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              lfunc_lfunctions •   Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 1, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 0, 'Lhash': '1257223690831075685', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 988.8673786315368, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, -1]], [43, [1, -1]]], 'bad_primes': [2, 3, 5, 43], 'central_character': '123840.1', 'coefficient_field': '1.1.1.1', 'conductor': 123840, 'conductor_radical': 1290, 'degree': 2, 'euler_factors': [[1], [1], [1, -1], [1, 0, 7], [1, -5, 11], [1, -3, 13], [1, -3, 17], [1, -4, 19], [1, 7, 23], [1, 8, 29], [1, -3, 31], [1, 0, 37], [1, 3, 41], [1, -1], [1, 0, 47], [1, 9, 53], [1, 8, 59], [1, 0, 61], [1, 11, 67], [1, -8, 71], [1, 4, 73], [1, -8, 79], [1, 9, 83], [1, -4, 89], [1, -13, 97]], 'gamma_factors': [[], [0]], 'index': 141, 'label': '2-123840-1.1-c1-0-141', 'leading_term': '9.22675330449', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'EllipticCurve/Q/123840/fj', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 2.105536026156508, 3.084367757570301, 2.357207408598374, 0.573187702069097, -0.6044666452603393, -0.1377304059692463, 0.9172145199952355, 0.342150703079983, -2.354136833088378, -4.693927325831558, -3.975300579342019, -0.9596166799880221, 0.7953802126803798, -0.2675064981326647, -1.495718385415203, -0.1666362178996749, 1.938770033136015, 1.02933444293733, -2.400419859464625, -3.65035359430664, -0.9226923328952235, 1.807253803213463, 1.200513641439967, -0.3076058644386285, 0.5699481503156252, 1.776357202707726, -0.09424315010734362, -2.663111340431439, -1.257960258583659, 2.406216554523427, 2.609471105887677, -0.2446931723583244, -0.2792659546703559, 3.046644078630702, 3.907836400147198, 0.8706618991691223, -0.949017639614683, -0.07457315583195566, -0.8348596975332628, -3.416535920601214, -2.643792086693088, 1.126346600913657, 1.396958056993871, -2.139401452405315, -2.78634826753743, 0.2329441697205646, 0.9998528327466015, -0.4731203143459236, 1.235535601054851, 4.388950438915064, 2.698425476349612, -1.392511616254665, -0.8748402263563779, 2.143649185913721, 1.484473340848054, -0.6169310476013974, 0.06428829660740687, -0.07556175740680549, -3.247065740364977, -3.316371742454169, 1.244932040065095, 2.413792063775684, -1.470930744045166, -2.291083528807226, 1.0221134876205, 1.426477473780417, -0.3606053420031425, 1.403767998850772, 3.559235100803034, 1.350578766028301, -0.1580101318644016, 2.446463881344896, 2.957616511624106, 0.08015392427513332, 0.7107117711118508, 3.574152703524416, 1.447008528185987, -2.051002786159461, -0.0287435042671592, 2.43163027478509, 0.1994690253644372, -0.7827827766066826, 1.407490093388845, -0.05301288146611657, -3.646004712933556, -1.880195759793093, 1.581545857998692, 0.3547452868364155, -0.86196043834587, 0.7895561600692674, -0.4203026845003262, -2.676394664576545, 0.9930182694259537, 4.9031522763956, 1.476122236459942, -2.137951561572029, -0.2735990804150604, 0.0555737686030646, -2.420890845218405, -0.9450004976749494, 1.560494927052899, -0.3818807947689515, -1.382400680341344, 0.4211412043092696, -1.797988441877773, -5.028275544006918, -1.593045636437706, 2.018533332155451, -0.6634818503381297, -1.814917169200174, 1.25754238264894, 0.904508306203759, -1.116333936226394, 0.348180804274851, -1.032385284584031, -6.623617701704542, -6.305274135484916, -0.9196351579128141, 0.2502162929330476, -0.1402063526453914], 