# Stored data for newform 150.6.g.a, downloaded from the LMFDB on 25 April 2024.
{"label": "150.6.g.a", "space_label": "150.6.g", "level": 150, "weight": 6, "hecke_orbit": 1, "hecke_orbit_code": 412417523862, "dim": 20, "is_polredabs": false, "trace_hash": 398933892863229170, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[7, [100958609795235984, 8167718788477620, -864743821499495, -66684308302480, 17548207095, 65226626294, 1080778560, 499140, -64540, -90, 1]]], "qexp_display": "q-4\\beta _{6}q^{2}-9\\beta _{7}q^{3}+2^{4}\\beta _{7}q^{4}+(-5+\\cdots)q^{5}+\\cdots", "char_order": 5, "char_parity": 1, "char_degree": 4, "char_conductor": 25, "char_orbit_label": "g", "char_is_real": false, "Nk2": 5400, "analytic_conductor": 24.057572971947096, "hecke_ring_index": 2500000000, "level_radical": 30, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": 0, "analytic_rank_proved": true, "char_values": [150, 5, [101, 127], [5, 2]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [2, 3, 5], "conrey_indexes": [31, 61, 91, 121], "field_disc": 1645306521547097472990587580657799521851933426140167236328125, "field_disc_factorization": [[5, 15], [326004351581, 2], [22522934813101, 2]], "field_poly": [45940690246932155189634577205, -10498749516125580450644510315, 11299132807307021058314145735, -1622318535480468844324766865, 865137734840778899106150416, -65050346450081546072582845, 22144208384329171616972475, -395836369710607771806480, 100084099910299358028076, -750799480917962811625, 150954604904063839080, -433752716999522710, 72521519492275041, -105918997871590, 15161344295580, -12026298320, 1505002471, -605415, 67300, -10, 1], "hecke_ring_index_factorization": [[2, 8], [5, 10]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "18.491", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1165.214", "prec": 27}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "129789.248", "prec": 34}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 5, "sato_tate_group": "5.2.3.c5", "trace_display": [20, 45, -55, 180], "traces": [0, 20, 20, 45, -80, -55, -180, 180, 320, -405, 220, 380, 720, -230, -920, -630, -1280, 2870, -6480, 1560, 1120, 2880, -720, 760, 11520, 1725, 7320, 3645, -5120, 12000, 5220, -1710, -20480, -1620, 20620, -22440, -6480, -5595, -5240, 2070, -9280, -2820, -11520, 66020, 2880, -8505, 21960, -19630, 11520, -61780, 100, -41130, -3680, 62735, -14580, 66590, 20480, 51660, -48000, 105100, 15120, 34790, -28560, 18630, -20480, -44345, 13680, -19470, 73120, 49410, -81240, -111720, 25920, -198830, -104120, 60975, -91840, 144740, 41220, 71210, -26880, -32805, 166680, -288690, -33120, 338735, 39920, 108225, -24320, 114225, 17820, -155800, -87840, 97740, 78520, -416900, -46080, -446970, -123380, -90720, -108400, 206230, -185580, 594470, -73280, -131940, -250940, 548620, 58320, 102360, 541240, 50355, 58880, 300835, 47160, -422270, -192400, 92745, 266000, -94590, -31680, -543525, -123260, 