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lfunc_lfunctions • Show schema
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{'Lhash': '472527532129169577632202026651', 'a10': [-2.6623004110726667, 7.229949724389427e-62], 'a2': [-1.3311502055363333, 2.305619788494683], 'a3': [0.3974945724953006, 1.6858226670788297], 'a4': [-2.543921739398845, -4.406201703117792], 'a5': [0.5, 0.8660254037844386], 'a6': [-4.41599108298653, -1.327611837615394], 'a7': [-0.7233692971714146, 1.2529123753362799], 'a8': [8.220766962931142, 0.0], 'a9': [-2.6839961296735564, 1.3402107207067737], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.671248518244905, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.3974945724953006, -1.6858226670788297]]], [5, [[1.0, 0], [-0.5, -0.8660254037844386]]], [13, [[1.0, 0], [0.5, 0.8660254037844386]]]], 'bad_primes': [3, 5, 13], 'central_character': '585.196', 'coefficient_field': 'CDF', 'conductor': 585, 'conductor_radical': 195, 'conjugate': '3064897527905619654357477039969', 'degree': 2, 'euler_factors': [[[1.0, 0], 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[-7.756732538137822, -13.435054856777402], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-585-9.7-c1-0-5', '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/585/2/i/h/196/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.4900906419437503, 0.30371528606023024, 0.14052743608929738, -0.002390653387095024, -0.12546383616335638, -0.22664166903364302, -0.3019415223304622, -0.3463508364971683, -0.3549284323400101, -0.3239738828360524, -0.2521511029654515, -0.14145156747820437, 0.0021260882204221887, 0.16830683101786315, 0.3427951876893649, 0.5081378604555158, 0.6452178859786141, 0.7353278784693638, 0.7626783909784762, 0.7171022777043721, 0.5966308546991103, 0.40955819976715097, 0.17559154671154578, -0.07427873188717157, 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'5.19126652853948179884469411770055', '6.64155857590913126521941469446161', '7.87495180836221416866486066411113', '8.439753367915034478112092914864585', '9.071095806316538194758248788467017', '10.21776449130217465444863662987415'], 'prelabel': '2-585-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': 0.40814155986034123, 'root_number': '0.2845929572130675 + 0.9586484489658976*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.20407077993', 'prec': 44}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.37275849673726745289202299225', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.49830497678016125634671969876', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.83754714555895636909729542633', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.671248518244905, 'bad_primes': [3, 5, 13], 'central_character': '9.7', 'conductor': 585, 'conductor_radical': 195, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/585/2/i/h/196/1'], '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': '2-585-9.7-c1-0-5', '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': '2-585-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': 0.20407077993017061, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.37275849673726745289202299225', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '472527532129169577632202026651', 'Lhash_array': ['472527532129169577632202026651'], 'label': '2-585-9.7-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/2/i/h/196/1'}