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lfunc_lfunctions • Show schema
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{'Lhash': '1537683213883368036657185548835', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.9364173644786657, -1.4570938609104185], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.5029892835187904, 5.2675420908885675], 'a8': [0.0, 0.0], 'a9': [-1.2462450390056592, -2.7288959860635553], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.419972322510946, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-0.9364173644786657, 1.4570938609104185]]], [67, [[1.0, 0], [-3.5692984957949854, 7.366146091947651]]]], 'bad_primes': [2, 3, 67], 'central_character': '804.353', 'coefficient_field': 'CDF', 'conductor': 804, 'conductor_radical': 402, 'conjugate': '1596321884823510154605774251909', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.9364173644786657, 1.4570938609104185]], [[1.0, 0], [0, 0], [-4.7974648680724865, 1.4086627842071484]], [[1.0, 0], [0.5029892835187904, 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109.81470722056021]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 11, 'label': '2-804-201.152-c1-0-11', '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/804/2/ba/a/353/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.9340757802499884, 1.9383464734741878, 1.9196023856707487, 1.8701029771847026, 1.7788920745890948, 1.6337534842150927, 1.4233940995363745, 1.1395631536871746, 0.7789328125340139, 0.3446178723082255, -0.15278961825474224, -0.6948122079136948, -1.25544669981671, -1.8023990364019622, -2.299230470169094, -2.708347466940627, -2.9946434901391825, -3.1294723879792032, -3.0945207125795795, -2.885071637433506, -2.512136544474274, -2.002987306843363, -1.399759815487702, -0.7560128619657905, -0.13139820113405223, 0.41510372000697066, 0.8326443485078575, 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'8.729886575074537345962170781044470', '9.581710769461863285729440660938141', '10.20576713426313346301491724710067'], 'prelabel': '2-804-201.152-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.533766430141292, 'root_angle': 0.101674063651684, 'root_number': '0.9494181807303314 + 0.3140145189297908*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0508370318258', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.21301817204718841709713289958', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.02804534073877247561669024329', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.12128796947432618383429084398', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.419972322510946, 'bad_primes': [2, 3, 67], 'central_character': '201.152', 'conductor': 804, 'conductor_radical': 402, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/804/2/ba/a/353/1'], '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': '2-804-201.152-c1-0-11', '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': '2-804-201.152-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.533766430141292, 'root_angle': 0.050837031825842, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.21301817204718841709713289958', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1537683213883368036657185548835', 'Lhash_array': ['1537683213883368036657185548835'], 'label': '2-804-201.152-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/804/2/ba/a/353/1'}