Formats: - HTML - YAML - JSON - 2026-08-15T01:16:01.144169
  • lfunc_lfunctions • Show schema
    {'Lhash': '1430297487451327332176103019072', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [2.3722813232690143, 0.0], 'a6': [0.0, 0.0], 'a7': [4.372281323269014, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 41.394448407831774, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '5184.1', 'coefficient_field': 'CDF', 'conductor': 5184, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.3722813232690143, 0], [5.0, 0]], [[1.0, 0], [-4.372281323269014, 0], [7.0, 0]], [[1.0, 0], [-1.0, 0], [11.0, 0]], [[1.0, 0], [-0.3722813232690143, 0], [13.0, 0]], [[1.0, 0], [-5.372281323269014, 0], [17.0, 0]], [[1.0, 0], [0.6277186767309857, 0], [19.0, 0]], [[1.0, 0], [-0.3722813232690143, 0], [23.0, 0]], [[1.0, 0], 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'GL2', 'index': 51, 'label': '2-72e2-1.1-c1-0-51', 'leading_term': '3.3899575017751455165010764855308', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/5184/2/a/bp/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 24}, 'plot_values': [3.3899575017751453, 3.382377678463522, 3.35956660856889, 3.3213186763197085, 3.2673211333831214, 3.197196750491594, 3.1105592583206456, 3.007077857373615, 2.886546679796822, 2.7489550155734634, 2.594554313106009, 2.423918351735644, 2.2379934832051576, 2.038136386408506, 1.826137331570781, 1.6042274835768893, 1.375069283415401, 1.1417294361780503, 0.9076345130994531, 0.6765096531607685, 0.4523013331369993, 0.2390856651239344, 0.04096417360083891, -0.1380505091598872, -0.294156123618296, -0.4238861036660762, -0.5242350278385733, -0.5927801939634331, -0.6277951094266639, -0.6283506040333967, 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'7.63561085502536896843565875863512', '8.151351780896868803537957614360853'], 'prelabel': '2-72e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.433851755195466, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.12830577068619285268915328276', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '1.76974501336820173402615237861', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.64027965529731933882660872674', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 41.394448407831774, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 5184, 'conductor_radical': 6, 'degree': 2, 'index': 51, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5184/2/a/bp/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': '2-72e2-1.1-c1-0-51', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-72e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.433851755195466, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.12830577068619285268915328276', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1430297487451327332176103019072', 'Lhash_array': ['1430297487451327332176103019072'], 'factors': ['2-72e2-1.1-c1-0-51'], 'label': '2-72e2-1.1-c1-0-51', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5184/2/a/bp/1/2'}