-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1559462563173543884219056844263,2236107130258056390824931497292', 'a10': 0, 'a2': 0, 'a3': -2, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -4, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 230.1767299768598, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]], [19, [1, -2, 1]]], 'bad_primes': [2, 5, 19], 'central_character': '1900.1', 'coefficient_field': '1.1.1.1', 'conductor': 3610000, 'conductor_radical': 190, 'degree': 4, 'euler_factors': [[1], [1, 2, 4, 6, 9], [1], [1, 4, 18, 28, 49], [1, 0, 10, 0, 121], [1, -2, 24, -26, 169], [1, 0, 22, 0, 289], [1, -2, 1], [1, 0, 34, 0, 529], [1, 0, 46, 0, 841], [1, -4, 54, -124, 961], [1, 10, 96, 370, 1369], [1, 12, 118, 492, 1681], [1, 4, 42, 172, 1849], [1, 12, 82, 564, 2209], [1, -18, 184, -954, 2809], [1, 0, 70, 0, 3481], [1, -4, 18, -244, 3721], [1, 10, 156, 670, 4489], [1, 12, 166, 852, 5041], [1, -8, 150, -584, 5329], [1, 8, 126, 632, 6241], [1, 0, 154, 0, 6889], [1, 24, 310, 2136, 7921], [1, -2, -48, -194, 9409], [1, 12, 130, 1212, 10201], [1, 10, 156, 1030, 10609], [1, 6, 148, 642, 11449], [1, 8, 126, 872, 11881], [1, -6, -8, -678, 12769]], 'euler_factors_factorization': [[1], [[[1, 2, 4, 6, 9], 1]], [1], [[[1, 2, 7], 2]], [[[1, 0, 10, 0, 121], 1]], [[[1, -2, 24, -26, 169], 1]], [[[1, 0, 22, 0, 289], 1]], [[[1, -1], 2]], [[[1, 0, 34, 0, 529], 1]], [[[1, 0, 46, 0, 841], 1]], [[[1, -4, 54, -124, 961], 1]], [[[1, 10, 96, 370, 1369], 1]], [[[1, 6, 41], 2]], [[[1, 4, 42, 172, 1849], 1]], [[[1, 12, 82, 564, 2209], 1]], [[[1, -18, 184, -954, 2809], 1]], [[[1, 0, 70, 0, 3481], 1]], [[[1, -4, 18, -244, 3721], 1]], [[[1, 10, 156, 670, 4489], 1]], [[[1, 12, 166, 852, 5041], 1]], [[[1, -8, 150, -584, 5329], 1]], [[[1, 8, 126, 632, 6241], 1]], [[[1, 0, 154, 0, 6889], 1]], [[[1, 24, 310, 2136, 7921], 1]], [[[1, -2, -48, -194, 9409], 1]], [[[1, 12, 130, 1212, 10201], 1]], [[[1, 10, 156, 1030, 10609], 1]], [[[1, 6, 148, 642, 11449], 1]], [[[1, 8, 126, 872, 11881], 1]], [[[1, -6, -8, -678, 12769], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 5, 'label': '4-1900e2-1.1-c1e2-0-5', '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': 2, 'origin': 'ModularForm/GL2/Q/holomorphic/1900/2/a/d', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.025390625', 'prec': 37}, 'plot_values': [1.191442026796307e-120, 0.003684643433735003, 0.01472809111763278, 0.033098617031890556, 0.05874166749357635, 0.09157850850326817, 0.13150217941297607, 0.1783759530627469, 0.23202649553766058, 0.29224303749053365, 0.35876773599838885, 0.4312963875295107, 0.5094663485460129, 0.592859487847775, 0.6809883843748205, 0.7733020348430393, 0.8691713779267881, 0.9678980562874399, 1.0687005862060364, 1.1707262321651277, 1.2730393248814142, 1.3746360491496252, 1.474436491579004, 1.57130187408515, 1.6640318720002423, 1.7513835520688414, 1.8320753347568703, 1.904806624631057, 1.9682694969761216, 2.021167751478048, 2.0622369891939427, 2.0902615934694966, 2.104103343436654, 2.1027146493268187, 2.0851752463972315, 2.0506999086317315, 1.998682115062227, 1.9286944607406822, 1.8405375277299303, 1.7342313280075143, 1.6100669938613434, 1.468587842074669, 1.3106409787014828, 1.137346977413582, 0.9501481294984369, 0.7507662803532218, 0.5412443025413713, 0.32389231806417074, 