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lfunc_lfunctions • Show schema
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{'Lhash': '2919964342905162429907195000640', 'a10': [3.5642964526484384, -2.5367189571488074], 'a2': [0.0, -1.9564842074456095], 'a3': [0.0, -2.374411991745167], 'a4': [-1.8278304539840746, 0.0], 'a5': [1.2965701166894434, 1.8217864673193516], 'a6': [-4.645499563818894, 0.0], 'a7': [0.0, -0.10548115418746036], 'a8': [0.0, -0.33684699778323834], 'a9': [-2.637832306543251, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.028705352606672, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-1.2965701166894434, -1.8217864673193516]]], [151, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [5, 151], 'central_character': '755.454', 'coefficient_field': 'CDF', 'conductor': 755, 'conductor_radical': 755, 'conjugate': '750569669652623041872559623173', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.9564842074456095], [-2.0, 0]], [[1.0, 0], [0, 2.374411991745167], [-3.0, 0]], [[1.0, 0], [-1.2965701166894434, -1.8217864673193516]], 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-0.1613359652103734, 0.23754042368286227], 'positive_zeros': ['2.30344571475724335479193053624956', '4.13076391829023292831830808739423', '4.81549028704613558768175132585414', '5.48283156288264770024786769912931', '6.33869695206672308289244071646711', '7.47302252010540429260970160665839', '8.429122148026983952915657287650564', '9.153768137315088015664788482040276', '9.680706959171208510698098855587795', '10.68760554063911794556980808905427'], 'prelabel': '2-755-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4553422068230475, 'root_angle': -0.6968864220423648, 'root_number': '-0.5798437837024859 - 0.814727676283054*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.348443211021', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.30344571475724335479193053625', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.13076391829023292831830808739', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.81549028704613558768175132585', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.028705352606672, 'bad_primes': [5, 151], 'central_character': '5.4', 'conductor': 755, 'conductor_radical': 755, 'degree': 2, 'index': 67, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/755/2/b/d/454/9'], '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': '2-755-5.4-c1-0-67', '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': '2-755-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4553422068230475, 'root_angle': -0.3484432110211824, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.30344571475724335479193053625', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2919964342905162429907195000640', 'Lhash_array': ['2919964342905162429907195000640'], 'label': '2-755-5.4-c1-0-67', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/755/2/b/d/454/9'}