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lfunc_lfunctions • Show schema
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{'Lhash': '522486035811986830389635598506,1469446917752942236290358251380', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 477.2944672800165, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [19, [1, -8, 19]]], 'bad_primes': [2, 3, 19], 'central_character': '2736.1', 'coefficient_field': '1.1.1.1', 'conductor': 7485696, 'conductor_radical': 114, 'degree': 4, 'euler_factors': [[1], [1], [1, 1, -4, 5, 25], [1, 0, 14, 0, 49], [1, 8, 38, 88, 121], [1, -1, -12, -13, 169], [1, -3, -8, -51, 289], [1, -8, 19], [1, 5, 2, 115, 529], [1, -7, 20, -203, 841], [1, 8, 78, 248, 961], [1, -20, 174, -740, 1369], [1, 5, -16, 205, 1681], [1, 5, -18, 215, 1849], [1, -7, 2, -329, 2209], [1, -11, 68, -583, 2809], [1, 3, -50, 177, 3481], [1, 11, 60, 671, 3721], [1, 3, -58, 201, 4489], [1, 11, 50, 781, 5041], [1, 15, 152, 1095, 5329], [1, 13, 90, 1027, 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'2.91629299416387880212151279329134', '3.12014877904489795241903560322905', '3.80394392294044327547846539699898', '4.39502527415872780641166664416871', '4.75054825821794167386846614078898', '5.11424772070726881081185604944314', '5.55715079039399319366086991755949', '5.92280105664678155302966185312844', '6.13773872994092676326782427872589', '6.88361181659730053854982346489940', '7.36794017330594851920613005948728', '7.52076972315539384232848272679493', '7.87920015256553347887430123904308', '8.140789053064287855912961104240022', '8.466716316120410172825665480837074', '9.054705403434683266982623551207595'], 'prelabel': '4-2736e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.67408493643647, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 128889153233540312, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.41216880717598192294647371678', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.15918922571281169518201343187', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.79115706186670023341258478109', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 477.2944672800165, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 7485696, 'conductor_radical': 114, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -8, 0, 1, 0, 0, 0, 3, 0, 8, 0, 0, 0, -5, 0, 5, 0, 0, 0, 7, 0, -8, 0, 0, 0, 0, 0, 20, 0, 0, 0, -5, 0, -5, 0, 0, 0, 7, 0, -14, 0, 0, 0, 11, 0, 8, 0, 0, 0, -3, 0, -11, 0, 0, 0, -1, 0, -3, 0, 0, 0, -11, 0, -15, 0, 0, 0, 0, 0, -13, 0, 0, 0, 0, 0, -3, 0, 0, 0, 3, 0, 0, 0, 0, 0, -8, 0, 5, 0, 0, 0], 'euler11': [1, 8, 38, 88, 121], 'euler13': [1, -1, -12, -13, 169], 'euler17': [1, -3, -8, -51, 289], 'euler19': [1, -8, 19, 0, 0], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 5, 2, 115, 529], 'euler29': [1, -7, 20, -203, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 8, 78, 248, 961], 'euler37': [1, -20, 174, -740, 1369], 'euler41': [1, 5, -16, 205, 1681], 'euler43': [1, 5, -18, 215, 1849], 'euler47': [1, -7, 2, -329, 2209], 'euler5': [1, 1, -4, 5, 25], 'euler53': [1, -11, 68, -583, 2809], 'euler59': [1, 3, -50, 177, 3481], 'euler61': [1, 11, 60, 671, 3721], 'euler67': [1, 3, -58, 201, 4489], 'euler7': [1, 0, 14, 0, 49], 'euler71': [1, 11, 50, 781, 5041], 'euler73': [1, 15, 152, 1095, 5329], 'euler79': [1, 13, 90, 1027, 6241], 'euler83': [1, 0, 166, 0, 6889], 'euler89': [1, -3, -80, -267, 7921], 'euler97': [1, -5, -72, -485, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 1, -4, 5, 25], [1, 0, 14, 0, 49], [1, 8, 38, 88, 121], [1, -1, -12, -13, 169], [1, -3, -8, -51, 289], [1, -8, 19, 0, 0], [1, 5, 2, 115, 529], [1, -7, 20, -203, 841], [1, 8, 78, 248, 961], [1, -20, 174, -740, 1369], [1, 5, -16, 205, 1681], [1, 5, -18, 215, 1849], [1, -7, 2, -329, 2209], [1, -11, 68, -583, 2809], [1, 3, -50, 177, 3481], [1, 11, 60, 671, 3721], [1, 3, -58, 201, 4489], [1, 11, 50, 781, 5041], [1, 15, 152, 1095, 5329], [1, 13, 90, 1027, 6241], [1, 0, 166, 0, 6889], [1, -3, -80, -267, 7921], [1, -5, -72, -485, 9409]], 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2736/2/s/g'], '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': '4-2736e2-1.1-c1e2-0-15', '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': '4-2736e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.67408493643647, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 128889153233540312, 'z1': {'__RealLiteral__': 0, 'data': '0.41216880717598192294647371678', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '522486035811986830389635598506,1469446917752942236290358251380', 'Lhash_array': ['522486035811986830389635598506', '1469446917752942236290358251380'], 'label': '4-2736e2-1.1-c1e2-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2736/2/s/g'}