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lfunc_lfunctions • Show schema
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{'Lhash': '1542914687979336627289355661457', 'a10': [-0.0018257435532653386, 0.0], 'a2': [0.5836593444218303, 0.0], 'a3': [0.0, 0.0], 'a4': [-1.659341769669079, 0.0], 'a5': [-0.00312809787201113, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-2.1358090183004754, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 45.77823547880006, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 7, 13], 'central_character': '5733.1', 'coefficient_field': 'CDF', 'conductor': 5733, 'conductor_radical': 273, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5836593444218303, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.00312809787201113, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.942490627563364, 0], [11.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-5.87686835027439, 0], [17.0, 0]], [[1.0, 0], [-5.387668266543876, 0], [19.0, 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'5.49495992042771558809749552176211', '5.98902807391960222904929011634996', '7.19024436685164387200938695460724', '7.930714442140383202756211455101764'], 'prelabel': '2-5733-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.765961533943277, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.21714507743817447388971584550', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.60811834821611335556670557077', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.34036971670311239933780657285', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 45.77823547880006, 'bad_primes': [3, 7, 13], 'central_character': '1.1', 'conductor': 5733, 'conductor_radical': 273, 'degree': 2, 'index': 140, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5733/2/a/bw/1/7'], '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': '2-5733-1.1-c1-0-140', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-5733-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.765961533943277, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.21714507743817447388971584550', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1542914687979336627289355661457', 'Lhash_array': ['1542914687979336627289355661457'], 'label': '2-5733-1.1-c1-0-140', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5733/2/a/bw/1/7'}