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lfunc_lfunctions • Show schema
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{'Lhash': '475656333702872439246841197201', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-1.618033988749895, -0.6180339887498949], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0.38196601125010515, -2.618033988749895], 'a8': [0, 0], 'a9': [2.23606797749979, 2.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 16.768584424468887, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.618033988749895, 0.6180339887498949]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-0.38196601125010515, 2.618033988749895]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '2100.1301', 'coefficient_field': 'CDF', 'conductor': 2100, 'conductor_radical': 210, 'conjugate': '1359895240715092942850051885895', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.618033988749895, 0.6180339887498949]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.38196601125010515, 2.618033988749895]], [[1.0, 0], [0, -0.7639320225002103], 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'positive_zeros': ['0.37522668597895561859101613654112', '2.00370046655772203039439130270200', '3.06128127042124562001491501700340', '4.41155848360113745784466762464206', '4.90378206557587266961397513435788', '5.76125100715861922226080258357464', '6.63955837358218650738017122754015', '7.04691225749923885595152150451155', '8.564904972544385185852518611929004', '8.888252870865168735430367294573628'], 'prelabel': '2-2100-21.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.0949462053205155, 'root_angle': -0.337744820847781, 'root_number': '0.487950036474266589677192318120050094796906317307372997 - 0.872871560943969525064389941662477807425610776527232743*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1688724104238905', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.37522668597895561859101613654', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.00370046655772203039439130270', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.06128127042124562001491501700', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 16.768584424468887, 'bad_primes': [2, 3, 5, 7], 'central_character': '21.20', 'conductor': 2100, 'conductor_radical': 210, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2100/2/d/g/1301/1'], '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': '2-2100-21.20-c1-0-8', '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': '2-2100-21.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.0949462053205155, 'root_angle': -0.1688724104238905, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.37522668597895561859101613654', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '475656333702872439246841197201', 'Lhash_array': ['475656333702872439246841197201'], 'label': '2-2100-21.20-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2100/2/d/g/1301/1'}