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lfunc_lfunctions • Show schema
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{'Lhash': '1187375666404482545226241590937', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.6420736324815003, 0.0], 'a4': [0.0, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-3.5877414504720115, 0.0], 'a8': [0.0, 0.0], 'a9': [-2.5877414504720115, 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], [-0.6420736324815003, 0], [3.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [3.5877414504720115, 0], [7.0, 0]], [[1.0, 0], [0, 0], [11.0, 0]], [[1.0, 0], [-1.3579263675184998, 0], [13.0, 0]], [[1.0, 0], [-5.587741450472011, 0], [17.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-4.871888715435012, 0], [23.0, 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0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 8, 'label': '2-1520-1.1-c1-0-8', 'leading_term': '1.7597776568913009610353101128870', '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/1520/2/a/s/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.759777656891301, 1.7543738101958797, 1.7380297694498223, 1.7103579070453505, 1.6707443241525617, 1.6183945107667295, 1.5523925622598318, 1.471770092040005, 1.375580830048356, 1.2629771189866992, 1.133284973331154, 0.9860749070064055, 0.8212262529292824, 0.6389831271487292, 0.440000512199286, 0.22537916134046546, -0.0033118114319764997, -0.2440256544690784, -0.4942428698724276, -0.7509909501432298, -1.010879405560902, -1.2701502334676533, -1.5247436215737797, -1.7703782583466567, 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'6.12575812990272592151877704280251', '6.96388599860259865490311383984128', '7.971444700519335383311694286707382', '8.812606540766630275302888546548133', '9.388537738170172236817791929181101'], 'prelabel': '2-1520-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.483857216826577, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.936674243037242236417885398167', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.76465589888172096731859452112', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.06860030542496379244206288580', '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': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1520/2/a/s/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': '2-1520-1.1-c1-0-8', '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': '2-1520-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.483857216826577, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.936674243037242236417885398167', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1187375666404482545226241590937', 'Lhash_array': ['1187375666404482545226241590937'], 'label': '2-1520-1.1-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1520/2/a/s/1/2'}