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lfunc_lfunctions • Show schema
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{'Lhash': '3382787962846711270960635645035', 'a10': [-4.9236559641895665, -2.311950666283163], 'a2': [1.7201018556186332, -1.7201018556186332], 'a3': [0.42286383907265185, -0.42286383907265185], 'a4': [0.0, -3.91750078740533], 'a5': [-0.759171699447736, -2.103249469453787], 'a6': [-1.3335708257996183e-60, -1.4547377485257749], 'a7': [1.8255517746463026, -1.8255517746463026], 'a8': [-3.298296662566098, -3.298296662566098], 'a9': [0.0, 2.6423723472094767], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.8309493222874655, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0.759171699447736, 2.103249469453787]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 11], 'central_character': '605.362', 'coefficient_field': 'CDF', 'conductor': 605, 'conductor_radical': 55, 'conjugate': '1617205881313854847223027911954', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.7201018556186332, 1.7201018556186332], [0, -2.0]], [[1.0, 0], 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{'__RealLiteral__': 0, 'data': '0.417546964108', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.66854917454199910447752228523', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.69458866472730119267253235867', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.49160627873919350652061976407', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.8309493222874655, 'bad_primes': [5, 11], 'central_character': '55.32', 'conductor': 605, 'conductor_radical': 55, 'degree': 2, 'index': 43, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/605/2/e/b/362/15'], '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': '2-605-55.32-c1-0-43', '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': '2-605-55.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1979420652709356, 'root_angle': 0.4175469641084613, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.66854917454199910447752228523', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3382787962846711270960635645035', 'Lhash_array': ['3382787962846711270960635645035'], 'label': '2-605-55.32-c1-0-43', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/605/2/e/b/362/15'}