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lfunc_lfunctions • Show schema
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{'Lhash': '2512314756989156197786339148090', 'a10': [2.7546264487008836, 1.553072158052406], 'a2': [-0.07491210790312818, 1.4122280892580739], 'a3': [-1.680355949223934, -0.42000462367423036], 'a4': [-1.9887763521790203, -0.21158596601265872], 'a5': [0.9934686262441856, -2.003252377676984], 'a6': [0.7190213333549414, -2.3415824397574565], 'a7': [0.5962371451462168, -2.2251873190455007], 'a8': [0.4477910731855052, -2.7927554770826917], 'a9': [2.6471922321845365, 1.411514536185105], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.4373072363830477, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.07491210790312818, -1.4122280892580739]]], [3, [[1.0, 0], [1.680355949223934, 0.42000462367423036]]], [5, [[1.0, 0], [-0.9934686262441856, 2.003252377676984]]]], 'bad_primes': [2, 3, 5], 'central_character': '180.103', 'coefficient_field': 'CDF', 'conductor': 180, 'conductor_radical': 30, 'conjugate': 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'3.65977868883752779557817852941179', '5.15138169714863451721320589841595', '6.08442002050523472805647946958840', '7.57169989841704993986949175924866', '9.196135926337636852931641742903440', '10.05848361710289362503333259619010', '10.68089349300123496634087672642319', '12.01593049847979222140987107259052', '12.06469736517967706632382434499408'], 'prelabel': '2-180-180.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.198877490147783, 'root_angle': 0.12353053022755492, 'root_number': '0.9256363301322479 + 0.3784143025036239*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0617652651138', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.98186689339857205357679202413', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.65977868883752779557817852941', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.15138169714863451721320589842', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.4373072363830477, 'bad_primes': [2, 3, 5], 'central_character': '180.103', 'conductor': 180, 'conductor_radical': 30, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/180/2/x/a/103/17'], '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': '2-180-180.103-c1-0-17', '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': '2-180-180.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.198877490147783, 'root_angle': 0.06176526511377746, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.98186689339857205357679202413', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2512314756989156197786339148090', 'Lhash_array': ['2512314756989156197786339148090'], 'label': '2-180-180.103-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/180/2/x/a/103/17'}