# Stored data for newform 225.10.a.k, downloaded from the LMFDB on 23 April 2024.
{"label": "225.10.a.k", "space_label": "225.10.a", "level": 225, "weight": 10, "hecke_orbit": 11, "hecke_orbit_code": 45035996441477345, "dim": 2, "is_polredabs": true, "nf_label": "2.2.241.1", "trace_hash": 2183804230484398866, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [-302, -31, 1]], [7, [22579200, 14112, 1]]], "qexp_display": "q+(15-\\beta )q^{2}+(255-31\\beta )q^{4}+(-6944+\\cdots)q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 22500, "fricke_eigenval": -1, "atkin_lehner_string": "-+", "analytic_conductor": 115.88306313687146, "hecke_ring_index": 3, "level_radical": 15, "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": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.002", "prec": 17}, "analytic_rank_proved": true, "char_values": [225, 1, [101, 127], [1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [3, 5], "conrey_indexes": [1], "field_disc": 241, "field_disc_factorization": [[241, 1]], "field_poly": [-60, -1, 1], "hecke_ring_index_factorization": [[3, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.027", "prec": 17}, {"__RealLiteral__": 0, "data": "1.882", "prec": 17}, {"__RealLiteral__": 0, "data": "0.238", "prec": 17}, {"__RealLiteral__": 0, "data": "9.124", "prec": 17}, {"__RealLiteral__": 0, "data": "1.770", "prec": 17}, {"__RealLiteral__": 0, "data": "62.090", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "9.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [5, 1]], "trace_display": [31, 0, 0, -14112], "traces": [0, 2, 31, 0, 541, 0, 0, -14112, 26133, 0, 0, 21512, 0, -24284, -461664, 0, 387265, -156956, 0, -95896, 0, 0, 2901532, -735264, 0, 0, 5419166, 0, -11348064, 2678212, 0, 10782432, -6402523, 0, 5722622, 0, 0, -21968332, -7698404, 0, 0, -26060372, 0, 7191160, 85429972, 0, 17095392, -31580240, 0, 73282930, 0, 0, 173093786, 3131116, 0, 0, -242454240, 0, 224332958, 35494664, 0, 341497340, 1485504, 0, -205120471, 0, 0, 288195816, 210362042, 0, 0, -210286064, 0, 232663084, -125240234, 0, -218512364, -727042176, 0, -24755040, 0, 0, 129742346, -372082152, 0, 0, 873146372, 0, 894861492, 427639116, 0, -1126859328, 684362592, 0, 1647543896, 0, 0, -1771658884, 4564085351, 0, 0, -13599948, 0, -1469639680, 1067833866, 0, -144213718, -1917700440, 0, 4399626844, 0, 0, -2950934112, -500500892, 0, 0, 6391897178, 0, 5265955036, -719337024, 0, 1596739018, 6323709346, 0, -2218260096, 0, 0, 559536496, -2440052067, 0, 0, 7367132760, 0, 2068133760, 3353730828, 0, -101715414, -351233004, 0, 5471279896, 0, 0, 1669922168, 13462706320, 0, 0, 2339373578, 0, 730902466, -13802924012, 0, 2934835664, -2737696908, 0, -32002572672, 0, 0, -9268965436, 20275067520, 0, 0, -1194181632, 0, 5026602248, 9494690846, 0, 2106508980, -26987368608, 0, 10057372974, 0, 0, 25557393932, 5267294748, 0, 0, 6474140644, 0, -3185399046, 21546417560, 0, 32720455852, -55410215616, 0, -2797742880, 0, 0, 17623863184, 57705711176, 0, 0, 56903984992, 0, 10117853372, -12873233342, 0, 126097230581, 24450454668, 0, 8938670672, 0, 0, -83000522778, -59849294400, 0, 0, -42875356208, 0, 508044002, -15741511264, 0, -44546044088, -5128159618, 0, -65279507124, 0, 0, -38976989184, 62832309266, 0, 0, 45488431112, 0, 78440081936, 24478979616, 0, -80862468610, -17510926888, 0, 44547133836, 0, 0, 78688997706, 27314769300, 0, 0, 155790726676, 0, -49630004928, -92647177504, 0, -80077991452, 79994335931, 0, 124320548326, 0, 0, -32032644272, 101300163840, 0, 0, -71964607704, 0, 59560518528, 170249954648, 0, -130684675231, 121761355140, 0, 106788314304, 0, 0, 34198393044, -344617408, 0, 0, 87535969920, 0, 43444534308, -72726014044, 0, -82081403392, -23060042110, 0, -14181433530, 0, 0, -51108709548, 169574182244, 0, 0, 12750144204, 0, 136184280216, 95927660648, 0, 239827255736, 64338087744, 0, -163529251226, 0, 0, 23661333278, -170976988788, 0, 0, -235599940110, 0, -302286019978, 161188737984, 0, -221357904768, -35458688888, 0, -24153184604, 0, 0, 42321830920, -839400895872, 0, 0, -456768783888, 0, 91452054668, -381091625810, 0, 633725651520, -436543656580, 0, 461726199568, 0, 0, -130241147904, -39188634032, 0, 0, -400924434116, 0, -212968781970, -255866252544, 0, -167682106056, 143439030300, 