Formats: - HTML - YAML - JSON - 2026-10-17T02:59:25.763719
  • lfunc_lfunctions • Show schema
    {'Lhash': '5283969117177855887966553783642', 'a10': [7.3484692283495345, -1.3179845261382144e-60], 'a2': [-1.224744871391589, -0.7071067811865476], 'a3': [2.449489742783178, -1.7320508075688772], 'a4': [1.0, 1.7320508075688772], 'a5': [-4.5, 2.598076211353316], 'a6': [-4.224744871391589, 0.3892695359907653], 'a7': [-3.1742346141747673, 5.497935626894489], 'a8': [0.0, -2.8284271247461903], 'a9': [3.0, -8.48528137423857], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.4904644758485345, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 7}, 'bad_lfactors': [[2, [[1.0, 0], [1.224744871391589, 0.7071067811865476]]], [3, [[1.0, 0], [-2.449489742783178, 1.7320508075688772]]]], 'bad_primes': [2, 3], 'central_character': '18.11', 'coefficient_field': 'CDF', 'conductor': 18, 'conductor_radical': 6, 'conjugate': '3907741983852841512117967697984', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.224744871391589, 0.7071067811865476]], [[1.0, 0], [-2.449489742783178, 1.7320508075688772]], [[1.0, 0], [4.5, -2.598076211353316], [12.5, -21.650635094610966]], [[1.0, 0], [3.1742346141747673, -5.497935626894489], [-24.5, -42.4352447854375]], [[1.0, 0], [-8.174234614174766, -4.719396554912959], [60.5, 104.78907385791707]], [[1.0, 0], [9.848469228349535, 17.05804908028005], [-84.5, 146.35829323957014]], [[1.0, 0], [0, 1.9070234711746934], [-289.0, 0]], [[1.0, 0], [-4.696938456699068, 0], [361.0, 0]], [[1.0, 0], [-8.174234614174766, 4.719396554912959], [264.5, -458.12743860196804]], [[1.0, 0], [2.848469228349534, 1.6445644757659692], [420.5, 728.3273645827129]], [[1.0, 0], [-20.5227038425243, -35.54636576394112], [-480.5, 832.2504130368455]], [[1.0, 0], [-17.30306154330093, 0], [1369.0, 0]], [[1.0, 0], [53.5454076850486, -30.914455540831067], [840.5, -1455.7887037616413]], [[1.0, 0], [0.47729615747569853, -0.8267011950053057], [-924.5, -1601.280971597427]], [[1.0, 0], [12.21964229922337, 7.05501377085755], [1104.5, 1913.050116959825]], [[1.0, 0], [0, 9.535117355873467], [-2809.0, 0]], [[1.0, 0], [-79.26504998427197, 45.76369794574857], [1740.5, -3014.634430573631]], [[1.0, 0], [-37.5454076850486, 65.03055370139117], [-1860.5, -3222.4805274818964]], [[1.0, 0], [15.477296157475699, 26.807463308538466], [-2244.5, 3887.5880375883453]], [[1.0, 0], [0, -85.9026497240206], [-5041.0, 0]], [[1.0, 0], [96.0908153700972, 0], [5329.0, 0]], [[1.0, 0], [14.871173070873835, -25.757627326903567], [-3120.5, -5404.864545018681]], [[1.0, 0], [76.12882692912616, 43.95299872062142], [3444.5, 5966.049006670998]], [[1.0, 0], [0, 41.376570889557954], [-7921.0, 0]], [[1.0, 0], [47.93928459844674, -83.03327660301392], [-4704.5, -8148.433024207783]], [[1.0, 0], [136.7724461102916, 78.96560857950045], [5100.5, 8834.325144005059]], [[1.0, 0], [14.568111527572905, 25.23270933608612], [-5304.5, 9187.66350874911]], [[1.0, 0], [0, -171.8052994480412], [-11449.0, 0]], [[1.0, 0], [-116.27244611029161, 0], [11881.0, 0]], [[1.0, 0], [-175.16632302368976, 101.13232375068422], [6384.5, -11058.278380923497]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-18-9.2-c2-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/18/3/d/a/11/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 27}, 'plot_values': [0.7192481084154976, 0.7389836550201353, 0.7708794309511865, 0.8150736093288529, 0.8712713413627645, 0.9387630430142908, 1.016420524493178, 