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lfunc_lfunctions • Show schema
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{'Lhash': '4132561033988533155741133945536', 'a10': [1.6855439326707928, -5.099757495043888], 'a2': [0.635665185148849, 1.2633011408170578], 'a3': [0.7071067811865476, -0.7071067811865476], 'a4': [-1.1918595447793592, 1.6060731071524543], 'a5': [-2.685543932670793, -2.685543932670793], 'a6': [1.3427719663353965, 0.4438056403694898], 'a7': [0.0, 2.1589416510366775], 'a8': [-2.786577606704886, -0.48475276359281166], 'a9': [0.0, -1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.38328192970214603, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.635665185148849, -1.2633011408170578]]], [3, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]]], 'bad_primes': [2, 3], 'central_character': '48.37', 'coefficient_field': 'CDF', 'conductor': 48, 'conductor_radical': 6, 'conjugate': '4895401280392129640719728715887', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.635665185148849, -1.2633011408170578]], [[1.0, 0], 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0, 'data': '-0.109283656212', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.26001583815327479995642235752', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.23338644021661599711126263758', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.67926877056311355946931200854', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.38328192970214603, 'bad_primes': [2, 3], 'central_character': '16.5', 'conductor': 48, 'conductor_radical': 6, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/48/2/j/a/37/3'], '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': '2-48-16.5-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': '2-48-16.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6190976737980414, 'root_angle': -0.10928365621194125, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.26001583815327479995642235752', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4132561033988533155741133945536', 'Lhash_array': ['4132561033988533155741133945536'], 'label': '2-48-16.5-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/48/2/j/a/37/3'}