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lfunc_lfunctions • Show schema
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{'Lhash': '5269452124129753591630258332412', 'a10': [1.5615528128088303, 0.0], 'a2': [1.5615528128088303, 0.0], 'a3': [-2.5615528128088303, 0.0], 'a4': [0.4384471871911697, 0.0], 'a5': [1.0, 0.0], 'a6': [-4.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [-2.4384471871911697, 0.0], 'a9': [3.5615528128088303, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.27947640707448146, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-1.0, 0]]], [7, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [5, 7], 'central_character': '35.1', 'coefficient_field': 'CDF', 'conductor': 35, 'conductor_radical': 35, 'conjugate': '5269452124129753591630258332412', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.5615528128088303, 0], [2.0, 0]], [[1.0, 0], [2.5615528128088303, 0], [3.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-2.5615528128088303, 0], [11.0, 0]], [[1.0, 0], [-4.56155281280883, 0], [13.0, 0]], [[1.0, 0], [4.56155281280883, 0], 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'13.94588673316197709173832397867650', '15.47778975023287695392669568728728', '16.54043015310824634377959576392741'], 'prelabel': '2-35-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5286552818940538, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '4.15686477265978088320503087188', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.75333263909241173971323500780', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.44771243960593321795590797896', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.27947640707448146, 'bad_primes': [5, 7], 'central_character': '1.1', 'conductor': 35, 'conductor_radical': 35, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/35/2/a/b/1/2'], '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': '2-35-1.1-c1-0-2', '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': '2-35-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5286552818940538, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '4.15686477265978088320503087188', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '5269452124129753591630258332412', 'Lhash_array': ['5269452124129753591630258332412'], 'label': '2-35-1.1-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/35/2/a/b/1/2'}