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lfunc_lfunctions • Show schema
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{'Lhash': '2061653880239852766940751045068', 'a10': [-2.0589593669928203, 0.0], 'a2': [-1.0, 0.0], 'a3': [0.32690855942394315, 0.0], 'a4': [1.0, 0.0], 'a5': [2.0589593669928203, 0.0], 'a6': [-0.32690855942394315, 0.0], 'a7': [1.0, 0.0], 'a8': [-1.0, 0.0], 'a9': [-2.893130793775362, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 36.715214849384736, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [11, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 11, 19], 'central_character': '4598.1', 'coefficient_field': 'CDF', 'conductor': 4598, 'conductor_radical': 418, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [-0.32690855942394315, 0], [3.0, 0]], [[1.0, 0], [-2.0589593669928203, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0], [7.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-6.117918733985641, 0], [13.0, 0]], [[1.0, 0], [0.2393136749274759, 0], [17.0, 0]], [[1.0, 0], [1.0, 0]], 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'5.35025874919038164279144063585618', '5.90634494275886850279670167206980', '6.33829326689684011131067476091205', '7.43290586456537180330379986315866', '8.130594610897071403329398947360964'], 'prelabel': '2-4598-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.059308116392889, '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': '1.62635814621842171700154043797', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.02719851857888953669281908130', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.27053568894918616204758428957', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 36.715214849384736, 'bad_primes': [2, 11, 19], 'central_character': '1.1', 'conductor': 4598, 'conductor_radical': 418, 'degree': 2, 'index': 141, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4598/2/a/bq/1/3'], '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': '2-4598-1.1-c1-0-141', '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': '2-4598-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.059308116392889, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.62635814621842171700154043797', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2061653880239852766940751045068', 'Lhash_array': ['2061653880239852766940751045068'], 'label': '2-4598-1.1-c1-0-141', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4598/2/a/bq/1/3'}