Formats: - HTML - YAML - JSON - 2026-08-13T03:46:11.676478
  • lfunc_lfunctions • Show schema
    {'Lhash': '1884180934944551834295718851771', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.5, -0.8660254037844386], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [2.598076211353316, 4.5], 'a8': [0.0, 0.0], 'a9': [1.5, -2.598076211353316], '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], [-1.5, 0.8660254037844386]]], [37, [[1.0, 0], [-5.0, 3.4641016151377544]]]], 'bad_primes': [2, 3, 37], 'central_character': '444.245', 'coefficient_field': 'CDF', 'conductor': 444, 'conductor_radical': 222, 'conjugate': '2305738689289717601694052329644', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [4.330127018922194, 2.5]], [[1.0, 0], [-2.598076211353316, -4.5], [-3.5, 6.06217782649107]], [[1.0, 0], [0, 0], [11.0, 0]], [[1.0, 0], [0.03589838486224541, 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['1.48635667794053151497638489992529', '3.15088367685776090174303619579307', '4.29949189951232798577420508261527', '4.89848701180947344926063676419541', '6.69670621028378898455155362506757', '7.68417107390136938149518762025929', '8.206655838172893104963125937297782', '9.368213070418357287519897994431756', '10.27571188425527282388698082214125', '10.85283724201053514863457982439564'], 'prelabel': '2-444-111.23-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8829120663867578, 'root_angle': -0.007984714092532276, 'root_number': '0.9987417776743943 - 0.05014839506694861*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.00798471409253', 'prec': 40}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.48635667794053151497638489993', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '3.15088367685776090174303619579', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '4.29949189951232798577420508262', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 3.5453578497448506, 'bad_primes': [2, 3, 37], 'central_character': '111.23', 'conductor': 444, 'conductor_radical': 222, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/444/2/w/b/245/1'], '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': '2-444-111.23-c1-0-6', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-444-111.23-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8829120663867578, 'root_angle': -0.007984714092532276, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.48635667794053151497638489993', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1884180934944551834295718851771', 'Lhash_array': ['1884180934944551834295718851771'], 'factors': ['2-444-111.23-c1-0-6'], 'label': '2-444-111.23-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/444/2/w/b/245/1'}