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lfunc_lfunctions • Show schema
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{'Lhash': '4153435994222836595290166828305', 'a10': [-3.9850393876480803, 3.343845080402438], 'a2': [1.3285346092799104, 0.31486848653545224], 'a3': [1.39366406649483, -1.0284456571745022], 'a4': [-0.12140323640542629, -0.060970996933056805], 'a5': [-2.27524585524333, 3.056185567901534], 'a6': [2.1753560736066544, -0.9275047539638771], 'a7': [-1.4595801329586435, -0.959980955219638], 'a8': [-2.2339088997638665, -1.8744721338755037], 'a9': [0.8845990604778124, -2.8666155134935294], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6467882563723715, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.39366406649483, 1.0284456571745022]]]], 'bad_primes': [3], 'central_character': '81.16', 'coefficient_field': 'CDF', 'conductor': 81, 'conductor_radical': 3, 'conjugate': '4099555508011700836210664164632', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.3285346092799104, -0.31486848653545224], [1.7872652806468246, 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'root_angle': -0.0034903014450860127, 'root_number': '0.9997595425653159 - 0.021928452968472456*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.00349030144509', 'prec': 57}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.27648327818016003597296667282', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.32192579132361819043541267015', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.35080421307036370973486692685', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6467882563723715, 'bad_primes': [3], 'central_character': '81.16', 'conductor': 81, 'conductor_radical': 3, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/81/2/g/a/16/7'], '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': '2-3e4-81.16-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': '2-3e4-81.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8042314693994332, 'root_angle': -0.0034903014450860127, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.27648327818016003597296667282', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4153435994222836595290166828305', 'Lhash_array': ['4153435994222836595290166828305'], 'factors': ['2-3e4-81.16-c1-0-5'], 'label': '2-3e4-81.16-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/81/2/g/a/16/7'}