-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '628353349920138470232348184677,1558726958024334721599046703766', 'a10': 0, 'a2': 0, 'a3': 3, 'a4': 0, 'a5': 1, 'a6': 0, 'a7': 1, 'a8': 0, 'a9': 2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3823.7096107228735, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [11, [1]]], 'bad_primes': [2, 11], 'central_character': '7744.1', 'coefficient_field': '1.1.1.1', 'conductor': 59969536, 'conductor_radical': 22, 'degree': 4, 'euler_factors': [[1], [1, -3, 7, -9, 9], [1, -1, 9, -5, 25], [1, -1, 3, -7, 49], [1], [1, -7, 37, -91, 169], [1, 7, 45, 119, 289], [1, -1, 27, -19, 361], [1, -4, 30, -92, 529], [1, -15, 113, -435, 841], [1, 5, 57, 155, 961], [1, 3, 65, 111, 1369], [1, 15, 137, 615, 1681], [1, 0, 86, 0, 1849], [1, -5, 99, -235, 2209], [1, 3, 77, 159, 2809], [1, -9, 107, -531, 3481], [1, -7, 133, -427, 3721], [1, 8, 70, 536, 4489], [1, 15, 197, 1065, 5041], [1, -13, 157, -949, 5329], [1, -21, 257, -1659, 6241], [1, 3, -43, 249, 6889], [1, 8, 174, 712, 7921], [1, 9, 113, 873, 9409], [1, -11, 81, -1111, 10201], [1, 9, 215, 927, 10609], [1, 3, 115, 321, 11449], [1, 16, 262, 1744, 11881], [1, -15, 181, -1695, 12769]], 'euler_factors_factorization': [[1], [[[1, -3, 7, -9, 9], 1]], [[[1, -1, 9, -5, 25], 1]], [[[1, -1, 3, -7, 49], 1]], [1], [[[1, -7, 37, -91, 169], 1]], [[[1, 7, 45, 119, 289], 1]], [[[1, -1, 27, -19, 361], 1]], [[[1, -4, 30, -92, 529], 1]], [[[1, -15, 113, -435, 841], 1]], [[[1, 5, 57, 155, 961], 1]], [[[1, 3, 65, 111, 1369], 1]], [[[1, 15, 137, 615, 1681], 1]], [[[1, 0, 43], 2]], [[[1, -5, 99, -235, 2209], 1]], [[[1, 3, 77, 159, 2809], 1]], [[[1, -9, 107, -531, 3481], 1]], [[[1, -7, 133, -427, 3721], 1]], [[[1, 8, 70, 536, 4489], 1]], [[[1, 15, 197, 1065, 5041], 1]], [[[1, -13, 157, -949, 5329], 1]], [[[1, -21, 257, -1659, 6241], 1]], [[[1, 3, -43, 249, 6889], 1]], [[[1, 8, 174, 712, 7921], 1]], [[[1, 9, 113, 873, 9409], 1]], [[[1, -11, 81, -1111, 10201], 1]], [[[1, 9, 215, 927, 10609], 1]], [[[1, 3, 115, 321, 11449], 1]], [[[1, 16, 262, 1744, 11881], 1]], [[[1, -15, 181, -1695, 12769], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 14, 'label': '4-88e4-1.1-c1e2-0-14', 'leading_term': '6.0764744970083181223155483747768976373554071027184075213440000000000000000000000000000000', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/7744/2/a/db', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.025390625', 'prec': 37}, 'plot_values': [6.076474497008318, 6.050217442959285, 5.999659060003977, 5.905844145887174, 5.7706358296912175, 5.5997960978979044, 5.393780577117642, 5.152289779707323, 4.876720939452042, 4.56895614090349, 4.230769082238288, 3.8641239327457337, 3.471396029554911, 3.0552438629290144, 2.6186329087994866, 2.1647879466567077, 1.6972741270498997, 1.2198959570941768, 0.736762032368188, 0.2521675793947338, -0.22934720221125798, -0.703135359982116, -1.1644014239468623, -1.608351402892087, -2.030170670757431, -2.4251779237820483, -2.7888245426020255, -3.1168429021479143, -3.4052657424080843, -3.6505590674519888, -3.849657041911512, -4.000070196918907, -4.099928510528529, -4.148057092438925, -4.1440178760864645, -4.088147303561462, -3.9815857541610953, -3.8262749109847753, -3.624963931072468, -3.3811679415621807, -3.0991411588708817, -2.783802036307636, -2.440666063660056, -2.0757470861549563, -1.6954462020495575, -1.3064422571954848, -0.9155377871118048, -0.5295542136150454, -0.15514068710410245, 