0, -181892340576, 0, 0, 376966306012, 15149707785, 0, 0, -276264872064, 0, -715531037760, 276005622828, 0, -24253966350, -257041579256, 0, -508956091012, 0, 0, 149933673716, -796244399676, 0, 0, -188551584786, 0, 235243532980, 85887040944, 0, -605194946502, 29188596074, 0, -1481076225216, 0, 0, 244009852752, -116756712864, 0, 0, 21081953088, 0, -161935494380, 159350754104, 0, 98108784264, 944474821064, 0, 817602979640, 0, 0, 936586722512, 837722806512, 0, 0, -57196796990, 0, -27021867962, 539628025524, 0, 271961767872, 1776891189549, 0, 384392609178, 0, 0, -286139497820, -536972883512, 0, 0, -122414615460, 0, -1016112163392, -2570160217038, 0, -2542953067200, 273465404624, 0, -217819061324, 0, 0, -1020511709648, -1306786803840, 0, 0, 571516032298, 0, -433944935696, 882799414456, 0, 558831059276, -1312381330996, 0, -5153570610, 0, 0, -2640437360064, -1620947628444, 0, 0, 741421715328, 0, 84404188, -745049346048, 0, 1023879950006, -127947646080, 0, 980492152880, 0, 0, 151222744252, 805279246824, 0, 0, 980375001256, 0, 2016015988896, 671328473468, 0, 983444407984, -2401631339590, 0, 1835941887124, 0, 0, -122381617172, 1457579664474, 0, 0, -3719759004, 0, -559260106320, 682944669218, 0, -1464164799162, 2055535804280, 0, -1784129510016, 0, 0, 1590864297972, 1881014389216, 0, 0, -1387469377728, 0, 93990857584, 2171043717120, 0, 1417136552872, -242087093042, 0, 2144509220081, 0, 0, 1481109288416, 4708464630774, 0, 0, 1442595899080, 0, 1164630732104, -698965582408, 0, 1938916933632, 379602687744, 0, -891973552216, 0, 0, -1443806091732, -824638555936, 0, 0, 285533548416, 0, 5160245929928, -265594079356, 0, -1357884174528, -3866796466187, 0, -977260196754, 0, 0, 4720828013248, 2804642906688, 0, 0, -2877560854292, 0, 1220994911800, -486947695236, 0, 2896912825936, -2091812982336, 0, -2583457344430, 0, 0, 2279306977920, 3168400867352, 0, 0, 3499630897284, 0, 3103889140654, 8906208643528, 0, -3435631385988, -3901386437072, 0, 1197292532554, 0, 0, -3275627112152, -365865508590, 0, 0, -1175611718192, 0, -4452893061120, -6271026629658, 0, 4107830871404, 1452883066524, 0, 3983120982128, 0, 0, -3132453318150, -1621211005992, 0, 0, 6644154213876, 0, -1569586733016, -3550208916084, 0, 2620743535768, 4607476600616, 0, 397004626368, 0, 0, 935487394556, -3814748634643, 0, 0, 861684421248, 0, -422744282192, 2737302077550, 0, 3959179682586, 6558122677800, 0, 431802426240, 0, 0, -4060256294102, 4469217234980, 0, 0, -6472252576798, 0, 21839514048, -1637883788912, 0, 4285070169268, -9678952596096, 0, -1715534844968, 0, 0, -3945910783184, -222269378380, 0, 0, 11803776293984, 0, 7252314145012, -1164854637796, 0, -14455183720320, 3988120141716, 0, -2254729568744, 0, 0, -11344477835928, -819129205440, 0, 0, 14050807090714, 0, -9867357658550, 3342852976936, 0, -403920943216, 4613984452800, 0, -10952614237214, 0, 0, 17430499121924, 12562128003512, 0, 0, -4161567079812, 0, 9181289160, -3786697442304, 0, -510954272968, 1025302871584, 0, 11548765983776, 0, 0, -13484243929676, -7481338466788, 0, 0, -4566358358602, 0, -15209002061568, -7220362928680, 0, -2980720876756, -7039431571308, 0, -2979977460804, 0, 0, 3818468260800, 28684849824, 0, 0, 6113370753008, 0, 2141474750844, 1597980784562, 0, -1642407383205, -1876288699572, 0, 9233229708864, 0, 0, 7781407310592, -13733103320568, 0, 0, -34378326601920, 0, 2077195658108, -1068052719976, 0, -6194206159672, -1858004853930, 0, -14194219875748, 0, 0, 6058425276056, -1166232540638, 0, 0, -6536609861180, 0, -179722745200, -8218098638716, 0, -9637329316626, 18640859315904, 0, -14885955896116, 0, 0, 3242247031998, -8315718709248, 0, 0, 2767801834780, 0, 12141662295336, -4741365037152, 0, 14871268403712, -8784814184445, 0, -5966449250626, 0, 0, 859717110464, -23792698560960, 0, 0, 5163511253360, 0, 9969955575620, 7983597995592, 0, 4781260880352, 463529567136, 0, 9933680791496, 0, 0, 1306468287936, -10038709265600, 0, 0, -27070291897018, 0, 1238862108584, 21495647972736, 0, 5863720464128, -4193764005016, 0, 20180431009276, 0, 0, 28325347073044, 15249934164340, 0, 0, -25961306231796, 0, -29842699884480, 17084351549552, 0, 17823010073016, 24770193493648, 0, 8658729245572, 0, 0, -3897849914810, -18663551999988, 0, 0, -19662973240746, 0, 1335722673126, -1807365508880, 0, 