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lfunc_lfunctions • Show schema
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{'Lhash': '1750926672458187064971457526100', 'a10': [2.106635446053043, 1.7676770258080934], 'a2': [0.766044443118978, -0.6427876096865394], 'a3': [1.6463272029847453, 0.5992140977491794], 'a4': [0.17364817766693036, -0.984807753012208], 'a5': [0.477535487009408, 2.7082383256987446], 'a6': [1.6463272029847453, -0.5992140977491794], 'a7': [-1.9174134779619656, 3.3210575629474723], 'a8': [-0.5, -0.8660254037844386], 'a9': [0.05320239498927743, 0.044642110013250656], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.3377468044895218, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.766044443118978, 0.6427876096865394]]], [11, [[1.0, 0], [-0.5, -0.8660254037844386]]], [19, [[1.0, 0], [2.8469167056832863, -3.3007673760659695]]]], 'bad_primes': [2, 11, 19], 'central_character': '418.177', 'coefficient_field': 'CDF', 'conductor': 418, 'conductor_radical': 418, 'conjugate': '3047820136928961472059750428964', 'degree': 2, 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0, 'data': '-0.0787610655055', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.38123759981097948775621202023', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.26892475659701790097431772230', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.07525903551322820667774907700', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.3377468044895218, 'bad_primes': [2, 11, 19], 'central_character': '19.6', 'conductor': 418, 'conductor_radical': 418, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/418/2/j/d/177/4'], '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': '2-418-19.6-c1-0-6', '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': '2-418-19.6-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8269501373845762, 'root_angle': -0.07876106550548555, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.38123759981097948775621202023', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1750926672458187064971457526100', 'Lhash_array': ['1750926672458187064971457526100'], 'label': '2-418-19.6-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/418/2/j/d/177/4'}