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lfunc_lfunctions • Show schema
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{'Lhash': '138018308859078224271289091764', 'a10': [0, 0], 'a2': [-1.0, 1.0], 'a3': [-1.224744871391589, -1.224744871391589], 'a4': [0, -2.0], 'a5': [0, 0], 'a6': [2.449489742783178, 0], 'a7': [-1.8708286933869707, 1.8708286933869707], 'a8': [2.0, 2.0], 'a9': [0, 3.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 28.61042775783118, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, -1.0]]], [3, [[1.0, 0], [1.224744871391589, 1.224744871391589]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.8708286933869707, -1.8708286933869707]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1050.43', 'coefficient_field': 'CDF', 'conductor': 1050, 'conductor_radical': 210, 'conjugate': '1635711476212916910497624545690', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, -1.0]], [[1.0, 0], [1.224744871391589, 1.224744871391589]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.8708286933869707, -1.8708286933869707]], [[1.0, 0], 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0.229752920547361183523937369381462718715990937285509727*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.4631040955873917', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.10887724806364564108526052772', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.48835637141135122108096506599', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.93529251967143498411733825290', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 28.61042775783118, 'bad_primes': [2, 3, 5, 7], 'central_character': '5.3', 'conductor': 1050, 'conductor_radical': 210, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1050/3/l/b/43/1'], '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': '2-1050-5.3-c2-0-1', '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': '2-1050-5.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.348871634076778, 'root_angle': -0.4631040955873917, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.10887724806364564108526052772', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '138018308859078224271289091764', 'Lhash_array': ['138018308859078224271289091764'], 'label': '2-1050-5.3-c2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1050/3/l/b/43/1'}