9410878482496, -1018787236416, 0, 17271908685689, 0, 0, -16453772816120, 6781575404238, 0, 0, 19906988165568, 0, 1360534375864, 15126389095454, 0, -18523280229992, 17868424144700, 0, 18548876947040, 0, 0, 8101213557714, -497505070928, 0, 0, 17506647893376, 0, -19964447657118, 3298381283500, 0, -15521670211656, -66263193259200, 0, -21654246578792, 0, 0, -4707724209056, -5399975035546, 0, 0, 17852358059604, 0, -13119700619488, -24005976817872, 0, -57841117649280, -5059810909496, 0, 9822662890620, 0, 0, -11076649084238, 20028965738180, 0, 0, -10146575641136, 0, 35499111855524, -5642369345360, 0, 5391295409806, 41687093395450, 0, -31329152002396, 0, 0, -23641443889056, 433007150486, 0, 0, 13731806685888, 0, 17143066334868, -89677624051008, 0, -33555313721916, -15188204166860, 0, 13726531442360, 0, 0, -15240093413184, -16337224771600, 0, 0, 9819005662514, 0, -14911361998848, 48653703665280, 0, -9448771883952, 56206228428102, 0, -1065586296960, 0, 0, 9402174141348, 2211657922840, 0, 0, -28360459769956, 0, -10289887788760, -4864665461708, 0, 61500975958284, 42310696280640, 0, -40141368642816, 0, 0, 13919207832376, -10726742116928, 0, 0, 61543370437920, 0, 4994151225922, -13484478772800, 0, -1695173761768, -12479138449432, 0, -24011819348694, 0, 0, 2644360842840, 60591493147324, 0, 0, 6552659029376, 0, 14643000944736, -33548773643254, 0, 35830071493134, -34064243853696, 0, -21676372123600, 0, 0, -13019269882482, 28895772708128, 0, 0, 6716199684792, 0, 7002481469290, 64658661218236, 0, -23150499161048, -51125210327022, 0, 66534410994916, 0, 0, 8332826592492, -54803948717952, 0, 0, 4777167788068, 0, 23601418037568, 11112413708836, 0, 46582184212880, -864026718984, 0, -9595331338984, 0, 0, -18596004396480, 26081199901684, 0, 0, 22369623860944, 0, 19401531978240, 4435460197056, 0, 30550701433282, -44307659536276, 0, 9311678320618, 0, 0, -18807856790944, 34067316974025, 0, 0, 31491971321928, 0, -57593683969920, 50855177192128, 0, 67051403705374, 7233387045604, 0, -18639404722896, 0, 0, 34238628063164, 10652416504416, 0, 0, 14625374287036, 0, -14941077757528, 17367245541504, 0, -22230051400736, -48629933554176, 0, -3355508927232, 0, 0, -6870053549196, 68447283763996, 0, 0, -101971644735744, 0, 32677173593488, -29645421225852, 0, -47799486327296, 953918429680, 0, 63553991984740, 0, 0, -3656168889984, 20993487370988, 0, 0, 45928119836424, 0, -36693649540994, -36958203063864, 0, 86368390511420, -40368117335616, 0, -10473760592615, 0, 0, 110701045995840, -55864950678774, 0, 0, -1489870758576, 0, -113569356962772, 55608266791520, 0, 64518384103488, -19050663917000, 0, -91429487601952, 0, 0, -90979580914294, 117181748134080, 0, 0, 40619566803332, 0, 77144512836636, -48161220296244, 0, -47448681966888, 89876667259696, 0, 24543905332608, 0, 0, -2575704708864, -60992718962441, 0, 0, -8351705710668, 0, 137445415534400, 40282965072000, 0, -32887035207596, 15487188168176, 0, -34050381017380, 0, 0, 54803215757940, 6871246918120, 0, 0, 111493026309514, 0, 269018752186940, 46595314293168, 0, 67754159039232, -118803461884926, 0, -103705884836912, 0, 0, -42214019397712, -2994155276462, 0, 0, 78637848394072, 0, 19484622090292, -48573871482004, 0, -6677605997118, -35509546384300, 0, 118584496304064, 0, 0, -35306415110728, 37266055335120, 0, 0, -211781281904640, 0, -183668996514318, -51666708258220, 0, -196192346487600, 91750351942668, 0, 164087421829362, 0, 0, -24435819237564, 73328443866760, 0, 0, -28713930347104, 0, -52064356116344, -99783583145490, 0, -95651385544140, 63124518596832, 0, -44561109211052, 0, 0, 177370081784796, -63394633083904, 0, 0, -36286725099640, 0, 12262578481914, -30989079734448, 0, 71791730785152, 158055437814308, 0, 183356570688744, 0, 0, -151315335514944, -1203855008832, 0, 0, 66281136844064, 0, 44370952383100, 70313322044098, 0, -83916064916473, -57637369904808, 0, -22276821757648, 0, 0, 2993286877056, -12532962161912, 0, 0, -4605209284504, 0, 43912187715254, 137466613380096, 0, -148017039726840, 158639737805646, 0, 42306133312716, 0, 0, -104821381852512, -18855170622720, 0, 0, 28628447323652, 0, -39439159282656, 88667071484306, 0, 33592362762718, -100512150589416, 0, 55067720901080, 0, 0, -201469333375086, -145773016612972, 0, 0, -33172610041152, 0, -251453989914568, 