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lfunc_lfunctions • Show schema
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{'Lhash': '1550159088529971197375661220131', 'a10': [-3.3998398409808823, 1.23744050338938], 'a2': [0.9396926207859084, 0.3420201433256687], 'a3': [-0.21464095176528675, -1.2172893274919125], 'a4': [0.766044443118978, 0.6427876096865394], 'a5': [-2.771574832097448, 2.3256274193932005], 'a6': [0.21464095176528675, -1.2172893274919125], 'a7': [1.618033988749895, -2.802517076888147], 'a8': [0.5, 0.8660254037844386], 'a9': [1.3833552937067208, -0.5035001503238263], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.765199025936447, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.9396926207859084, -0.3420201433256687]]], [19, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 19], 'central_character': '722.99', 'coefficient_field': 'CDF', 'conductor': 722, 'conductor_radical': 38, 'conjugate': '1595999411664157105445930188161', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.9396926207859084, -0.3420201433256687]], [[1.0, 0], 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[-83.63264324994584, -30.439792755984517]], [[1.0, 0], [8.098302944910424, 2.947541220017724], [74.30631098254086, 62.35039813959431]], [[1.0, 0], [2.712043140886599, -15.380760958929077], [-94.90895469937675, -34.544034475892545]], [[1.0, 0], [7.326237921249264, 12.68941630794152], [-51.5, 89.20061658979718]], [[1.0, 0], [4.708203932499369, -8.154848423484497], [-53.5, -92.66471820493493]], [[1.0, 0], [8.452872864983615, -7.0928025033961895], [18.927651365695407, -107.34404507833068]], [[1.0, 0], [9.854101966249685, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 14, 'label': '2-722-19.4-c1-0-14', '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/722/2/e/q/99/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.070358207725154, 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'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.22285990181433165721710624350', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.04547317561988738218934204925', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.13264707632212056300595588076', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.765199025936447, 'bad_primes': [2, 19], 'central_character': '19.4', 'conductor': 722, 'conductor_radical': 38, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/722/2/e/q/99/1'], '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': '2-722-19.4-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': '2-722-19.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.401082886102945, 'root_angle': -0.012576317548384237, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.22285990181433165721710624350', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1550159088529971197375661220131', 'Lhash_array': ['1550159088529971197375661220131'], 'label': '2-722-19.4-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/722/2/e/q/99/1'}