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lfunc_lfunctions • Show schema
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{'Lhash': '839773883223419860183440712459', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.8660254037844386, 0.5], 'a4': [0.5, 0.8660254037844386], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.834063921426284, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.8660254037844386, -0.5]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5, 7], 'central_character': '3675.2774', 'coefficient_field': 'CDF', 'conductor': 3675, 'conductor_radical': 105, 'conjugate': '1802053859543740278735007288698', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0.8660254037844386, -0.5]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, -1.0], [-1.0, 0]], [[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 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['0.66246478570059125016810864411777', '1.71567785294318915552831204670008', '2.64389787921711101402887745289652', '3.91130683483380075218868320429827', '5.07587083301006102929593675467175', '5.52187759384646165642743226718123', '6.19194121835197976168501001974306', '6.84418602362574487617387465762923', '7.64698468749278219105202131006436', '8.211653793453758075988065845457620'], 'prelabel': '2-3675-105.44-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3542761614332153, 'root_angle': -0.32270190478750393, 'root_number': '-0.44107805798755475947471979793640 - 0.89746874416991663891051365387399*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.32270190478750393', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.66246478570059125016810864412', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.71567785294318915552831204670', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.64389787921711101402887745290', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.834063921426284, 'bad_primes': [3, 5, 7], 'central_character': '105.44', 'conductor': 3675, 'conductor_radical': 105, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3675/1/p/a/2774/1'], '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': '2-3675-105.44-c0-0-2', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3675-105.44-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3542761614332153, 'root_angle': -0.32270190478750393, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.66246478570059125016810864412', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '839773883223419860183440712459', 'Lhash_array': ['839773883223419860183440712459'], 'factors': ['2-3675-105.44-c0-0-2'], 'label': '2-3675-105.44-c0-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3675/1/p/a/2774/1'}