Formats: - HTML - YAML - JSON - 2026-09-08T07:44:28.455061
  • lfunc_lfunctions • Show schema
    {'Lhash': '2225694198240779843184157448966', 'a10': [-0.5, -0.8660254037844386], 'a2': [-0.5, -0.8660254037844386], 'a3': [0.0, 0.0], 'a4': [0.5, -0.8660254037844386], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.5, 2.598076211353316], 'a8': [-3.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.096325623691686, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [4.0, 1.7320508075688772]]]], 'bad_primes': [3, 19], 'central_character': '513.505', 'coefficient_field': 'CDF', 'conductor': 513, 'conductor_radical': 57, 'conjugate': '1062110064760027412981714576060', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, 0.8660254037844386], [-1.0, 1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0], [5.0, 0]], [[1.0, 0], [1.5, -2.598076211353316], [-3.5, -6.06217782649107]], [[1.0, 0], [-1.5, 2.598076211353316], [-5.5, -9.526279441628825]], [[1.0, 0], [-3.0, 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6.564862772557948, 7.261386494527277], 'positive_zeros': ['1.75576313996937568804761698360346', '3.47959918976036542031719361535362', '4.33990420847873951360144415562974', '6.13226787349324150529786119100024', '6.58985942488832300076487238506465', '7.45918675433093412309689321841346', '8.396419621598843879061991890147868', '9.422274484681160721014995885667855', '9.977551879038831302476544619923510', '11.22764068267892271213048943579608'], 'prelabel': '2-513-171.106-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.023938147200078, 'root_angle': 0.3089378683198909, 'root_number': '-0.36191147265799595 + 0.9322124682488003*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.30893786832', 'prec': 37}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.75576313996937568804761698360', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '3.47959918976036542031719361535', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '4.33990420847873951360144415563', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 4.096325623691686, 'bad_primes': [3, 19], 'central_character': '171.106', 'conductor': 513, 'conductor_radical': 57, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/513/2/g/b/505/1'], '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': '2-513-171.106-c1-0-10', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-513-171.106-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.023938147200078, 'root_angle': 0.3089378683198909, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.75576313996937568804761698360', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '2225694198240779843184157448966', 'Lhash_array': ['2225694198240779843184157448966'], 'factors': ['2-513-171.106-c1-0-10'], 'label': '2-513-171.106-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/513/2/g/b/505/1'}