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lfunc_lfunctions • Show schema
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{'Lhash': '2462424624103798360039899284810', 'a10': [-0.5675246226377348, 3.332191559795313], 'a2': [1.4601517547289513, 0.39124648350650926], 'a3': [-0.8529802835021635, 1.5074563462855464], 'a4': [0.24691852841294915, 0.14255847884712244], 'a5': [0.20788264466906686, 2.2263837957650954], 'a6': [-1.835267652228673, 1.8673894927855272], 'a7': [2.369494270055207, -1.1770713250162632], 'a8': [-1.8330475234505998, -1.8330475234505998], 'a9': [-1.5448492719131375, -2.5716610832435616], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8384292212234444, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.8529802835021635, -1.5074563462855464]]], [5, [[1.0, 0], [-0.20788264466906686, -2.2263837957650954]]], [7, [[1.0, 0], [-2.369494270055207, 1.1770713250162632]]]], 'bad_primes': [3, 5, 7], 'central_character': '105.32', 'coefficient_field': 'CDF', 'conductor': 105, 'conductor_radical': 105, 'conjugate': 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['1.94251051800903210010206832643179', '4.29748543976028554220766308479116', '5.31037862863709781698238387966089', '6.38816928945126939974966677220721', '8.256074449985967076812318599343129', '8.889221555283975603234675284920903', '11.15114605802926037586254613799084', '11.73712095609489215452410432687304', '12.68660767633995106029380051960060', '13.37685217783887738515015390753039'], 'prelabel': '2-105-105.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9156578079301484, 'root_angle': -0.33518966421218144, 'root_number': '0.4949410084243451 - 0.8689265781295289*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.167594832106', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.94251051800903210010206832643', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.29748543976028554220766308479', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.31037862863709781698238387966', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8384292212234444, 'bad_primes': [3, 5, 7], 'central_character': '105.32', 'conductor': 105, 'conductor_radical': 105, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/105/2/x/a/32/10'], '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': '2-105-105.32-c1-0-3', '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': '2-105-105.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9156578079301484, 'root_angle': -0.16759483210609072, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.94251051800903210010206832643', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2462424624103798360039899284810', 'Lhash_array': ['2462424624103798360039899284810'], 'label': '2-105-105.32-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/105/2/x/a/32/10'}