# Stored data for newform 225.6.a.k, downloaded from the LMFDB on 05 May 2024.
{"label": "225.6.a.k", "space_label": "225.6.a", "level": 225, "weight": 6, "hecke_orbit": 11, "hecke_orbit_code": 45035996374368481, "dim": 2, "is_polredabs": true, "nf_label": "2.2.145.1", "trace_hash": 1277350696915326464, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [-30, 5, 1]], [7, [-12900, 80, 1]]], "qexp_display": "q+(-2-\\beta )q^{2}+(8+5\\beta )q^{4}+(-30+\\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": 8100, "fricke_eigenval": 1, "atkin_lehner_string": "++", "analytic_conductor": 36.08635945792064, "hecke_ring_index": 1, "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": 145, "field_disc_factorization": [[5, 1], [29, 1]], "field_poly": [-36, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.958", "prec": 17}, {"__RealLiteral__": 0, "data": "0.024", "prec": 17}, {"__RealLiteral__": 0, "data": "9.341", "prec": 17}, {"__RealLiteral__": 0, "data": "0.262", "prec": 17}, {"__RealLiteral__": 0, "data": "61.936", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "5.2.3.c1", "atkin_lehner_eigenvals": [[3, 1], [5, 1]], "trace_display": [-5, 0, 0, -80], "traces": [0, 2, -5, 0, 21, 0, 0, -80, -255, 0, 0, 800, 0, 120, 1650, 0, -687, -1940, 0, -1512, 0, 0, -550, 1320, 0, 0, -6100, 0, -8090, 1300, 0, -5824, 13865, 0, 2530, 0, 0, 12560, 26980, 0, 0, 400, 0, -25680, 1150, 0, -39840, -18920, 0, -1414, 0, 0, 30260, -49460, 0, 0, -2850, 0, -96050, 63200, 0, -49116, -17340, 0, -26671, 0, 0, -6080, -8770, 0, 0, 65200, 0, -97740, -135800, 0, -131876, -3000, 0, -46288, 0, 0, 97600, 57360, 0, 0, -28600, 0, -115050, -87000, 0, -120800, 196560, 0, 60640, 0, 0, -10180, -112465, 0, 0, -266700, 0, -59920, 36900, 0, 79570, -218160, 0, -12668, 0, 0, 107230, 17140, 0, 0, 477650, 0, -86950, 31200, 0, 26898, -271610, 0, 98348, 0, 0, -135120, 32985, 0, 0, -16800, 0, 524480, 603900, 0, 268230, 467700, 0, -285032, 0, 0, -55700, -68000, 0, 0, -92050, 0, 653880, -197300, 0, 498816, -16020, 0, 529500, 0, 0, -803800, 310020, 0, 0, -783600, 0, 482000, -488800, 0, 634380, -241320, 0, -271386, 0, 0, 194360, 978300, 0, 0, -195050, 0, 826500, 461600, 0, 503716, 621000, 0, 160560, 0, 0, -822400, -265360, 0, 0, 880000, 0, 826100, -183350, 0, 565153, -178140, 0, -405168, 0, 0, 979950, -1908000, 0, 0, 684850, 0, -360220, -140800, 0, 68824, -298930, 0, 1281420, 0, 0, -405040, -699130, 0, 0, 69200, 0, 275120, -834450, 0, -52130, -1873360, 0, -872932, 0, 0, 669450, 564300, 0, 0, 308350, 0, -1391700, 1252400, 0, -1118676, 1092755, 0, 1456282, 0, 0, -1946720, 1029660, 0, 0, -38400, 0, -202800, -751150, 0, -773023, 1086420, 0, -2590400, 0, 0, 4100550, -1195480, 0, 0, -3335400, 0, -3007340, -2691100, 0, -2605776, 538790, 0, -403650, 0, 0, -1740080, 2226380, 0, 0, 1611000, 0, -1440800, 148100, 0, -2063000, 1956000, 0, -883674, 0, 0, 655730, 1731780, 0, 0, -661800, 0, -4227950, 3002400, 0, -828800, -2650640, 0, 1795372, 0, 0, 