0.10131907816757572, -0.12363241522532827, -0.3478665404000392, -0.5681081802440554, -0.780899574538006, -0.9826794985338325, -1.169796542167001, -1.3385908922165073, -1.4854239774754214, -1.6067588024135995, -1.6992044360369354, -1.759590481694056, -1.785023325814043, -1.7729502774415027, -1.7212229499144553, -1.628146923856604, -1.4925462456690535, -1.313795194545949, -1.0918767887574528, -0.8273943751284171, -0.521616374253438, -0.17646692703510952, 0.20545099950151688, 0.620884852728271, 1.0659383817680126, 1.5361176961715763, 2.026372304587152, 2.5311528673717927, 3.0444916980385996, 3.5600651648506343, 4.071315551951612, 4.5715094704888255, 5.053900141004364, 5.511772096418757, 5.938639896508376, 6.32826901286934, 6.674903971326561, 6.973255732503759, 7.218749557009896, 7.407470505553337, 7.536419215765315, 7.603409339901926, 7.607318167304877, 7.5479328083308515, 7.426182395080656, 7.243933432662423, 7.004191284585181, 6.710849090399402, 6.368848410023759, 5.98389012679321, 5.562547389387863, 5.111950614657888, 4.639850009369624, 4.154289779340814, 3.6636222078486447, 3.176188113075031, 2.7002892890487, 2.2438928426230365, 1.814573295125624, 1.4192574846696355, 1.0641513007143422, 0.7545393012577843, 0.494713466447126, 0.287837649921296, 0.13589654074016827, 0.03962980053664195, -0.0014815972273486014, 0.010787209523201844, 0.07344297577054062, 0.18233772226662942, 0.3322681088223988, 0.5170858737946569, 0.729862350490964, 0.9630271039373374, 1.208594622282155, 1.4583086801386609, 1.7039213506123383, 1.9373190443056905, 2.1508376982162876, 2.337347190423562, 2.4905816064497928, 2.6051618991313252, 2.676917160310607, 2.70283081828648, 2.6813283330159376, 2.612139477688804, 2.4965300703911715, 2.337081316853818, 2.137848045260988, 1.9040648595294356, 1.6422205050818472, 1.359708760608825, 1.0648173886779333, 0.766348339890215, 0.47352935053698736, 0.195632310824658, -0.05817507664650206, -0.2791826313380793, -0.4593205529177558, -0.5914563711825099, -0.6695812408498343, -0.6890277665852933, -0.6466261542001087, -0.5408284086042832, -0.37180190999373125, -0.14145583903647405, 0.1465553592889054, 0.4868960665421986, 0.8726553770499522, 1.2954832659644446, 1.7458141235669615, 2.21304692289147, 2.685882248245702, 3.1525115140210387, 3.601050747252825, 4.019700778633616, 4.3972497937097295, 4.723167610695727, 4.988140509255877, 5.184068326262084, 5.304590448967752, 5.344964068730218, 5.302540218591516, 5.176514184916552, 4.96831528178044, 4.681234763594815, 4.320702279749061, 3.893811006768003, 3.4094664662975993, 2.877841258450197, 2.3103967238150265, 1.7193089854105965, 1.1173790362935332, 0.5174764928219616, -0.06763277684275015, -0.6257794989182047, -1.1456064934579506, -1.6169586884373421, -2.031096915434698, -2.380956902502945, -2.661316593078232, -2.8689109365145464, -3.0025137284253027, -3.062912036617023, -3.0528744543518713, -2.9770059408299705, -2.841589105022662, -2.654354939598558, -2.4242004657841747, -2.1609213397249194, -1.874825710151626, -1.5764794947363006, -1.276250404404021, -0.9841150385343657, -0.7091767385513849, -0.45957558224959044, -0.2420276079270077, -0.06186521051622779, 0.07735735152075364, 0.17368305487421834, 0.2270443380920403, 0.2389505476157522, 0.212656041777106, 0.15274279549680772, 