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lfunc_lfunctions • Show schema
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{'Lhash': '2803174892666524198418705700620', 'a10': [0.5107963250361076, -0.884725187282005], 'a2': [0.9396926207859084, 0.3420201433256687], 'a3': [0.0, 0.0], 'a4': [0.766044443118978, 0.6427876096865394], 'a5': [0.17739770200297025, -1.0060723622114052], 'a6': [0.0, 0.0], 'a7': [2.0428852112740636, -1.7141842273175867], 'a8': [0.5, 0.8660254037844386], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.293576512744743, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.9396926207859084, -0.3420201433256687]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '162.145', 'coefficient_field': 'CDF', 'conductor': 162, 'conductor_radical': 6, 'conjugate': '2722849662072295422127898180514', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.9396926207859084, -0.3420201433256687]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.17739770200297025, 1.0060723622114052], [-4.698463103929542, 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'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.24229688523698948603732589841', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.293576512744743, 'bad_primes': [2, 3], 'central_character': '27.4', 'conductor': 162, 'conductor_radical': 6, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/162/2/e/b/145/2'], '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': '2-162-27.4-c1-0-2', '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': '2-162-27.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1373550513119213, 'root_angle': -0.02932157708699618, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.21131508332172688628203670088', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2803174892666524198418705700620', 'Lhash_array': ['2803174892666524198418705700620'], 'label': '2-162-27.4-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/2/e/b/145/2'}