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lfunc_lfunctions • Show schema
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{'Lhash': '2127297335358898525596695458898', 'a10': [-3.362408046308094, -2.8213953515246404], 'a2': [-0.9730448705798238, 0.23061587074244017], 'a3': [0.8778978455056078, -1.4930825070492963], 'a4': [0.8936326403234123, -0.44879918020046217], 'a5': [2.62111535655589, 3.5207689340695385], 'a6': [-0.5099054730088313, 1.6552934509009694], 'a7': [-1.5052904174955035, 0.9900450823080953], 'a8': [-0.766044443118978, 0.6427876096865394], 'a9': [-1.458590745713224, -2.6215478322013777], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.293576512744743, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.9730448705798238, -0.23061587074244017]]], [3, [[1.0, 0], [-0.8778978455056078, 1.4930825070492963]]]], 'bad_primes': [2, 3], 'central_character': '162.157', 'coefficient_field': 'CDF', 'conductor': 162, 'conductor_radical': 6, 'conjugate': '2612903861940558322232367508637', 'degree': 2, 'euler_factors': [[[1.0, 0], 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1.1373550513119213, 'root_angle': -0.051627515466431524, 'root_number': '0.986875585747104 - 0.16148243946730068*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0258137577332', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.67814170164546701544060441049', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.70164752861829993639222543237', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.10542052736703458464545806286', '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': '81.76', 'conductor': 162, 'conductor_radical': 6, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/162/2/g/a/157/3'], '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': '2-162-81.76-c1-0-1', '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': '2-162-81.76-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1373550513119213, 'root_angle': -0.025813757733215762, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.67814170164546701544060441049', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2127297335358898525596695458898', 'Lhash_array': ['2127297335358898525596695458898'], 'label': '2-162-81.76-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/2/g/a/157/3'}