25380, -173760, -203875, -58320, -759190, 81920, 207270, -1301820, 603360, 161280, 1900, -142320, 40095, 329920, -107580, 27360, -68080, 234560, -187380, 446880, -315300, -103680, 358800, -84780, -405, -89520, -855270, 62100, 454700, -83840, 232470, 1163040, -386710, -164880, 1325010, -284840, 487260, 56320, 1183530, 131220, -533570, -45120, -240660, -657440, 644480, 103680, 319185, -192040, 126360, -368480, -984015, 1800, -1642700, -286720, -945900, 148200, 409230, -71280, -1674300, 1517600, -277335, -48640, 1312660, 257040, 885450, 333120, -167670, -235200, -710070, 184320, 789770, 1787880, 842130, 720, -1227475, -123120, -2176480, -110400, 289980, -531020, 4546460, -413280, -408635, -2377880, 766260, 293120, 2788850, 488160, 679450, -866240, -1019070, -125880, -2974520, -233280, 1195210, 3851160, -190755, 427840, -1166865, -267120, -1771240, -184320, 271350, 1729960, 261620, -224640, -492255, -1482520, 2616840, -3200, -2524765, 74520, 4189660, 1681600, 831060, -234640, -3500440, 126720, -1451335, 2174100, -1180980, 493040, -2294035, 851580, -3606020, -456960, -2237940, 308000, 2468320, 298080, 3749480, -1318040, 149310, -327680, -1303470, -829080, 7632820, -1497120, -974025, 147360, -3498330, 218880, -6213420, 1060400, 333450, -515520, 1977335, 204120, 3059410, 734720, 1402200, -1493880, -5289300, -1362240, 1577395, -1582480, -138510, -867840, -4655635, -85680, -2074970, 1811680, -4138200, 780600, 2290830, 414720, -5477505, -699900, -1778895, 339120, 14939230, 1620, 4328750, 474880, -131220, 763880, 335780, -482400, 9435900, 1447000, 2122830, 399360, 8174040, -929880, -14798340, -4652160, 5776020, -470360, -5776250, -132480, -6282270, -2479140, -2113290, -1477440, -7588320, -618840, 7629910, -225280, 2752020, -2577520, -3315690, 2099520, -13337100, 976080, -921240, -1513920, -12868380, -709560, -1361220, 3978560, -601020, 7077080, 4705710, -529920, 2409680, -2924240, -2707515, -265440, -62590, -505440, 27264240, 1473920, 2042280, 1053360, 3787740, 1731600, 13796070, -1782200, 1334070, -389120, -5520780, -2586600, -2380560, -592800, -646740, -1636920, 1828470, -362880, 2590365, -6850300, -7269525, -2492800, -2832670, 1252440, -625730, 2421760, 1916055, -1196840, 1629010, 246240, 10798580, 1384000, 23625, 152320, -7875935, -933120, -11768870, 7356800, -2965590, 13212080, -19734080, -737280, 405870, -383080, -808380, 3162480, -14845330, -2970720, -12247050, -2880, 10197360, 4909900, 27171750, 233280, 13322220, 2050920, -4737600, 857600, 34236050, 1280880, -12318250, -3773920, 951345, -18185840, 45910580, 1653120, -4676415, -5931460, 968220, -10268480, -10125350, -246240, 8362080, 235520, -3560580, 5333200, 6519980, 3756960, -7596590, 247000, 1686420, 1100160, -22744825, -108720, -22158930, -4892480, -3175200, -8177120, -19132900, -3732480, -11588545, -998840, -3226050, 1637760, -15402830, -7157880, -9642420, 1261440, 2498445, 4667460, 30855520, 1068480, 