Formats: - HTML - YAML - JSON - 2026-09-07T12:11:51.646359
  • lfunc_lfunctions • Show schema
    {'Lhash': '1211052592379348100939611479353', 'a10': [0.0, 0.0], 'a2': [-1.618033988749895, 0.0], 'a3': [0.0, 0.0], 'a4': [0.6180339887498949, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-3.3281310261040553, 0.0], 'a8': [2.23606797749979, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 66.47545968271595, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [37, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 5, 37], 'central_character': '8325.1', 'coefficient_field': 'CDF', 'conductor': 8325, 'conductor_radical': 555, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.618033988749895, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.3281310261040553, 0], [7.0, 0]], [[1.0, 0], [1.148961141749635, 0], [11.0, 0]], [[1.0, 0], [-1.8590581791037952, 0], [13.0, 0]], [[1.0, 0], [-2.679888294749375, 0], [17.0, 0]], [[1.0, 0], [1.82083011564558, 0], [19.0, 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'7.66107929343233983899936702970061'], 'prelabel': '2-8325-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.15324841291592, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.955352044294625566107567176805', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.00440731005532945276369167414', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.04743478881423332314246460637', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 66.47545968271595, 'bad_primes': [3, 5, 37], 'central_character': '1.1', 'conductor': 8325, 'conductor_radical': 555, 'degree': 2, 'index': 135, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8325/2/a/bt/1/1'], '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': '2-8325-1.1-c1-0-135', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-8325-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.15324841291592, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.955352044294625566107567176805', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1211052592379348100939611479353', 'Lhash_array': ['1211052592379348100939611479353'], 'factors': ['2-8325-1.1-c1-0-135'], 'label': '2-8325-1.1-c1-0-135', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8325/2/a/bt/1/1'}