34625390993776, 0, -53177233499932, 70839959680358, 0, -253562370477696, 0, 0, 53571588053792, 19001304842136, 0, 0, -13445095914432, 0, -74932829424828, -5974602304552, 0, 24377228378948, -100970471467260, 0, -6214921769664, 0, 0, 65497907635120, -102533900395648, 0, 0, 146555132977910, 0, -44998078264876, -242203844052252, 0, 103349840870400, -159418337774976, 0, -126428865479610, 0, 0, 48981881984532, -276353668962076, 0, 0, -27786053270632, 0, -178495328522864, -255757368297288, 0, 4606950237120, 138031264992752, 0, 16619428419524, 0, 0, 416370088331854, -129916911922560, 0, 0, -177856952980422, 0, -54660359296468, 66338028580008, 0, 99466971869368, 233262577140232, 0, 13778854522560, 0, 0, -123808359294144, -247856873471834, 0, 0, -222008954606784, 0, -7441405840608, 440905634794030, 0, 292463466199592, -98128006155588, 0, 175265781075904, 0, 0, 62946186979746, 169633344705592, 0, 0, -26912346501348, 0, -42307562787840, -151329153763092, 0, 2987102153656, -7609969315288, 0, -172091973730048, 0, 0, 60049816679324, 275305738042864, 0, 0, -283629085897964, 0, 299977895664864, -48761889507948, 0, 37860318027826, -109433919250616, 0, -98858494570752, 0, 0, 128894907023566, -442263152264280, 0, 0, -417747150874368, 0, -36216039716300, -204703452800016, 0, -125282972280620, 154051959287242, 0, -183009136438788, 0, 0, -175887288479216, -64968666977076, 0, 0, 97270232716752, 0, -77567377709952, 30129315480000, 0, -296128014305760, -413739308054016, 0, -89548344607232, 0, 0, 544340287299400, 157296681241920, 0, 0, 80301181334178, 0, -29625519941098, -18152555887808, 0, -23450303959488, 97777905943203, 0, -285692877492582, 0, 0, 110844201294720, 255378580809408, 0, 0, -24671809707300, 0, 317963964289376, 299239249761792, 0, -80303237705124, 148338710570048, 0, 24110343797310, 0, 0, -915466606729920, 216848255205180, 0, 0, 41873879666668, 0, -5141197186412, -173734373985984, 0, 83961888862796, -344444809954292, 0, 43515715473126, 0, 0, -3898902156560, -386042084504428, 0, 0, -166722004482096, 0, 88245730218240, -54243299206508, 0, 70727570352742, 388633039608256, 0, -186241414629392, 0, 0, -254599396162786, -98472038966208, 0, 0, 55126398595480, 0, -494838180880428, -52386551081220, 0, 88411106291376, -131545884883446, 0, 874749513089088, 0, 0, -82074299164552, -131375011968134, 0, 0, 676045843671716, 0, 119153231207152, 73982220124614, 0, 85608170348544, 56539296297080, 0, 258040724516140, 0, 0, 257940765578940, 311239673837172, 0, 0, 358355252557176, 0, -438367285747248, -258296552462144, 0, -110180566128288, 550809935230464, 0, -145238300952375, 0, 0, 94438523370400, 313304982148110, 0, 0, 333851907270024, 0, 163432043059044, 340650156449680, 0, -252308151361728, -496658472489216, 0, 69063583241384, 0, 0, 49582572144904, 153621241966080, 0, 0, 418880819010862, 0, 196249468785432, -384594460535032, 0, 224572810922848, 8710111670112, 0, 365267268167856, 0, 0, 453626440154496, 31251282271564, 0, 0, 130772835157100, 0, -294511477861768, 36073306777536, 0, -285506228270992, -417302758737936, 0, -437406569561052, 0, 0, -805172594987758, 186011541420332, 0, 0, 203079437359464, 0, 816991250366592, 216287029243656, 0, -117146483568000, 150257470332208, 0, 283170074318344, 0, 0, -24467840611248, 427253648864116, 0, 0, 69052862313360, 0, -107360078732328, 500550289740230, 0, 301051333370140, 392184422589304, 0, -128525440682016, 0, 0, -253158452450310, 82643767815768, 0, 0, -959124508695360, 0, 756579334175472, 259582892812384, 0, 287523464405976, 376591522895976, 0, 429534773788472, 0, 0, -28299456170920, 88790286552638, 0, 0, -135198735322752, 0, 88144467275968, 81053308788054, 0, -136199400383334, -196904431817856, 0, 22794966102492, 0, 0, -329936594911490, 286749803141412, 0, 0, -71914482493134, 0, 27340760413160, -228386596046896, 0, -500733253939968, -71128628571424, 0, -88694375582016, 0, 0, 411233804378672, 57481383931069, 0, 0, 202422127296728, 0, 275841039719732, -65862574820836, 0, 320774990195358, -27260430196512, 0, -55566070597544, 0, 0, 885177953868096, 258778171461712, 0, 0, 998161472726660, 0, 529007356501274, -348491820749184, 0, 72202211405872, -44652684328104, 0, 859078208916706, 0, 0, -733775035288892, -8978221602128, 0, 0, -820360204617604, 0, -486154772510400, 