Formats: - HTML - YAML - JSON - 2026-10-07T18:24:43.760459
  • lfunc_lfunctions • Show schema
    {'Lhash': '2798394856984196424932397319909', 'a10': [-4.133869836976943, 4.38507761460598], 'a2': [-1.2635392884920482, 0.6351916769267436], 'a3': [0.04471806801994335, -1.7314734460547074], 'a4': [1.1930630671259828, -1.605179279040177], 'a5': [4.004335878004041, -1.45745906759769], 'a6': [1.043314485904959, 2.216189270685352], 'a7': [-1.467229170219552, 0.2587120895922], 'a8': [-0.4878855409409134, 2.7860308144277215], 'a9': [-2.9960005887851273, -0.15485629467080025], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.7247686836596572, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [1.2635392884920482, -0.6351916769267436]]], [3, [[1.0, 0], [-0.04471806801994335, 1.7314734460547074]]]], 'bad_primes': [2, 3], 'central_character': '216.59', 'coefficient_field': 'CDF', 'conductor': 216, 'conductor_radical': 6, 'conjugate': '1566662172175620954725502524838', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.2635392884920482, -0.6351916769267436]], [[1.0, 0], [-0.04471806801994335, 1.7314734460547074]], [[1.0, 0], [-4.004335878004041, 1.45745906759769], [3.83022221559489, -3.2139380484326967]], [[1.0, 0], [1.467229170219552, -0.2587120895922], [6.5778483455013586, -2.3941410032796813]], [[1.0, 0], [-1.578352302586374, 4.336487311300272], [-8.426488874308758, -7.070663706551932]], [[1.0, 0], [2.8269250638076855, -3.3689981007874255], [-2.2574263096700946, -12.802500789158705]], [[1.0, 0], [-2.433813322669739, -1.4051627770006714], [8.5, 14.722431864335457]], [[1.0, 0], [-0.5168256265619657, -0.8951682438589437], [-9.5, 16.454482671904334]], [[1.0, 0], [-0.345538718942558, 1.9596474547129226], [-21.612930278075893, -7.866463296490381]], [[1.0, 0], [0.7832660537362424, -0.6572382568037646], [5.03579715234098, -28.559424837354033]], [[1.0, 0], [6.0488335599891006, 1.0665725584409136], [29.13047124436316, 10.602624443095731]], [[1.0, 0], [-5.155894114770081, -2.9767568550757137], [18.5, 32.04293994002423]], [[1.0, 0], [-2.775885397046408, 3.3081713945598614], [-7.119575284344144, -40.37711787350053]], [[1.0, 0], [2.281641036910018, 0.8304494227155202], [32.93991105411605, 27.639867216521193]], [[1.0, 0], [-0.8062790425560495, -4.5726356755868975], [-44.16555317693769, 16.07494673630643]], [[1.0, 0], [-3.145440358050289, 0], [53.0, 0]], [[1.0, 0], [-2.7745820447407707, -7.623101516349503], [-45.196622144019706, 37.92446897150582]], [[1.0, 0], [2.255752708262518, -0.3977500642728726], [57.32124986794041, -20.863228742865793]], [[1.0, 0], [-7.241117383914653, -6.076018926154176], [11.634427903684333, 65.98211945181794]], [[1.0, 0], [2.217700070074932, -3.8411691973188415], [-35.5, -61.48780366869514]], [[1.0, 0], [-6.1206656080085455, -10.601303809210254], [-36.5, 63.21985447626402]], [[1.0, 0], [-2.198721178865737, -2.6203338640262186], [-13.718206035687498, 77.79981248796443]], [[1.0, 0], [-3.2322397908029905, -3.8520333828154216], [-14.412798746355218, 81.73904350001327]], [[1.0, 0], [3.1414974311250345, -1.8137443875185566], [44.5, -77.07626093681505]], [[1.0, 0], [5.202809764899564, 1.8936678889729797], [74.30631098254086, 62.35039813959431]], [[1.0, 0], [1.0415098344561882, 5.906695789104431], [-94.90895469937675, 34.544034475892545]], [[1.0, 0], [0.5188670115912792, 1.4255753980469394], [-78.90257764125474, 66.20712379771355]], [[1.0, 0], [0, -3.8419589678724946], [-107.0, 0]], [[1.0, 0], [0, 0.07907186478970095], [-109.0, 0]], [[1.0, 0], [4.708969525702987, 12.937787440768899], [-86.56302207244451, 72.63499989457894]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 