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lfunc_lfunctions • Show schema
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{'Lhash': '4819690206174966528496654106357', 'a10': 0, 'a2': 0, 'a3': -3, 'a4': 0, 'a5': -2, 'a6': 0, 'a7': -4, 'a8': 0, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7346236985957799, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [23, [1, -1]]], 'bad_primes': [2, 23], 'central_character': '92.1', 'coefficient_field': '1.1.1.1', 'conductor': 92, 'conductor_radical': 46, 'degree': 2, 'euler_factors': [[1], [1, 3, 3], [1, 2, 5], [1, 4, 7], [1, -2, 11], [1, 5, 13], [1, -4, 17], [1, 2, 19], [1, -1], [1, 7, 29], [1, 3, 31], [1, -2, 37], [1, 9, 41], [1, 8, 43], [1, -9, 47], [1, -2, 53], [1, 0, 59], [1, 2, 61], [1, -14, 67], [1, 3, 71], [1, 3, 73], [1, 6, 79], [1, -8, 83], [1, -12, 89], [1, 0, 97], [1, -2, 101], [1, 8, 103], [1, -2, 107], [1, 0, 109], [1, 20, 113]], 'euler_factors_factorization': [[1], [[[1, 3, 3], 1]], [[[1, 2, 5], 1]], [[[1, 4, 7], 1]], [[[1, -2, 11], 1]], [[[1, 5, 13], 1]], [[[1, -4, 17], 1]], 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6.503685647459941, 5.109133676966179, 3.449069080359493, 1.8188797146621059, 0.4966754890817511, -0.31229312378404117, -0.5156166741794669], 'positive_zeros': ['3.80206517892802911800653447978629', '5.32154529144374630720020311490963', '6.53483233561451653204235369888904', '7.41247065200411840033758437727312', '9.520156045863341826363538518982104', '10.38750929477444084894724644026546', '11.67692432657301101982140211332126', '12.21704194536701599614180308969151', '13.03943744344058701436939538545268'], 'prelabel': '2-92-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.8571019184413134, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 696553967368558014, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.80206517892802911800653447979', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.32154529144374630720020311491', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.53483233561451653204235369889', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7346236985957799, 'bad_primes': [2, 23], 'central_character': '1.1', 'conductor': 92, 'conductor_radical': 46, 'degree': 2, 'dirichlet_coefficients': [1, 0, -3, 0, -2, 0, -4, 0, 6, 0, 2, 0, -5, 0, 6, 0, 4, 0, -2, 0, 12, 0, 1, 0, -1, 0, -9, 0, -7, 0, -3, 0, -6, 0, 8, 0, 2, 0, 15, 0, -9, 0, -8, 0, -12, 0, 9, 0, 9, 0, -12, 0, 2, 0, -4, 0, 6, 0, 0, 0, -2, 0, -24, 0, 10, 0, 14, 0, -3, 0, -3, 0, -3, 0, 3, 0, -8, 0, -6, 0, 9, 0, 8, 0, -8, 0, 21, 0, 12, 0, 20, 0, 9, 0, 4, 0, 0, 0, 12, 0], 'euler11': [1, -2, 11], 'euler13': [1, 5, 13], 'euler17': [1, -4, 17], 'euler19': [1, 2, 19], 'euler2': [1, 0, 0], 'euler23': [1, -1, 0], 'euler29': [1, 7, 29], 'euler3': [1, 3, 3], 'euler31': [1, 3, 31], 'euler37': [1, -2, 37], 'euler41': [1, 9, 41], 'euler43': [1, 8, 43], 'euler47': [1, -9, 47], 'euler5': [1, 2, 5], 'euler53': [1, -2, 53], 'euler59': [1, 0, 59], 'euler61': [1, 2, 61], 'euler67': [1, -14, 67], 'euler7': [1, 4, 7], 'euler71': [1, 3, 71], 'euler73': [1, 3, 73], 'euler79': [1, 6, 79], 'euler83': [1, -8, 83], 'euler89': [1, -12, 89], 'euler97': [1, 0, 97], 'euler_factors': [[1, 0, 0], [1, 3, 3], [1, 2, 5], [1, 4, 7], [1, -2, 11], [1, 5, 13], [1, -4, 17], [1, 2, 19], [1, -1, 0], [1, 7, 29], [1, 3, 31], [1, -2, 37], [1, 9, 41], [1, 8, 43], [1, -9, 47], [1, -2, 53], [1, 0, 59], [1, 2, 61], [1, -14, 67], [1, 3, 71], [1, 3, 73], [1, 6, 79], [1, -8, 83], [1, -12, 89], [1, 0, 97]], 'index': 1, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/92/a', 'ModularForm/GL2/Q/holomorphic/92/2/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/92/2/a/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, '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': '2-92-1.1-c1-0-1', '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': '2-92-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.8571019184413134, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 696553967368558014, 'z1': {'__RealLiteral__': 0, 'data': '3.80206517892802911800653447979', 'prec': 103}}
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lfunc_instances • Show schema
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id: 9962570
{'Lhash': '4819690206174966528496654106357', 'Lhash_array': ['4819690206174966528496654106357'], 'factors': ['2-92-1.1-c1-0-1'], 'label': '2-92-1.1-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/92/2/a/a'}
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id: 24546595
{'Lhash': '4819690206174966528496654106357', 'Lhash_array': ['4819690206174966528496654106357'], 'factors': ['2-92-1.1-c1-0-1'], 'label': '2-92-1.1-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/92/2/a/a/1/1'}
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id: 21935
{'Lhash': '696553967368558014', 'Lhash_array': ['696553967368558014'], 'factors': ['2-92-1.1-c1-0-1'], 'label': '2-92-1.1-c1-0-1', 'type': 'ECQ', 'url': 'EllipticCurve/Q/92/a'}