0.20130933420456748, 0.5338757623789278, 0.8371577570388746, 1.1065034176427335, 1.3380043000292599, 1.528720070229403, 1.676611961995136, 1.7807446487645788, 1.8411545659257877, 1.8590127126298592, 1.8364303937477628, 1.7765703057944249, 1.6833992102472148, 1.561740243887602, 1.4169885066900014, 1.2551045339228815, 1.0823139201095509, 0.905049514875495, 0.7296592319543037, 0.5623118269640418, 0.40873736363097785, 0.27411738394108887, 0.16287981721733163, 0.07859802303404276, 0.02385629268483434, 0.00018291433965750194, 0.007994292945115099, 0.04658448523801632, 0.1141462012417732, 0.20783325538096162, 0.3238464707437641, 0.4575767436636789, 0.6037344952867273, 0.7565705549685754, 0.9100206503353927, 1.0579904368212063, 1.194482765120843, 1.3139234652982668, 1.4112395867424574, 1.4821955061201886, 1.5233952792402046, 1.5325955457282805, 1.5086142195888892, 1.4515882957606998, 1.3627833535938834, 1.2447708704767144, 1.1011468808440124, 0.9366141750437336, 0.7566320270343735, 0.5674023931845433, 0.3754838501193289, 0.18769571915829963, 0.010736373090667094, -0.14896712911441848, -0.2855947886407288, -0.39410067218111977, -0.47046595549473763, -0.5118397462916942, -0.516683459679309, -0.4848441695127837, -0.4175798772583662, -0.31753240891095524, -0.1886413167944703, -0.03599760166869201, 0.13432786691804904, 0.31555017287192866, 0.5003863173730977, 0.6814212259463778, 0.8513173917629259, 1.003243780470176, 1.1310264233232818, 1.229589966465322, 1.2950029388012065, 1.3248762914021481, 1.3182715676918797, 1.276004495466148, 1.200405029228715, 1.0954870278676683, 0.9665731145964263, 0.820312258361516, 0.6642058018257531, 0.5064804475483246, 0.3555706120197081, 0.21988086876363033, 0.10729041565627669, 0.024861897770439935, -0.021566252967053324, -0.02765282497359389, 0.009180609370632177, 0.08957019278125897, 0.21211857518926072, 0.37337484638639956, 0.5679205340431182, 0.7885530330450512, 1.026519355611175, 1.271915549857565, 1.5140089999452138, 1.74182977488333, 1.9445005563600837, 2.1119603767609396, 2.235212085798424, 2.30709094811873, 2.3223456353772858, 2.278349345325417, 2.1749518281672096, 2.0150329242582496, 1.8040975615307013, 1.550592065864299, 1.265256321026648, 0.961159915177647, 0.6528688030811068, 0.3562062595764841, 0.08732772139117922, -0.1377368916612205, -0.30398410436226614, -0.3980102134021065, -0.40876878214481616, -0.32812408861495806, -0.15136429600460072, 0.12241217712823199, 0.49009038016094714, 0.9444536665414831, 1.4742937542043688, 2.064723313163289, 2.697552218146916, 3.3520369636175738, 4.005417145642314, 4.634071985933124, 5.214069451598292, 5.722631319352169, 6.1385286262639305, 6.443699956631701, 6.623336406776913, 6.667464046139771, 6.5705998864098705, 6.333106355108632, 5.960362321526879, 5.4637275799557665, 4.859250484214879, 4.168140730549414, 3.415114844931181, 2.628357204900396, 1.8376724059573672, 1.0740042535450682, 0.36760692321350746, -0.25272595293904726, -0.7612508251742489, -1.1361231078420773, -1.3605564516411754, -1.4235124370774068, -1.3203034672627074, -1.0529019289000112, -0.6299513361598444, -0.06652978789870113, 0.6163640992303724, 1.3926701589602735, 2.2321440040986587, 3.101808852314531, 3.966962773369036, 