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lfunc_lfunctions • Show schema
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{'Lhash': '755695506583810627314478831574', 'a10': [-2.080706687830873, 0.8189381412633545], 'a2': [0.8005412409243604, 0.599277666511347], 'a3': [-1.199046331634375, 0.44722115969031506], 'a4': [0.28173255684142967, 0.9594929736144974], 'a5': [-1.1749201755623, 1.9025148044250941], 'a6': [-1.2278956912460952, -0.36054270551472245], 'a7': [-4.1011578761213165, -0.8921522872345052], 'a8': [-0.3494641795990983, 0.9369497249997617], 'a9': [-1.0295433833316738, 0.8921044199239687], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.8365592464894498, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8005412409243604, -0.599277666511347]]], [5, [[1.0, 0], [1.1749201755623, -1.9025148044250941]]], [23, [[1.0, 0], [4.754479208033352, -0.6284325424248388]]]], 'bad_primes': [2, 5, 23], 'central_character': '230.43', 'coefficient_field': 'CDF', 'conductor': 230, 'conductor_radical': 230, 'conjugate': 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[32.817786027149026, 71.86092763300695]], [[1.0, 0], [9.402178991486775, 0.672457113199601], [82.15517967611741, 11.812131576682667]], [[1.0, 0], [-1.0692435611977038, 2.3413168124663364], [-58.28260532113037, -67.26171211752899]], [[1.0, 0], [0.46054681965416605, -0.03293895863058069], [96.01267986245047, -13.804539312508659]], [[1.0, 0], [-1.105098920798866, -1.2753521408765272], [-14.373798665601798, 99.9719656299742]], [[1.0, 0], [-1.744574776048834, -2.3304790652948983], [-29.01845335466726, 98.82777628229323]], [[1.0, 0], [0.2663394854382005, -0.714083795152274], [-80.86520445590564, -70.07009853214551]], [[1.0, 0], [7.547115847801918, 2.2160331581896453], [91.69663507859875, 58.929849102660135]], [[1.0, 0], [-9.05110221252003, -6.775570246714117], [31.835778923081556, 108.4227060184382]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-230-115.43-c1-0-0', '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/230/2/l/a/43/8', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.8072266132672066, 0.6444957498410727, 0.48438755011082424, 0.3198856501169446, 0.14481672354137246, -0.045454640805280375, -0.2535536574928909, -0.47981357789408474, -0.7221333093754504, -0.975942688547648, -1.2342725246116906, -1.487947184275887, -1.7259251202742518, -1.935808862433975, -2.1045336073472405, -2.219225376242489, -2.26819803434955, -2.2420354361278783, -2.134682896347666, -1.944453655008827, -1.6748437330041388, -1.3350452240656965, -0.9400558998090698, -0.5103035108411218, -0.07073669698694941, 0.3506201345223213, 0.7245960057536137, 1.0231753762643958, 1.222003622891264, 1.3028768086545712, 1.255962358898167, 1.0814856629232665, 0.7906341414984327, 0.4054780571822047, -0.04221391962772667, -0.5132807759401647, 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'rational': False, 'root_analytic_conductor': 1.355197124587213, 'root_angle': -0.42648836256015965, 'root_number': '-0.8952130655544006 - 0.44563838171851006*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.42648836256', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.59613864139515593806353628792', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.02038787859571899858105775647', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.23865796289510395256874135390', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.8365592464894498, 'bad_primes': [2, 5, 23], 'central_character': '115.43', 'conductor': 230, 'conductor_radical': 230, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/230/2/l/a/43/8'], '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': '2-230-115.43-c1-0-0', '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': '2-230-115.43-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.355197124587213, 'root_angle': -0.42648836256015965, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.59613864139515593806353628792', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '755695506583810627314478831574', 'Lhash_array': ['755695506583810627314478831574'], 'factors': ['2-230-115.43-c1-0-0'], 'label': '2-230-115.43-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/230/2/l/a/43/8'}