25, 'label': '2-6e3-216.59-c1-0-25', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/216/2/v/b/59/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, 'plot_values': [0.9925449105442951, 1.0588450525694106, 1.1312106165511482, 1.2089334749612675, 1.2893535083498573, 1.36811774566804, 1.4395514544388297, 1.4970726761975282, 1.5336293284782212, 1.542167914417702, 1.516148790898992, 1.450112752750368, 1.3402865896207277, 1.1851971686290808, 0.9862475458603575, 0.7481962932584254, 0.4794739121917776, 0.1922690890177047, -0.09767627488886543, -0.3716100711694723, -0.6086752886596841, -0.7871715960574929, -0.886130741145718, -0.8871232974620116, -0.7761743309664757, -0.545630075139499, -0.1957915870979808, 0.26388051486116737, 0.8141795017897099, 1.4263453234528267, 2.0631472048855253, 2.6808946431698115, 3.232326481438744, 3.670228763133024, 3.951532545436255, 4.041554115986976, 3.917974213500758, 3.5741213890467733, 3.0211368747702374, 2.288659823160965, 1.4237830077806528, 0.4881844562584008, -0.446471908362225, -1.3045714957245786, -2.0135308232043956, -2.511074763260496, -2.7520529460141443, -2.714010546448947, -2.400790281700635, -1.8435975571918377, -1.099201158414536, -0.24524736408921965, 0.6269955162868235, 1.4218120202835434, 2.0491999920741115, 2.4348905155566145, 2.5290346554016807, 2.312444522584798, 1.7995063163503406, 1.0372459833552934, 0.10048671116029861, -0.9164626733589326, -1.910673549661655, -2.7827190819804963, -3.4485225289338417, -3.849370290589547, -3.958711557678291, -3.784756183330901, -3.3684355596187947, -2.7769373468933973, -2.0936736205059234, -1.4060955660203176, -0.7931355381227284, -0.3141703660086118, -0.001224352435788037, 0.14432411757886224, 0.14994717258920257, 0.06530567784175086, -0.04824352642315758, -0.1302513320000764, -0.13373703306965104, -0.035458374758526506, 0.15807090062397283, 0.4101354497220212, 0.6593503402085631, 0.8305300736490577, 0.8492478871884424, 0.6576519280762881, 0.22869280096047223, -0.42401887146399303, -1.2429401175626038, -2.131116783479212, -2.9644030279272027, -3.609892963106482, -3.947841049424213, -3.893497696278142, -3.4150059242436037, -2.5438886094843247, -1.3756864482651332, -0.059849197293840944, 1.2202008095375634, 2.2741285503079327, 2.9347332062989304, 3.0860483176081073, 2.684585309039152, 1.7697057493289963, 0.46076949473801204, -1.0591173087641568, -2.5706001996907055, -3.852594864511782, -4.718177750823155, -5.045719167453035, -4.79972533543028, -4.037473409061664, -2.899913917830898, -1.5880733179664264, -0.32882186174317374, 0.6641142047930372, 1.227020553021888, 1.2743111138664835, 0.8127420974968067, -0.0609488754131584, -1.1786158793902433, -2.332098738659631, -3.311606540522317, -3.943893760767265, -4.123032731241722, -3.827983222842619, -3.1237077390856576, -2.145797325006946, -1.0718274594532136, -0.08530265148297457, 0.660474053095489, 1.071275835197758, 1.1277522663189192, 0.8850659136003495, 0.45667418616892375, -0.014073041759328282, -0.38823707652104056, -0.5639203213448468, -0.4999779038768731, -0.22547912753751592, 0.1673027872330707, 0.544942118697533, 0.7651212529058029, 0.7118767767731341, 0.32578203675981515, -0.3780174102378743, -1.3084120471220793, -2.314406560955047, -3.2155390175039615, -3.8401602321640698, -4.063123022592314, -3.8343334336266848, -3.191468190246573, -2.2535982597034243, -1.1967352376982563, -0.2164746352747993, 0.5140167918288964, 0.8811789251178959, 0.8548403230788274, 0.4929935846388503, -0.07370821905124621, -0.6742603008092259, -1.1389043490358988, -1.340145961039615, -1.2232711034527848, -0.8187840912661246, -0.23344210712057073, 