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lfunc_lfunctions • Show schema
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{'Lhash': '573950562270253038753372261282', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 67.07433769787555, '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], [0, 0]]], [7, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '8400.1', 'coefficient_field': 'CDF', 'conductor': 8400, 'conductor_radical': 210, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [5.4185507188738455, 0], [11.0, 0]], [[1.0, 0], [-4.340172973252067, 0], [13.0, 0]], [[1.0, 0], [-1.0783777456217782, 0], [17.0, 0]], [[1.0, 0], [4.340172973252067, 0], [19.0, 0]], [[1.0, 0], [6.340172973252067, 0], [23.0, 0]], [[1.0, 0], 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[[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-8400-1.1-c1-0-4', 'leading_term': '0.85810205628325837440345701019590', '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/8400/2/a/dh/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [0.8581020562832584, 0.8486579850265956, 0.820342226067282, 0.7732099730425467, 0.7073722244619479, 0.6230228602590554, 0.5204738064835562, 0.40019583135593284, 0.262862171913112, 0.10939204069264206, -0.05900891070804288, -0.24081392035725796, -0.4341487015180001, -0.6367753887653103, -0.8460885402982004, -1.0591244572977145, -1.2725846332080353, -1.4828736920861971, -1.6861517194517552, -1.8784004336323523, -2.0555021929782087, -2.2133303885474054, -2.3478493391646693, -2.455221394722258, -2.531918575004315, -2.5748357376933586, 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'5.23348397665148064140240375067460', '5.70917907657490054648972227718011', '6.28964707019974493132793197467840', '7.06398339613357458168138953429174', '7.85209432911951650163840398208550'], 'prelabel': '2-8400-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.189892410641031, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.45276716010462051671441067729', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.77737058994670304910461619279', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.58528366037530987558107251950', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 67.07433769787555, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 8400, 'conductor_radical': 210, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8400/2/a/dh/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': '2-8400-1.1-c1-0-4', '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': '2-8400-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.189892410641031, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.45276716010462051671441067729', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '573950562270253038753372261282', 'Lhash_array': ['573950562270253038753372261282'], 'label': '2-8400-1.1-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8400/2/a/dh/1/1'}