758640, -2641500, 0, 0, 1114800, 0, -1478860, 3227500, 0, -1457524, 385700, 0, -1336000, 0, 0, 4377600, 724240, 0, 0, 3884500, 0, -938400, 1023600, 0, -1476616, -3286620, 0, 4450440, 0, 0, -3503580, -17535, 0, 0, -2967600, 0, -918880, 4109400, 0, -3211350, -1407680, 0, -3191532, 0, 0, 5266150, -142020, 0, 0, -3958500, 0, -665350, -6841200, 0, 3614874, 411110, 0, -2863400, 0, 0, -1630160, -2463120, 0, 0, 1096800, 0, 4779000, -278500, 0, 2292240, 7502000, 0, 3146328, 0, 0, -5259500, 3582120, 0, 0, 2284750, 0, 937110, -4107300, 0, -111120, 1224285, 0, 1997430, 0, 0, -822960, 3211120, 0, 0, -814200, 0, 2202560, -4366350, 0, 9424500, 2936000, 0, -6797612, 0, 0, -3304410, -1107000, 0, 0, 1951300, 0, 8535800, 37600, 0, 1556316, -3373660, 0, 6702870, 0, 0, -5923360, -5970780, 0, 0, -769200, 0, 7690740, -1933800, 0, 3520986, -12690720, 0, -1735728, 0, 0, 5313800, -24240, 0, 0, -3963350, 0, 9266590, 11601800, 0, 2132000, 226370, 0, -1943680, 0, 0, -1736340, -7410870, 0, 0, 3995100, 0, 4733680, -5550550, 0, 6523650, -225280, 0, 12017200, 0, 0, -8697450, -12128000, 0, 0, 6896100, 0, -610900, -896400, 0, 9105600, 9919090, 0, -5517571, 0, 0, 11111600, 9811890, 0, 0, 8336800, 0, 1708600, 10643600, 0, 246044, -462000, 0, -2094888, 0, 0, -7868850, 12265400, 0, 0, -13152000, 0, 4025990, 6594500, 0, -2818400, -7186775, 0, 2302110, 0, 0, -7301200, 19758000, 0, 0, 3019000, 0, -14240160, -20469150, 0, 208760, 6670080, 0, 6414674, 0, 0, 15628040, -7864000, 0, 0, -4523100, 0, 5115350, -2885600, 0, 1730324, 12418840, 0, -13001290, 0, 0, 4989840, 1082850, 0, 0, -30678800, 0, 5737520, 11507400, 0, -10561836, -8829300, 0, 5883200, 0, 0, -19861500, -9433920, 0, 0, 397500, 0, -9278700, 2734200, 0, -16910696, 10451000, 0, -8544000, 0, 0, 21163340, 6709985, 0, 0, 13261200, 0, -20665600, 15489450, 0, -17177610, -6174960, 0, -5805056, 0, 0, -10056360, 3631940, 0, 0, 21534350, 0, -13526400, -6227600, 0, 8925676, -12834000, 0, 12255568, 0, 0, 7319280, -14959540, 0, 0, -2202400, 0, -9584640, 5370800, 0, -4315500, -16398660, 0, 6435832, 0, 0, 11054700, 15660000, 0, 0, 18765550, 0, -14529900, -8842400, 0, -13405296, 4153020, 0, -33548650, 0, 0, 9195160, -32837500, 0, 0, 3980400, 0, -20174960, -20320800, 0, -22560680, 15430600, 0, 26701000, 0, 0, -20386500, 6689060, 0, 0, 5285600, 0, -16809600, 12435200, 0, -5813724, -10216860, 0, -14313420, 0, 0, 47629200, -21769560, 0, 0, -27534400, 0, 13228900, -9777850, 0, 630447, 9584820, 0, -3768800, 0, 0, -9563400, -6491520, 0, 0, -18458100, 0, 3717080, 558800, 0, -6523224, 14100150, 0, 14186560, 0, 0, -3543200, 36781630, 0, 0, -13889900, 0, -42903360, -2468650, 0, -7551510, 16932000, 0, 7751388, 0, 0, 5611500, 12233760, 0, 0, 2403550, 0, 27508200, -42686400, 0, 13097800, -44115585, 0, -3062982, 0, 0, 1206320, 12531000, 0, 0, 27879200, 0, 33680000, -12052950, 0, 16203120, 9342000, 0, 13438968, 0, 0, -36837300, -3890600, 0, 0, 2784500, 0, 3037300, 23446800, 0, -3038784, 7232720, 