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lfunc_lfunctions • Show schema
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{'Lhash': '1753614576255054759703949023651', 'a10': [-1.8843671526381416, 3.263819648483159], 'a2': [-0.5, 0.8660254037844386], 'a3': [-1.3008395659415772, 2.2531202207066565], 'a4': [0.5, 0.8660254037844386], 'a5': [3.768734305276283, 0.0], 'a6': [-1.3008395659415772, -2.2531202207066565], 'a7': [-0.08352758669656445, -0.14467402399206386], 'a8': [-3.0, 0.0], 'a9': [-1.8843671526381416, -3.263819648483159], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.14186074890431, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [0.5, -0.8660254037844386]]], [13, [[1.0, 0], [-0.19916043405842287, 3.6000465443526783]]]], 'bad_primes': [11, 13], 'central_character': '143.100', 'coefficient_field': 'CDF', 'conductor': 143, 'conductor_radical': 143, 'conjugate': '3698051811045128719988613778344', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, -0.8660254037844386], [-1.0, -1.7320508075688772]], [[1.0, 0], [1.3008395659415772, 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'group': 'GL2', 'index': 4, 'label': '2-143-13.9-c1-0-4', '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/143/2/e/a/100/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.9572176437698836, 0.8751832370801746, 0.8022951889964893, 0.7339984713389017, 0.6658221084572046, 0.5938572448288912, 0.5151209956154655, 0.42781331994392396, 0.33149961721839616, 0.2272474852826698, 0.11772867266158717, 0.007280031759089294, -0.09809427115640806, -0.19080233827106274, -0.26184908258082, -0.30114491714288766, -0.29795043565606905, -0.2414587353765024, -0.1215044895298671, 0.07062535582682046, 0.34131938573546783, 0.6937627090545724, 1.127118497328364, 1.6358465853154436, 2.2092396517252295, 2.831254850763872, 3.4807083172978666, 4.1318811248414695, 4.755558183000116, 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'11.62569672545782006515828101109011', '12.72826992280505370952037309872463'], 'prelabel': '2-143-13.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0685788454317773, 'root_angle': -0.730367559166666, 'root_number': '-0.6621775933786469 - 0.749346938892302*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.365183779583', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.38335798203332353205906776523', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.33448561716203863438677919592', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.45577233419780419919168320201', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.14186074890431, 'bad_primes': [11, 13], 'central_character': '13.9', 'conductor': 143, 'conductor_radical': 143, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/143/2/e/a/100/1'], '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': '2-143-13.9-c1-0-4', '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': '2-143-13.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0685788454317773, 'root_angle': -0.365183779583333, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.38335798203332353205906776523', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1753614576255054759703949023651', 'Lhash_array': ['1753614576255054759703949023651'], 'label': '2-143-13.9-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/143/2/e/a/100/1'}