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lfunc_lfunctions • Show schema
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{'Lhash': '161174494036718351319225390660', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-1.0, 0], 'a4': [0, 0], 'a5': [0, 4.0], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.38732305983134, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 13], 'central_character': '4056.337', 'coefficient_field': 'CDF', 'conductor': 4056, 'conductor_radical': 78, 'conjugate': '2316926584794106615475233749563', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, -4.0], [-5.0, 0]], [[1.0, 0], [0, 0], [-7.0, 0]], [[1.0, 0], [0, -2.0], [-11.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.0, 0], [17.0, 0]], [[1.0, 0], [0, -8.0], [-19.0, 0]], [[1.0, 0], [4.0, 0], [23.0, 0]], [[1.0, 0], [6.0, 0], [29.0, 0]], [[1.0, 0], [0, 4.0], [-31.0, 0]], [[1.0, 0], [0, 6.0], [-37.0, 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'-0.5547001962252291220183417334569993763463533190531148020 + 0.8320502943378436830275126001854990645195299785796722030*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3435835209054994', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.12714425726434420776516908787', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.02532474988957540364259615939', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.05941343744698439545371308178', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32.38732305983134, 'bad_primes': [2, 3, 13], 'central_character': '13.12', 'conductor': 4056, 'conductor_radical': 78, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4056/2/c/d/337/2'], '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': '2-4056-13.12-c1-0-0', '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': '2-4056-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.690986123672358, 'root_angle': 0.3435835209054994, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.12714425726434420776516908787', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '161174494036718351319225390660', 'Lhash_array': ['161174494036718351319225390660'], 'label': '2-4056-13.12-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4056/2/c/d/337/2'}