0, -28093000, 0, 0, -1078320, -18856820, 0, 0, 5579400, 0, -14109280, 24537500, 0, 30958560, -1892000, 0, 3341212, 0, 0, -13075950, -877260, 0, 0, 3177150, 0, 40927050, 31249600, 0, 28226000, 34190400, 0, -5894291, 0, 0, -6218400, -9630870, 0, 0, -871200, 0, 28605040, 39774800, 0, -15245264, 1016540, 0, 17925520, 0, 0, 9395700, -45824000, 0, 0, 9469200, 0, 31185450, -16487600, 0, -9883384, -43306500, 0, -39994000, 0, 0, -10281920, 52281230, 0, 0, -10177500, 0, 7021520, 2824350, 0, 45745500, -75258080, 0, 29527988, 0, 0, -34399260, 5083580, 0, 0, -42397400, 0, 29206150, 10558000, 0, 78606702, 53169610, 0, 16730652, 0, 0, 22124080, 14565110, 0, 0, 60907200, 0, 45149440, -5024700, 0, 21191220, -3679220, 0, -16126728, 0, 0, -20644800, 27805400, 0, 0, -41104450, 0, 10479080, -14629200, 0, -47460800, 8192370, 0, 74663040, 0, 0, -20993000, -6216680, 0, 0, -16526200, 0, -14587120, -26707400, 0, -11680920, 33668280, 0, -16374200, 0, 0, 19266510, 18572320, 0, 0, -32200050, 0, -5143300, 37046400, 0, 49386760, 34400000, 0, -2101830, 0, 0, 30768640, 13465120, 0, 0, 41313200, 0, 38499600, -33579550, 0, 38800214, 81843000, 0, -14106432, 0, 0, -16843350, -4672000, 0, 0, -9457650, 0, 26922650, -53799800, 0, -36051016, -33746850, 0, -23009740, 0, 0, -6356660, -57999000, 0, 0, -11371700, 0, -49430400, -17801450, 0, -25418000, -54760560, 0, 21047600, 0, 0, 7845300, -45761180, 0, 0, 549700, 0, -37892100, -3396000, 0, -26262814, -65452000, 0, -47358098, 0, 0, -22127920, -13869495, 0, 0, 50054400, 0, 41677280, -1570250, 0, -4820654, -5668340, 0, -22620000, 0, 0, 27806950, 22329240, 0, 0, 84236500, 0, -49324560, 29822400, 0, -3772016, -34218180, 0, 44133000, 0, 0, -35116040, 18554020, 0, 0, -41940000, 0, -63577600, 39421050, 0, -46256800, 23286160, 0, -65463668, 0, 0, 66165600, -19680820, 0, 0, 27028350, 0, -73326250, 74270400, 0, 14955084, -50359500, 0, 84250161, 0, 0, -18321280, -13683390, 0, 0, -83176800, 0, 5474020, 9872000, 0, -93609200, 60263320, 0, -35139312, 0, 0, 37634500, -86532000, 0, 0, 42650300, 0, -34384950, -94171800, 0, -69966904, 1347160, 0, 21023640, 0, 0, -48024640, -64269485, 0, 0, 12887100, 0, -59697040, -48653400, 0, 24416000, -8248000, 0, -20956788, 0, 0, 34466980, 141796000, 0, 0, -20194550, 0, -40211150, -58780800, 0, -19210560, 98206590, 0, -56882648, 0, 0, 43428080, 12751270, 0, 0, -14674400, 0, 46724160, 50907800, 0, -66522150, -39652300, 0, 56512000, 0, 0, 161933800, 106851720, 0, 0, -55674600, 0, -54056840, -40933300, 0, -100416000, 22717380, 0, -16485150, 0, 0, -65459240, 54196000, 0, 0, -25043200, 0, -118710960, 96085500, 0, 45728040, 57530760, 0, 2825068, 0, 0, 894100, -13267000, 0, 0, -16494700, 0, -98411700, -12940800, 0, 82510000, 6258740, 0, 28767000, 0, 0, 9361280, 38808000, 0, 0, 34534400, 0, 56478180, -1995950, 0, -31782577, -53940000, 0, -89076304, 0, 0, -22678200, -19599440, 0, 0, -1826500, 0, 15071690, 86595600, 0, -115370824, 82424490, 0, 139261020, 0, 