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lfunc_lfunctions • Show schema
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{'Lhash': '1639615722877447637107068724013', 'a10': [4.414213562373095, 0.0], 'a2': [1.0, 0.0], 'a3': [1.0, 0.0], 'a4': [1.0, 0.0], 'a5': [4.414213562373095, 0.0], 'a6': [1.0, 0.0], 'a7': [0.0, 0.0], 'a8': [1.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 44.604434569087246, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [-1.0, 0]]], [7, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 7, 19], 'central_character': '5586.1', 'coefficient_field': 'CDF', 'conductor': 5586, 'conductor_radical': 798, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-4.414213562373095, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0], [11.0, 0]], [[1.0, 0], [-2.8284271247461903, 0], [13.0, 0]], [[1.0, 0], [4.242640687119285, 0], [17.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-0.585786437626905, 0], [23.0, 0]], [[1.0, 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 87, 'label': '2-5586-1.1-c1-0-87', 'leading_term': '6.06970010786956197240420697451', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/5586/2/a/br/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [6.069700107869562, 6.06032675443237, 6.0320576825268315, 5.984458785504628, 5.9168487323733805, 5.828359148554752, 5.71801305771297, 5.584816553178668, 5.427858168263528, 5.246410368886506, 5.040027911725936, 4.808638381291776, 4.552620925699878, 4.272869960694442, 3.9708413425212057, 3.6485791912080323, 3.3087221698008125, 2.9544886011183236, 2.589640347968486, 2.218425912426741, 1.8455037376733812, 1.4758472285755804, 1.1146335440251849, 0.7671187474522924, 0.43850241847422233, 0.13378531031029822, 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'5.18381745550539759255671621656421', '6.08043676093827681145388475942155', '6.51414938393302704117793400697994', '7.12468328331029410010459424238451', '8.427138323035753333615975731447833'], 'prelabel': '2-5586-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.67865514674079, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.29342874336370697819299494079', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.09191329426343172937934388991', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.69873100326959008744893713363', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 44.604434569087246, 'bad_primes': [2, 3, 7, 19], 'central_character': '1.1', 'conductor': 5586, 'conductor_radical': 798, 'degree': 2, 'index': 87, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5586/2/a/br/1/2'], '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': '2-5586-1.1-c1-0-87', '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': '2-5586-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.67865514674079, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.29342874336370697819299494079', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1639615722877447637107068724013', 'Lhash_array': ['1639615722877447637107068724013'], 'label': '2-5586-1.1-c1-0-87', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5586/2/a/br/1/2'}