19354975, -4599640, -5567445, 942080, -3831530, -558900, 36134880, 4813360, -1209600, 2267320, 23723690, 898560, 23393580, 1969020, 3757995, -3630720, -5490625, 5210640, -16481890, -3078400, 2407590, -7496840, -18491650, -2371680, 14179050, -1247440, 11540610, 4598400, 6726670, 1521360, -2653250, 1149760, -4385340, -10747440, -10823230, 645120, -572225, 21529240, -5799420, 12923600, -5237940, -1180980, -13520850, -2226560, 4802130, -5249260, -22273150, -3406320, 7088130, 14424080, 4996890, -437760, -3366130, 5916960, 14538160, -42000, -20246220, 11195920, -5452500, 1658880, -6207560, -14997920, 18904410, 5272160, 24331585, -5414940, -11836640, 1310720, -954990, -21908520, -18988320, 1437120, -34925620, 5085920, 2370060, 5281280, 14506475, -3888000, 34919450, -18128640, 13882050, -3478880, -36070980, -414720, -7368315, 24111880, -5819850, 8422400, -7731860, 4112100, -13912490, -2277120, -868320, -11694440, -3232060, -1691280, -45069765, -12237640, 688950, -2938880, 41173825, 12438000, -2417360, -1721280, -10628010, 20399200, 40655020, 437760, -51298780, 3641920, -8467965, 6329920, 84558850, 554040, 23867590, -6679040, -7969050, -26456960, -44697570, -2998080, 22055230, 2956880, -2099520, 193280, -53217140, -7810200, 35216650, 5644800, 6390630, 18034080, -31388350, 6635520, -34370810, -27027680, 4415895, 5735200, -34744940, 17950680, -9717510, 12725120, -8506620, 9951380, 6634180, -4441680, -23264630, -971600, 8843400, -1899520, 72066290, 524880, 7861680, 9897680, -14408730, 3522480, -15419920, 993600, 42746350, 28035200, -1577070, 2150400, 84962460, -8491320, 95615440, -1597440, 37991160, 4403040, -45041550, -6680880, -15877065, -28063040, -14768460, -9263360, -25751765, 3406320, -80282520, -4280160, 4002210, -12409200, -13301880, 4216320, -15144375, -26457920, -25099650, -20516640, -32983435, 7270560, 8718300, -2704640, 555750, 17974280, -22264290, 7796160, -69930910, -12774440, 9171630, -1146880, -54183950, -11008080, 32299640, 10310080, 25069680, 11062360, 147980, 2099520, 14714920, 30290400, 26008560, -8537120, -31834760, 13645260, -12794160, 6055680, 28776870, 51473520, 47381710, -8883360, 4972850, -20550120, -26577315, -10519040, 12890250, 1812780, -27142280, 35993280, -10349190, -21360840, 107147200, -2949120, 43617145, -6480720, 18225, -33607840, -29399000, -3045240, -18575660, 9626560, 5101470, 55229760, -20980620, 1697760, -2557465, -3062160, -6411330, -2554880, 37893435, -5735520, -84456810, -4213440, 23655240, -15150960, -1721500, 6912000, -8070185, 19468620, -11709990, -24679200, -28626810, -670680, -76785190, 737280, 25298010, 22083120, 125222260, 10346400, 103524970, -36511160, -7479540, -7310400, -40037030, 2111760, 32204810, 1543680, -24181740, -6483680, -69920970, 3006720, 84829810, -12222460, 13062015, -1224800, -4404500, -19022400, -79745000, -22112000, -2657205, 18651080, 27618050, 18894240, -45674470, 27358120, -33030360, -778240, -90862890, 913680, 