0, -72543600, -28929360, 0, 0, -20546500, 0, -3064560, 107221400, 0, -4344730, -104726880, 0, -125948000, 0, 0, 67646550, 218660, 0, 0, 61627200, 0, 49336600, -19683200, 0, 143942724, -147524590, 0, 65827600, 0, 0, -66677600, -50966640, 0, 0, -54444000, 0, 101133400, -114260650, 0, 151359276, -16012380, 0, -10427280, 0, 0, 61174400, -135460360, 0, 0, -46583800, 0, -28371280, 104679900, 0, -84056224, 29740500, 0, -49747830, 0, 0, -60453080, -7859380, 0, 0, 105572600, 0, 6670400, -57503100, 0, -126585000, 102092000, 0, 77949468, 0, 0, -90870030, -8691000, 0, 0, 91522500, 0, 108804400, 47234400, 0, 16093200, -48426260, 0, 26586428, 0, 0, 13259360, 166971850, 0, 0, -44548800, 0, 192980480, -25847300, 0, 166859500, -31060620, 0, -140584688, 0, 0, 58326600, -60246560, 0, 0, 36810300, 0, 78141600, 89543400, 0, 127477816, 111354920, 0, 70802800, 0, 0, -118371100, 7487500, 0, 0, 64775500, 0, -15687920, -107260500, 0, 62526230, -2392640, 0, -13794000, 0, 0, -16256800, -41058000, 0, 0, 82000800, 0, -18532450, -130420800, 0, 28137316, 108447910, 0, 54037532, 0, 0, -14025840, 23074740, 0, 0, -94881600, 0, 115612160, -204072000, 0, -3855960, -96390000, 0, -46399200, 0, 0, -124533100, 38681760, 0, 0, -213104250, 0, 55896410, -14955200, 0, 53956000, 40865715, 0, 107171310, 0, 0, 5902800, 10393500, 0, 0, -64987800, 0, -29373200, 53752200, 0, 223081740, -69429400, 0, 90524886, 0, 0, 94128260, -33889140, 0, 0, -160116200, 0, 139392200, 38167200, 0, 124005324, 12172660, 0, -117842850, 0, 0, -33756560, -68117440, 0, 0, -71971200, 0, 60170720, -87248000, 0, -177525086, -75827000, 0, 155399728, 0, 0, 56869150, 166361040, 0, 0, 331880800, 0, -17686650, 61197600, 0, -80528160, 38041590, 0, -248215500, 0, 0, 57703920, -173171270, 0, 0, 147560900, 0, -56851920, 63379500, 0, 54766080, 153102560, 0, 31935532, 0, 0, -63251850, -132246780, 0, 0, -123858600, 0, 156845400, -19731200, 0, 74451000, -97588500, 0, 213348177, 0, 0, -77764560, -79257390, 0, 0, 174184800, 0, 60279160, 168622150, 0, 59039800, 49225440, 0, -186452088, 0, 0, 50106800, 169308000, 0, 0, -48704000, 0, 63525070, 1770800, 0, -165588176, -224236560, 0, 207717000, 0, 0, -66784960, 37226380, 0, 0, 138686600, 0, -165156160, 181992900, 0, -110904800, -26387640, 0, -58014268, 0, 0, -23480500, -22831180, 0, 0, 125866500, 0, -246223800, -202879200, 0, 97169728, 199898860, 0, -133737520, 0, 0, 202392000, 125461000, 0, 0, -104439600, 0, 64902000, 260192600, 0, 87991444, -139472000, 0, 55157568, 0, 0, -123150900, 34407840, 0, 0, 55320900, 0, -84664500, -83736800, 0, -129732904, -161957040, 0, -174287000, 0, 0, 24273400, 47187770, 0, 0, -300717600, 0, -72409200, -144477750, 0, -246021330, 106968000, 0, 97361972, 0, 0, -7987170, -184021380, 0, 0, -196420650, 0, -148025600, 158312000, 0, -76515800, 19625000, 0, -170729760, 0, 0, -36692560, 12585445, 0, 0, -189337600, 0, -91186120, 76518500, 0, 8744130, 205525440, 0, 237686632, 0, 0, 14975700, 191289400, 0, 0, 47259800, 