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lfunc_lfunctions • Show schema
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{'Lhash': '2319068993710819417939700846288', 'a10': [-0.17364817766693036, 0.3007674663608706], 'a2': [0.17364817766693036, 0.984807753012208], 'a3': [-0.23887785891483007, 1.35474365837288], 'a4': [-0.9396926207859084, 0.3420201433256687], 'a5': [0.266044443118978, 0.22323779409789932], 'a6': [-1.3756427629952728, -1.064664768090358e-60], 'a7': [-0.3659821128117296, -0.307095455877804], 'a8': [-0.5, -0.8660254037844386], 'a9': [1.040810113935924, 0.378823900995891], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5908929749574752, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.17364817766693036, -0.984807753012208]]], [37, [[1.0, 0], [-2.4232242061012816, -5.579245867226574]]]], 'bad_primes': [2, 37], 'central_character': '74.9', 'coefficient_field': 'CDF', 'conductor': 74, 'conductor_radical': 74, 'conjugate': '4626140503306636917906089402275', 'degree': 2, 'euler_factors': [[[1.0, 0], 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['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.82942286564869793950187444219', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.01169869595108353775807037165', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.85147533168094710322640210041', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5908929749574752, 'bad_primes': [2, 37], 'central_character': '37.9', 'conductor': 74, 'conductor_radical': 74, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/74/2/f/b/9/1'], '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': '2-74-37.9-c1-0-0', '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': '2-74-37.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7686956321961738, 'root_angle': -0.2375632464779882, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.82942286564869793950187444219', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2319068993710819417939700846288', 'Lhash_array': ['2319068993710819417939700846288'], 'label': '2-74-37.9-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/74/2/f/b/9/1'}