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lfunc_lfunctions • Show schema
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{'Lhash': '520409505759106875165539707999', 'a10': [3.749328485881446, -4.490656561752178], 'a2': [-1.0855826152061663, -0.9063721010501927], 'a3': [0.07097064205054754, -0.07097064205054754], 'a4': [0.3569792288757184, 1.9678835916159516], 'a5': [0.0, 4.136632715787682], 'a6': [-0.14137030514833004, 0.012718685251858179], 'a7': [-1.0528816295119523, -0.43611785051733504], 'a8': [1.3961043406979665, -2.4598562295151107], 'a9': [0.0, 2.989926335933866], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.343861869957655, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0855826152061663, 0.9063721010501927]]], [17, [[1.0, 0], [-3.5902198092659847, -2.0273928383897672]]]], 'bad_primes': [2, 17], 'central_character': '544.77', 'coefficient_field': 'CDF', 'conductor': 544, 'conductor_radical': 34, 'conjugate': '2694389244147728435870582472437', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0855826152061663, 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{'__RealLiteral__': 0, 'data': '3.99911640025453358715112921135', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.343861869957655, 'bad_primes': [2, 17], 'central_character': '544.77', 'conductor': 544, 'conductor_radical': 34, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/544/2/x/a/77/15'], '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': '2-544-544.77-c1-0-5', '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': '2-544-544.77-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0841933379505977, 'root_angle': -0.3407419862989734, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.41053071379874840595605524370', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '520409505759106875165539707999', 'Lhash_array': ['520409505759106875165539707999'], 'factors': ['2-544-544.77-c1-0-5'], 'label': '2-544-544.77-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/544/2/x/a/77/15'}