0, -197228080, -57607200, 0, -27638400, 31875120, 0, -196862230, 0, 0, 171428400, -35806400, 0, 0, -87366400, 0, -156946720, -45350100, 0, -90861500, 144797880, 0, -167496988, 0, 0, -51751120, 25794620, 0, 0, 108837450, 0, 37228600, -79627200, 0, -226304604, 14227860, 0, 201379500, 0, 0, 328928720, 194098000, 0, 0, 136116000, 0, -11047200, -202026400, 0, -247810926, 84226380, 0, -173344000, 0, 0, 188307750, 163422720, 0, 0, -17914850, 0, 50010270, 16556200, 0, 79008800, -226513500, 0, 188494360, 0, 0, -120537580, -36502770, 0, 0, 171454400, 0, -323641680, 125501700, 0, 101451290, 88892240, 0, 273303628, 0, 0, -55702200, 306000, 0, 0, -146105950, 0, -212198000, 105037200, 0, -97536402, -317156755, 0, -268960682, 0, 0, 187195040, 20039340, 0, 0, 260652000, 0, -113094560, -82209150, 0, -334374010, 112067220, 0, 237175512, 0, 0, -450643200, -325692000, 0, 0, -75214200, 0, 36970220, -158866900, 0, -49864000, 115419060, 0, -266378510, 0, 0, 248676600, -345992180, 0, 0, 153961600, 0, 26975840, 104762400, 0, 161190200, -297160000, 0, 193404800, 0, 0, 190140770, 33792340, 0, 0, 78160200, 0, 80734200, -138027200, 0, 329132716, 171606000, 0, -35842542, 0, 0, 220023120, -347933760, 0, 0, 41000800, 0, -192678940, -109975500, 0, 34554856, -157761000, 0, -150107632, 0, 0, -322756300, -131344000, 0, 0, -178952900, 0, -58204200, 472906600, 0, -265068000, 58453080, 0, 99540240, 0, 0, 35729860, -13468500, 0, 0, -33186000, 0, 226459280, -5597850, 0, -275987840, -56967840, 0, -42145372, 0, 0, -130355330, 294590000, 0, 0, 2512900, 0, 156882600, 56906400, 0, 216329684, -23335700, 0, -176264000, 0, 0, -138205920, -6397990, 0, 0, -23337600, 0, 158160080, -256588200, 0, 298497120, -128477280, 0, 188062560, 0, 0, 7908800, -128710600, 0, 0, 256449000, 0, 171370430, -215300400, 0, 236743776, 197637630, 0, -379129500, 0, 0, -19585200, 484931380, 0, 0, -7779600, 0, -59119920, 76226550, 0, -170962000, -267282040, 0, 154498314, 0, 0, 37820890, 35673560, 0, 0, -542120150, 0, 140044300, -122474400, 0, -127651204, 161421140, 0, -143357850, 0, 0, -204820640, 115499260, 0, 0, 106411200, 0, -58669140, -171343950, 0, 265960600, 52346580, 0, 211761712, 0, 0, -253891550, 75396000, 0, 0, 181344000, 0, 424421350, -277004400, 0, 316561792, 151346000, 0, 349125720, 0, 0, 222319040, 210643000, 0, 0, -90625700, 0, 376008000, -82970700, 0, 332721910, 411007520, 0, -354143520, 0, 0, -182361900, -178658340, 0, 0, 191253300, 0, 316948500, 301849200, 0, -16328840, 251442635, 0, 309048800, 0, 0, 14358400, 78529590, 0, 0, -147772800, 0, -180465040, 191052850, 0, 54560537, 365858000, 0, 212747200, 0, 0, -226834650, -757488000, 0, 0, -371393400, 0, -14371950, 257916300, 0, 135325024, -264377470, 0, -122560670, 0, 0, 216515520, 237075000, 0, 0, -247133600, 0, 142216960, -155708350, 0, 320839920, -381120000, 0, 194413000, 0, 0, -424599700, 532738380, 0, 0, 196215600, 0, 333369600, 356452800, 0, -6458000, -403663360, 0, -102728548, 0, 0, 