Formats: - HTML - YAML - JSON - 2026-10-12T15:55:39.449692
  • lfunc_lfunctions • Show schema
    {'Lhash': '2097104296863765663263939645789', 'a10': [0.0, 0.0], 'a2': [1.7320508075688772, 0.0], 'a3': [0.7922869913932613, 0.0], 'a4': [1.0, 0.0], 'a5': [0.0, 0.0], 'a6': [1.3722813232690143, 0.0], 'a7': [5.0486755979242774, 0.0], 'a8': [-1.7320508075688772, 0.0], 'a9': [-2.3722813232690143, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.78915414654283, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [29, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [5, 29], 'central_character': '725.1', 'coefficient_field': 'CDF', 'conductor': 725, 'conductor_radical': 145, 'conjugate': '2097104296863765663263939645789', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.7320508075688772, 0], [2.0, 0]], [[1.0, 0], [-0.7922869913932613, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-5.0486755979242774, 0], [7.0, 0]], [[1.0, 0], [-0.6277186767309857, 0], [11.0, 0]], [[1.0, 0], [-4.256388606531016, 0], [13.0, 0]], [[1.0, 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'7.966456191943061039151056298762858', '8.549660987843968837369683831600137', '9.302839726138712244168518576583930', '10.86266736190830404089155385472332'], 'prelabel': '2-725-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.406066114333276, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.65432359396682364961687111457', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '3.02214980313415212572016383877', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.96555899274983907686224242528', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 5.78915414654283, 'bad_primes': [5, 29], 'central_character': '1.1', 'conductor': 725, 'conductor_radical': 145, 'degree': 2, 'index': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/725/2/a/g/1/4'], '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': '2-725-1.1-c1-0-25', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-725-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.406066114333276, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.65432359396682364961687111457', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '2097104296863765663263939645789', 'Lhash_array': ['2097104296863765663263939645789'], 'factors': ['2-725-1.1-c1-0-25'], 'label': '2-725-1.1-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/725/2/a/g/1/4'}