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lfunc_lfunctions • Show schema
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{'Lhash': '151904933530028591093196996707', 'a10': [0, 0], 'a2': [0, -2.0], 'a3': [0, 0], 'a4': [-4.0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, 19.0], 'a8': [0, 8.0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 79.65257850774987, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 2.0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '1350.649', 'coefficient_field': 'CDF', 'conductor': 1350, 'conductor_radical': 30, 'conjugate': '2079007080557362241172079003694', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 2.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -19.0], [-343.0, 0]], [[1.0, 0], [-12.0, 0], [1331.0, 0]], [[1.0, 0], [0, -50.0], [-2197.0, 0]], [[1.0, 0], [0, -126.0], [-4913.0, 0]], [[1.0, 0], [29.0, 0], [6859.0, 0]], [[1.0, 0], [0, -18.0], [-12167.0, 0]], [[1.0, 0], [102.0, 0], [24389.0, 0]], [[1.0, 0], [265.0, 0], [29791.0, 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'rational': False, 'root_analytic_conductor': 8.924829326533358, 'root_angle': -0.8524163823495667, 'root_number': '-0.89442719099991587856366946749251049417624734384461028971 - 0.4472135954999579392818347337462552470881236719223051449*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.42620819117478337', 'prec': 67}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.11983186337203598265607456313', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.10393907569220871718466853577', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.79981347286704247038586335848', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 79.65257850774987, 'bad_primes': [2, 3, 5], 'central_character': '5.4', 'conductor': 1350, 'conductor_radical': 30, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1350/4/c/m/649/1'], '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': '2-1350-5.4-c3-0-4', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-1350-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.924829326533358, 'root_angle': -0.42620819117478337, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.11983186337203598265607456313', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '151904933530028591093196996707', 'Lhash_array': ['151904933530028591093196996707'], 'label': '2-1350-5.4-c3-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1350/4/c/m/649/1'}