0.0651599778445063, -0.04325701051313503, -0.16486152174085686, -0.2916900410469248, -0.4156211054118616, -0.5288310356393344, -0.6239936633291852, -0.6946508207375505, -0.7354033500509424, -0.7421620032228287, -0.7122810076896674, -0.6446724397914785, -0.5398416932163932, -0.39986855536061844, -0.22831825820053372, -0.03011251444176549, 0.18869156232876236, 0.4211002837416354, 0.6595241352053645, 0.8959950789115848, 1.1225958098031168, 1.3316404998825633, 1.5161471083052422, 1.6699312097698407, 1.7880683839189042, 1.86686331615513, 1.9042499436501907, 1.8996167530729464, 1.8541013664586539, 1.7702751989737047, 1.6523053983103446, 1.505524435527947, 1.3364534412811715, 1.152301394933505, 0.9608667164421063, 0.7700233802334957, 0.5875384862974119, 0.4206066206806466, 0.2756365412725297, 0.15788946973040513, 0.07129518760055951, 0.018235188927112102, -0.0005542158969946588, 0.013965152416685838, 0.059168407532761674, 0.13087177608852393, 0.2235235263564381, 0.3304327506728424, 0.4441136061183144, 0.5565846612377083, 0.6598361275806917, 0.7461321297473308, 0.8085460814408202, 0.8411951370905016, 0.8397719161420035, 0.801648802328616, 0.7263282255357253, 0.6153735728924488, 0.4727070175732682, 0.3043509809790367, 0.11852191141114359, -0.07480259570122606, -0.26401582724396366, -0.4364438808347692, -0.578689051412875, -0.6772514127130993, -0.7190319021669642, -0.691930545978718, -0.5854252841991315, -0.3910636470746762, -0.103011499984976, 0.28163086359244954, 0.7624230655349348, 1.3354860677982994, 1.9933429426964657, 2.725043326323158, 3.516327775540735, 4.349940402913568, 5.206154275656607, 6.063199478004503, 6.898139076798299, 7.687310805809269, 8.40749387650201, 9.036247662196725, 9.553266584463175, 9.940502008689265, 10.183572542246031, 10.271576613750234, 10.198414040241518, 9.962234302763374, 9.566534818147067, 9.019238845976615, 8.333466004436772, 7.526287032225217, 6.619108939922509, 5.636203382303071, 4.604705860458731, 3.553052254076168, 2.5106502290560364, 1.5063779891189784, 0.5680374293012967, -0.27893359138441115, -1.012081038047448, -1.612883278336151, -2.0672844342962113, -2.366223820649428, -2.505933986969789, -2.488030373073085, -2.3194592897346094, -2.012191515959576, -1.5827584494767284, -1.051652915748892, -0.4424556364079761, 0.21890820934282043, 0.9053851240436067, 1.5895089617082792, 2.244837042412615, 2.846468654662872, 3.3725414775346634, 3.804412490507218, 4.128042923612251, 4.333752517366163, 4.417336549182399, 4.379370467137958, 4.225943415290605, 3.9675607913677777, 3.6194390014659445, 3.2001172092297487, 2.731328354279433, 2.2364778476337395, 1.7401749022845032, 1.2667573383580202, 0.8396236906144388, 0.47997571003284106, 0.2061260813629995, 0.03259443153743595, -0.030428165113209327, 0.022447631303146538, 0.19158878790321468, 0.47230294442983395, 0.8550415843444179, 1.3257312263514405, 1.8664420675006723, 2.4559563841453667, 3.0708698164509873, 3.6862245239303473, 4.276940887422034, 4.818330076705664, 5.2877012132682175, 5.664586337638019, 5.932340838410236, 6.077960705068479, 6.093496843919398, 5.975412435621797, 5.725664073658576, 5.350624799721028, 4.861741191554368, 4.274122186703733, 3.606751548538627, 2.88090126184256, 2.119950981551149, 1.3478175188596293, 