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lfunc_lfunctions • Show schema
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{'Lhash': '358849489666541352366508684802', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-0.06952102901436853, -0.12041395444735635], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [-3.4078544376305344, 0], 'a8': [0, 0], 'a9': [1.4903336530495666, -2.581333607311577], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.17157638404328, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [2.14436989454077, 3.794954249445862]]]], 'bad_primes': [2, 5, 19], 'central_character': '1900.501', 'coefficient_field': 'CDF', 'conductor': 1900, 'conductor_radical': 190, 'conjugate': '1628603322697434229408359694028', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.06952102901436853, 0.12041395444735635], [-1.5, 2.598076211353316]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.4078544376305344, 0], [7.0, 0]], [[1.0, 0], [-0.18569002096784967, 0], [11.0, 0]], [[1.0, 0], 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'9.285968043376489066214094808667075'], 'prelabel': '2-1900-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8950707803637252, 'root_angle': -0.5959632370190361, 'root_number': '-0.296931298173552891938348702189861266969545316305526420 - 0.954898844990907204427491732138816512662198368503566014*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.29798161850951804', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.28308233325644593303004767071', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.98525737789912676768419921692', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.08122204026303428931669490698', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.17157638404328, 'bad_primes': [2, 5, 19], 'central_character': '19.7', 'conductor': 1900, 'conductor_radical': 190, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1900/2/i/e/501/4'], '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': '2-1900-19.7-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': 0, 'prelabel': '2-1900-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8950707803637252, 'root_angle': -0.29798161850951804, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.28308233325644593303004767071', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '358849489666541352366508684802', 'Lhash_array': ['358849489666541352366508684802'], 'label': '2-1900-19.7-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1900/2/i/e/501/4'}