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lfunc_lfunctions • Show schema
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{'Lhash': '736114181592635110478655394870', 'a10': [6.7905978192997765, 0.0], 'a2': [-2.3565467481833218, 0.0], 'a3': [0.0, 0.0], 'a4': [3.5533125763733886, 0.0], 'a5': [-2.881588419383021, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [-3.6604537007649665, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 63.888306657226465, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.0, 0]]], [127, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 7, 127], 'central_character': '8001.1', 'coefficient_field': 'CDF', 'conductor': 8001, 'conductor_radical': 2667, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.3565467481833218, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.881588419383021, 0], [5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-2.0909882453190116, 0], [11.0, 0]], [[1.0, 0], [-0.9090317347473138, 0], [13.0, 0]], [[1.0, 0], [3.785245359126901, 0], [17.0, 0]], [[1.0, 0], 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'3.33697438485626410044651041367201', '4.12933757304175571877286197986082', '5.01496546733689218939916010574812', '6.13818597316258719661068081617633', '6.87159314465596665701450874938113', '7.39100332148714772609520861372404', '7.77940796879501699382725006716749'], 'prelabel': '2-8001-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.993016117663373, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.58069169963719039884993237432', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.26599008885749193927498486531', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.53913540803195117725710099057', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 63.888306657226465, 'bad_primes': [3, 7, 127], 'central_character': '1.1', 'conductor': 8001, 'conductor_radical': 2667, 'degree': 2, 'index': 59, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8001/2/a/s/1/4'], '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': '2-8001-1.1-c1-0-59', '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': '2-8001-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.993016117663373, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.58069169963719039884993237432', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '736114181592635110478655394870', 'Lhash_array': ['736114181592635110478655394870'], 'label': '2-8001-1.1-c1-0-59', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8001/2/a/s/1/4'}