Formats: - HTML - YAML - JSON - 2026-09-23T03:32:29.153894
  • lfunc_lfunctions • Show schema
    {'Lhash': '1075343677049522287313526273038,2287235975771527172454371593798', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5164630229397681, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, 0, 1]]], 'bad_primes': [2, 3, 5], 'central_character': '1440.1', 'coefficient_field': '1.1.1.1', 'conductor': 2073600, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1], [1], [1, 0, 1], [1, 0, 0, 0, 1], [1, 0, 2, 0, 1], [1, 2, 2, 2, 1], [1, -2, 2, -2, 1], [1, 0, -2, 0, 1], [1, 0, 0, 0, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, -2, 2, -2, 1], [1, 0, 2, 0, 1], [1, 0, 0, 0, 1], [1, 0, 0, 0, 1], [1, 2, 2, 2, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, 0, 0, 0, 1], [1, 0, 2, 0, 1], [1, -2, 2, -2, 1], [1, 0, -2, 0, 1], [1, 0, 0, 0, 1], [1, 0, -2, 0, 1], [1, -2, 2, -2, 1], [1, -4, 6, -4, 1], [1, 0, 0, 0, 1], [1, 0, 0, 0, 1], [1, 0, 2, 0, 1], [1, -2, 2, -2, 1]], 'euler_factors_factorization': [[1], [1], [[[1, 0, 1], 1]], [[[1, 0, 0, 0, 1], 1]], [[[1, 0, 1], 2]], [[[1, 1], 2], [[1, 0, 1], 1]], [[[1, -1], 2], [[1, 0, 1], 1]], [[[1, -1], 2], [[1, 1], 2]], [[[1, 0, 0, 0, 1], 1]], [[[1, -1], 2], [[1, 1], 2]], [[[1, 0, 1], 2]], [[[1, -1], 2], [[1, 0, 1], 1]], [[[1, 0, 1], 2]], [[[1, 0, 0, 0, 1], 1]], [[[1, 0, 0, 0, 1], 1]], [[[1, 1], 2], [[1, 0, 1], 1]], [[[1, -1], 2], [[1, 1], 2]], [[[1, 0, 1], 2]], [[[1, 0, 0, 0, 1], 1]], [[[1, 0, 1], 2]], [[[1, -1], 2], [[1, 0, 1], 1]], [[[1, -1], 2], [[1, 1], 2]], [[[1, 0, 0, 0, 1], 1]], [[[1, -1], 2], [[1, 1], 2]], [[[1, -1], 2], [[1, 0, 1], 1]], [[[1, -1], 4]], [[[1, 0, 0, 0, 1], 1]], [[[1, 0, 0, 0, 1], 1]], [[[1, 0, 1], 2]], [[[1, -1], 2], [[1, 0, 1], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 0, 'label': '4-1440e2-1.1-c0e2-0-0', 'leading_term': '1.00717197338149604157781673713949610806102471731917166876536025000000000000000000000000000', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 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{'__RealLiteral__': 0, 'data': '2.38113606625636665596598092352', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 0.5164630229397681, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 2073600, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0], 'euler11': [1, 0, 2, 0, 1], 'euler13': [1, 2, 2, 2, 1], 'euler17': [1, -2, 2, -2, 1], 'euler19': [1, 0, -2, 0, 1], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 0, 0, 1], 'euler29': [1, 0, -2, 0, 1], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, 2, 0, 1], 'euler37': [1, -2, 2, -2, 1], 'euler41': [1, 0, 2, 0, 1], 'euler43': [1, 0, 0, 0, 1], 'euler47': [1, 0, 0, 0, 1], 'euler5': [1, 0, 1, 0, 0], 'euler53': [1, 2, 2, 2, 1], 'euler59': [1, 0, -2, 0, 1], 'euler61': [1, 0, 2, 0, 1], 'euler67': [1, 0, 0, 0, 1], 'euler7': [1, 0, 0, 0, 1], 'euler71': [1, 0, 2, 0, 1], 'euler73': [1, -2, 2, -2, 1], 'euler79': [1, 0, -2, 0, 1], 'euler83': [1, 0, 0, 0, 1], 'euler89': [1, 0, -2, 0, 1], 'euler97': [1, -2, 2, -2, 1], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, 1, 0, 0], [1, 0, 0, 0, 1], [1, 0, 2, 0, 1], [1, 2, 2, 2, 1], [1, -2, 2, -2, 1], [1, 0, -2, 0, 1], [1, 0, 0, 0, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, -2, 2, -2, 1], [1, 0, 2, 0, 1], [1, 0, 0, 0, 1], [1, 0, 0, 0, 1], [1, 2, 2, 2, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, 0, 0, 0, 1], [1, 0, 2, 0, 1], [1, -2, 2, -2, 1], [1, 0, -2, 0, 1], [1, 0, 0, 0, 1], [1, 0, -2, 0, 1], [1, -2, 2, -2, 1]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1440/1/bh/b'], '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': '4-1440e2-1.1-c0e2-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0], 'nu_real_doubled': [0, 0], 'order_of_vanishing': 0, 'prelabel': '4-1440e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.8477344030954056, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e2-0', 'trace_hash': 854958978964053772, 'z1': {'__RealLiteral__': 0, 'data': '0.848296586500977528890620058934', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1075343677049522287313526273038,2287235975771527172454371593798', 'Lhash_array': ['1075343677049522287313526273038', '2287235975771527172454371593798'], 'factors': ['2-1440-5.2-c0-0-0', '2-1440-5.3-c0-0-2'], 'label': '4-1440e2-1.1-c0e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1440/1/bh/b'}