Formats: - HTML - YAML - JSON - 2026-08-11T16:53:03.812417
  • lfunc_lfunctions • Show schema
    {'Lhash': '3625371211643089572589360022832', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.1583123951777, 1.1583123951777], 'a4': [0.0, -2.0], 'a5': [-1.6583123951777, 1.5], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, -0.31662479035539987], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.43917721111704233, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[5, [[1.0, 0], [1.6583123951777, -1.5]]], [11, [[1.0, 0], [3.3166247903554, 0]]]], 'bad_primes': [5, 11], 'central_character': '55.43', 'coefficient_field': 'CDF', 'conductor': 55, 'conductor_radical': 55, 'conjugate': '3990693274327132718641142895861', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [0, 2.0]], [[1.0, 0], [-1.1583123951777, -1.1583123951777], [0, 3.0]], [[1.0, 0], [1.6583123951777, -1.5]], [[1.0, 0], [0, 0], [0, 7.0]], [[1.0, 0], [3.3166247903554, 0]], [[1.0, 0], [0, 0], [0, -13.0]], [[1.0, 0], [0, 0], [0, 17.0]], [[1.0, 0], [0, 0], 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'15.46383208499094676616911500459046'], 'prelabel': '2-55-55.43-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6627044674038665, 'root_angle': -0.028924834305293346, 'root_number': '0.983530675170194 - 0.18074128194538827*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0289248343053', 'prec': 40}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.85991361577896401400185087078', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '4.69283492377536908539427929709', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '7.17128803580651590665461554075', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 0.43917721111704233, 'bad_primes': [5, 11], 'central_character': '55.43', 'conductor': 55, 'conductor_radical': 55, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/55/2/e/b/43/2'], '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': '2-55-55.43-c1-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-55-55.43-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6627044674038665, 'root_angle': -0.028924834305293346, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.85991361577896401400185087078', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '3625371211643089572589360022832', 'Lhash_array': ['3625371211643089572589360022832'], 'factors': ['2-55-55.43-c1-0-0'], 'label': '2-55-55.43-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/55/2/e/b/43/2'}