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lfunc_lfunctions • Show schema
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{'Lhash': '1237005670945858517033737978778', 'a10': [0.5543054892880653, -0.32002842345375176], 'a2': [-0.4164901068804828, -0.4164901068804828], 'a3': [-1.4348928116687827, -0.9700941289489671], 'a4': [0.0, -1.653071981741368], 'a5': [-0.2812516575592303, 1.049645475724011], 'a6': [0.19358405304388365, 1.001653267944052], 'a7': [-0.25881904510252074, 0.9659258262890683], 'a8': [-1.5214683401175595, 1.5214683401175595], 'a9': [1.1178347619574895, 2.7839621845419242], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.5397479255428665, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.4348928116687827, 0.9700941289489671]]], [7, [[1.0, 0], [0.25881904510252074, -0.9659258262890683]]], [13, [[1.0, 0], [-3.082050642241485, -1.8710862723719741]]]], 'bad_primes': [3, 7, 13], 'central_character': '819.470', 'coefficient_field': 'CDF', 'conductor': 819, 'conductor_radical': 273, 'conjugate': 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['0.975825413345875012389483275741142', '3.22620381327372216702655038804839', '4.09614652088136885206718574780079', '4.95186581377479669180388663518563', '6.14065795305038159510290052238092', '6.95181555709927131596352133549514', '7.74913050546292564752668756782198', '8.977288304690913152548946642370760', '9.251547484587836383952007571657820', '10.46092044590577945138895835439486'], 'prelabel': '2-819-117.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5572930855775735, 'root_angle': 0.36590259238201733, 'root_number': '0.40892835296617047 + 0.9125664919009328*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.182951296191', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.975825413345875012389483275741', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '3.22620381327372216702655038805', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.09614652088136885206718574780', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.5397479255428665, 'bad_primes': [3, 7, 13], 'central_character': '117.2', 'conductor': 819, 'conductor_radical': 273, 'degree': 2, 'index': 31, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/819/2/ew/a/470/33'], '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': '2-819-117.2-c1-0-31', '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': '2-819-117.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5572930855775735, 'root_angle': 0.18295129619100867, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.975825413345875012389483275741', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1237005670945858517033737978778', 'Lhash_array': ['1237005670945858517033737978778'], 'label': '2-819-117.2-c1-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/819/2/ew/a/470/33'}