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lfunc_lfunctions • Show schema
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{'Lhash': '88412931827888959277119614399', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-4.330127018922194, 2.5], 'a4': [0.0, 0.0], 'a5': [-4.5, 7.794228634059948], 'a6': [0.0, 0.0], 'a7': [-6.928203230275509, 1.0], 'a8': [0.0, 0.0], 'a9': [8.0, -13.856406460551018], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.103557921670651, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [6.928203230275509, -1.0]]]], 'bad_primes': [2, 7], 'central_character': '224.191', 'coefficient_field': 'CDF', 'conductor': 224, 'conductor_radical': 14, 'conjugate': '4126214989015138622095680374136', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [4.330127018922194, -2.5], [4.5, -7.794228634059948]], [[1.0, 0], [4.5, -7.794228634059948], [-12.5, -21.650635094610966]], [[1.0, 0], [6.928203230275509, -1.0]], [[1.0, 0], [2.598076211353316, -1.5], [60.5, -104.78907385791707]], [[1.0, 0], [-16.0, 0], 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'0.06974550543499209033988254261', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.15177743522728845530874508837', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.87853562400416745802203871703', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.103557921670651, 'bad_primes': [2, 7], 'central_character': '28.23', 'conductor': 224, 'conductor_radical': 14, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/224/3/r/a/191/1'], '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': '2-224-28.23-c2-0-0', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-224-28.23-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4705379822359848, 'root_angle': 0.2587657159681987, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.06974550543499209033988254261', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '88412931827888959277119614399', 'Lhash_array': ['88412931827888959277119614399'], 'label': '2-224-28.23-c2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/224/3/r/a/191/1'}