31107680, 15054160, -7995870, -6516040, 153205420, -984960, 52529425, 21043080, -23383890, 14167200, -13712480, 12640500, 103518180, 5329920, -14083380, 13270140, 70166990, 3732480, 133396390, 47075480, 7249230, 13884800, -69624740, -27330840, -36627510, -11361120, -17798940, -34499080, 35721140, -11796480, -85080030, -83698080, 43428555, -7850480, 36525860, -21390480, -110045050, -31912320, -68695380, -44327780, -43438010, 15122880, 45942270, 33781600, -8748000, 7896320, -82125840, -1326240, -36021900, -15721600, 31484970, -8034200, 24698710, -933120, 53910010, -53288880, 15709905, 25615520, -32461075, -9543600, -9171480, -1766400, -12502350, 28000200, -100352660, 2803680, 31998990, 49273000, 88217010, 15095680, 80453515, 2755620, -100726280, -67539840, -381240, 9167280, -87154370, 11877120, 49214040, 23945960, 27985500, 26255040, 107340050, -2849580, 123930140, -6055680, -56812050, -84860400, -37152160, -7115040, 8122105, 73854480, 8194320, -7495680, -13971350, -2450880, 57360510, 44621600, -5205060, -4371720, 96088670, -12925440, -61766885, 30386360, 35254890, -988000, 62500660, 6360120, 34655680, -13859840, -50655420, -41958200, -70092880, -16305120, -3767565, -85518480, 9335250, 19569920, 103496840, 12700800, 71969730, -44568320, -20617470, -32631000, -80710070, -3732480, -137401695, 5546880, -60812280, -46237440, -124848560, 33368400, -24352560, -24258240, 16010055, 73376320, -91284750, -51158880, -186484550, -55467320, 44835930, 15792640, 59832050, 20016720, -57370730, 47248560, -8650350, 25513320, -115697360, -3222720, 13471910, 9960400, 2493180, 18398560, 169209940, 22269780, 171849800, 5242880, -6414570, 45844420, 2205520, -32400, -24260, 58812480, -20617650, 5413760, 216714565, 4838400, 233361860, -9069280, 10753155, -34129960, -122928550, -3018240, -60000700, 88675480, -78276960, 11397920, 97970020, 13326120, -152344730, 10196480, -3450690, -20144800, 119015450, -42053760, -107726200, -137412640, -51984180, -12288000, -56022060, 11832840, 62871430, 20817760, -27920700, -25885800, -21325080, 1192320, -12712615, -82963200, 56540430, -44974240, 11437475, -46162440, -14930560, -18393600, -14805990, 33923920, -45173870, 13296960, -114289850, 6693000, -217474020, -3754240, -145791970, -20326140, 198775140, 42989760, 194823360, 43292920, 76658590, -5345280, -5960675, -8223300, 2549070, -23221360, -314788645, 42607080, -62908040, 33817600, 24890310, -52302740, 132604960, 4723920, 130362020, -56904800, -61929225, -33589760, 94308100, 23600880, 99098130, 58720640, 30701835, 50842400, -128687820, -1624320, 77191010, -20450920, -8027730, 14214880, 197865160, -21575160, 55364780, 1751040, 67973580, 13464520, 130322600, 41571360, 79552830, 68301360, -18975870, -22472000], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 25, 4, 1, 5, 0]], "char_orbit_index": 7, "prim_orbit_index": 4, "minimal_twist": "150.6.g.a", "char_is_minimal": true, "conrey_index": 