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lfunc_lfunctions • Show schema
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{'Lhash': '3542956945445094804265673014717', 'a10': [-34.53674665295593, -83.37908216980979], 'a2': [3.437715134911702, -3.437715134911702], 'a3': [0.0, 0.0], 'a4': [0.0, -15.635770697601963], 'a5': [7.103895116386423, -17.1503199356561], 'a6': [0.0, 0.0], 'a7': [5.36561071565564, 12.953730160150254], 'a8': [-26.24960449386155, -26.24960449386155], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.027292230878318, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [-56.05660666281031, 42.079173583270034]]]], 'bad_primes': [3, 17], 'central_character': '153.145', 'coefficient_field': 'CDF', 'conductor': 153, 'conductor_radical': 51, 'conjugate': '1642256222786455731702130762832', 'degree': 2, 'euler_factors': [[[1.0, 0], [-3.437715134911702, 3.437715134911702], [0, -8.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-7.103895116386423, 17.1503199356561], [-88.38834764831844, 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'5.51655969753273430533218379291527', '6.35536631580808082245743513053630', '7.28629006142288597686087829547487', '8.116209186628264530245146178848657', '10.14537119001287666829286955964279', '10.81855958100183973251856756904816', '12.27360176497015209573288861989635', '13.46645264014564476271029436452158'], 'prelabel': '2-153-17.9-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.004545261912078, 'root_angle': 0.7802227851739939, 'root_number': '-0.7709591872373639 + 0.6368845512448101*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.390111392587', 'prec': 47}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.79490022314288842611266018592', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.00023650876041296610517886531', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.51655969753273430533218379292', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.027292230878318, 'bad_primes': [3, 17], 'central_character': '17.9', 'conductor': 153, 'conductor_radical': 51, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/153/4/l/a/145/3'], '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': '2-153-17.9-c3-0-19', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-153-17.9-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.004545261912078, 'root_angle': 0.39011139258699695, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.79490022314288842611266018592', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3542956945445094804265673014717', 'Lhash_array': ['3542956945445094804265673014717'], 'label': '2-153-17.9-c3-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/153/4/l/a/145/3'}