Formats: - HTML - YAML - JSON - 2026-07-18T15:45:35.818689
  • lfunc_lfunctions • Show schema
    {'Lhash': '855394631315461461156732543039', 'a10': [2.0, 0.0], 'a2': [-0.45685025174785665, 0.0], 'a3': [0.0, 0.0], 'a4': [-1.79128784747792, 0.0], 'a5': [-4.3778021186334675, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [1.7320508075688772, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.5275177946066, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 7], 'central_character': '567.1', 'coefficient_field': 'CDF', 'conductor': 567, 'conductor_radical': 21, 'conjugate': '855394631315461461156732543039', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.45685025174785665, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.3778021186334675, 0], [5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [2.6457513110645907, 0], [11.0, 0]], [[1.0, 0], [-4.0, 0], [13.0, 0]], [[1.0, 0], [-3.4641016151377544, 0], [17.0, 0]], [[1.0, 0], [3.58257569495584, 0], 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'8.201420589479745284105441690783507', '8.633661634193135992434590262351935', '9.943032551241114955340318596668647', '10.69046576984660308297900147316519'], 'prelabel': '2-567-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1277964645629526, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.67478738318070858054725244698', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.21923382511238821807819438005', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.04238941355116605697051178395', 'prec': 103}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 4.5275177946066, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 567, 'conductor_radical': 21, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/567/2/a/i/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': '2-567-1.1-c1-0-0', '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': '2-567-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1277964645629526, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.67478738318070858054725244698', 'prec': 103}}
  • lfunc_instances • Show schema
    {'Lhash': '855394631315461461156732543039', 'Lhash_array': ['855394631315461461156732543039'], 'factors': ['2-567-1.1-c1-0-0'], 'label': '2-567-1.1-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/567/2/a/i/1/2'}