31, "id": null, "nf_label": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-5, 0, 0, 0, 0, 5, -7, 3, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, -1, 0], [-36, 0, 0, 0, 0, 36, -36, -36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [20, 1, -1, -1, -1, -22, 22, 0, 0, 1, 0, 0, -1, 1, 0, 0, -1, -2, 0, -1], [64, 0, 0, 0, 0, -64, 64, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -81, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [32, 0, 4, 4, 0, -12, 32, 40, 0, 0, 0, 0, 0, -4, 0, 4, 4, 4, -4, 0], [8, -2, -7, 0, 0, 0, -52, 8, 5, 5, -2, 0, 7, 9, -1, -9, 0, 0, 9, 2], [0, 0, 0, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -6, 4, 4, -2, 64, 55, 55, 4, -2, 2, 1, -2, 2, 0, 2, -4, 6, -2, 6], [-88, 4, 0, -8, 0, 0, -80, -88, 0, 0, 0, 0, 0, -4, -4, -4, 0, -8, -4, -4], [-63, 0, 0, -9, 0, 90, -18, -18, 0, 0, 0, 0, 0, -9, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -256, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-68, -13, -16, 14, 0, 389, -68, -389, 1, -12, 12, 12, -1, -5, 0, 1, -5, 0, 4, 0], [-324, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [292, -12, 4, 26, 4, -282, 292, 282, -5, -5, 17, 17, -14, -34, -4, 14, 21, 0, -21, 0], [112, 0, 0, 16, 0, -160, 32, 32, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0], [198, 0, 0, 9, -9, -198, 0, 18, -18, -9, 9, 0, -18, 0, 9, 9, -9, 0, -9, 0], [32, 0, 4, -4, -4, -32, 0, 240, -4, 4, -4, -8, -4, 4, -4, 0, 0, 12, 4, -12], [250, 7, 7, -28, 0, 0, 598, 250, 10, 10, 18, 0, -7, -13, -18, -4, 0, -28, -13, -7], [576, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [340, -50, -20, 40, 25, -270, 405, 340, 25, 0, 25, 25, 25, -20, 0, -10, 20, 5, 5, 0], [476, -24, 8, 8, 4, -220, 220, 0, 0, 0, 0, 8, -12, 12, -8, -8, -12, -20, 0, 0], [0, 0, 0, 0, 0, 0, -729, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-352, 0, 0, -16, 16, 352, 0, -32, 32, 16, -16, 0, 32, 0, -16, -16, 16, 0, 16, 0], [961, 0, -31, -24, 2, -961, 0, 483, 37, 24, -24, -22, 12, 53, -24, -55, -29, -29, 10, -45], [288, 0, 0, 0, 0, 72, 180, 0, 0, 0, 0, 0, 0, -36, 0, 36, 0, 0, 0, 0], [366, -65, -26, 61, -9, -720, 366, 720, 34, -19, 31, 31, 4, -19, 9, -4, 11, 0, -5, 0], [-1024, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-468, -18, 0, 27, -18, 540, -468, -540, 9, 18, 9, 9, -9, 9, 18, 9, 45, 0, -9, 0], [0, -52, -60, 32, 0, 1556, -1284, -1284, 0, -52, 0, 48, -8, -44, 0, -24, -20, -24, -8, 0], [-1484, 30, 33, -82, 20, -226, -1630, -44, 35, -20, -20, 15, 20, -24, -50, -58, -5, -77, -25, -15], [0, 0, 0, 0, 0, 0, 1296, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 20, 19, 108, -91, -1265, -73, -73, -112, -92, 91, 63, -144, -187, 0, 153, 37, 41, -144, -21], [0, 0, -40, 68, 16, -1128, -40, -40, -32, -32, -16, 68, 0, -52, 0, -4, 84, -36, 0, -48], [495, 0, -18, 45, 0, 0, 1071, 495, 36, 36, 18, 0, 18, -18, 9, 27, 0, 45, -18, 0], [-512, 0, 0, 0, 0, -128, -320, 0, 0, 0, 0, 0, 0, 64, 0, -64, 0, 0, 0, 0], [0, 9, 102, 157, -34, 1554, 1059, 