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lfunc_lfunctions • Show schema
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{'Lhash': '2480567780832775064042028354224', 'a10': [-1.0258230917681992, -1.7767777145199122], 'a2': [-0.3959289259707918, -0.6857690159675882], 'a3': [0.6591414397448032, 1.601727992641431], 'a4': [0.6864805711592304, -1.1890192276566893], 'a5': [2.590927372262454, 0.0], 'a6': [0.8374422670604532, -1.0861892203411272], 'a7': [-0.3730879538324292, 0.6462072917296791], 'a8': [-2.670905764838727, 0.0], 'a9': [-2.131065124822296, 2.111530590298453], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.3654418745638952, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.6591414397448032, -1.601727992641431]]], [19, [[1.0, 0], [-3.8939938582129288, -1.9587781477747779]]]], 'bad_primes': [3, 19], 'central_character': '171.106', 'coefficient_field': 'CDF', 'conductor': 171, 'conductor_radical': 57, 'conjugate': '2562062602380888569675817711681', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.3959289259707918, 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'8.732089901467421455345160288052368', '9.272190597476128013432112450572317', '10.92148081377030961061609655233102', '11.93471836719889990382803022883502', '12.97772842025074563663931467926469'], 'prelabel': '2-171-171.106-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1685212341091176, 'root_angle': 0.05428766259769105, 'root_number': '0.9854916147363465 + 0.16972412110347918*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0271438312988', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.95682294504981935436964407910', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.41079853015847432658914766786', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.78630243014799546697249862588', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.3654418745638952, 'bad_primes': [3, 19], 'central_character': '171.106', 'conductor': 171, 'conductor_radical': 57, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/171/2/g/c/106/6'], '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': '2-171-171.106-c1-0-9', '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': '2-171-171.106-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1685212341091176, 'root_angle': 0.027143831298845525, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.95682294504981935436964407910', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2480567780832775064042028354224', 'Lhash_array': ['2480567780832775064042028354224'], 'label': '2-171-171.106-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/171/2/g/c/106/6'}