Formats: - HTML - YAML - JSON - 2026-09-11T04:57:15.315715
  • lfunc_lfunctions • Show schema
    {'Lhash': '995424996510360989105811110228', 'a10': [1.0, -3.0], 'a2': [0.0, -1.4142135623730951], 'a3': [-1.0, 1.4142135623730951], 'a4': [-2.0, 0.0], 'a5': [2.1213203435596424, 0.7071067811865476], 'a6': [2.0, 1.4142135623730951], 'a7': [1.0, 0.0], 'a8': [0.0, 2.8284271247461903], 'a9': [-1.0, -2.8284271247461903], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.3537168848937777, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 1.4142135623730951]]], [3, [[1.0, 0], [1.0, -1.4142135623730951]]], [5, [[1.0, 0], [-2.1213203435596424, -0.7071067811865476]]], [7, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '420.239', 'coefficient_field': 'CDF', 'conductor': 420, 'conductor_radical': 210, 'conjugate': '2192530855199639945452519794873', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.4142135623730951]], [[1.0, 0], [1.0, -1.4142135623730951]], [[1.0, 0], [-2.1213203435596424, 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'7.982460779226936813288556093110422', '9.061367907453524573939195644925103', '10.27232604482245198757885544973823', '10.85548826180716822731874985962271'], 'prelabel': '2-420-60.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8313156158602968, 'root_angle': -0.10083517081756482, 'root_number': '0.8059214472523273 - 0.5920224834064279*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.100835170818', 'prec': 40}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.78525186382678588737342378224', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '2.73054577108713646790079187748', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '5.02982559733495413126446465533', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 3.3537168848937777, 'bad_primes': [2, 3, 5, 7], 'central_character': '60.59', 'conductor': 420, 'conductor_radical': 210, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/420/2/l/a/239/2'], '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': '2-420-60.59-c1-0-16', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-420-60.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8313156158602968, 'root_angle': -0.10083517081756482, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.78525186382678588737342378224', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '995424996510360989105811110228', 'Lhash_array': ['995424996510360989105811110228'], 'factors': ['2-420-60.59-c1-0-16'], 'label': '2-420-60.59-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/420/2/l/a/239/2'}