4.793088150640665, 5.546722254159575, 6.1976033992617925, 6.719151064104408, 7.090578602132249, 7.296787870386425, 7.3301762660125735, 7.189846924828762, 6.882885230370885, 6.422903171082079, 5.830650552464269, 5.132030433388336, 4.358028029942573, 3.5424315668807322, 2.721186461040702, 1.9301136530118168, 1.2039051494137218, 0.574137808267844, 0.0681979142723029, -0.2921604159245132, -0.49165382386353, -0.522213736983763, -0.3833169760635475, -0.08200635316770474, 0.3674697395831051, 0.9442510799687128, 1.621975838125706, 2.369762091985921, 3.153989003183563, 3.9393622754242754, 4.691162330615045, 5.376068731795625, 5.964583109357773, 6.431328007741971, 6.757318537374805, 6.929546898368335, 6.942805002110116, 6.798499917902923, 6.5058155477946125, 6.079851366786952, 5.5420387265068864, 4.9178272278691315, 4.2364158591295045, 3.528302132000921, 2.8245215880817494, 2.1544059165811382, 1.5446196330060349, 1.0174376326464223, 0.5899054184612235, 0.27284989218319927, 0.07046101537244848, -0.019889693467654984, -0.007437868309917319, 0.09251944456857102, 0.25953945008624907, 0.46908628939407765, 0.6940753090418135, 0.9061158143117102, 1.077471317352138, 1.1821420028128222, 1.1979335910256705, 1.1070660812546096, 0.898011554452013, 0.5654161050458644, 0.11140478426045276, -0.4552526766885157, -1.1185701553280403, -1.8568472371755465, -2.642886060616801, -3.445933487864483, -4.232582456328971, -4.968834564678968, -5.62144087959856, -6.159740274394074, -6.557101311582395, -6.792239187063505, -6.850394359639487, -6.723941419890562, -6.412987415749687, -5.9252364478470465, -5.275801757797783, -4.486448760803147, -3.5845671510427497, -2.602048802090433, -1.573527992625137, -0.5352306555801281, 0.4772710652942318, 1.4298925489678647, 2.292435496660449, 3.0388227728164883, 3.64930120618983, 4.109918920128824, 4.4142369904677565, 4.562047054328756, 4.560409047246454, 4.42176299059719, 4.164255122914601, 3.809520275900393, 3.382404444438668, 2.9087572011865492, 2.4147735364302734, 1.9251265869658372, 1.4622113910321843, 1.0448699908902335, 0.6878134305222684, 0.40106236258983025, 0.18975525225217268, 0.05427729259508908, -0.009449439617113609, -0.009314046053909772, 0.04372287877720276, 0.1365433685520131, 0.2549157172754502, 0.38437700434322924, 0.5113635874623266, 0.6238032540376053, 0.7121016673134749, 0.7692777958464189, 0.7916208826629347, 0.7783289306051424, 0.7317424629955259, 0.6565744584304726, 0.5597406117544486, 0.4493690582496357, 0.33435226367139376, 0.22337255955120586, 0.1243706268061468, 0.043807947728442355, -0.013737253812354954, -0.045921646189599555, -0.052744920334149986, -0.036476052899682, -0.0013867389211153953, 0.046669349893514574, 0.10086332068312519, 0.15398552244802055, 0.1992517449241645, 0.23085136218753174, 0.24474269593571324, 0.23894894814021375, 0.2141204881574738, 0.1734444668906679, 0.12280365120909621, 0.0702762760104449, 0.02582611377814929, 0.0004889760766046992, 0.005661498841598297, 0.0521666514128333, 0.1493349046974759, 0.30418529486466195, 0.5205775960567223, 0.7987229290077529, 1.1347034392608493, 1.5204395616397428, 1.9438147130150818, 2.3890951442947426, 2.837771041218355, 3.269282620483974, 3.662523718653666, 3.9966127124000232, 4.252840136075378, 4.41516866518087, 4.472284972338861, 4.417539048763907, 4.250716517518368, 3.9772336949693874, 