1059, -61, -52, 34, 70, -131, -116, 0, 121, 132, 60, -131, -27], [-720, 36, 0, -36, 0, -72, -720, 72, -72, -36, 36, 36, 0, -72, 0, 0, 0, 0, -36, 0], [3562, 23, 41, -191, 36, -522, 522, 0, 0, 82, 0, 79, 31, -31, -79, -79, 36, -125, 0, -82], [832, 32, 0, -48, 32, -960, 832, 960, -16, -32, -16, -16, 16, -16, -32, -16, -80, 0, 16, 0], [-162, 0, 81, 0, 0, 0, 648, 405, 0, 0, 0, 0, 0, 0, 0, 0, 0, 81, 0, 0], [1000, 0, 12, -72, 144, -1000, 0, -1392, 100, 72, -72, 72, 56, -84, -72, -60, 156, -96, 32, -112], [-1618, 0, -78, -81, 205, 1618, 0, -928, 132, 81, -81, 124, 285, -46, -81, -159, 127, 37, 127, -109], [0, 0, 0, 0, 0, 0, -2304, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2473, 11, -258, -67, -2, -1232, 1232, 0, 0, 176, 0, -29, -34, 34, 29, 29, -130, -277, 0, -176], [280, -100, 20, 180, 0, -1360, 0, -260, -100, -200, 0, 100, -100, -100, 100, 120, 60, 20, -60, -100], [-612, 117, 81, -72, 108, -2889, 2889, 0, 0, 117, 0, 0, -45, 45, 0, 0, 99, -18, 0, -117], [-880, 0, 32, -80, 0, 0, -1904, -880, -64, -64, -32, 0, -32, 32, -16, -48, 0, -80, 32, 0], [4675, 0, -7, -2, 134, -4675, 0, 1478, -125, 2, -2, 132, 131, -125, -2, -9, 127, -206, 18, -159], [0, 0, 0, 0, 0, 0, 0, 2916, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1594, -95, 87, 180, -25, 6482, 1398, -1858, -130, -135, 120, 50, -125, -290, -165, -39, 104, -53, -289, 10], [1280, -64, 0, 64, 0, 128, 1280, -128, 128, 64, -64, -64, 0, 128, 0, 0, 0, 0, 64, 0], [2628, 0, 81, -189, 189, -90, 90, 0, 0, 108, 0, 36, 63, -63, -36, -36, 27, -117, 0, -108], [-1912, -52, 56, -160, 88, -1932, -1912, 1932, 148, -84, -96, -96, 212, 48, -88, -212, -188, 0, 40, 0], [0, -284, -198, 33, 99, 6864, -7078, -7078, 5, -279, -99, 69, 16, -284, 0, 3, -152, 8, 16, -94], [288, 0, -144, 0, 0, 0, -1152, -720, 0, 0, 0, 0, 0, 0, 0, 0, 0, -144, 0, 0], [159, -207, 290, 616, 0, 0, -6481, 159, -278, -278, 176, 0, -290, -42, -140, 282, 0, 616, -42, 207], [0, -212, 40, 292, -36, -2880, 1416, 1416, -84, -296, 36, 124, -128, -184, 0, 132, 44, 48, -128, -48], [0, -81, 81, 81, 0, 162, -1782, -1782, 0, -81, 0, -81, -81, 0, 0, 0, 0, 0, -81, 0], [0, 0, 0, 0, 0, 0, 4096, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1969, 85, 145, -41, 40, -16761, -458, 442, -255, 135, -40, 80, -210, -116, -50, -63, 303, -275, -138, -180], [0, 36, 288, 216, -72, 2160, -288, -288, -180, -144, 72, 36, -324, -252, 0, 288, 180, 108, -324, -108], [510, -226, -153, -275, 245, -2712, 510, 2712, 669, 714, -443, -443, 501, 882, -245, -501, 190, 0, 596, 0], [1088, -208, -144, 128, -192, 5136, -5136, 0, 0, -208, 0, 0, 80, -80, 0, 0, -176, 32, 0, 208], [5382, 63, -90, -252, 162, -3132, 5382, 3132, -225, 90, 162, 162, 189, -126, -162, -189, 9, 0, -72, 0], [-1080, -220, -8, 0, 60, 176, 5760, 6344, 540, 260, -200, -80, 280, 364, -120, -212, 88, 32, 372, 160], [-8998, 0, 376, -60, 158, 8998, 0, -4650, -62, 60, -60, 98, -704, -474, -60, 316, 534, -20, -147, -139], [0, 0, 0, 0, 0, 0, 