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lfunc_lfunctions • Show schema
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{'Lhash': '1716997514126574037496960825564', 'a10': [-1.0, 0.0], 'a2': [0.5, 0.8660254037844386], 'a3': [0.5, -0.8660254037844386], 'a4': [-0.5, 0.8660254037844386], 'a5': [-0.5, 0.8660254037844386], 'a6': [1.0, 3.111507638930571e-61], 'a7': [0.5811388300841897, -1.0065619799569532], 'a8': [-1.0, 0.0], 'a9': [1.0, 1.7320508075688772], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.9544648747873756, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, -0.8660254037844386]]], [5, [[1.0, 0], [0.5, -0.8660254037844386]]], [37, [[1.0, 0], [2.9188611699158105, 5.336688998879146]]]], 'bad_primes': [2, 5, 37], 'central_character': '370.211', 'coefficient_field': 'CDF', 'conductor': 370, 'conductor_radical': 370, 'conjugate': '2260347881591787956323655560069', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [-0.5, 0.8660254037844386], [-1.5, -2.598076211353316]], [[1.0, 0], [0.5, 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'rational': False, 'root_analytic_conductor': 1.7188556875978203, 'root_angle': -0.2791543579956318, 'root_number': '0.6394687317169924 - 0.7688171051402676*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.139577178998', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.35447221325611620025392050118', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.20139536268897994387666769347', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.05048485559214208465038423359', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.9544648747873756, 'bad_primes': [2, 5, 37], 'central_character': '37.26', 'conductor': 370, 'conductor_radical': 370, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/370/2/e/e/211/2'], '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': '2-370-37.26-c1-0-6', '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': '2-370-37.26-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7188556875978203, 'root_angle': -0.1395771789978159, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.35447221325611620025392050118', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1716997514126574037496960825564', 'Lhash_array': ['1716997514126574037496960825564'], 'label': '2-370-37.26-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/370/2/e/e/211/2'}