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lfunc_lfunctions • Show schema
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{'Lhash': '1762443880712440502059628090658', 'a10': [0.0, 0.0], 'a2': [0.9588153640963352, 0.0], 'a3': [-0.8993422462520215, 0.0], 'a4': [-1.0806730975728123, 0.0], 'a5': [0.0, 0.0], 'a6': [-0.8623031632873479, 0.0], 'a7': [0.7616454095393694, 0.0], 'a8': [-2.9537966977110606, 0.0], 'a9': [-2.191183524106368, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 24.15474661143733, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 11], 'central_character': '3025.1', 'coefficient_field': 'CDF', 'conductor': 3025, 'conductor_radical': 55, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.9588153640963352, 0], [2.0, 0]], [[1.0, 0], [0.8993422462520215, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.7616454095393694, 0], [7.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.2581865760139292, 0], [13.0, 0]], [[1.0, 0], [-0.782845389267868, 0], [17.0, 0]], [[1.0, 0], 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'4.63915519498066382880102423436376', '5.19037294505689481400629216363540', '5.97244188184095116515910095475852', '6.43095899002244517006821628046659', '7.68371565313522279119697768287141', '8.374044450960680278384772606386534'], 'prelabel': '2-55e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.914747868552092, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.39032307514004876322652223127', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.97363365110048232926336205414', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.56029034501942871247333548526', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 24.15474661143733, 'bad_primes': [5, 11], 'central_character': '1.1', 'conductor': 3025, 'conductor_radical': 55, 'degree': 2, 'index': 106, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3025/2/a/bi/1/7'], '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': '2-55e2-1.1-c1-0-106', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-55e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.914747868552092, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.39032307514004876322652223127', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1762443880712440502059628090658', 'Lhash_array': ['1762443880712440502059628090658'], 'label': '2-55e2-1.1-c1-0-106', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3025/2/a/bi/1/7'}