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lfunc_lfunctions • Show schema
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{'Lhash': '4262255404727592946551779899939', 'a10': [-2.602000229739967, -2.157586520375112], 'a2': [-0.39124648350650926, -1.4601517547289513], 'a3': [-0.879005349228273, -1.4924307675828992], 'a4': [-0.24691852841294915, 0.14255847884712244], 'a5': [1.8241636033720645, -1.2932235491718533], 'a6': [-1.835267652228673, 1.8673894927855272], 'a7': [-1.1770713250162632, 2.369494270055207], 'a8': [-1.8330475234505998, -1.8330475234505998], 'a9': [-1.4546991920561636, 2.623709256116452], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8384292212234444, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.879005349228273, 1.4924307675828992]]], [5, [[1.0, 0], [-1.8241636033720645, 1.2932235491718533]]], [7, [[1.0, 0], [1.1770713250162632, -2.369494270055207]]]], 'bad_primes': [3, 5, 7], 'central_character': '105.2', 'coefficient_field': 'CDF', 'conductor': 105, 'conductor_radical': 105, 'conjugate': 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-1.9584187364755898], 'positive_zeros': ['3.36232665685655901241319687430666', '5.25421233589555496593630846364080', '6.38046539980900763529485975757944', '7.14220743513215475832518816371459', '8.833165568335685518595688298253699', '9.828015966412588325421936373741092', '10.81741786145503840120653668215384', '11.79821094049667137042577187372450', '13.61571878366485080399089341271739', '14.27465968985452144741059649515924'], 'prelabel': '2-105-105.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9156578079301484, 'root_angle': 0.3756565167353787, 'root_number': '-0.7100175839458376 + 0.7041839464853736*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.375656516735', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.36232665685655901241319687431', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.25421233589555496593630846364', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.38046539980900763529485975758', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8384292212234444, 'bad_primes': [3, 5, 7], 'central_character': '105.2', 'conductor': 105, 'conductor_radical': 105, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/105/2/x/a/2/3'], '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': '2-105-105.2-c1-0-10', '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': '2-105-105.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9156578079301484, 'root_angle': 0.3756565167353787, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.36232665685655901241319687431', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4262255404727592946551779899939', 'Lhash_array': ['4262255404727592946551779899939'], 'factors': ['2-105-105.2-c1-0-10'], 'label': '2-105-105.2-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/105/2/x/a/2/3'}