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lfunc_lfunctions • Show schema
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{'Lhash': '4428770801630607797952009857302', 'a10': [-31.622776601683793, 0.0], 'a2': [0.0, -2.8284271247461903], 'a3': [4.324555320336759, -7.8929222269921695], 'a4': [-8.0, 0.0], 'a5': [0.0, -11.180339887498949], 'a6': [-22.32455532033676, -12.231689570505937], 'a7': [-8.052668077979448, 0.0], 'a8': [0.0, 22.627416997969522], 'a9': [-43.59644256269407, -68.2667576194865], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.101098892515331, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 2.8284271247461903]]], [3, [[1.0, 0], [-4.324555320336759, 7.8929222269921695]]], [5, [[1.0, 0], [0, 11.180339887498949]]]], 'bad_primes': [2, 3, 5], 'central_character': '30.11', 'coefficient_field': 'CDF', 'conductor': 30, 'conductor_radical': 30, 'conjugate': '1652474956705881089805974497067', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 2.8284271247461903]], [[1.0, 0], [-4.324555320336759, 7.8929222269921695]], [[1.0, 0], 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.101098892515331, 'bad_primes': [2, 3, 5], 'central_character': '3.2', 'conductor': 30, 'conductor_radical': 30, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/30/5/d/a/11/2'], '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': '2-30-3.2-c4-0-2', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-30-3.2-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7609937230198554, 'root_angle': 0.3297735124159186, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '3.49368414359070737381560866339', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4428770801630607797952009857302', 'Lhash_array': ['4428770801630607797952009857302'], 'label': '2-30-3.2-c4-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/30/5/d/a/11/2'}