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lfunc_lfunctions • Show schema
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{'Lhash': '1603280361615703201149146340580', 'a10': [2.9169492680076226, -1.2212317420824743], 'a2': [0.2212317420824743, -1.3968022466674206], 'a3': [0.0, 0.0], 'a4': [-1.902113032590307, -0.6180339887498949], 'a5': [1.1755705045849463, 1.902113032590307], 'a6': [0.0, 0.0], 'a7': [1.902113032590307, 1.902113032590307], 'a8': [-1.2840790438404124, 2.520147021340202], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.8746144727660954, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.2212317420824743, 1.3968022466674206]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.1755705045849463, -1.902113032590307]]]], 'bad_primes': [2, 3, 5], 'central_character': '360.163', 'coefficient_field': 'CDF', 'conductor': 360, 'conductor_radical': 30, 'conjugate': '2190382756800907578512045346831', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.2212317420824743, 1.3968022466674206]], [[1.0, 0], [0, 0]], [[1.0, 0], 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'z1': {'__RealLiteral__': 0, 'data': '1.26476519738723477677176822607', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.72688406204262459653840886439', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.79858600404903128705383254023', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.8746144727660954, 'bad_primes': [2, 3, 5], 'central_character': '40.3', 'conductor': 360, 'conductor_radical': 30, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/360/2/w/c/163/2'], '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': '2-360-40.3-c1-0-9', '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': '2-360-40.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6954688061908114, 'root_angle': 0.075, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.26476519738723477677176822607', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1603280361615703201149146340580', 'Lhash_array': ['1603280361615703201149146340580'], 'label': '2-360-40.3-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/360/2/w/c/163/2'}