Formats: - HTML - YAML - JSON - 2026-07-18T21:19:43.413204
  • lfunc_lfunctions • Show schema
    {'Lhash': '3200751005903084886799530112348', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 1.7320508075688772], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, -3.4641016151377544], 'a8': [0.0, 0.0], 'a9': [-3.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.38328192970214603, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, -1.7320508075688772]]]], 'bad_primes': [2, 3], 'central_character': '48.47', 'coefficient_field': 'CDF', 'conductor': 48, 'conductor_radical': 6, 'conjugate': '4608386772293848630934601103137', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -1.7320508075688772]], [[1.0, 0], [0, 0], [-5.0, 0]], [[1.0, 0], [0, 3.4641016151377544], [-7.0, 0]], [[1.0, 0], [0, 0], [11.0, 0]], [[1.0, 0], [2.0, 0], [13.0, 0]], [[1.0, 0], [0, 0], [-17.0, 0]], [[1.0, 0], [0, -3.4641016151377544], [-19.0, 0]], [[1.0, 0], [0, 0], [23.0, 0]], 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'root_angle': -0.08333333333333334, 'root_number': '0.8660254037844386 - 0.5*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0833333333333', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.52494733590377164458054694339', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.37448383935061293331068662521', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.74418422965018797428766625394', 'prec': 103}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 0.38328192970214603, 'bad_primes': [2, 3], 'central_character': '12.11', 'conductor': 48, 'conductor_radical': 6, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/48/2/c/a/47/2'], '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': '2-48-12.11-c1-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-48-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6190976737980414, 'root_angle': -0.08333333333333334, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.52494733590377164458054694339', 'prec': 103}}
  • lfunc_instances • Show schema
    {'Lhash': '3200751005903084886799530112348', 'Lhash_array': ['3200751005903084886799530112348'], 'factors': ['2-48-12.11-c1-0-0'], 'label': '2-48-12.11-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/48/2/c/a/47/2'}