1.1026624560592386, 1.1953936506073917, 1.2919309786178712, 1.3889319527051698, 1.4823422235747572, 1.5673773090168475, 1.638552662581733, 1.689774694459603, 1.7145032341232525, 1.7059927629677458, 1.6576152287516703, 1.5632612275535955, 1.4178088481611875, 1.2176407891233685, 0.9611809945898171, 0.6494127730001918, 0.2863321516209016, -0.12071575376656746, -0.5608720531206416, -1.0198235360139918, -1.4801307165774766, -1.9218544837596077, -2.3234903814801036, -2.663192604054548, -2.920238354945397, -3.076649634007984, -3.118856994528085, -3.0392622298288106, -2.8375385634390167, -2.5215019107084276, -2.107398722283991, -1.619487160113123, -1.088839427734797, -0.5513621937193377, -0.045114793942441465, 0.3929058059353874, 0.7302578855010564, 0.9424977818079391, 1.0161977275514107, 0.9511529283325576, 0.7614254578335651, 0.47495409201619504, 0.131587291934918, -0.22043692088391512, -0.529350214519528, -0.7456450374847452, -0.8282186858257928, -0.7501678604016305, -0.5034798015370737, -0.10190527268991995, 0.41856263623467643, 1.0019452834280018, 1.5772993811790839, 2.0661712175461835, 2.3917908155319916, 2.4889973715279816, 2.3136705571353073, 1.8503684564560599, 1.1169718590387905, 0.16541475150951698, -0.9219753607160973, -2.0404407900881565, -3.0743608248361056, -3.911144509165474, -4.455718503226355, -4.643636173617706, -4.450860417352864, -3.8985942299656746, -3.052131364500483, -2.013509851380491, -0.9086673585280173, 0.1293159649949294, 0.9785896473918113, 1.5458173471363066, 1.7796669843005075, 1.6782342238605117, 1.2889658897394904, 0.7007874135340655, 0.029406885029466017, -0.6020386836045477, -1.0839240484651038, -1.339156202158623, -1.3369138210450648, -1.0984932519462962, -0.6939107843850173, -0.22949728481695764, 0.17163386488131507, 0.3929600750668212, 0.3475933168640953, -0.003338776738832879, -0.6406640280305417, -1.4877939649755016, -2.422401631196937, -3.2974339177306122, -3.9678382997274757, -4.318069699712899, -4.285021245927478, -3.8716389644966207, -3.148083011432848, -2.2396310585385804, -1.303158620827333, -0.49645736941181723, 0.053648164085091175, 0.2778538605406412, 0.17981981308631273, -0.1632675542130202, -0.6158633109545696, -1.0125269073581495, -1.1942772508115156, -1.0454393775674546, -0.5230474710935016, 0.32799144224791876, 1.3780926058280856, 2.4349362610080285, 3.280507361647781, 3.7160971165752077, 3.606000016777769, 2.9104130044287992, 1.6998836610198707, 0.14727411026832257, -1.5020966522912576, -2.9766841762585345, -4.032066302843413, -4.500219851049514, -4.324015129144978, -3.5691051977345576, -2.410139502090633, -1.0938448969749723, 0.11326041779585819, 0.9811419549328371, 1.364029444868911, 1.2289671660680894, 0.6586850232649364, -0.17176599425896072, -1.0390261152825089, -1.725570978824729, -2.070987528009429, -2.0080153739839504, -1.574669619101215, -0.899661377854059, -0.16503457338647518, 0.44422818185394897, 0.7904231819824208, 0.8198435560655557, 0.5760331521902258, 0.18568440284117094, -0.1794263688811198, -0.35445663913874215, -0.23329916098192896, 0.19449036081807472, 0.8328225426137122, 1.4987622931258135, 1.9690434491379802, 2.0420473719440766, 1.5989574144151635, 0.6470593952351189, -0.6679788178468555, -2.0863545971846156, -3.290832920697206, -3.9828380143433115, -3.9589295662352666, -3.1675408378203014, -1.7301000819343109, 0.08063130997114398, 1.9011465325144357, 3.3624011088886996, 4.178321513317123, 4.214759830513499, 