Formats: - HTML - YAML - JSON - 2026-09-15T03:22:08.660976
  • lfunc_lfunctions • Show schema
    {'Lhash': '2214526649666349619990967058245', 'a10': [0.0, 0.0], 'a2': [3.0, 0.0], 'a3': [-3.720153254455275, 0.0], 'a4': [1.0, 0.0], 'a5': [0.0, 0.0], 'a6': [-11.160459763365825, 0.0], 'a7': [25.600766272276374, 0.0], 'a8': [-21.0, 0.0], 'a9': [-13.160459763365825, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 33.92609825330087, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 7}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [-23.0, 0]]]], 'bad_primes': [5, 23], 'central_character': '575.1', 'coefficient_field': 'CDF', 'conductor': 575, 'conductor_radical': 115, 'degree': 2, 'euler_factors': [[[1.0, 0], [-3.0, 0], [8.0, 0]], [[1.0, 0], [3.720153254455275, 0], [27.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-25.600766272276374, 0], [343.0, 0]], [[1.0, 0], [-12.600766272276376, 0], [1331.0, 0]], [[1.0, 0], [8.160459763365825, 0], [2197.0, 0]], [[1.0, 0], [-76.04107278118693, 0], [4913.0, 0]], [[1.0, 0], [103.36199230791857, 0], 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'6.87322720082784842523604662897322', '8.147521030609398738643487918778394', '8.851912615893465499607307107092381', '10.10173519987673804045235701879942'], 'prelabel': '2-575-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.824611425091023, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.74695349749185104224762682292', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '3.30311822301414627958047823141', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '4.42210390595879919469799024763', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 33.92609825330087, 'bad_primes': [5, 23], 'central_character': '1.1', 'conductor': 575, 'conductor_radical': 115, 'degree': 2, 'index': 82, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/575/4/a/h/1/1'], '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': '2-575-1.1-c3-0-82', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-575-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.824611425091023, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.74695349749185104224762682292', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '2214526649666349619990967058245', 'Lhash_array': ['2214526649666349619990967058245'], 'factors': ['2-575-1.1-c3-0-82'], 'label': '2-575-1.1-c3-0-82', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/575/4/a/h/1/1'}