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lfunc_lfunctions • Show schema
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{'Lhash': '3410661009561452292459758666061', 'a10': [116.72766999631601, -66.75791331652655], 'a2': [3.8033635569738244, 3.8033635569738244], 'a3': [-3.6742346141747673, 3.6742346141747673], 'a4': [0.0, 12.931148693033164], 'a5': [6.569153320639729, -24.121488856410338], 'a6': [-27.94890006264818, -2.3668389522308404e-60], 'a7': [16.61489056308844, 16.61489056308844], 'a8': [11.671957222689155, -11.671957222689155], 'a9': [0.0, -27.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.5505494462576654, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [3.6742346141747673, -3.6742346141747673]]], [5, [[1.0, 0], [-6.569153320639729, 24.121488856410338]]]], 'bad_primes': [3, 5], 'central_character': '15.7', 'coefficient_field': 'CDF', 'conductor': 15, 'conductor_radical': 15, 'conjugate': '6009495845141974522916790981798', 'degree': 2, 'euler_factors': [[[1.0, 0], [-3.8033635569738244, -3.8033635569738244], [0, 16.0]], 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[{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/15/5/f/a/7/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [1.6143326157706865, 1.5519995554372117, 1.4918350717438151, 1.4322720337538484, 1.37143361277005, 1.3072092971751244, 1.2373415593224935, 1.159524262826893, 1.0715142160796938, 0.9712571427145521, 0.857028550004819, 0.7275884596919611, 0.5823467747000786, 0.4215333351893231, 0.24636367810440518, 0.05918841322209478, -0.13638873414219713, -0.33544144704683226, -0.5317184693394945, -0.717726929310578, -0.8849181294153162, -1.0239887929472973, -1.1253046767832744, -1.1794450411356687, -1.1778558747383931, -1.1135874397517072, -0.9820783617364739, -0.781935195145019, -0.515644478049906, -0.19014530239471664, 0.1828139779773408, 0.5866095015157075, 1.000031409939798, 1.3979767047327347, 1.7525667559074753, 2.0346766321660676, 2.215823187717027, 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True, 'rational': False, 'root_analytic_conductor': 1.2452106031742844, 'root_angle': -0.3415734234030739, 'root_number': '0.4774161737472842 - 0.878677299720724*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.170786711702', 'prec': 50}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.69053713140465725591469529110', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.18962143882425666349782604269', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.43025333046922290462064908300', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.5505494462576654, 'bad_primes': [3, 5], 'central_character': '5.2', 'conductor': 15, 'conductor_radical': 15, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/15/5/f/a/7/4'], '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': '2-15-5.2-c4-0-0', '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': '2-15-5.2-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2452106031742844, 'root_angle': -0.17078671170153695, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '2.69053713140465725591469529110', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3410661009561452292459758666061', 'Lhash_array': ['3410661009561452292459758666061'], 'label': '2-15-5.2-c4-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/15/5/f/a/7/4'}