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lfunc_lfunctions • Show schema
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{'Lhash': '1040464713410305205294966269084', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-3.1231056256176606, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 44.0774219157468, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [23, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '5520.1', 'coefficient_field': 'CDF', 'conductor': 5520, 'conductor_radical': 690, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [3.1231056256176606, 0], [7.0, 0]], [[1.0, 0], [-3.1231056256176606, 0], [11.0, 0]], [[1.0, 0], [-2.0, 0], [13.0, 0]], [[1.0, 0], [1.1231056256176606, 0], [17.0, 0]], [[1.0, 0], [4.0, 0], [19.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-2.0, 0], [29.0, 0]], 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'2.46928511508088796250489347549', '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/5520/2/a/bs/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [2.469285115080888, 2.459790308007835, 2.4312471778950857, 2.3834890719061614, 2.3162691292322592, 2.2293042991889145, 2.1223325811959564, 1.995179655267008, 1.8478306481021232, 1.6805026877124587, 1.4937140820448183, 1.2883463375637871, 1.065695734875724, 0.8275117363140315, 0.5760200710713235, 0.31392890336823365, 0.044417030994513086, -0.2288964114651374, -0.5020007504061716, -0.7705605567111092, -1.0299993730221153, -1.2755988104572147, -1.5026109079666488, -1.7063811256571566, -1.8824788473273097, -2.02683181568501, -2.1358605369160113, -2.206608390938812, -2.2368629908704665, -2.225264269298944, 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'7.33877564468612088455253059728609', '8.378773464612410435369465851806579'], 'prelabel': '2-5520-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.639082912251269, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.820781935671373985353206185677', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.02040657616326832427191301053', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.79026582685072621342139630451', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 44.0774219157468, 'bad_primes': [2, 3, 5, 23], 'central_character': '1.1', 'conductor': 5520, 'conductor_radical': 690, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5520/2/a/bs/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': '2-5520-1.1-c1-0-22', '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': '2-5520-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.639082912251269, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.820781935671373985353206185677', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1040464713410305205294966269084', 'Lhash_array': ['1040464713410305205294966269084'], 'label': '2-5520-1.1-c1-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5520/2/a/bs/1/1'}