222392240, -219741000, 0, 0, 234894400, 0, 244792420, 415820700, 0, -88580324, -120569660, 0, 116071488, 0, 0, 144870000, -5242800, 0, 0, 16713500, 0, 76579650, -158042800, 0, 120775224, 206753200, 0, -598626920, 0, 0, 108233180, 52438370, 0, 0, 225857600, 0, 125362960, 148788000, 0, 377939090, -212761200, 0, 76267372, 0, 0, -13478530, 400455360, 0, 0, 353442250, 0, -213642150, 19389600, 0, -145668000, -724560110, 0, 257434300, 0, 0, -364356000, -86993415, 0, 0, -326234400, 0, 26463160, 191696400, 0, -183681990, -63211060, 0, -94964000, 0, 0, 446965800, -126705960, 0, 0, -111275850, 0, -34757600, -218105100, 0, -224278992, 210738000, 0, 288884260, 0, 0, -241323040, -424689020, 0, 0, -82152600, 0, 70962560, -194210500, 0, 262135500, 238982600, 0, -28501812, 0, 0, -184771180, -240504000, 0, 0, 228991050, 0, 248253300, 1305600, 0, 290810000, 422374260, 0, 177443160, 0, 0, 166635760, -118458360, 0, 0, 333220800, 0, -326342780, 537847200, 0, 308518077, 367061000, 0, -378240000, 0, 0, -133903350, 417440000, 0, 0, -170652050, 0, -291489880, -331360800, 0, 130181224, -106352000, 0, -70280500, 0, 0, -161484940, 40652770, 0, 0, -417163900, 0, 28648080, -155768700, 0, -1005134000, -15927440, 0, 115002400, 0, 0, 357626850, 18516300, 0, 0, 206826950, 0, 27274800, 165912800, 0, -395970516, 402499200, 0, -494493598, 0, 0, -40214400, 279096840, 0, 0, -322250400, 0, -69840800, -633210650, 0, 17413590, 232242000, 0, 346557832, 0, 0, -297064850, 294584000, 0, 0, -72341800, 0, -264518680, -118103200, 0, 360522400, -118546950, 0, 406020350, 0, 0, -5158320, -772755000, 0, 0, -237074400, 0, 49312560, -748311400, 0, -482525640, -454350120, 0, -277252254, 0, 0, 266897960, 291157420, 0, 0, 157445400, 0, -461681950, -667116000, 0, -583713124, 182962500, 0, 181167492, 0, 0, -113577600, 100084350, 0, 0, 98516400, 0, -670110000, 352217700, 0, -282746400, -395075060, 0, -568170512, 0, 0, 742014200, -64634800, 0, 0, 422843300, 0, -62896500, 119946000, 0, 161062984, -209772360, 0, -194553120, 0, 0, 259487520, 398914130, 0, 0, -443971200, 0, 432634880, 212542500, 0, 203745500, 242192240, 0, -118328132, 0, 0, 431290100, -466253620, 0, 0, 486590100, 0, -531634200, 691488800, 0, -243330284, -60405000, 0, 2527692, 0, 0, -506113520, -99457000, 0, 0, -278791200, 0, -501112920, 80277600, 0, -216504000, -338048020, 0, 350865112, 0, 0, -120268900, -7967560, 0, 0, 362337350, 0, -32346930, 94721700, 0, -472787296, 72161235, 0, 423690000, 0, 0, -219103360, -48888440, 0, 0, -36502400, 0, -333874800, 86868600, 0, -322180520, -11396000, 0, -478168200, 0, 0, 50463700, -851496740, 0, 0, -612657350, 0, -545331600, -110308800, 0, -219596996, 2730660, 0, -105168510, 0, 0, 454147680, -683955180, 0, 0, 732352800, 0, -103409040, 317601000, 0, 156256912, 372172460, 0, -230592800, 0, 0, 406384250, 228039440, 0, 0, -161253450, 0, -757875880, -309212400, 0, 390745976, 14459770, 0, 443384460, 0, 0, 690960460, 360400000, 0, 0, 843247300, 0, 