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lfunc_lfunctions • Show schema
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{'Lhash': '2955916279242664254365620441211', 'a10': [2.8294856768758665, -1.7835689536052088], 'a2': [0.6790795724897525, 1.3327687030423347], 'a3': [-2.328573443469295, -1.1864674304644824], 'a4': [-0.13955284545133564, 0.19207801342952624], 'a5': [-0.20364466910457948, -2.226775437430835], 'a6': [4.372999309135092e-61, -3.909155603644231], 'a7': [1.6362581126122084, -0.2591578253925667], 'a8': [2.6040079248794816, 0.41243433778269384], 'a9': [2.251193561200039, 3.0985021171168503], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.2376812313298466, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0.20364466910457948, 2.226775437430835]]], [31, [[1.0, 0], [-4.649924840314755, -3.062384525075811]]]], 'bad_primes': [5, 31], 'central_character': '155.23', 'coefficient_field': 'CDF', 'conductor': 155, 'conductor_radical': 155, 'conjugate': '1510795297742854994387549020348', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'0.8920208068039176 + 0.45199433650089893*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0746436407806', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.33180679180089323183135397076', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.17764179931994912581315307526', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.85333095171432082398273390584', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.2376812313298466, 'bad_primes': [5, 31], 'central_character': '155.23', 'conductor': 155, 'conductor_radical': 155, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/155/2/r/a/23/11'], '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': '2-155-155.23-c1-0-8', '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': '2-155-155.23-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1125112275073212, 'root_angle': 0.07464364078060225, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.33180679180089323183135397076', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2955916279242664254365620441211', 'Lhash_array': ['2955916279242664254365620441211'], 'label': '2-155-155.23-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/155/2/r/a/23/11'}