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lfunc_lfunctions • Show schema
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{'Lhash': '5011176479963871683386426601201', 'a10': [-1.790399486684281, 2.606620355571686], 'a2': [-0.1630265941698591, -1.404785510173484], 'a3': [-1.6282044610619582, -0.940044283889871], 'a4': [-1.946844659186752, 0.4580347945255021], 'a5': [-1.6849298877563785, -1.4700378475894005], 'a6': [-1.055119961030798, 2.4405302524710755], 'a7': [0.6039599160623225, 2.5758944892580504], 'a8': [0.9608280966697108, 2.6602273152214004], 'a9': [0.267366511348041, 0.4630923818972478], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.1179056282979258, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.1630265941698591, 1.404785510173484]]], [5, [[1.0, 0], [1.6849298877563785, 1.4700378475894005]]], [7, [[1.0, 0], [-0.6039599160623225, -2.5758944892580504]]]], 'bad_primes': [2, 5, 7], 'central_character': '140.59', 'coefficient_field': 'CDF', 'conductor': 140, 'conductor_radical': 70, 'conjugate': 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'6.19978364568557463645230798535099', '7.43266633089005818259954943664034', '8.061226527930424063280730753240181', '10.15063180184454835613457387543233', '10.28268665595349689290749637240280', '11.66436506624502845738388595232123', '12.74298367178618259419816217532757', '14.21802440918870075896184970491053'], 'prelabel': '2-140-140.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0573105637881075, 'root_angle': -0.792186542824227, 'root_number': '-0.7943465347053258 - 0.6074648819492701*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.396093271412', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.95312121420654334453369607135', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.92926293196669225164354649440', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.19978364568557463645230798535', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.1179056282979258, 'bad_primes': [2, 5, 7], 'central_character': '140.59', 'conductor': 140, 'conductor_radical': 70, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/140/2/s/b/59/8'], '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': '2-140-140.59-c1-0-19', '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': '2-140-140.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0573105637881075, 'root_angle': -0.3960932714121135, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.95312121420654334453369607135', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '5011176479963871683386426601201', 'Lhash_array': ['5011176479963871683386426601201'], 'label': '2-140-140.59-c1-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/140/2/s/b/59/8'}