Formats: - HTML - YAML - JSON - 2026-08-11T23:59:08.161678
  • lfunc_lfunctions • Show schema
    {'Lhash': '2145251094588912338457430584434', 'a10': [27.293785387156422, 0], 'a2': [-2.7293785387156424, 4.72742230214359], 'a3': [0, 0], 'a4': [-10.89901441520307, -18.877646719557312], 'a5': [-2.5, -4.330127018922194], 'a6': [0, 0], 'a7': [5.903257858452785, -10.224742541020467], 'a8': [75.32008753258042, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 23.89577355232496, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 7}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [2.5, 4.330127018922194]]]], 'bad_primes': [3, 5], 'central_character': '405.136', 'coefficient_field': 'CDF', 'conductor': 405, 'conductor_radical': 15, 'conjugate': '182258792838941754805319317238', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.7293785387156424, -4.72742230214359], [-4.0, -6.928203230275509]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.5, 4.330127018922194]], [[1.0, 0], [-5.903257858452785, 10.224742541020467], [-171.5, -297.04671349806245]], 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'10.15571800033788564991915020000692', '11.09713299437413921032792824206279'], 'prelabel': '2-405-9.7-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.8883303440259604, 'root_angle': 0.2777777777777778, 'root_number': '-0.1736481776669303488517166267693147960003756771840693873 + 0.9848077530122080593667430245895230136706432517198424188*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.2777777777777778', 'prec': 54}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.69230472040377580775777739907', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.42568079306610098152788029925', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.86097591586383647691639689788', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 23.89577355232496, 'bad_primes': [3, 5], 'central_character': '9.7', 'conductor': 405, 'conductor_radical': 15, 'degree': 2, 'index': 40, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/405/4/e/q/136/1'], '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': '2-405-9.7-c3-0-40', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-405-9.7-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.8883303440259604, 'root_angle': 0.2777777777777778, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.69230472040377580775777739907', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '2145251094588912338457430584434', 'Lhash_array': ['2145251094588912338457430584434'], 'factors': ['2-405-9.7-c3-0-40'], 'label': '2-405-9.7-c3-0-40', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/405/4/e/q/136/1'}