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lfunc_lfunctions • Show schema
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{'Lhash': '3424607086989614155364443506273', 'a10': [0.18648297893368146, -1.05759752809474], 'a2': [-0.8936326403234123, -0.44879918020046217], 'a3': [-1.4136224771186576, -1.0008353971482575], 'a4': [0.5971585917027862, 0.8021231927550437], 'a5': [0.30800162675107357, 1.028797079497593], 'a6': [0.8140850808923265, 1.5288117873265283], 'a7': [-2.0649895391552704, -4.787183840146463], 'a8': [-0.17364817766693036, -0.984807753012208], 'a9': [0.9966570156301795, 2.8296068266095107], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.293576512744743, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.8936326403234123, 0.44879918020046217]]], [3, [[1.0, 0], [1.4136224771186576, 1.0008353971482575]]]], 'bad_primes': [2, 3], 'central_character': '162.13', 'coefficient_field': 'CDF', 'conductor': 162, 'conductor_radical': 6, 'conjugate': '460905640509071853238564311379', 'degree': 2, 'euler_factors': [[[1.0, 0], 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0.944899210094262, 'root_number': '-0.9850548369988867 + 0.1722410174874052*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.472449605047', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.70153864666891934332298071249', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.10913381130699535969531624078', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.64414699627172635435127476983', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.293576512744743, 'bad_primes': [2, 3], 'central_character': '81.13', 'conductor': 162, 'conductor_radical': 6, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/162/2/g/a/13/2'], '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': '2-162-81.13-c1-0-6', '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': '2-162-81.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1373550513119213, 'root_angle': 0.472449605047131, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.70153864666891934332298071249', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3424607086989614155364443506273', 'Lhash_array': ['3424607086989614155364443506273'], 'label': '2-162-81.13-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/2/g/a/13/2'}