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lfunc_lfunctions • Show schema
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{'Lhash': '1822916283772419842740632055509', 'a10': [5.1789725137953, -8.97024352489617], 'a2': [-0.5619035183745328, 0.973245442776403], 'a3': [-3.0, 0.0], 'a4': [3.368528872076642, 5.834463153199427], 'a5': [-9.216835888084425, 0.0], 'a6': [1.6857105551235985, -2.919736328329209], 'a7': [2.790306215486583, 4.832952133897994], 'a8': [-16.56160919385677, 0.0], 'a9': [9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.859383911153868, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [3.0, 0]]], [67, [[1.0, 0], [-282.5855303956405, -470.0089552455512]]]], 'bad_primes': [3, 67], 'central_character': '201.163', 'coefficient_field': 'CDF', 'conductor': 201, 'conductor_radical': 201, 'conjugate': '167623299881822755558762534377', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5619035183745328, -0.973245442776403], [-4.0, -6.928203230275509]], [[1.0, 0], [3.0, 0]], [[1.0, 0], [9.216835888084425, 0], [125.0, 0]], 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0], [593.0343978501907, 1027.1657077125456], [-721448.5, 1249585.457044355]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 20, 'label': '2-201-67.29-c3-0-20', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/201/4/e/b/163/8', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.264886078639572, 0.482740532655659, 0.6646546282738548, 0.8065634903826048, 0.9045294487303549, 0.954830881571276, 0.9541747822952563, 0.9000218140909275, 0.7909997679488348, 0.6273700850859862, 0.4115028917477008, 0.14830919092544545, -0.15442508073902667, -0.48585887508879755, -0.8321217171633497, -1.176588560062057, -1.5004330427502324, -1.78346884414474, -2.005264346124161, -2.1464876254819356, -2.1904088659139282, -2.1244582861570875, -1.9417128303122422, -1.6421676549111037, 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'8.019548964761293884657465010844429', '9.772892583945704523217000023044223', '10.34117225445237412736696188106982', '11.20164175720500808192945063037221', '12.16053651483802222389853736313619'], 'prelabel': '2-201-67.29-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.443745622306309, 'root_angle': 0.5272897395250714, 'root_number': '-0.0856282578708564 + 0.9963271558348704*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.263644869763', 'prec': 47}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.43802738975883395017531410839', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.28372845044655881906793386500', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.92723041154703978296582789851', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.859383911153868, 'bad_primes': [3, 67], 'central_character': '67.29', 'conductor': 201, 'conductor_radical': 201, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/201/4/e/b/163/8'], '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': '2-201-67.29-c3-0-20', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-201-67.29-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.443745622306309, 'root_angle': 0.2636448697625357, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.43802738975883395017531410839', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1822916283772419842740632055509', 'Lhash_array': ['1822916283772419842740632055509'], 'label': '2-201-67.29-c3-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/201/4/e/b/163/8'}