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lfunc_lfunctions • Show schema
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{'Lhash': '3206944954283541649142821812146', 'a10': -1, 'a2': 1, 'a3': 0, 'a4': 1, 'a5': -1, 'a6': 0, 'a7': -4, 'a8': 1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.892959669170495, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1]], [41, [1, -1]]], 'bad_primes': [2, 3, 41], 'central_character': '738.1', 'coefficient_field': '1.1.1.1', 'conductor': 738, 'conductor_radical': 246, 'degree': 2, 'euler_factors': [[1, -1], [1], [1, 1, 5], [1, 4, 7], [1, 4, 11], [1, 5, 13], [1, 1, 17], [1, 3, 19], [1, -8, 23], [1, 0, 29], [1, -7, 31], [1, 4, 37], [1, -1], [1, 6, 43], [1, -8, 47], [1, 14, 53], [1, -7, 59], [1, 8, 61], [1, 5, 67], [1, -7, 71], [1, -1, 73], [1, 14, 79], [1, -15, 83], [1, 13, 89], [1, -12, 97], [1, -6, 101], [1, 9, 103], [1, 11, 107], [1, 6, 109], [1, 8, 113]], 'euler_factors_factorization': [[[[1, -1], 1]], [1], [[[1, 1, 5], 1]], [[[1, 4, 7], 1]], [[[1, 4, 11], 1]], [[[1, 5, 13], 1]], 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1.9014037416617462, 1.2244951893671427, 0.46027673787511264, -0.10203557902782369, -0.30974914642552726, -0.1981737124337841, 0.0358247184011764, 0.12668702492811001], 'positive_zeros': ['2.52983349963007098615023775562100', '3.21932604526646441119983264062096', '4.47420705672619953222926321067415', '5.33330380381551699100541521376737', '6.45057299417612122047272522501704', '7.14649800311416056102761154095052', '8.019240374239258929238557865380026', '9.244347738098059429850983472639880', '10.08266600804786671706131769377086'], 'prelabel': '2-738-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.427541898540681, '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': 2001969451693504258, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.52983349963007098615023775562', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.21932604526646441119983264062', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.47420705672619953222926321067', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.892959669170495, 'bad_primes': [2, 3, 41], 'central_character': '1.1', 'conductor': 738, 'conductor_radical': 246, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, 1, -1, 0, -4, 1, 0, -1, -4, 0, -5, -4, 0, 1, -1, 0, -3, -1, 0, -4, 8, 0, -4, -5, 0, -4, 0, 0, 7, 1, 0, -1, 4, 0, -4, -3, 0, -1, 1, 0, -6, -4, 0, 8, 8, 0, 9, -4, 0, -5, -14, 0, 4, -4, 0, 0, 7, 0, -8, 7, 0, 1, 5, 0, -5, -1, 0, 4, 7, 0, 1, -4, 0, -3, 16, 0, -14, -1, 0, 1, 15, 0, 1, -6, 0, -4, -13, 0, 20, 8, 0, 8, 3, 0, 12, 9, 0, -4], 'euler11': [1, 4, 11], 'euler13': [1, 5, 13], 'euler17': [1, 1, 17], 'euler19': [1, 3, 19], 'euler2': [1, -1, 0], 'euler23': [1, -8, 23], 'euler29': [1, 0, 29], 'euler3': [1, 0, 0], 'euler31': [1, -7, 31], 'euler37': [1, 4, 37], 'euler41': [1, -1, 0], 'euler43': [1, 6, 43], 'euler47': [1, -8, 47], 'euler5': [1, 1, 5], 'euler53': [1, 14, 53], 'euler59': [1, -7, 59], 'euler61': [1, 8, 61], 'euler67': [1, 5, 67], 'euler7': [1, 4, 7], 'euler71': [1, -7, 71], 'euler73': [1, -1, 73], 'euler79': [1, 14, 79], 'euler83': [1, -15, 83], 'euler89': [1, 13, 89], 'euler97': [1, -12, 97], 'euler_factors': [[1, -1, 0], [1, 0, 0], [1, 1, 5], [1, 4, 7], [1, 4, 11], [1, 5, 13], [1, 1, 17], [1, 3, 19], [1, -8, 23], [1, 0, 29], [1, -7, 31], [1, 4, 37], [1, -1, 0], [1, 6, 43], [1, -8, 47], [1, 14, 53], [1, -7, 59], [1, 8, 61], [1, 5, 67], [1, -7, 71], [1, -1, 73], [1, 14, 79], [1, -15, 83], [1, 13, 89], [1, -12, 97]], 'index': 17, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/738/g', 'ModularForm/GL2/Q/holomorphic/738/2/a/g/1/1', 'ModularForm/GL2/Q/holomorphic/738/2/a/g'], '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': '2-738-1.1-c1-0-17', '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': '2-738-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.427541898540681, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2001969451693504258, 'z1': {'__RealLiteral__': 0, 'data': '2.52983349963007098615023775562', 'prec': 103}}
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lfunc_instances • Show schema
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id: 13890267
{'Lhash': '3206944954283541649142821812146', 'Lhash_array': ['3206944954283541649142821812146'], 'factors': ['2-738-1.1-c1-0-17'], 'label': '2-738-1.1-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/738/2/a/g'}
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id: 24550380
{'Lhash': '3206944954283541649142821812146', 'Lhash_array': ['3206944954283541649142821812146'], 'factors': ['2-738-1.1-c1-0-17'], 'label': '2-738-1.1-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/738/2/a/g/1/1'}
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id: 34808
{'Lhash': '2001969451693504258', 'Lhash_array': ['2001969451693504258'], 'factors': ['2-738-1.1-c1-0-17'], 'label': '2-738-1.1-c1-0-17', 'type': 'ECQ', 'url': 'EllipticCurve/Q/738/g'}