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lfunc_lfunctions • Show schema
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{'Lhash': '2808758439552991323199612349424', 'a10': [1.1071598716887676, 1.9176571498663846], 'a2': [-1.1071598716887676, -1.9176571498663846], 'a3': [0.5, 0.8660254037844386], 'a4': [-1.4516059629557767, 2.5142552804093508], 'a5': [-1.0, 0.0], 'a6': [1.1071598716887676, -1.9176571498663846], 'a7': [1.9182676891547494, -3.322537100133768], 'a8': [2.0, 0.0], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.5570828394149683, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.5, -0.8660254037844386]]], [5, [[1.0, 0], [1.0, 0]]], [13, [[1.0, 0], [-0.5333382738010272, 3.5658870264912967]]]], 'bad_primes': [3, 5, 13], 'central_character': '195.16', 'coefficient_field': 'CDF', 'conductor': 195, 'conductor_radical': 195, 'conjugate': '1070063857831398855965641715352', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.1071598716887676, 1.9176571498663846], [-1.0, 1.7320508075688772]], [[1.0, 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-195-13.3-c1-0-6', '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/195/2/i/e/16/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.7346840353901796, 0.8375270262228878, 0.94944946392696, 1.0716506832879058, 1.2033741851477293, 1.3418059023257718, 1.4821028787569197, 1.6174947595751157, 1.7394364302755492, 1.837823100756707, 1.9012955075187763, 1.917663751404373, 1.8744691519560823, 1.7596889493108352, 1.5625713788698323, 1.2745701025115825, 0.8903284069116211, 0.4086463202126044, -0.16665052010692344, -0.8260309432690495, -1.5538607996449512, -2.3283759716051855, -3.1220986209918418, -3.9027441041126103, -4.634630951058761, -5.280563206610515, -5.804106110018918, -6.17212656022357, 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'10.79649521973391521442938040297105', '12.15467051053215860583698753199294', '12.75884035768605959003960532479267'], 'prelabel': '2-195-13.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2478312543829668, 'root_angle': 0.7952173214641223, 'root_number': '-0.8000944002894793 + 0.5998741123147576*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.397608660732', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.21571972517292930436742978165', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.70117616664576129164671919450', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.86269997654287025339570558372', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.5570828394149683, 'bad_primes': [3, 5, 13], 'central_character': '13.3', 'conductor': 195, 'conductor_radical': 195, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/195/2/i/e/16/1'], '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': '2-195-13.3-c1-0-6', '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': '2-195-13.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2478312543829668, 'root_angle': 0.39760866073206114, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.21571972517292930436742978165', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2808758439552991323199612349424', 'Lhash_array': ['2808758439552991323199612349424'], 'label': '2-195-13.3-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/195/2/i/e/16/1'}