0, -5184, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-8801, -366, -621, -180, 0, 0, 13363, -8801, 67, 67, 280, 0, 621, -267, 66, -411, 0, -180, -267, 366], [-5352, 80, -536, 68, 112, 292, -292, 0, 0, -4, 0, 364, 248, -248, -364, -364, 12, -348, 0, 4], [3645, 225, -90, -585, 450, -585, 1215, 585, 225, 675, -225, 0, 450, 135, -225, -405, 360, -315, 315, -450], [-4672, 0, -144, 336, -336, 160, -160, 0, 0, -192, 0, -64, -112, 112, 64, 64, -48, 208, 0, 192], [17420, -307, 214, 643, 0, 0, 23312, 17420, 173, 173, 168, 0, -214, -206, 70, 628, 0, 643, -206, 307], [1980, 0, -144, 36, 36, -1980, 0, -2304, -36, -36, 36, 72, 108, 72, 36, -108, -108, -216, -36, -216], [6542, 0, -460, 77, -170, -6542, 0, 5384, -138, -77, 77, -93, 568, 553, 77, -383, -630, 1114, 380, 883], [-512, 0, 256, 0, 0, 0, 2048, 1280, 0, 0, 0, 0, 0, 0, 0, 0, 0, 256, 0, 0], [-6561, 0, 0, 0, 0, 6561, -6561, -6561, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [10452, 36, -76, 492, -144, -4236, 4236, 0, 0, -72, 0, 136, -164, 164, -136, -136, 36, -28, 0, 72], [-21494, 336, -159, -1208, -179, 3372, -21494, -3372, -360, -293, 24, 24, 872, 89, 179, -872, -801, 0, 135, 0], [0, 144, -144, -144, 0, -288, 3168, 3168, 0, 144, 0, 144, 144, 0, 0, 0, 0, 0, 144, 0], [14213, 310, 1059, -434, -420, -2584, -8126, -5353, -175, 115, 280, -315, -775, -107, 330, 773, 360, -186, -505, 395], [-2088, 328, 376, -500, 0, 0, -14248, -2088, 80, 80, -316, 0, -376, 104, -172, 184, 0, -500, 104, -328], [0, 522, 126, 99, -198, 4347, -8649, -8649, -603, -81, 198, 216, -729, -747, 0, 342, 423, -261, -729, -405], [0, -64, -512, -384, 128, -3840, 512, 512, 320, 256, -128, -64, 576, 448, 0, -512, -320, -192, 576, 192], [6051, 650, 89, 63, 0, 0, -4692, 6051, -371, -371, 296, 0, -89, -576, 390, 762, 0, 63, -576, -650], [1620, 0, 0, 0, 0, -1620, 2268, -972, 0, 0, 0, 0, 0, 324, 0, 0, -324, 0, 324, 0], [0, -403, -213, 629, 398, 8944, 20052, 20052, 1235, 832, -398, -256, 1051, 425, 0, 15, 624, 1250, 1051, 837], [-9568, -112, 160, 448, -288, 5568, -9568, -5568, 400, -160, -288, -288, -336, 224, 288, 336, -16, 0, 128, 0], [3294, 477, 207, -576, 198, 3186, -3186, 0, 0, 585, 0, -81, 81, -81, 81, 81, 315, -189, 0, -585], [2760, -204, -184, 388, -496, 3712, 2760, -3712, 528, -112, -324, -324, -184, 1140, 496, 184, -896, 0, 508, 0], [-35068, 410, 1066, -228, -525, 16040, -13782, -27070, -260, -245, 390, -50, -345, 245, 770, 750, 397, -54, -297, -380], [0, 0, 0, 0, 0, 0, 0, 9216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-25785, 0, 155, 982, -1396, 25785, 0, 12039, -325, -982, 982, -414, -2263, 259, 982, 1137, -1241, 354, -357, 1449], [-4928, 704, -44, -1108, 0, 0, 9892, -4928, -776, -776, 116, 0, 44, -1104, 108, -64, 0, -1108, -1104, -704], [-4212, -81, 0, -324, -81, -648, 648, 0, 0, 162, 0, -162, 0, 0, 162, 162, 0, 0, 0, -162], [-6480, -400, 160, 1040, -800, 1040, -2160, -1040, -400, -1200, 400, 0, -800, -240, 400, 720, -640, 560, -560, 800]]}