Formats: - HTML - YAML - JSON - 2026-08-14T22:33:12.749089
  • lfunc_lfunctions • Show schema
    {'Lhash': '3135228418275166133520523175981', 'a10': [-4135.889749451189, -1.0144046397437963e-58], 'a2': [7.115948860193663, 12.325184969917267], 'a3': [45.717188595525904, -9.845743594118039], 'a4': [-37.27345636178298, 64.55952019230952], 'a5': [-145.30352278763527, 251.67308398692646], 'a6': [446.67178704147415, 493.4109978381256], 'a7': [-555.9395946417696, -962.9156238587914], 'a8': [760.7388709571463, 0.0], 'a9': [1993.1226661577673, -900.2394335109708], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.811465229357097, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 7}, 'bad_lfactors': [[3, [[1.0, 0], [-45.717188595525904, 9.845743594118039]]]], 'bad_primes': [3], 'central_character': '9.4', 'coefficient_field': 'CDF', 'conductor': 9, 'conductor_radical': 3, 'conjugate': '4672494058135722246840804154301', 'degree': 2, 'euler_factors': [[[1.0, 0], [-7.115948860193663, -12.325184969917267], [-64.0, 110.85125168440814]], [[1.0, 0], 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'positive_zeros': ['2.47325912811518858821550330101234', '4.43771397850938260922690859734996', '8.276013555757405353068412327270679', '10.03617490511455521901862043912604', '12.32568613250580131213756304168411', '12.92381657039604754444817662013878', '14.89788919144736616683792895214623', '16.26957314914959050142803339279995', '18.87292620970793225420762467188669', '19.90104823983494680296731421902572'], 'prelabel': '2-3e2-9.4-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6767424457432623, 'root_angle': -0.1786316749102974, 'root_number': '0.4335426562654589 - 0.9011330452260033*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.17863167491', 'prec': 37}, 'spectral_label': 'c7-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.47325912811518858821550330101', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '4.43771397850938260922690859735', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '8.276013555757405353068412327271', 'prec': 103}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 2.811465229357097, 'bad_primes': [3], 'central_character': '9.4', 'conductor': 9, 'conductor_radical': 3, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9/8/c/a/4/5'], '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': '2-3e2-9.4-c7-0-2', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'prelabel': '2-3e2-9.4-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6767424457432623, 'root_angle': -0.1786316749102974, 'self_dual': False, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '2.47325912811518858821550330101', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '3135228418275166133520523175981', 'Lhash_array': ['3135228418275166133520523175981'], 'factors': ['2-3e2-9.4-c7-0-2'], 'label': '2-3e2-9.4-c7-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9/8/c/a/4/5'}