276844689535734, 0, 277412417251304, -661961615480928, 0, -412510065112044, 0, 0, 756089639006976, 310175443983452, 0, 0, -77061353433126, 0, -17199375457270, 591429201798552, 0, 322563256476524, -494791378725228, 0, -1168074877233600, 0, 0, -281337509952904, -728709378913592, 0, 0, 230076781841088, 0, 206811931315968, -131826721009264, 0, -121657223223886, 670676179815948, 0, -357655023044528, 0, 0, 399615483849750, 46319778176832, 0, 0, -333725387396480, 0, -302636256447632, 248734090685752, 0, 856674338467808, -1518649418321280, 0, -1011520634887588, 0, 0, 263270713811852, 493955429304450, 0, 0, -160119291096256, 0, 292700718274960, -1027873263499494, 0, 340237963683982, -491844380394088, 0, -168469642163252, 0, 0, -251084868084912, 310993532075520, 0, 0, 915084590485484, 0, -173689889675800, -118818502670016, 0, -52571510195978, 573197596450457, 0, 1174945372810990, 0, 0, 341227030205376, -730699202859900, 0, 0, 35709036676464, 0, -512967149142588, -950196569771232, 0, -26445288920018, 648664169974404, 0, 111243235279112, 0, 0, -179257418950464, -516929854321104, 0, 0, -321949040824986, 0, -2225514499967808, 306703985217956, 0, 842499752262928, -403293210571596, 0, -977929716510634, 0, 0, -621511424632536, 916447579585780, 0, 0, -143558630108660, 0, -440839126704616, -628141456027584, 0, -836559222506792, -661913854784752, 0, 271373287530240, 0, 0, 304371450658454, -420648572515892, 0, 0, -542969366446080, 0, 944551484213760, 771076017105376, 0, -324397375444004, 702191001323928, 0, 847090390643246, 0, 0, -354248638766840, -6164169528960, 0, 0, -35787094776320, 0, 221751922555148, 307915826493246, 0, -137341956496760, 581333718559104, 0, -347983286541312, 0, 0, -914369014721390, 281119198113872, 0, 0, 625317451850092, 0, 462004927946772, 631018802077816, 0, -277424413249536, 1737421612873764, 0, 989712625762416, 0, 0, -976008226215780, -1830243047415552, 0, 0, -42427577462424, 0, -165828177551392, 968665672385016, 0, -170642704342432, -784975951923192, 0, 548409661862460, 0, 0, 1614380975913888, -1079819335117792, 0, 0, 13839708575302, 0, 554803857878400, -217486412748864, 0, -1456517715053292, 1618942871764, 0, -593376617609032, 0, 0, 386575093069232, -162634368571006, 0, 0, -235075130920392, 0, -124467893590124, -270364315116876, 0, 274852813497180, 551847967119360, 0, -116877435155760, 0, 0, -1651816111213472, 330748826034416, 0, 0, -166114425661872, 0, -1014311843334754, -528911156396160, 0, -477783911677264, 765411806781918, 0, -858412478915712, 0, 0, 269547178156416, -1219254331526120, 0, 0, -647673364219392, 0, 1390418395952, -402816216966102, 0, -221331357200912, 515867718961472, 0, -444371165997174, 0, 0, 325646812555752, -385595454719752, 0, 0, -702654847867406, 0, 442673081815394, -225094205894472, 0, -937901942253492, -750825434371012, 0, -94214516813118, 0, 0, -804160168737960, 1630904221943596, 0, 0, -416667249522432, 0, -627171201889892, -1338888652527798, 0, -1324255213153152, 1523730007960236, 0, 641904022489648, 0, 0, 1938051848104046, -434621133172800, 0, 0, -201631023117504, 0, 288152698682420, -193500079839300, 0, 1683691387389504, 1049034688863920, 0, 436936926772260, 0, 0, 1168090311661056, 540862477539412, 0, 0, 1469866999804132, 0, -194109156437904, -173880798969024, 0, 315477241542614, 47959753595960, 0, 343649315235456, 0, 0, -844899060829872, -349235033044428, 0, 0, 145528310730240, 0, 173062342458432, 474871626995856, 0, -510469070973304, -1312489799355073, 0, -1671136121727676, 0, 0, 1463124063807776, -807548971210662, 0, 0, -429764732393976, 0, -599299639553692, 401953564139968, 0, 358845716058533, -304497585646744, 0, 1587883580063424, 0, 0, 722979285647196, 198248357332176, 0, 0, -2155398133069440, 0, 1265477542388608, -229238550169980, 0, 603071696217184, -1005424668319786, 0, 993294922637822, 0, 0, 185575834386944, 154641088136616, 0, 0, -72652011101192, 0, -468224315770208, 758452331151284, 0, -1110924625484448, 655973026438464, 0, -2029756750240, 0, 0, 208814149156276, -1305627735612756, 0, 0, -466942389869976, 0, 91618324956288, -764511735718200, 0, -1976375004202368, -2284954828319968, 0, -718086191187456, 0, 0, -738563298932056, -183737341170432, 0, 0, -779911792944464, 0, -283289070521748, 2005611350246550, 0, 