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lfunc_lfunctions • Show schema
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{'Lhash': '753466006444359620256670925820', 'a10': [-1.0, 0.0], 'a2': [-1.0, 0.0], 'a3': [-2.5072087334429263, 0.0], 'a4': [1.0, 0.0], 'a5': [1.0, 0.0], 'a6': [2.5072087334429263, 0.0], 'a7': [0.0, 0.0], 'a8': [-1.0, 0.0], 'a9': [3.2860956330524824, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 43.03936668947015, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [7, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 5, 7, 11], 'central_character': '5390.1', 'coefficient_field': 'CDF', 'conductor': 5390, 'conductor_radical': 770, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [2.5072087334429263, 0], [3.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-0.4562613822365466, 0], [13.0, 0]], [[1.0, 0], [0.5423314916937079, 0], [17.0, 0]], [[1.0, 0], [-8.414082706443523, 0], [19.0, 0]], [[1.0, 0], 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'3.70328912851617108777420414786669', '4.85974356202334660030341062919703', '5.42663351812685531433161528621134', '6.05948725964015248142452830746542', '6.65813351167467774886747327304367', '7.40253452396240439817430220650176', '8.101822676056184083400221353802668'], 'prelabel': '2-5390-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.560439519534507, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.59437987589695824458176678839', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.50467573202222255381572945579', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.61701621211682451993562995318', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 43.03936668947015, 'bad_primes': [2, 5, 7, 11], 'central_character': '1.1', 'conductor': 5390, 'conductor_radical': 770, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5390/2/a/ck/1/1'], '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': '2-5390-1.1-c1-0-17', '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': '2-5390-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.560439519534507, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.59437987589695824458176678839', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '753466006444359620256670925820', 'Lhash_array': ['753466006444359620256670925820'], 'label': '2-5390-1.1-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5390/2/a/ck/1/1'}