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lfunc_lfunctions • Show schema
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{'Lhash': '3672044302371143834454700481663', 'a10': [0.16602093066783216, 2.2298961972657354], 'a2': [0.5, -0.8660254037844386], 'a3': [0.6868327580795662, -2.5632947494556046], 'a4': [-0.5, -0.8660254037844386], 'a5': [-1.8481362893005266, 1.2587264421511453], 'a6': [-1.8764619913760383, -1.8764619913760383], 'a7': [0.5242098762756722, -1.9563778920902035], 'a8': [-1.0, 0.0], 'a9': [-3.500664523662171, -2.0211096050789275], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.9544648747873756, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, 0.8660254037844386]]], [5, [[1.0, 0], [1.8481362893005266, -1.2587264421511453]]], [37, [[1.0, 0], [-4.850454174971004, 3.6705713855619746]]]], 'bad_primes': [2, 5, 37], 'central_character': '370.97', 'coefficient_field': 'CDF', 'conductor': 370, 'conductor_radical': 370, 'conjugate': '1071517570472915277821684087179', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, 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[[1.0, 0], [4.261280270205152, 2.4602513110953854], [56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 17, 'label': '2-370-185.97-c1-0-17', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/370/2/q/f/97/8', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.401648693615568, 1.6332315337218057, 1.8903720178345955, 2.176790245740744, 2.4927585825892873, 2.8347359011244646, 3.195345350098284, 3.5635858881090305, 3.925220810207311, 4.263343666167459, 4.559150160842604, 4.792941337931111, 4.945358479317763, 4.998814068624673, 4.939043547614982, 4.756665126743077, 4.4486044601947645, 4.01922215236813, 3.4809790658058017, 2.8544906538489268, 2.1678589476492105, 1.4552291173764471, 0.7545937317987754, 0.10495603317237917, -0.4569450328489187, 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'8.349938394727327644285043874556512', '9.020276561213244277707391773624801', '9.636618304790533874123535940967552', '11.03327034124782536935211163381804', '11.73833110397170268186875617160553'], 'prelabel': '2-370-185.97-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7188556875978203, 'root_angle': 0.9374919121454697, 'root_number': '-0.9807803230865091 + 0.19511524247562748*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.468745956073', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.89673219238015931195200301451', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.16979849109866009857392240442', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.69815102750783855626899536155', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.9544648747873756, 'bad_primes': [2, 5, 37], 'central_character': '185.97', 'conductor': 370, 'conductor_radical': 370, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/370/2/q/f/97/8'], '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': '2-370-185.97-c1-0-17', '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': '2-370-185.97-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7188556875978203, 'root_angle': 0.46874595607273484, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.89673219238015931195200301451', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3672044302371143834454700481663', 'Lhash_array': ['3672044302371143834454700481663'], 'label': '2-370-185.97-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/370/2/q/f/97/8'}