2309180242649236, -845652461429924, 0, 723261077780768, 0, 0, -3435626505523968, -559509029683752, 0, 0, 281147901411512, 0, -1018802313248796, 732113267180876, 0, 1329837181487000, -1308609979399616, 0, 14302250290280, 0, 0, -172394437800964, 1043056896844430, 0, 0, 1387369171731776, 0, 1440592530554016, 625848092530560, 0, 648701811290890, -414135032835480, 0, -506464050862436, 0, 0, 253602298486760, 295609801638432, 0, 0, -1081728379106054, 0, -1937766911536836, 1328335585902096, 0, -1156242925009976, 1593824910294946, 0, -966255960753216, 0, 0, -415042117490880, 1032558314001165, 0, 0, -274074721083072, 0, 2085736935603060, 1393292660993280, 0, 906364619796474, 290132621608436, 0, 549375814009376, 0, 0, -86975757231720, 1627830632442000, 0, 0, -2340926707548726, 0, 732482387755040, -1295092682225964, 0, -180240305674064, 1670061853212480, 0, 1016373618347972, 0, 0, 1723767542971776, -1487210343416288, 0, 0, -652963440195012, 0, 929365105433288, -2216079228941794, 0, 4116207421892160, -1107659854686880, 0, 1901026290629204, 0, 0, 1002797639425292, -582592488081408, 0, 0, 1354603378053036, 0, -855588633066246, -1304493638236968, 0, 741292756336000, 289279722032484, 0, 689135857225008, 0, 0, 2671242867699896, 1200141791601408, 0, 0, 353146463426976, 0, -679352703811716, 174773313614592, 0, -1348248245505371, 97990885297880, 0, -2619936697817456, 0, 0, -996692930092698, -397980074568976, 0, 0, 2007828520994512, 0, 450334337362560, 690887524405212, 0, 703786805456392, -1684862273579396, 0, -1877940702079544, 0, 0, -894823074668212, 1519145626747090, 0, 0, 477384078585092, 0, 1812828795310480, -1017442584981564, 0, -1613360390576020, 442741765772368, 0, 109245996849024, 0, 0, 60968561136378, -15935861451180, 0, 0, 6469277502654260, 0, -451589800330776, 1171148779846112, 0, -516861481538332, -185345794135296, 0, -2961424727375226, 0, 0, 275801300808240, -1700877457016112, 0, 0, 1591065678138048, 0, -135648567357112, -3704306037475784, 0, -1296608924956614, 4178222356702464, 0, 1467940204663240, 0, 0, 1611841877741492, 546185722542800, 0, 0, 1743138248325110, 0, -817908322390204, -1503492414753472, 0, -3475144952250048, -75864977096262, 0, -3335799647646074, 0, 0, -616709239655704, 4639159610342208, 0, 0, -1886587735267584, 0, 2204200174473688, -847620407612248, 0, 1329175469887368, 2756921124715536, 0, 2471487292404514, 0, 0, -5630112196208640, -3131757279343412, 0, 0, -1977255103276638, 0, -647408272118570, 4017958054318656, 0, -1559081120221476, -3948930623456808, 0, 1135625244588764, 0, 0, -1179698923554000, 4781604632740182, 0, 0, 1034560756588608, 0, -4468743372038400, -250948346193522, 0, 1436726353622680, -393600290746436, 0, -1415931333716480, 0, 0, -781425221470736, 3665483128135544, 0, 0, 2365181607646556, 0, -629289493000002, -629869247570952, 0, 1703494911762040, -2624738640610020, 0, 762102073895904, 0, 0, -3546513228784744, -2130341353030378, 0, 0, 254905821515520, 0, 1447838824627008, 2862910088498556, 0, -3085856647828160, -1156167663766264, 0, -417083205776708, 0, 0, 1093156896145576, -3054183673614652, 0, 0, 1125683805316974, 0, 782221003360536, -124114287826096, 0, 3534195610562260, 3880892853500544, 0, 4349362429732268, 0, 0, -42309859537584, 2634826103198024, 0, 0, 3449423296814400, 0, 781174397504020, 634614835727232, 0, 697217283161280, -166049365488268, 0, -393003121673720, 0, 0, 2137712595684400, 5598217704834608, 0, 0, 240346982133602, 0, 1983260630510278, -841250030819916, 0, -1533076901053776, -2442685773657489, 0, 464985779081268, 0, 0, 2177805340077696, -1455394648880312, 0, 0, -1951838239803104, 0, -2170051841915712, -88161835273344, 0, 1487234535229340, -789208021098320, 0, -38140597511448, 0, 0, -53985188559304, -4715511870780932, 0, 0, -852754346261042, 0, 3740604073178112, 4391023725325560, 0, 1554639946614220, -1643358115633044, 0, -654442624895202, 0, 0, 937530243360472, -65715629643804, 0, 0, -1673976858316992, 0, -2951608716668392, -4469582029964880, 0, -675188798814720, 632987015717228, 0, -1708994936488896, 0, 0, -753478221937538, 208090362118832, 0, 0, -839857290505632, 0, 1749140314882106, 12326008472064, 0, 1751030684083368, 102827626298458, 0, 295490028706932, 0, 0, -1135480509374868, -813986124990380, 0, 0, -398897974899932, 