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lfunc_lfunctions • Show schema
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{'Lhash': '1584194335687889884372967867052', 'a10': [4.82842712474619, 0.0], 'a2': [2.414213562373095, 0.0], 'a3': [0.0, 0.0], 'a4': [3.8284271247461903, 0.0], 'a5': [2.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [4.414213562373095, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 38.73543002052313, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 7, 11], 'central_character': '4851.1', 'coefficient_field': 'CDF', 'conductor': 4851, 'conductor_radical': 231, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.414213562373095, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.0, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0.8284271247461901, 0], [13.0, 0]], [[1.0, 0], [-4.414213562373095, 0], [17.0, 0]], [[1.0, 0], [-7.242640687119285, 0], [19.0, 0]], [[1.0, 0], [-7.0, 0], [23.0, 0]], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 115, 'label': '2-4851-1.1-c1-0-115', 'leading_term': '7.0508492704016341389727636326363', '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/4851/2/a/be/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [7.050849270401634, 7.042193528289132, 7.016085030480538, 6.9721087720662664, 6.909601934703805, 6.827695444460724, 6.725368879316388, 6.601515840086819, 6.455016549928699, 6.284814342870861, 6.089992805252826, 5.86985059168001, 5.623971290254314, 5.352286107223485, 5.055127538032798, 4.733272564146837, 4.387974250981989, 4.020980920879316, 3.634542342504339, 3.23140262425416, 2.8147797347518266, 2.388331807535743, 1.9561106262722812, 1.5225029347976118, 1.0921604734378718, 0.6699199068666349, 0.2607140742565555, 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'5.76757748163586321867570624091192', '6.63016547074526999917319745606161', '7.22062686295560240153687977721541', '7.987364910507144321020014733147576'], 'prelabel': '2-4851-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.223779400052924, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.24970897769674826198021931009', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.27893739810726249470998704493', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.14110669469976902497524644594', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 38.73543002052313, 'bad_primes': [3, 7, 11], 'central_character': '1.1', 'conductor': 4851, 'conductor_radical': 231, 'degree': 2, 'index': 115, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4851/2/a/be/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': '2-4851-1.1-c1-0-115', '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': '2-4851-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.223779400052924, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.24970897769674826198021931009', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1584194335687889884372967867052', 'Lhash_array': ['1584194335687889884372967867052'], 'label': '2-4851-1.1-c1-0-115', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4851/2/a/be/1/2'}