375469680, -191893450, 0, -107268970, -220944000, 0, -43015612, 0, 0, -328622400, 97564860, 0, 0, -234227800, 0, -252296300, 142129600, 0, -354585702, -216318410, 0, 719771598, 0, 0, -958274400, 239826000, 0, 0, -5184000, 0, -246313280, -13019000, 0, -248541296, -175772220, 0, 109268000, 0, 0, 876001500, -178930520, 0, 0, -596860500, 0, 556664690, 269654400, 0, 137416000, -519027060, 0, -663757290, 0, 0, -492072840, 900609600, 0, 0, 557500400, 0, 703717280, -301467200, 0, 27602120, 176076120, 0, 49298656, 0, 0, 252088280, 44537000, 0, 0, -162133200, 0, 53135850, 86868800, 0, -514939680, 475110660, 0, -121543500, 0, 0, 230630720, 281536470, 0, 0, -152450400, 0, -194239620, -445403100, 0, 26425236, 539348700, 0, -885910400, 0, 0, 175754900, 297560000, 0, 0, -7961500, 0, -266712300, 1311436800, 0, 459780880, 601605000, 0, 876002000, 0, 0, -881885600, 188019130, 0, 0, -546207200, 0, 271375600, 52939050, 0, 336841500, 359962320, 0, -298434000, 0, 0, 343095300, 481752000, 0, 0, -526337200, 0, 567173850, -541036800, 0, -71319284, -23239000, 0, 268941892, 0, 0, -846162960, -358391460, 0, 0, -239666400, 0, 342459400, 265229700, 0, 244082850, -902432000, 0, -60098632, 0, 0, -182131200, 6734920, 0, 0, -998036400, 0, 110846180, 253103700, 0, 645449216, 495937500, 0, 82829790, 0, 0, 512382480, 634638020, 0, 0, -134854800, 0, 384408000, -299593800, 0, 949458520, -438936320, 0, -257360600, 0, 0, -143701580, -509255520, 0, 0, 402189600, 0, -348981900, -656939200, 0, -836070000, 156429860, 0, 94410120, 0, 0, -200166080, -384875200, 0, 0, 492135600, 0, 36452300, 148201750, 0, -90839500, 105496220, 0, 15989520, 0, 0, -361574750, -108589200, 0, 0, 405995850, 0, 114355500, -751339800, 0, 103480000, -326009270, 0, -119109320, 0, 0, -326578980, -468375000, 0, 0, 529102300, 0, 1135481440, 552248800, 0, 894867000, 254944000, 0, 551362000, 0, 0, -2253600, -554947740, 0, 0, 67791850, 0, 608706300, -486840000, 0, 699900192, -1020452890, 0, -530612102, 0, 0, -910798800, 313444140, 0, 0, -305022400, 0, -345673120, 856595450, 0, 247536660, -132707380, 0, -182580088, 0, 0, 487181100, 156450280, 0, 0, 390799200, 0, 925101600, 740710000, 0, 823691584, 294486120, 0, 1001355000, 0, 0, -26055280, 321869000, 0, 0, 654992400, 0, 134457520, 677734300, 0, -231481320, 827010600, 0, -204917668, 0, 0, 1039063450, -1136420, 0, 0, 613537650, 0, 712589200, 275122400, 0, -129391200, 290032500, 0, 54941091, 0, 0, -319645120, -555026190, 0, 0, -182485600, 0, 98991260, -1122528000, 0, -44429900, -663152000, 0, -167021888, 0, 0, -632414700, 777468000, 0, 0, 959992000, 0, 531210600, -607246800, 0, 297809784, -1102425660, 0, 742776800, 0, 0, 682696800, -1537576215, 0, 0, 261042300, 0, 260257440, 303954900, 0, -12417870, 799416000, 0, -516505812, 0, 0, -182328360, 216819780, 0, 0, -698078600, 0, -286652700, -14616000, 0, -174657000, -331078910, 0, -47816852, 0, 0, -744087600, -378154050, 0, 0, -630404000, 0, -584798800, -795074200, 0, 