Formats: - HTML - YAML - JSON - 2026-08-16T01:46:05.863686
  • lfunc_lfunctions • Show schema
    {'Lhash': '1462730183863200378319958471913', 'a10': [-174.0695532433431, 0.0], 'a2': [6.962782129733725, 0.0], 'a3': [22.67007854064203, 0.0], 'a4': [16.4803349861393, 0.0], 'a5': [-25.0, 0.0], 'a6': [157.84681774244234, 0.0], 'a7': [169.11757845623234, 0.0], 'a8': [-108.06004621796296, 0.0], 'a9': [270.93246103887833, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 97.0322109868533, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 7}, 'bad_lfactors': [[5, [[1.0, 0], [25.0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 11], 'central_character': '605.1', 'coefficient_field': 'CDF', 'conductor': 605, 'conductor_radical': 55, 'degree': 2, 'euler_factors': [[[1.0, 0], [-6.962782129733725, 0], [32.0, 0]], [[1.0, 0], [-22.67007854064203, 0], [243.0, 0]], [[1.0, 0], [25.0, 0]], [[1.0, 0], [-169.11757845623234, 0], [16807.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [25.31815003433785, 0], [371293.0, 0]], [[1.0, 0], [-2016.261619853946, 0], [1419857.0, 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'positive_zeros': ['1.15389065693642128540366040840270', '2.50276639446408260070475465164769', '3.28815642239942390571580646310184', '4.18046044807616754086161375599908', '4.95531130268212627103075726626103', '6.00236740346807402904008456136771', '7.55505727217138371996493853381560', '7.939860316033248673269686000263164', '8.852676470672192572612983371396911', '9.703144090170684433175352267449244'], 'prelabel': '2-605-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.850492931161025, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.15389065693642128540366040840', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.50276639446408260070475465165', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.28815642239942390571580646310', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 97.0322109868533, 'bad_primes': [5, 11], 'central_character': '1.1', 'conductor': 605, 'conductor_radical': 55, 'degree': 2, 'index': 123, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/605/6/a/c/1/3'], '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': '2-605-1.1-c5-0-123', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-605-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.850492931161025, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.15389065693642128540366040840', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1462730183863200378319958471913', 'Lhash_array': ['1462730183863200378319958471913'], 'factors': ['2-605-1.1-c5-0-123'], 'label': '2-605-1.1-c5-0-123', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/605/6/a/c/1/3'}