0, -705198967003664, -2752112971068598, 0, 484311013383910, -752901936095232, 0, 2621016047581164, 0, 0, 1514268608863680, 3825889309080948, 0, 0, -7451118091680088, 0, 6128352940475144, -878213021249024, 0, 7307977841133410, -3813468723708722, 0, 1296174014544818, 0, 0, 829073288837424, -4385622374904960, 0, 0, 1373738526775944, 0, -952342507873088, -413974086784784, 0, 495506737839160, -2511283991858652, 0, 1858118211743920, 0, 0, -100976197379904, -711738856193312, 0, 0, -1653570747970290, 0, 643428593027528, 4100742272221056, 0, -822238352105440, 1250484043153812, 0, -4801702563110034, 0, 0, 654737745130036, 19134169411392, 0, 0, 110553013154924, 0, 2085334719289920, -448357885047920, 0, 850110774312016, 4116378581374128, 0, -3288797760199680, 0, 0, 3020223151862690, 286164756898880, 0, 0, 117816722639796, 0, -4285125707280498, 1222668112668104, 0, -229096860628608, 4074419468036496, 0, 560985566295168, 0, 0, -707114545818520, -4756800059628270, 0, 0, 5012501695363008, 0, -4723896119529236, 1174726420940262, 0, -8093470528388116, 329049974275164, 0, -3386577137752176, 0, 0, 617475194884756, -399279625526080, 0, 0, -4195658966131912, 0, -6987599557546248, 104955838031328, 0, -429252118790368, 314832590493120, 0, 3816805759544968, 0, 0, 4801883919599456, 2195834599123486, 0, 0, -3942668647257944, 0, 5886018852076032, 4214317030482462, 0, -3934215970312320, -1758311631783360, 0, -1266592689266888, 0, 0, -2008215922521518, -3027551508898560, 0, 0, -2396470263347068, 0, 2707322613149292, 2295639616697904, 0, -2573013557700812, -3769267877926972, 0, 7315963289422552, 0, 0, 4136817065578848, 1839353956240320, 0, 0, -776711514391656, 0, 418903823217896, -2520770936943168, 0, -6704596515596106, 3439691404955104, 0, 62800835479704, 0, 0, 1594383751066752, 2424485454204496, 0, 0, -957099585056592, 0, 10007669863010890, -259226914182444, 0, -1431815488908144, 7325029273194984, 0, 1576182985003074, 0, 0, -1568601406451132, 583051114645136, 0, 0, -267963378191400, 0, -4175905878212016, 2825260883132646, 0, -1161912804548284, -839053818672992, 0, -2662857263275776, 0, 0, -836210812265388, -3208585270048128, 0, 0, -331678842872832, 0, -7507456602142038, -4849999676558824, 0, -1081717943599848, -453392030328460, 0, -489002063046936, 0, 0, -3718524397890656, -5550164788664128, 0, 0, -508015181790240, 0, -2717100716162884, -5843792674646510, 0, 6109237022735824, -494558440900468, 0, -1736606660157504, 0, 0, -4488867631850122, 66888300308496, 0, 0, 2970537326493408, 0, 542839304490820, 1147590077801628, 0, 6644122196789952, 2744750936888086, 0, -74606504349988, 0, 0, 445912435452940, -2869863835878144, 0, 0, -456907322504444, 0, 1951638658302736, 1423436108079526, 0, -5889255748054644, 3288274514797984, 0, 2626579312632704, 0, 0, -6030371349031680, 1129627868569620, 0, 0, 393578983817500, 0, -7935258394956504, -7905414304771200, 0, -747895730060576, 2415244679144726, 0, 5401562122023262, 0, 0, 1575074803997632, -3252264022438884, 0, 0, 1504601485873040, 0, -6346274331841920, -1413619245434200, 0, 1861970649279612, 1333412767731524, 0, 6849080736632328, 0, 0, -1903243942100904, 8488441084489600, 0, 0, 2308525582669056, 0, 132130445112000, -1058008545384632, 0, -366436912053824, -5013097378298208, 0, -13709825791345152, 0, 0, 5276354445239060, -5402692774219360, 0, 0, -6994752794894592, 0, 2791244221120920, 15590741048149720, 0, 715895435255040, 1517861616688080, 0, -5195533072156284, 0, 0, 2039626923682278, -8022698657351732, 0, 0, 3911075964394662, 0, 135432811651808, -9551989624943128, 0, -2807085357575048, -82284666198336, 0, 1820909395980567, 0, 0, -8092468192535032, -8462458575359922, 0, 0, 7704173558747120, 0, 54276700404428, 490067339552640, 0, 5977757766230208, -823967445572288, 0, -1324963591060160, 0, 0, 2418066310435794, -2233228722258240, 0, 0, 4903400990935984, 0, -726635385031680, 4889445533407404, 0, -3882271939928008, 394551328460436, 0, 723395741503888, 0, 0, -746502635096064, -4355388599236479, 0, 0, -9162831129611436, 0, -2782649841628912, -14915221633368000, 0, 7084427470383138, -4303097689556496, 0, 2695155219924092, 0, 0, -2520601224871460, 181806658715844, 0, 0, 64913958416188, 0, -5700909746806848, 3804416217426240, 0, -1551595184517984, 8581776635727610, 