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lfunc_lfunctions • Show schema
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{'Lhash': '1673101117467092965496757399464', 'a10': [11.583123951776999, 0.0], 'a2': [-2.3166247903554, 0.0], 'a3': [-5.0, 0.0], 'a4': [-2.6332495807107996, 0.0], 'a5': [-5.0, 0.0], 'a6': [11.583123951776999, 0.0], 'a7': [0.0, 0.0], 'a8': [24.6332495807108, 0.0], 'a9': [-2.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.455467951406456, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [5.0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 7], 'central_character': '245.1', 'coefficient_field': 'CDF', 'conductor': 245, 'conductor_radical': 35, 'conjugate': '1673101117467092965496757399464', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.3166247903554, 0], [8.0, 0]], [[1.0, 0], [5.0, 0], [27.0, 0]], [[1.0, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-46.2664991614216, 0], [1331.0, 0]], [[1.0, 0], [-61.332495807107996, 0], [2197.0, 0]], [[1.0, 0], [101.332495807108, 0], [4913.0, 0]], [[1.0, 0], 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'6.22942758318084413538326499999489', '7.11204992735264282915461643906759', '8.688520042377446474929939395401762', '8.882492241037928788796798324180387', '10.34679310526481175010457988521249', '11.17640015452778181744863073084668'], 'prelabel': '2-245-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.802034712020191, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.31984406205137736308868858378', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.78191278706345279968320018666', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.86943917233339096392053040151', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.455467951406456, 'bad_primes': [5, 7], 'central_character': '1.1', 'conductor': 245, 'conductor_radical': 35, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/245/4/a/i/1/1'], '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': '2-245-1.1-c3-0-18', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-245-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.802034712020191, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.31984406205137736308868858378', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1673101117467092965496757399464', 'Lhash_array': ['1673101117467092965496757399464'], 'label': '2-245-1.1-c3-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/245/4/a/i/1/1'}