0.5884943495652349, -0.13531021628113984, -0.8027603152896481, -1.3958839975970003, -1.900122363472935, -2.3048467004191426, -2.6037228790526603, -2.7947248591518865, -2.8802125957566864, -2.8664914042341665, -2.7635645450866773, -2.584357291982867, -2.3441745732996178, -2.059756597530133, -1.7485344377432197, -1.4277026167878704, -1.1134094963502845, -0.8200184503559989, -0.5593868936717744, -0.3404445148091292, -0.16870125638872088, -0.04620676680964896, 0.028614175934494834, 0.060630258399522186, 0.057804828489334166, 0.03057067719935764, -0.008696380924187397, -0.04646683286320681, -0.06880840607146553, -0.062185040522346434, -0.01427919857860414, 0.08534748572366023, 0.24453656082019415, 0.46812215807652213, 0.757484833878974, 1.1104439311628767, 1.521209459503487, 1.9805604924333877, 2.476257207287776, 2.9934212972490855, 3.5153932843307936, 4.024179928440052, 4.5016664629949945, 4.929971465768216, 5.292863783268338, 5.575872647517119, 5.7677260318065935, 5.860102178046001, 5.848906297996344, 5.7336122602714275, 5.518228031398521, 5.210251350163826, 4.821234880700012, 4.365452903033129, 3.860053402822839, 3.3235898455183412, 2.7758248569335993, 2.236310608973371, 1.7239725466365659, 1.2559175278770147, 0.8469639817540282, 0.5088189102182166, 0.24972564894803853, 0.07408589467940062, -0.0176329355566335, -0.028834259133639028, 0.03345934668745785, 0.15902795468267572, 0.335061067852362, 0.546790923383062, 0.7783894362586578, 1.0136303872315033, 1.236949358201081, 1.4339516303474438, 1.5924719309916837, 1.7027797412937982, 1.7584734197279308, 1.7562981984702162, 1.696741501358416, 1.5834587047929969, 1.4234969445735492, 1.226403887984385, 1.0040838669919412, 0.7697293787930405, 0.5373903410970745, 0.32090372957951646, 0.1333181197180036, -0.0140036183297355, -0.11192962409968978, -0.15414517326583246, -0.13749631677953084, -0.06219253791408631, 0.06818331557585855, 0.24684660451865464, 0.46419859672440517, 0.7082825604119674, 0.9655498734067256, 1.221448319916324, 1.4614663324114125, 1.6716698120195037, 1.8398623837095804, 1.9558940600316401, 2.0127463542535096, 2.0064807075085174, 1.9370681858692895, 1.8079191286476808, 1.626326917269735, 1.402607828589635, 1.1501077927032137, 0.8840646823620623, 0.6212203564098543, 0.378578741884034, 0.17275365009736934, 0.018821346637138168, -0.07040104960383142, -0.08522673453967022, -0.019669264280160647, 0.12808738398312053, 0.35547253129502704, 0.6554986268426508, 1.0170394205700517, 1.4251807458140346, 1.8620420215547713, 2.3073590094781893, 2.7397881876641295, 3.137516815190101, 3.4799080738096606, 3.7478896317462564, 3.9256669286053656, 4.000782348774015, 3.96583388348512, 3.8177133082150037, 3.558452679069366, 3.195022709135859, 2.7413410612890603, 2.2136297102611384, 1.6267639891491403, 1.002882447559814], 'positive_zeros': ['1.23019904924336113712124714625738', '1.76397749494652932195956149680453', '2.89224244568729188193746483028435', '2.91027176429740671157007530436162', '3.65016321528989332605373908980582', '3.89784477540040678313905319586908', '4.61810810306989325090843943910454', '5.21542994543241923041358277048231', '5.39853823930531554967607062417245', '5.76729417529343455527964321079187', '6.44578648275118741177808487896613', '6.45545676362758861993359922642811', '6.92184041146793511736874997927411', '7.16762095013087082325732917163565', '7.938551033620986159704715607337543', '8.243704919932355411372816219043300', '8.818686164756380864525594806133475', '8.855511533935697558017854457237998'], 