Formats: - HTML - YAML - JSON - 2026-08-19T23:22:17.355982
  • lfunc_lfunctions • Show schema
    {'Lhash': '5430045262500736485219941785551', 'a10': [-7.3484692283495345, -3.099159144529227e-60], 'a2': [1.224744871391589, 0.7071067811865476], 'a3': [-2.449489742783178, -1.7320508075688772], 'a4': [1.0, 1.7320508075688772], 'a5': [-4.5, 2.598076211353316], 'a6': [-1.775255128608411, -3.85337115112852], 'a7': [4.174234614174767, -7.229986434463366], 'a8': [0.0, 2.8284271247461903], 'a9': [3.0, 8.48528137423857], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.4904644758485345, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 7}, 'bad_lfactors': [[2, [[1.0, 0], [-1.224744871391589, -0.7071067811865476]]], [3, [[1.0, 0], [2.449489742783178, 1.7320508075688772]]]], 'bad_primes': [2, 3], 'central_character': '18.11', 'coefficient_field': 'CDF', 'conductor': 18, 'conductor_radical': 6, 'conjugate': '5636740175974194115510880033355', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.224744871391589, -0.7071067811865476]], [[1.0, 0], [2.449489742783178, 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'17.07151883426733925435835553088182', '18.56032922514210106998866923710689'], 'prelabel': '2-18-9.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7003316898788277, 'root_angle': -0.02630894620691859, 'root_number': '0.986368379649002 - 0.1645521790454389*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0263089462069', 'prec': 40}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '4.28355042116739765382981373077', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '5.85459802292309601854744857078', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '8.547550303254200435591441805699', 'prec': 103}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 0.4904644758485345, 'bad_primes': [2, 3], 'central_character': '9.2', 'conductor': 18, 'conductor_radical': 6, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/18/3/d/a/11/2'], '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': '2-18-9.2-c2-0-1', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-18-9.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7003316898788277, 'root_angle': -0.02630894620691859, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '4.28355042116739765382981373077', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '5430045262500736485219941785551', 'Lhash_array': ['5430045262500736485219941785551'], 'factors': ['2-18-9.2-c2-0-1'], 'label': '2-18-9.2-c2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/18/3/d/a/11/2'}