384, -666770426, -1100979792, -195428862, 22966464, 205386078, 10579176, 946943214, 22282240, 1559729682, 1106368432, 71752030, 120232512, 1460494036, -1032832296, 212792130, 7742592, -426806562, -88807032, -177236512, -466828192, 308154456, 317286704, 1791224262, -143594496, -403284638, 960324176, -199911384, 606268416, 69638468, -234221868, -1084959374, -44184832, -68057208, 736935880, 1539573816, 138754080, -2143720386, -807105936, -46805526, 108574720, 651821776, -370843128, -140530776, -965653632, -83861136, -166978368, -307616064, 26002944, 733453650, -7836616, -756244350, -461587520, -76970010, -509327352, -156551892, -227369472, 30469284, -1179629064, -298712140, -31958208, 132340980, 751417824, 447802380, 119231488, 1206735858, -186285096, -1395248014, -80256352, 312798600, -278175736, 963009740, 29196288, 201858714, 41801744, 117831834, -118010080, -542532442, -567760392, 173757550, -339520000, -261494910, -362760664, 775228226, -104591088, -221935508, 597599136, -979547634, 182359808, 1384289132, -98566056, -736940366, -79130400, -543077298, 156789632, 258204450, -43140096, -1690327750, 18129048, 70228278, -505790496, -629178634, -205375824, -73528530, 290166784, -61924860, 468853152, -2628159660, -84966048, 1455611642, 642112120, -153661536, -204689280, 1079814298, -1424212632, -1146012670, -141578688, -368789454, 483235928, -977651582, -2363904, 129593898, -195783708, -241839702, 469299840, 739361770, -556572528, 531186338, -401472000, -95603166, 437069608, 1379526190, 73464768, 1778709158, 451345008, -79433784, 22503424, -621311316, 78836976, 1600787308, 36985024, -25466994, 201499488, -387813422, 84030336, 14760704, -390800008, -880565256, 508983648, 1625729994, -556578288, -1658330128, -231981568, 342446904, -757093968, 254957056, 55404000, -67775070, 300949712, 112186170, -216291968, -153637892, -43756128, 2116925406, -481330432, -39017538, 464123192, 1301915544, -150884352, -693787956, -765177480, -55162440, -533482496, -111757232, -244235736, 255433010, 29980288, -962709192, -344461648, -1406094876, -15569280, -60000806, 342312584, 394896870, -258785280, -472101410, 219419136, -862569274, -275460192, -409967586, 460605568, -808515360, -47495808, 1184829303, -271711744, -80054298, -362592800, 369365474, -474765624, -555607076, -33816576, 135429084, -349938864, 433128164, 312236064, -1022783814, 1091778608, -333070164, 223277696, 1124389248, 64572552, 1098820888, -162161280, -579967380, -1812250312, 970961322, 40101120, -8761456, -784485096, -63654822, -177040480, 200923160, -213885936, -1222710108, -214775040, 818643222, 2450591120, -1206712326, -23903424, 271050738, -155802024, -340462134, 323532800, 848155500, -638791632, 1491314660, 81341760, 280229058, -12577488, 59101588, -51757056, -1699407974, 727155296, 317859426, -431625024, 948918434, -184611960, -298134756, -89810944, 607949280, -120987888, 1045765870, 82846080, 156352240, -7375896, -455639418, 6934528, 2338642370, -734020632, -797404746, 234244704, -285700770, 467787840, 703680364, 55074816, -122560528, 621726032, 649692441, 327500352, -566667124, -129899736, 2079527516, -120727104, -142497630, 1212687872, -279604363, 192216096, -1796989742, 467857560, -711139212, -228921344, 938946916, -423706464, -1762351640, 253029728, 532866204, 660478568, -1297837710, 106699968, -2383109658, -529315968, 314169678, -46853824, 116071366, -1128487104, 672130938, 362575872, -313559550, 402720168, 417184632, 42515280, 59067014, 394021192, 113660982, 637560448, 310092430, 124872984, -1008375358, -133167840, -735797358, -535783680, -524015314, -165371904, -237776184, -104375624, 17114328, 983362208, 836200476, -165105864, 106460136, 27686528, 353627622, -427113376, 608684240, -781267968, -1917600020, -439673280, -337588236, -21331968, 622652540, -216075960, -948773574, 192448960, 609015132, -124856508, 1704798138, 28200960, 133954586, 739581696, -253982736, -133446272, 477367330, -576609120, -1775427068, -155390464, 9799218, -35914992, 16762454, 494904096, -1290419342, 384419448, -759799998, 244319616, -272167328, -181736784, 775561242, -442540256, -528857244, -458186400, -4023655416, 44089344, 1339501734, -700138424, -55921428, -22460000, 2103562816, -396272088, -292457594, 90476288, 1413128394, 752716168, -914419000, 137414880, -763781332, 526745016, -555318972, 154420736, -371472458, -135857952, -990601500, -322085952, 32909976, -1028534784, -787507348, -278975232]