0.37823829934872094, 0.8552087464726489, 1.073632394095398, 0.9818963042714499, 0.6173704457642559, 0.09957092231513687, -0.39989108198776707, -0.7042579095834368, -0.6844583379129883, -0.3045741473771101, 0.3524057919622562, 1.0868908875386878, 1.6151083765220515, 1.626504904909424, 0.8546019327799571, -0.8542496671280666, -3.490341223279777, -6.861235268604387, -10.610099720887392, -14.270082557632598, -17.34487050211815, -19.399319152785214, -20.14124595456751, -19.47689722576551, -17.52801857135045, -14.60670761975097, -11.153447570755747, -7.651783140540599, -4.538120937620541, -2.1259264385364083, -0.5599581023287168, 0.1910097606093944, 0.3035479601959789, 0.040282475223399505, -0.3225034060391884, -0.5624545018943728, -0.5580367492389436, -0.30473367870168433, 0.10128348448070526, 0.5054726568751042, 0.7502554763706931, 0.7275285004252341, 0.41388024509245075, -0.1207715323053935, -0.7328360470248996, -1.2468082732268628, -1.506838004352797, -1.4231668880485773, -1.000007106911782, -0.33669890540730835, 0.39845209804635, 1.0144844242987858, 1.351251956368338, 1.3248712483417289, 0.9520366325244437, 0.345930307965875, -0.3155360436521986, -0.8404568069349543, -1.078316509181758, -0.96403592804508, -0.5375924707252728, 0.06711890310918432, 0.6617282351830925, 1.0603131216274286, 1.1374528937391934, 0.8700785191678888, 0.3497938911071258, -0.23959360251691872, -0.6746261693662841, -0.76102691680233, -0.3994256702294196, 0.3716979067173097, 1.3701968320844435, 2.3061817345141353, 2.852720254436737, 2.734072287239642, 1.8082126768965445, 0.12052924618742783, -2.0878818512914368, -4.4224873230585295, -6.419957801036678, -7.655262239635372, -7.844487982302965, -6.916788110691341, -5.036118990971906, -2.5660650810829155, 0.014226008259199424, 2.2220955375450457], 'positive_zeros': ['2.20754430004637706206690872151268', '3.30669181518177960696055978307509', '5.18963685833852583976346530160013', '6.40982179825645419856015150606148', '7.51259121123617063451463622103391', '9.250675786245978540246151569919377', '9.696329659420198585024845934657658', '10.15266345520366495595005057226447', '11.04846187156975270394422306998669', '12.38062823444956926430754233797812'], 'prelabel': '2-6e3-216.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3133044900782367, 'root_angle': 0.1695493845151286, 'root_number': '0.48423282747957486 + 0.8749391800526116*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.169549384515', 'prec': 40}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.20754430004637706206690872151', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '3.30669181518177960696055978308', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '5.18963685833852583976346530160', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 1.7247686836596572, 'bad_primes': [2, 3], 'central_character': '216.59', 'conductor': 216, 'conductor_radical': 6, 'degree': 2, 'index': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/216/2/v/b/59/6'], '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': '2-6e3-216.59-c1-0-25', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-6e3-216.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3133044900782367, 'root_angle': 0.1695493845151286, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.20754430004637706206690872151', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '2798394856984196424932397319909', 'Lhash_array': ['2798394856984196424932397319909'], 'factors': ['2-6e3-216.59-c1-0-25'], 'label': '2-6e3-216.59-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/216/2/v/b/59/6'}