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lfunc_lfunctions • Show schema
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{'Lhash': '1958697065413610751798937960866', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.8136065026483308, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [4.916381551744972, 0.0], 'a8': [0.0, 0.0], 'a9': [0.28916854644830997, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.137261107234623, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 5, 19], 'central_character': '1520.1', 'coefficient_field': 'CDF', 'conductor': 1520, 'conductor_radical': 190, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.8136065026483308, 0], [3.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-4.916381551744972, 0], [7.0, 0]], [[1.0, 0], [0.5783370928966199, 0], [11.0, 0]], [[1.0, 0], [6.391943595544951, 0], [13.0, 0]], [[1.0, 0], [0.7108314535516901, 0], [17.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-2.71083145355169, 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[113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 26, 'label': '2-1520-1.1-c1-0-26', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/1520/2/a/q/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-7.559991216464121e-61, 0.11112141486367579, 0.2220822337077644, 0.3326899356431944, 0.44268979332781766, 0.5517377489822228, 0.6593777259586767, 0.765024347462903, 0.8679517014497338, 0.9672884722033283, 1.0620194841385857, 1.150993487273413, 1.2329368585354137, 1.3064727904541154, 1.370145475145098, 1.4224487516746918, 1.4618586553572113, 1.4868692780309207, 1.4960313124880822, 1.4879926092302913, 1.4615400197952575, 1.4156417404628145, 1.349489307049751, 1.2625383304161908, 1.1545470082338027, 1.0256114064863662, 0.8761964787846048, 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'6.76096379848190048134819747909261', '7.38394875407072967812688464763171', '8.254614497709732878824615339163826', '8.860802365675483176211066258882783'], 'prelabel': '2-1520-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.483857216826577, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.54513954007592035166355729424', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.78532423606824347924427876538', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.40055200700155236134090076653', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.137261107234623, 'bad_primes': [2, 5, 19], 'central_character': '1.1', 'conductor': 1520, 'conductor_radical': 190, 'degree': 2, 'index': 26, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1520/2/a/q/1/1'], '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': '2-1520-1.1-c1-0-26', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-1520-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.483857216826577, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.54513954007592035166355729424', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1958697065413610751798937960866', 'Lhash_array': ['1958697065413610751798937960866'], 'label': '2-1520-1.1-c1-0-26', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1520/2/a/q/1/1'}