0, -9377005815051932, 0, 0, 1465992877708048, 924718015877454, 0, 0, -3995330193797744, 0, 8732126787689152, -722340859903000, 0, -5798841815298444, -4428811377065548, 0, -2362787197194816, 0, 0, -7709562086306280, 864381158959968, 0, 0, 5048567323994880, 0, -2953811583373508, -674117150636684, 0, -6136499975365648, -5043576501266826, 0, 8480207539197536, 0, 0, 1918514812205156, 5412635841810872, 0, 0, -7982752917518948, 0, -1168910181204312, -6519893210198566, 0, 2959806781929024, -1375937855119296, 0, -6560368875969890, 0, 0, 1746660132951880, 86659879073656, 0, 0, -8723926245900700, 0, 1675487790513570, -896041314713736, 0, -279743134519296, -764793375501720, 0, -9757761776440326, 0, 0, -5473615789086192, 23202654449421888, 0, 0, 1167838117479952, 0, 8989074461676636, 11542120910023012, 0, -946574632827794, -10898550934687380, 0, 3895731997435584, 0, 0, 21768250934773294, 5474433820142056, 0, 0, 7280922356665880, 0, -2205111039448290, 3870451223476992, 0, 3855307726355688, 4400154209746944, 0, 203696765944036, 0, 0, 6555143945253740, 7749469693276010, 0, 0, 220396523510564, 0, 1990257923747520, 4083332078845900, 0, 4332568360491126, -3361653739256672, 0, 322954319125568, 0, 0, 3705931765903032, -1847644107559812, 0, 0, -12593699200362768, 0, -6412387904798656, -9439932164864384, 0, 254317409201760, 6891557587323600, 0, 13952141627364864, 0, 0, 476424905696800, -7765405679234079, 0, 0, 16207596536748232, 0, 6868831704319232, 12703318434466304, 0, 5906041023563222, 705765384307812, 0, -2210644335077600, 0, 0, 8238022359240060, 7753859793355424, 0, 0, -6570908120952642, 0, 10379614256742640, -4349357029616252, 0, 5165782976039264, 374589384611904, 0, 6438535153141248, 0, 0, -5712519426669068, -6781866824813924, 0, 0, 4039251073659648, 0, 4372596805654080, 452722373286424, 0, 5633454036994560, -3906073193475792, 0, -13974572214862872, 0, 0, 10891614718456522, -11115754157047680, 0, 0, 4192500162410712, 0, -6523920289628996, 9282219832035464, 0, -1209712460012424, -1136389153380352, 0, -4301807930883360, 0, 0, -11340759437025984, 11225944104104976, 0, 0, 11474356215051568, 0, -975538156747924, 16830201443190912, 0, -1117283215795676, 5693922767126620, 0, 9237104097482384, 0, 0, -10107967406387606, 4173894496955096, 0, 0, -11744293479891740, 0, 509615165626560, 1986301687599180, 0, -1115328822668072, -6742564130624752, 0, -6415841363286888, 0, 0, 3558486238008792, -1585160865817938, 0, 0, -7108634827770880, 0, 1804385360095184, -7985839861772862, 0, 2863710245775466, -5355696691662848, 0, 15770465835989788, 0, 0, 3310229294377928, -3655081760867128, 0, 0, 20812642687089792, 0, 8481708132559164, -9642043995471856, 0], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "15.10.a.d", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0], [1, 0], [15, -1], [0, 0], [255, -31], [0, 0], [0, 0], [-6944, 224], [12947, -239], [0, 0], [0, 0], [9572, -2368], [0, 0], [-14814, -5344], [-225568, 10528], [0, 0], [193183, -899], [-82238, -7520], [0, 0], [-45084, 5728], [0, 0], [0, 0], [1427036, -47460], [-380768, -26272], [0, 0], [0, 0], [2674238, -70690], [0, 0], [-5534368, 279328], [1254818, -168576], [0, 0], [5467584, 152736], [-3243861, -85199], [0, 0], [2842270, -38082], [0, 0], [0, 0], [-11083414, -198496], [-3780836, 136732], [0, 0], [0, 0], [-13276234, -492096], [0, 0], [3244412, -702336], [42227996, -973980], [0, 0], [8527904, -39584], [-16775384, -1970528], [0, 0], [35060921, -3161088], [0, 0], [0, 0], [86012318, -1069150], [1654422, 177728], [0, 0], [0, 0], [-118920480, 4613280], [0, 0], [110190462, -3952034], [15573156, -4348352], [0, 0], [170273566, -950208], [-769152, -3023808], [0, 0], [-101389753, 2340965], [0, 0], [0, 0], [144611188, 1026560], [105380350, 398658], [0, 0], [0, 0], [-107415672, -4545280], [0, 0], [116915638, 1168192], [-58666378, 7907478], [0, 0], [-107738276, 3035812], [-353962112, 19117952], [0, 0], [-21902080, -19049120], [0, 0], [0, 0], [67572522, 5402698], [-189671220, -7260288], [0, 0], [0, 0], [429332292, -14481788], [0, 0], [430674668, -33512156], [218344134, 9049152], [0, 0], [-545935936, 34987456], [344326304, 4290016], [0, 0], [816395416, -14753064], [0, 0], [0, 0], [-892554882, -13450880], [2239223511, -85638329], [0, 0], [0, 0]]}