3.520605658701547, 2.3124052378156392, 0.9160823317486003, -0.3190719140862471, -1.111277984688808, -1.3175704658163605, -0.9662051682573982, -0.24142329603987797, 0.5749951838261089, 1.1888231100533657, 1.380927245165047, 1.0722031769445886, 0.34713994376265445, -0.5709736535970671, -1.3862256175896015, -1.8185280221414428, -1.6884911082226963, -0.9736322185952015, 0.18101438803493053, 1.50152835051401, 2.6620411333924245, 3.377515228541824, 3.4849231135896237, 2.9885866698367143, 2.0560033128263218, 0.9653435641180784, 0.02050419769492247, -0.540366433291324, -0.6147668066183116, -0.26254623808256183, 0.3188900136603598, 0.8630602685973134, 1.124837595713856, 0.9638260738250229, 0.39351264869568187, -0.4203845866842275, -1.212765921702468, -1.706858503751027, -1.7085486113334605, -1.176050898687434, -0.24071199348857883, 0.8299770798073536, 1.717288322744999, 2.1578934072703895, 2.0376275123354795, 1.4403532150737668, 0.6330892208162014, -0.011461129098579012, -0.1333021270513919, 0.49168945510719186, 1.8634143871774007, 3.7344328977922374, 5.663154948475295, 7.1307262141309655, 7.6883998775850015, 7.091382354343227, 5.377901152079992, 2.8680786020736453, 0.08139475939317833, -2.4034393889474117, -4.104467974587818, -4.761648329470189, -4.394222975410818, -3.2747567411328573, -1.8305364412522263, -0.5056243048336604, 0.3715549257748423, 0.673389453368702, 0.4861267707929335, 0.050656433565284924, -0.3447813453584518, -0.4801304791548071, -0.2858099870111876, 0.13689192757537727, 0.5631668607546891, 0.7408736207181713, 0.4987435227378433, -0.17484496270359998, -1.113501770502846, -2.0238466845816934, -2.589125643657528, -2.5883968330565925], 'positive_zeros': ['4.16831666093679399606816968693856', '7.22373635247377566575366078628512', '8.678128793745155372043192588380166', '9.880974393067798906745917632475362', '11.62936365107692201197538088819040', '13.68761001830931743560191895932746', '14.94911498001339251343967744903741', '16.26555310766820021965715127173310', '16.87382936778583479900571953794213', '19.13739471986139193363604939784521'], 'prelabel': '2-18-9.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7003316898788277, 'root_angle': 0.08186450176247415, 'root_number': '0.8706029278710484 + 0.49198632296269984*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0818645017625', 'prec': 40}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '4.16831666093679399606816968694', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '7.22373635247377566575366078629', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '8.678128793745155372043192588380', 'prec': 103}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 0.4904644758485345, 'bad_primes': [2, 3], 'central_character': '9.2', 'conductor': 18, 'conductor_radical': 6, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/18/3/d/a/11/1'], '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': '2-18-9.2-c2-0-0', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-18-9.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7003316898788277, 'root_angle': 0.08186450176247415, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '4.16831666093679399606816968694', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '5283969117177855887966553783642', 'Lhash_array': ['5283969117177855887966553783642'], 'factors': ['2-18-9.2-c2-0-0'], 'label': '2-18-9.2-c2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/18/3/d/a/11/1'}