Formats: - HTML - YAML - JSON - 2026-08-25T08:12:33.078468
  • lfunc_lfunctions • Show schema
    {'Lhash': '563261561909460000688162138844', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -1.0], 'a4': [0, 0], 'a5': [-0.3111078174659819, 2.2143197433775352], 'a6': [0, 0], 'a7': [0, -2.9032119259115534], 'a8': [0, 0], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.540253066809015, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 1.0]]], [5, [[1.0, 0], [0.3111078174659819, -2.2143197433775352]]], [11, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 5, 11], 'central_character': '1320.529', 'coefficient_field': 'CDF', 'conductor': 1320, 'conductor_radical': 330, 'conjugate': '1828145566610717829311582145481', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0.3111078174659819, -2.2143197433775352]], [[1.0, 0], [0, 2.9032119259115534], [-7.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, -3.525427560843517], [-13.0, 0]], [[1.0, 0], [0, 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'4.53972362805209278950085706964929', '5.19695785891404529443696917719692', '5.78072387244093963357085470612564', '7.02030583493400057771611653856800', '8.202077609863913971996039447338002', '8.614746459466346563295431919065232', '9.399659828379070234440703690138878'], 'prelabel': '2-1320-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.24657559080472, 'root_angle': -0.2277844404182969, 'root_number': '0.1391316456371063789875129308001809909212943459158301840 - 0.9902738940224116892131970920148430732365280939552459239*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2277844404182969', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.44433502560409759892080408373', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '2.27207150348960555401332890461', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.23332149944379316736874847088', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 10.540253066809015, 'bad_primes': [2, 3, 5, 11], 'central_character': '5.4', 'conductor': 1320, 'conductor_radical': 330, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1320/2/d/a/529/2'], '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': '2-1320-5.4-c1-0-6', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1320-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.24657559080472, 'root_angle': -0.2277844404182969, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.44433502560409759892080408373', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '563261561909460000688162138844', 'Lhash_array': ['563261561909460000688162138844'], 'factors': ['2-1320-5.4-c1-0-6'], 'label': '2-1320-5.4-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1320/2/d/a/529/2'}