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lfunc_lfunctions • Show schema
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{'Lhash': '1330280061434298040839812459800', 'a10': [0.0, -4.97979656976556], 'a2': [-1.902113032590307, 0.0], 'a3': [1.618033988749895, -0.6180339887498949], 'a4': [1.618033988749895, 0.0], 'a5': [0.0, 2.618033988749895], 'a6': [-3.0776835371752536, 1.1755705045849463], 'a7': [0.0, -0.7265425280053609], 'a8': [0.7265425280053609, 0.0], 'a9': [2.23606797749979, -2.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.8985695933724793, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.618033988749895, 0.6180339887498949]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 11], 'central_character': '363.362', 'coefficient_field': 'CDF', 'conductor': 363, 'conductor_radical': 33, 'conjugate': '1954669626033470187916475329857', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.902113032590307, 0], [2.0, 0]], [[1.0, 0], [-1.618033988749895, 0.6180339887498949]], [[1.0, 0], [0, -2.618033988749895], [-5.0, 0]], [[1.0, 0], [0, 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'positive_zeros': ['1.04940593346052354861744081710072', '2.62358248263222631889263992220328', '4.30629584074771619887681102996095', '5.32768893637914041006426421034500', '7.12926489809822006475952361768122', '8.105059545989767369649608798803124', '8.628602508929852529171193671037642', '9.303649115417189356463858982645039', '10.06310517462550578977403005717628', '10.90479867707244494349162031245880'], 'prelabel': '2-363-33.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7025186029446138, 'root_angle': -0.18643907532991164, 'root_number': '0.8333167023263508 - 0.5527958697602*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.093219537665', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.04940593346052354861744081710', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.62358248263222631889263992220', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.30629584074771619887681102996', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.8985695933724793, 'bad_primes': [3, 11], 'central_character': '33.32', 'conductor': 363, 'conductor_radical': 33, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/363/2/d/f/362/1'], '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': '2-363-33.32-c1-0-11', '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': '2-363-33.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7025186029446138, 'root_angle': -0.09321953766495582, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.04940593346052354861744081710', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1330280061434298040839812459800', 'Lhash_array': ['1330280061434298040839812459800'], 'label': '2-363-33.32-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/363/2/d/f/362/1'}