'prelabel': '4-1900e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.8950707803637257, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 1714166372383826827, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.23019904924336113712124714626', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.76397749494652932195956149680', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.89224244568729188193746483028', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 230.1767299768598, 'bad_primes': [2, 5, 19], 'central_character': '1.1', 'conductor': 3610000, 'conductor_radical': 190, 'degree': 4, 'dirichlet_coefficients': [1, 0, -2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 8, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, -10, 0, -4, 0, -12, 0, -4, 0, 0, 0, -12, 0, -2, 0, 0, 0, 18, 0, 0, 0, -4, 0, 0, 0, 4, 0, 0, 0, 0, 0, -10, 0, 0, 0, -12, 0, 8, 0, 0, 0, 0, 0, -8, 0, -1, 0, 0, 0, 0, 0, 0, 0, -24, 0, -8, 0, -8, 0, 0, 0, 2, 0, 0, 0], 'euler11': [1, 0, 10, 0, 121], 'euler13': [1, -2, 24, -26, 169], 'euler17': [1, 0, 22, 0, 289], 'euler19': [1, -2, 1, 0, 0], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 34, 0, 529], 'euler29': [1, 0, 46, 0, 841], 'euler3': [1, 2, 4, 6, 9], 'euler31': [1, -4, 54, -124, 961], 'euler37': [1, 10, 96, 370, 1369], 'euler41': [1, 12, 118, 492, 1681], 'euler43': [1, 4, 42, 172, 1849], 'euler47': [1, 12, 82, 564, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, -18, 184, -954, 2809], 'euler59': [1, 0, 70, 0, 3481], 'euler61': [1, -4, 18, -244, 3721], 'euler67': [1, 10, 156, 670, 4489], 'euler7': [1, 4, 18, 28, 49], 'euler71': [1, 12, 166, 852, 5041], 'euler73': [1, -8, 150, -584, 5329], 'euler79': [1, 8, 126, 632, 6241], 'euler83': [1, 0, 154, 0, 6889], 'euler89': [1, 24, 310, 2136, 7921], 'euler97': [1, -2, -48, -194, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 2, 4, 6, 9], [1, 0, 0, 0, 0], [1, 4, 18, 28, 49], [1, 0, 10, 0, 121], [1, -2, 24, -26, 169], [1, 0, 22, 0, 289], [1, -2, 1, 0, 0], [1, 0, 34, 0, 529], [1, 0, 46, 0, 841], [1, -4, 54, -124, 961], [1, 10, 96, 370, 1369], [1, 12, 118, 492, 1681], [1, 4, 42, 172, 1849], [1, 12, 82, 564, 2209], [1, -18, 184, -954, 2809], [1, 0, 70, 0, 3481], [1, -4, 18, -244, 3721], [1, 10, 156, 670, 4489], [1, 12, 166, 852, 5041], [1, -8, 150, -584, 5329], [1, 8, 126, 632, 6241], [1, 0, 154, 0, 6889], [1, 24, 310, 2136, 7921], [1, -2, -48, -194, 9409]], 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1900/2/a/d'], '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': '4-1900e2-1.1-c1e2-0-5', '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': 2, 'prelabel': '4-1900e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.8950707803637257, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1714166372383826827, 'z1': {'__RealLiteral__': 0, 'data': '1.23019904924336113712124714626', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1559462563173543884219056844263,2236107130258056390824931497292', 'Lhash_array': ['1559462563173543884219056844263', '2236107130258056390824931497292'], 'label': '4-1900e2-1.1-c1e2-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1900/2/a/d'}