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lfunc_lfunctions • Show schema
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{'Lhash': '1868448726335558354776979792407', 'a10': [-0.15403919162695467, 0.2668037062547239], 'a2': [0.15403919162695467, -0.2668037062547239], 'a3': [1.0526443551241094, 1.3754780483982099], 'a4': [0.9525438548858287, 1.649854353099771], 'a5': [-1.0, 0.0], 'a6': [0.5291311267186517, -0.06897188863934463], 'a7': [2.204330602186297, -1.463190553641253], 'a8': [1.2030731080911639, 0.0], 'a9': [-0.7838797232506962, 2.895778406487004], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.515287663670333, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.0526443551241094, -1.3754780483982099]]], [5, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [-2.204330602186297, 1.463190553641253]]]], 'bad_primes': [3, 5, 7], 'central_character': '315.256', 'coefficient_field': 'CDF', 'conductor': 315, 'conductor_radical': 105, 'conjugate': '2841426216936004143913079879425', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.15403919162695467, 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'5.68614338684269919440326351238413', '6.85599095656482535616681094458506', '7.46316590062154868766582210294628', '8.739158160891540019449811650879023', '9.307326922036224329493831341476321', '10.95133791899662721123211998432915', '11.44988496023841947615974713607003'], 'prelabel': '2-315-63.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5859658456821613, 'root_angle': -0.30443037435348275, 'root_number': '0.5764684354494405 - 0.8171194177906154*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.152215187177', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.47394615361611512375634585328', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.66994038418280432831061928690', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.48643239617733358600730433240', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.515287663670333, 'bad_primes': [3, 5, 7], 'central_character': '63.4', 'conductor': 315, 'conductor_radical': 105, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/315/2/k/b/256/7'], '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': '2-315-63.4-c1-0-15', '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': '2-315-63.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5859658456821613, 'root_angle': -0.15221518717674137, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.47394615361611512375634585328', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1868448726335558354776979792407', 'Lhash_array': ['1868448726335558354776979792407'], 'label': '2-315-63.4-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/315/2/k/b/256/7'}