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lfunc_lfunctions • Show schema
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{'Lhash': '2121514714287899609268821307409', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, -3.335132025215443], 'a6': [0, 0], 'a7': [0.6621534468619564, 2.5615528128088303], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.19568209498026, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-0.6621534468619564, -2.5615528128088303]]]], 'bad_primes': [2, 3, 7], 'central_character': '4032.3583', 'coefficient_field': 'CDF', 'conductor': 4032, 'conductor_radical': 42, 'conjugate': '498029750354611846383400644071', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 3.335132025215443], [-5.0, 0]], [[1.0, 0], [-0.6621534468619564, -2.5615528128088303]], [[1.0, 0], [0, 5.036796290982293], [-11.0, 0]], [[1.0, 0], [0, 6.040895836088439], [-13.0, 0]], [[1.0, 0], [0, 5.207984795063985], [-17.0, 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'2.28335257297788015383871544470373', '3.45328367842564057273192133205432', '4.32997591951236305404744360352808', '4.64569146717296744388286594754451', '6.28446286843277769483108441607216', '6.69108953334914184561704425655576', '7.04983508957811937613938737422091', '7.937682994986446520626750173144309', '8.671640870058663907401353995344463'], 'prelabel': '2-4032-28.27-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.674123905501206, 'root_angle': 0.9194804539592665, 'root_number': '-0.96817595897859321442884073150086873560824234898407670953 + 0.25027047859442269684147960522331891788226819373121661932*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.45974022697963324', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.67358001795284871352926495669', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.28335257297788015383871544470', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.45328367842564057273192133205', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32.19568209498026, 'bad_primes': [2, 3, 7], 'central_character': '28.27', 'conductor': 4032, 'conductor_radical': 42, 'degree': 2, 'index': 71, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4032/2/b/r/3583/4'], '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': '2-4032-28.27-c1-0-71', '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': '2-4032-28.27-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.674123905501206, 'root_angle': 0.45974022697963324, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.67358001795284871352926495669', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2121514714287899609268821307409', 'Lhash_array': ['2121514714287899609268821307409'], 'label': '2-4032-28.27-c1-0-71', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4032/2/b/r/3583/4'}