Formats: - HTML - YAML - JSON - 2026-09-07T14:47:15.804956
  • lfunc_lfunctions • Show schema
    {'Lhash': '686445319004392850701052575620', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, -0.540181513475453], 'a6': [0, 0], 'a7': [1.2360679774997898, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 42.54429419693821, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [37, [[1.0, 0], [2.23606797749979, -5.656854249492381]]]], 'bad_primes': [2, 3, 37], 'central_character': '5328.2737', 'coefficient_field': 'CDF', 'conductor': 5328, 'conductor_radical': 222, 'conjugate': '1504480503471891127137517995361', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0.540181513475453], [-5.0, 0]], [[1.0, 0], [-1.2360679774997898, 0], [7.0, 0]], [[1.0, 0], [-2.4721359549995796, 0], [11.0, 0]], [[1.0, 0], [0, -4.576491222541474], [-13.0, 0]], [[1.0, 0], [0, 3.368608638221643], [-17.0, 0]], [[1.0, 0], [0, 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'4.40619621260101854226819849962815', '5.09973056035468004875529107440553', '5.95556764502630114290514498568847', '6.61654960079336109074139066420118', '7.31785453109684594322747866655751', '8.141531567167490593853840646098872'], 'prelabel': '2-5328-37.36-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.522598730332735, 'root_angle': -0.19008852934542256, 'root_number': '0.36760731104690387418999830735290238251334474217075041439 - 0.9299811099505542455923755173026717440029768170044038508*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.19008852934542256', 'prec': 57}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.54150987573453156244915303246', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '1.67079387137310440153767295792', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.71461668321230136717715315945', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 42.54429419693821, 'bad_primes': [2, 3, 37], 'central_character': '37.36', 'conductor': 5328, 'conductor_radical': 222, 'degree': 2, 'index': 29, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5328/2/h/g/2737/2'], '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': '2-5328-37.36-c1-0-29', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-5328-37.36-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.522598730332735, 'root_angle': -0.19008852934542256, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.54150987573453156244915303246', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '686445319004392850701052575620', 'Lhash_array': ['686445319004392850701052575620'], 'factors': ['2-5328-37.36-c1-0-29'], 'label': '2-5328-37.36-c1-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5328/2/h/g/2737/2'}