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lfunc_lfunctions • Show schema
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{'Lhash': '1485439510205620363224900952866', 'a10': [-1.1310571369179996, -2.953084785952963], 'a2': [-1.3903253710379353, 0.2588346241294378], 'a3': [0.7071067811865476, 0.7071067811865476], 'a4': [1.8660092747035453, -0.7197286896604502], 'a5': [0.4040884214780632, 2.1992527248198117], 'a6': [-1.1661322158444234, -0.8000847799888302], 'a7': [1.815673855645715, 0.0], 'a8': [-2.408069332349, 1.4836448667387494], 'a9': [0.0, 1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.9164096485107303, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.3903253710379353, -0.2588346241294378]]], [3, [[1.0, 0], [-0.7071067811865476, -0.7071067811865476]]], [5, [[1.0, 0], [-0.4040884214780632, -2.1992527248198117]]]], 'bad_primes': [2, 3, 5], 'central_character': '240.229', 'coefficient_field': 'CDF', 'conductor': 240, 'conductor_radical': 30, 'conjugate': '2567003189965074097083199132398', 'degree': 2, 'euler_factors': 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-0.4171948438915308, 'root_number': '0.25721591172007163 - 0.9663539593534102*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.208597421946', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.17180515667186208380048204019', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.58144907407042171533325302707', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.48202575580082726764731411455', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.9164096485107303, 'bad_primes': [2, 3, 5], 'central_character': '80.69', 'conductor': 240, 'conductor_radical': 30, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/240/2/bl/a/229/2'], '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': '2-240-80.69-c1-0-5', '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': '2-240-80.69-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.384344483324411, 'root_angle': -0.2085974219457654, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.17180515667186208380048204019', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1485439510205620363224900952866', 'Lhash_array': ['1485439510205620363224900952866'], 'label': '2-240-80.69-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/240/2/bl/a/229/2'}