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lfunc_lfunctions • Show schema
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{'Lhash': '1725428783974072440958353349877', 'a10': [-1.2541553827811365, -0.6535245028620588], 'a2': [-0.6535245028620588, 1.2541553827811365], 'a3': [0, -1.0], 'a4': [-1.145811448317798, -1.6392425460876345], 'a5': [0, 1.0], 'a6': [1.2541553827811365, 0.6535245028620588], 'a7': [-1.0084918242499814, 0], 'a8': [2.8046807199952064, -0.3657404255577594], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.540253066809015, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.6535245028620588, -1.2541553827811365]]], [3, [[1.0, 0], [0, 1.0]]], [5, [[1.0, 0], [0, -1.0]]], [11, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [2, 3, 5, 11], 'central_character': '1320.661', 'coefficient_field': 'CDF', 'conductor': 1320, 'conductor_radical': 330, 'conjugate': '397340917456279931087156904083', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.6535245028620588, -1.2541553827811365]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 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'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.72003826214294677382247615112', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.61004495188926269764693044769', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 10.540253066809015, 'bad_primes': [2, 3, 5, 11], 'central_character': '8.5', 'conductor': 1320, 'conductor_radical': 330, 'degree': 2, 'index': 53, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1320/2/w/d/661/6'], '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': '2-1320-8.5-c1-0-53', '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': '2-1320-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.24657559080472, 'root_angle': 0.229362082018533, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.36112331242017641296543883199', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1725428783974072440958353349877', 'Lhash_array': ['1725428783974072440958353349877'], 'label': '2-1320-8.5-c1-0-53', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1320/2/w/d/661/6'}