3.609296494216025, 3.1643324436430587, 2.665339820388337, 2.1387230413716165, 1.6138317929361616, 1.1205254279421988, 0.6881109609086484, 0.34305237621048346, 0.10768669633971605, -0.0015128641048068913, 0.02502289951735489, 0.1890754773276113, 0.484283642360138, 0.8962201624696725, 1.4030280536709998, 1.9763330452401107, 2.582957682773446, 3.18632828528515, 3.749099638873421, 4.234568804511894, 4.609815821580876, 4.846601222428485, 4.924484926053434, 4.830775099279378, 4.563067905901194, 4.128017295676069, 3.5428534295610192, 2.8330125121631093, 2.0324196576907747, 1.180292359722325, 0.32026346808184564, -0.5031158015072656, -1.2460537077935372, -1.8686944896076998, -2.3370309162432905, -2.625190378281269, -2.7169393040206273, -2.6067000589309517, -2.3000818393977864, -1.8135401437794756, -1.1735870501179009, -0.4153279311025836, 0.41968562941269894, 1.2855296947261978, 2.1351202306211006, 2.922222893908733, 3.605171519375463, 4.148135682252722, 4.524650084553794, 4.717623385267306, 4.722015186059567, 4.543361991095161, 4.199136276467425, 3.715920496335251, 3.1293020560256455, 2.4801581591331177, 1.8133052834396335, 1.1735834760136508, 0.6037991434220739, 0.14135805017066025, -0.18376588062189222, -0.351223852580393, -0.3515497844029476, -0.18683812470897906, 0.12934639616480625, 0.572772349856461, 1.1102301160039416, 1.7014060107489526, 2.3020222570106297, 2.8660875881137997, 3.3499693080887347, 3.714210377501181, 3.9277612588439412, 3.968638591062185, 3.8274791470675646, 3.5065853637569253, 3.022108745870555, 2.401419656402001, 1.683553426003883, 0.9152602844369371, 0.14977835950996168, -0.5577405249305726, -1.1526355200201985, -1.5850661881308374, -1.8127757550327737, -1.8043487818657715, -1.541382061855858, -1.020095974876052, -0.25206072133118207, 0.736007916302238, 1.9035079182711323, 3.197679715543293, 4.55693894198177, 5.913436886135705, 7.198067600868175, 8.342926768857792, 9.287192071717328, 9.97853136486416, 10.378838001595241, 10.463857518662458, 10.227783447931692, 9.680774958912643, 8.851681330416937, 7.78361505553588, 6.5345136901989695, 5.171394001547264, 3.7689732658841297, 2.403546337542205, 1.1503510066060292, 0.07810216941861699, -0.7539140970832306, -1.299771191445517, -1.5290290454427973, -1.4286190973183723, -1.0033260307094751, -0.275606051851299, 0.7160564789490307, 1.9189269035963563, 3.269774055739282, 4.69740052279559, 6.1280103184274, 7.487483184274592, 8.707504139561365, 9.726657932168585, 10.496325087175826, 10.979974394023225, 11.157908558278468, 11.02460725882949, 10.591746251162002, 9.88384245236363, 8.939210738969503, 7.804902208534539, 6.5363928897828885, 5.191677585833064, 3.8281690492076375, 2.501037293946135, 1.2659870066831518, 0.1665134641688191], 'positive_zeros': ['0.49568339241665561965516318164865', '1.22961875909947075964043689470985', '1.87952360239325726074424120562232', '1.89102169066986657949081542495198', '2.56606872815428438599406148107734', '2.84930772006376650474154187005372', '3.41336210059589114060323167334988', '3.47427968337719988437449816480959', '4.09708066264688201555081130028608', '4.25534629753124895960908853154243', '4.91493553695740619634952612805713', '5.13157330502113449761910480894581', '5.74236086019323845437851966788511', '5.87052279417592678898386499116815', '6.56709069406392481227565134856311', '6.60450091025111048657716528747294', '6.91164469965237170516898834817777', '7.45273816920866126806638744202488', '8.017159273621646335754993029161977', '8.055497859635932336326992720295234'], 