Formats: - HTML - YAML - JSON - 2026-08-11T23:15:47.341671
  • lfunc_lfunctions • Show schema
    {'Lhash': '1510168480570052503689422594735', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.5, 0.8660254037844386], 'a4': [0.0, 0.0], 'a5': [-3.0, -1.7320508075688772], 'a6': [0.0, 0.0], 'a7': [-0.5, 0.8660254037844386], 'a8': [0.0, 0.0], 'a9': [-0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.5453578497448506, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0.5, -0.8660254037844386]]], [37, [[1.0, 0], [5.0, -3.4641016151377544]]]], 'bad_primes': [2, 3, 37], 'central_character': '444.85', 'coefficient_field': 'CDF', 'conductor': 444, 'conductor_radical': 222, 'conjugate': '1237764143833106091927495700605', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [3.0, 1.7320508075688772], [2.5, 4.330127018922194]], [[1.0, 0], [0.5, -0.8660254037844386], [-3.5, -6.06217782649107]], [[1.0, 0], [-6.0, 0], [11.0, 0]], 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'3.39698377254026474132856635670', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.89203993851820244067982668909', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 3.5453578497448506, 'bad_primes': [2, 3, 37], 'central_character': '37.11', 'conductor': 444, 'conductor_radical': 222, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/444/2/r/a/85/1'], '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': '2-444-37.11-c1-0-2', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-444-37.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8829120663867578, 'root_angle': 0.023412033375973876, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.19131287461873159632462798164', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1510168480570052503689422594735', 'Lhash_array': ['1510168480570052503689422594735'], 'factors': ['2-444-37.11-c1-0-2'], 'label': '2-444-37.11-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/444/2/r/a/85/1'}