83472960, -312024460, 0, 787266400, 0, 0, 856753200, -566887320, 0, 0, -532101600, 0, 443326400, 226996900, 0, 447613584, 147695130, 0, -343974500, 0, 0, 524028320, -371099320, 0, 0, -513399800, 0, 1116224080, -256565950, 0, 221142720, 179772000, 0, 413555454, 0, 0, -1573597280, 260647000, 0, 0, -470485450, 0, -564486600, -744628800, 0, 211409600, -619663800, 0, 89266590, 0, 0, 534931200, 1207213500, 0, 0, -1361625200, 0, -423409940, -151370600, 0, 850353574, 1049363220, 0, 110971920, 0, 0, -378692650, 320927680, 0, 0, 484734350, 0, -720664500, -770520000, 0, -88689016, -298297920, 0, -996471220, 0, 0, -835619740, -182533630, 0, 0, 1474313300, 0, 977648480, -131683850, 0, -656338890, 392067760, 0, -826256896, 0, 0, 778606200, 285516420, 0, 0, -698854200, 0, -6183800, 78464800, 0, -675468800, 1425112500, 0, 461746900, 0, 0, 5567280, -145190835, 0, 0, -158362400, 0, -533790800, 879604550, 0, -81154446, 39036180, 0, 278551200, 0, 0, 31062450, 504503720, 0, 0, -48867300, 0, -845523390, 215857900, 0, 158968000, -899013000, 0, 139864320, 0, 0, -173045160, 812744020, 0, 0, 459651600, 0, -570480640, -306292400, 0, -852702000, 246225720, 0, -574251000, 0, 0, 176160000, 584499000, 0, 0, 353000550, 0, -54689800, 74607200, 0, -924451800, 659936840, 0, 799962480, 0, 0, 1078955360, -1057269000, 0, 0, 417764800, 0, -651584380, 344923800, 0, -213009836, -240902060, 0, -1108688000, 0, 0, -293310100, -244403440, 0, 0, 460279300, 0, 167015700, 1273113600, 0, 578333176, 562305200, 0, -1012627320, 0, 0, 715080080, -143549130, 0, 0, -924222400, 0, 997432800, -741910500, 0, 94900910, -723812000, 0, 665765012, 0, 0, 154096900, -477052000, 0, 0, 1184225400, 0, -74888550, -84022000, 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": "45.6.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], [-2, -1], [0, 0], [8, 5], [0, 0], [0, 0], [-30, -20], [-132, 9], [0, 0], [0, 0], [410, -20], [0, 0], [20, 80], [780, 90], [0, 0], [-316, -55], [-986, 32], [0, 0], [-596, -320], [0, 0], [0, 0], [-100, -350], [408, 504], [0, 0], [0, 0], [-2920, -260], [0, 0], [-3840, -410], [10, 1280], [0, 0], [-3132, 440], [6836, 193], [0, 0], [820, 890], [0, 0], [0, 0], [5560, 1440], [12712, 1556], [0, 0], [0, 0], [880, -1360], [0, 0], [-13480, 1280], [-320, 1790], [0, 0], [-18960, -1920], [-9368, -184], [0, 0], [-1507, 1600], [0, 0], [0, 0], [14560, 1140], [-25034, 608], [0, 0], [0, 0], [-2520, 2190], [0, 0], [-46100, -3850], [32090, -980], [0, 0], [-27278, 5440], [-9576, 1812], [0, 0], [-10508, -5655], [0, 0], [0, 0], [1020, -8120], [-2128, -4514], [0, 0], [0, 0], [33340, -1480], [0, 0], [-51190, 4640], [-62960, -9880], [0, 0], [-62368, -7140], [2100, -7200], [0, 0], [-21804, -2680], [0, 0], [0, 0], [47200, 3200], [34044, -10728], [0, 0], [0, 0], [-19120, 9640], [0, 0], [-60600, 6150], [-39300, -8400], [0, 0], [-58200, -4400], [93984, 8592], [0, 0], [25360, 9920], [0, 0], [0, 0], [-6530, 2880], [-54586, -3293], [0, 0], [0, 0]]}