'prelabel': '4-88e4-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.863596589683347, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 518641659156267113, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.49568339241665561965516318165', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.22961875909947075964043689471', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.87952360239325726074424120562', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3823.7096107228735, 'bad_primes': [2, 11], 'central_character': '1.1', 'conductor': 59969536, 'conductor_radical': 22, 'degree': 4, 'dirichlet_coefficients': [1, 0, 3, 0, 1, 0, 1, 0, 2, 0, 0, 0, 7, 0, 3, 0, -7, 0, 1, 0, 3, 0, 4, 0, -8, 0, -6, 0, 15, 0, -5, 0, 0, 0, 1, 0, -3, 0, 21, 0, -15, 0, 0, 0, 2, 0, 5, 0, -2, 0, -21, 0, -3, 0, 0, 0, 3, 0, 9, 0, 7, 0, 2, 0, 7, 0, -8, 0, 12, 0, -15, 0, 13, 0, -24, 0, 0, 0, 21, 0, -14, 0, -3, 0, -7, 0, 45, 0, -8, 0, 7, 0, -15, 0, 1, 0, -9, 0, 0, 0], 'euler11': [1, 0, 0, 0, 0], 'euler13': [1, -7, 37, -91, 169], 'euler17': [1, 7, 45, 119, 289], 'euler19': [1, -1, 27, -19, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -4, 30, -92, 529], 'euler29': [1, -15, 113, -435, 841], 'euler3': [1, -3, 7, -9, 9], 'euler31': [1, 5, 57, 155, 961], 'euler37': [1, 3, 65, 111, 1369], 'euler41': [1, 15, 137, 615, 1681], 'euler43': [1, 0, 86, 0, 1849], 'euler47': [1, -5, 99, -235, 2209], 'euler5': [1, -1, 9, -5, 25], 'euler53': [1, 3, 77, 159, 2809], 'euler59': [1, -9, 107, -531, 3481], 'euler61': [1, -7, 133, -427, 3721], 'euler67': [1, 8, 70, 536, 4489], 'euler7': [1, -1, 3, -7, 49], 'euler71': [1, 15, 197, 1065, 5041], 'euler73': [1, -13, 157, -949, 5329], 'euler79': [1, -21, 257, -1659, 6241], 'euler83': [1, 3, -43, 249, 6889], 'euler89': [1, 8, 174, 712, 7921], 'euler97': [1, 9, 113, 873, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, -3, 7, -9, 9], [1, -1, 9, -5, 25], [1, -1, 3, -7, 49], [1, 0, 0, 0, 0], [1, -7, 37, -91, 169], [1, 7, 45, 119, 289], [1, -1, 27, -19, 361], [1, -4, 30, -92, 529], [1, -15, 113, -435, 841], [1, 5, 57, 155, 961], [1, 3, 65, 111, 1369], [1, 15, 137, 615, 1681], [1, 0, 86, 0, 1849], [1, -5, 99, -235, 2209], [1, 3, 77, 159, 2809], [1, -9, 107, -531, 3481], [1, -7, 133, -427, 3721], [1, 8, 70, 536, 4489], [1, 15, 197, 1065, 5041], [1, -13, 157, -949, 5329], [1, -21, 257, -1659, 6241], [1, 3, -43, 249, 6889], [1, 8, 174, 712, 7921], [1, 9, 113, 873, 9409]], 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7744/2/a/db'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-88e4-1.1-c1e2-0-14', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-88e4-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.863596589683347, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 518641659156267113, 'z1': {'__RealLiteral__': 0, 'data': '0.49568339241665561965516318165', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '628353349920138470232348184677,1558726958024334721599046703766', 'Lhash_array': ['628353349920138470232348184677', '1558726958024334721599046703766'], 'label': '4-88e4-1.1-c1e2-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7744/2/a/db'}