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lfunc_lfunctions • Show schema
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{'Lhash': '1144994364603630724580293325299', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-0.766044443118978, 0.6427876096865394], 'a6': [0.0, 0.0], 'a7': [0.5, -0.8660254037844386], 'a8': [0.0, 0.0], 'a9': [-0.9396926207859084, 0.3420201433256687], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7206498782420555, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 19], 'central_character': '1444.1345', 'coefficient_field': 'CDF', 'conductor': 1444, 'conductor_radical': 38, 'conjugate': '1850862935783462971327365047180', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [0.9396926207859084, -0.3420201433256687]], [[1.0, 0], [0.766044443118978, -0.6427876096865394], [0.17364817766693036, -0.984807753012208]], [[1.0, 0], [-0.5, 0.8660254037844386], [-0.5, -0.8660254037844386]], [[1.0, 0], [-0.5, 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'root_analytic_conductor': 0.8489109954771793, 'root_angle': -0.2653722833530496, 'root_number': '0.67214700850669915182666326631505 - 0.74041771923387631609049792348060*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.13268614167652476', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.903241290934177371385519360749', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.63241949588713765969114059666', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.50713896686204169279568213297', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7206498782420555, 'bad_primes': [2, 19], 'central_character': '19.15', 'conductor': 1444, 'conductor_radical': 38, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1444/1/j/a/1345/1'], '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': '2-38e2-19.15-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-38e2-19.15-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8489109954771793, 'root_angle': -0.1326861416765248, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.903241290934177371385519360749', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1144994364603630724580293325299', 'Lhash_array': ['1144994364603630724580293325299'], 'label': '2-38e2-19.15-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1444/1/j/a/1345/1'}