'positive_zeros': ['1.088328204035911', '1.529872409818570', '2.042241983153534', '3.090881089265647', '3.462457866806530', '4.017134977669014', '4.580830994471992', '5.314642225012623', '5.918382731186037', '6.161987250710188', '6.742457581626438', '7.332369158324665', '7.975277341127286', '8.277134106667691', '9.071908126213887', '9.528671761692463', '9.612069174866515', '10.42033097906636', '10.85609938550077', '11.47975030509923', '11.89971682534202', '12.14581906387692', '12.89901385798581', '13.31621667877346', '13.89765135305062', '14.23791690172230', '14.49087229736896', '15.18398525301916', '15.66178819636143', '16.17239505591384', '16.67007679014364', '16.87203283145274', '17.62982829225661', '17.78019508420312', '18.51001922895949', '18.68074514234986', '19.32963389758268', '19.75184969112776'], 'prelabel': '2-123840-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 31.44626175925426, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1257223690831075685, 'z1': {'__RealLiteral__': 0, 'data': '1.088328204035911', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.529872409818570', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.042241983153534', 'prec': 57}}
           
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              lfunc_search •   Show schema
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{'algebraic': True, 'analytic_conductor': 988.8673786315368, 'bad_primes': [2, 3, 5, 43], 'central_character': '1.1', 'conductor': 123840, 'conductor_radical': 1290, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 3, 0, 0, 0, 3, 0, 4, 0, 0, 0, -7, 0, 1, 0, 0, 0, -8, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 1, 0, 0, 0, 0, 0, -7, 0, 0, 0, -9, 0, 5, 0, 0, 0, -8, 0, 0, 0, 0, 0, 3, 0, -11, 0, 0, 0, 8, 0, -4, 0, 0, 0, 0, 0, 8, 0, 0, 0, -9, 0, 3, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 13, 0, 0, 0], 'euler11': [1, -5, 11], 'euler13': [1, -3, 13], 'euler17': [1, -3, 17], 'euler19': [1, -4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 7, 23], 'euler29': [1, 8, 29], 'euler3': [1, 0, 0], 'euler31': [1, -3, 31], 'euler37': [1, 0, 37], 'euler41': [1, 3, 41], 'euler43': [1, -1, 0], 'euler47': [1, 0, 47], 'euler5': [1, -1, 0], 'euler53': [1, 9, 53], 'euler59': [1, 8, 59], 'euler61': [1, 0, 61], 'euler67': [1, 11, 67], 'euler7': [1, 0, 7], 'euler71': [1, -8, 71], 'euler73': [1, 4, 73], 'euler79': [1, -8, 79], 'euler83': [1, 9, 83], 'euler89': [1, -4, 89], 'euler97': [1, -13, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, -1, 0], [1, 0, 7], [1, -5, 11], [1, -3, 13], [1, -3, 17], [1, -4, 19], [1, 7, 23], [1, 8, 29], [1, -3, 31], [1, 0, 37], [1, 3, 41], [1, -1, 0], [1, 0, 47], [1, 9, 53], [1, 8, 59], [1, 0, 61], [1, 11, 67], [1, -8, 71], [1, 4, 73], [1, -8, 79], [1, 9, 83], [1, -4, 89], [1, -13, 97]], 'index': 141, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/123840/fj'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-123840-1.1-c1-0-141', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-123840-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 31.44626175925426, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1257223690831075685, 'z1': {'__RealLiteral__': 0, 'data': '1.088328204035911', 'prec': 57}}
           
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              lfunc_instances •   Show schema
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{'Lhash': '1257223690831075685', 'Lhash_array': ['1257223690831075685'], 'factors': ['2-123840-1.1-c1-0-141'], 'label': '2-123840-1.1-c1-0-141', 'type': 'ECQ', 'url': 'EllipticCurve/Q/123840/fj'}