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lfunc_lfunctions • Show schema
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{'Lhash': '1137816249361596718989177679019', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-2.5107691794184643, 0.6727585740061302], 'a4': [0.0, 0.0], 'a5': [-2.912030521280131, -0.7802762265117925], 'a6': [0.0, 0.0], 'a7': [-1.4195510791419643, 2.2326833034953446], 'a8': [0.0, 0.0], 'a9': [3.25328156206559, -1.8782829856082146], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.577298010553363, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.4195510791419643, -2.2326833034953446]]]], 'bad_primes': [2, 7], 'central_character': '448.81', 'coefficient_field': 'CDF', 'conductor': 448, 'conductor_radical': 14, 'conjugate': '716050536642274667683357709542', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [2.5107691794184643, -0.6727585740061302], [2.598076211353316, -1.5]], [[1.0, 0], [2.912030521280131, 0.7802762265117925], [4.330127018922194, 2.5]], [[1.0, 0], 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'10.62514496455821480420561016261191', '11.20076646514558921185974365127297'], 'prelabel': '2-448-112.109-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8913746351670688, 'root_angle': 0.13043303623655542, 'root_number': '0.9172134872753588 + 0.3983960576614374*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0652165181183', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.897578756446565683485041429528', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '3.34209812670998242035932979813', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.40038335943765365694482965521', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.577298010553363, 'bad_primes': [2, 7], 'central_character': '112.109', 'conductor': 448, 'conductor_radical': 14, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/448/2/ba/c/81/2'], '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': '2-448-112.109-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': '2-448-112.109-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8913746351670688, 'root_angle': 0.06521651811827771, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.897578756446565683485041429528', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1137816249361596718989177679019', 'Lhash_array': ['1137816249361596718989177679019'], 'label': '2-448-112.109-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/448/2/ba/c/81/2'}