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lfunc_lfunctions • Show schema
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{'Lhash': '2010848113245862062889560802207', 'a10': [0.0, 1.0], 'a2': [-1.0, 0.0], 'a3': [-1.717309057610091, 0.2254985601957181], 'a4': [1.0, 0.0], 'a5': [0.0, -1.0], 'a6': [1.717309057610091, -0.2254985601957181], 'a7': [-0.6319888614806616, 0.0], 'a8': [-1.0, 0.0], 'a9': [2.8983007986993163, -0.7745014398042819], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.551472915212984, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [3, [[1.0, 0], [1.717309057610091, -0.2254985601957181]]], [5, [[1.0, 0], [0, 1.0]]], [19, [[1.0, 0], [2.434618115220182, 3.615609856309407]]]], 'bad_primes': [2, 3, 5, 19], 'central_character': '570.341', 'coefficient_field': 'CDF', 'conductor': 570, 'conductor_radical': 570, 'conjugate': '311269249438364280384300763037', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [1.717309057610091, -0.2254985601957181]], [[1.0, 0], [0, 1.0]], [[1.0, 0], 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['1.58627946287709440635346184145010', '3.16892241757326770472515507586115', '4.69727786318148801179807807166160', '5.78319576064876051973982060350557', '6.68822648906559804995211891890881', '7.38086915380182795400383525157124', '8.336763995504134748605021603835046', '9.679531477130327354710608079753176', '10.16252454680131926104099513450501', '10.96751690022756813056253123712838'], 'prelabel': '2-570-57.56-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.133418129484463, 'root_angle': 0.7698025786106373, 'root_number': '-0.749700768135178 + 0.6617769701776605*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.384901289305', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.58627946287709440635346184145', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.16892241757326770472515507586', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.69727786318148801179807807166', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.551472915212984, 'bad_primes': [2, 3, 5, 19], 'central_character': '57.56', 'conductor': 570, 'conductor_radical': 570, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/570/2/f/c/341/2'], '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': '2-570-57.56-c1-0-14', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-570-57.56-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.133418129484463, 'root_angle': 0.38490128930531864, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.58627946287709440635346184145', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2010848113245862062889560802207', 'Lhash_array': ['2010848113245862062889560802207'], 'label': '2-570-57.56-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/570/2/f/c/341/2'}