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lfunc_lfunctions • Show schema
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{'Lhash': '2120263707385969755134763030140', 'a10': [0, -328.030609207257], 'a2': [0, -10.33465184825053], 'a3': [12.520950231765784, 9.285785119937053], 'a4': [-74.80502882454809, 0], 'a5': [31.740847589634733, 0], 'a6': [95.96535635221473, -129.39966145457115], 'a7': [0, 0], 'a8': [0, 442.37507025603315], 'a9': [70.54838941271126, 232.5337066992062], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 23.57642151250816, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-12.520950231765784, -9.285785119937053]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7], 'central_character': '147.146', 'coefficient_field': 'CDF', 'conductor': 147, 'conductor_radical': 21, 'conjugate': '828884790359732259221074157698', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 10.33465184825053], [-32.0, 0]], [[1.0, 0], [-12.520950231765784, -9.285785119937053]], [[1.0, 0], [-31.740847589634733, 0], [3125.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], 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'0.4879665842950935', 'prec': 60}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.67259314751575459525657570244', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.86560714547947192078378353799', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.29563066432323496730273193861', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 23.57642151250816, 'bad_primes': [3, 7], 'central_character': '21.20', 'conductor': 147, 'conductor_radical': 21, 'degree': 2, 'index': 45, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/147/6/c/c/146/2'], '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': '2-147-21.20-c5-0-45', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-147-21.20-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.855555736731704, 'root_angle': 0.4879665842950935, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.67259314751575459525657570244', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2120263707385969755134763030140', 'Lhash_array': ['2120263707385969755134763030140'], 'label': '2-147-21.20-c5-0-45', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/147/6/c/c/146/2'}