Formats: - HTML - YAML - JSON - 2026-10-14T17:53:18.118706
  • lfunc_lfunctions • Show schema
    {'Lhash': '1496372182286578761694444146716', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [170.76734353812338, 0], 'a6': [0, 0], 'a7': [0, 374.3836717690617], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 66.2555760825171, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.0', 'prec': 7}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '288.127', 'coefficient_field': 'CDF', 'conductor': 288, 'conductor_radical': 6, 'conjugate': '822726793601691172315909153269', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-170.76734353812338, 0], [15625.0, 0]], [[1.0, 0], [0, -374.3836717690617], [-117649.0, 0]], [[1.0, 0], [0, 1358.2612100370245], [-1771561.0, 0]], [[1.0, 0], [2957.836717690617, 0], [4826809.0, 0]], [[1.0, 0], [-6656.089680296195, 0], [24137569.0, 0]], [[1.0, 0], [0, 9926.979485566357], [-47045881.0, 0]], [[1.0, 0], 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-4.105240620957223], 'positive_zeros': ['1.18042951426613140887910351418902', '2.13036245800400425760598257308824', '3.62402435092744844403636077152400', '4.97159283526502512917589109229684', '5.82539274889589546869652028666344', '7.12752641874690702743083772687368', '7.72561321347055364527812484167309', '9.381620460288814863673975850369394', '10.04519817984094906344563164343482', '10.40751521540254285748908736353338'], 'prelabel': '2-288-4.3-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.139752826868706, 'root_angle': 0.125, 'root_number': '0.7071067811865475244008443621048490392848359376884740366 + 0.7071067811865475244008443621048490392848359376884740366*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, 'spectral_label': 'c6-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.18042951426613140887910351419', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.13036245800400425760598257309', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.62402435092744844403636077152', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 66.2555760825171, 'bad_primes': [2, 3], 'central_character': '4.3', 'conductor': 288, 'conductor_radical': 6, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/288/7/g/b/127/4'], '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': '2-288-4.3-c6-0-20', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'prelabel': '2-288-4.3-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.139752826868706, 'root_angle': 0.125, 'self_dual': False, 'spectral_label': 'c6-0', 'z1': {'__RealLiteral__': 0, 'data': '1.18042951426613140887910351419', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1496372182286578761694444146716', 'Lhash_array': ['1496372182286578761694444146716'], 'factors': ['2-288-4.3-c6-0-20'], 'label': '2-288-4.3-c6-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/288/7/g/b/127/4'}