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lfunc_lfunctions • Show schema
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{'Lhash': '396591488605278542018824580640', 'a10': [3.4378767810667203, 0.0], 'a2': [-1.0, 0.0], 'a3': [-1.0, 0.0], 'a4': [1.0, 0.0], 'a5': [-3.4378767810667203, 0.0], 'a6': [1.0, 0.0], 'a7': [-0.8756627620176483, 0.0], 'a8': [-1.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.15181298389669, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [3, [[1.0, 0], [1.0, 0]]], [13, [[1.0, 0], [1.0, 0]]], [103, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 13, 103], 'central_character': '8034.1', 'coefficient_field': 'CDF', 'conductor': 8034, 'conductor_radical': 8034, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [3.4378767810667203, 0], [5.0, 0]], [[1.0, 0], [0.8756627620176483, 0], [7.0, 0]], [[1.0, 0], [4.128944249408686, 0], [11.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-2.91274999334633, 0], [17.0, 0]], [[1.0, 0], [-6.270544342743641, 0], 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'3.32763155216261600561771709713731', '4.31316725681119835651136358612010', '5.09723994294327699191927821565239', '5.74567810269351740502956900703827', '6.66775494634936895240423626894144', '7.41926217876655982354087006404551', '7.79723907784136109263029735605179'], 'prelabel': '2-8034-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.009482691403777, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.31285552070410861934162807343', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.42141121113758165444200392351', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.85548544470934900589785544821', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 64.15181298389669, 'bad_primes': [2, 3, 13, 103], 'central_character': '1.1', 'conductor': 8034, 'conductor_radical': 8034, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8034/2/a/ba/1/2'], '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': '2-8034-1.1-c1-0-3', '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': '2-8034-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.009482691403777, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.31285552070410861934162807343', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '396591488605278542018824580640', 'Lhash_array': ['396591488605278542018824580640'], 'label': '2-8034-1.1-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8034/2/a/ba/1/2'}