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lfunc_lfunctions • Show schema
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{'Lhash': '163270109363165208747062283486', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-78.06246951218786, 0.0], 'a6': [0.0, 0.0], 'a7': [49.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 161.6668903714845, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-49.0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '1008.1', 'coefficient_field': 'CDF', 'conductor': 1008, 'conductor_radical': 42, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [78.06246951218786, 0], [3125.0, 0]], [[1.0, 0], [-49.0, 0]], [[1.0, 0], [746.4372865853151, 0], [161051.0, 0]], [[1.0, 0], [-9.75012195124853, 0], [371293.0, 0]], [[1.0, 0], [1754.6871646340664, 0], [1419857.0, 0]], [[1.0, 0], [-603.2503658537456, 0], [2476099.0, 0]], [[1.0, 0], [3175.311859755945, 0], [6436343.0, 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['0.12879740626776010187684498022218', '1.88676019199566580932694813640529', '2.95253357705356951539059783139437', '4.01237752265643661341368729524449', '4.76886433875346986183380356998212', '5.68361873837266505510381473814411', '6.92497659327963682156438025706693', '7.902885696039227995944884136849100', '7.991562951016727310602571774333353', '9.110013411779934129236227630655889'], 'prelabel': '2-1008-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.714829545514345, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.12879740626776010187684498022', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.88676019199566580932694813641', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.95253357705356951539059783139', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 161.6668903714845, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 1008, 'conductor_radical': 42, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1008/6/a/bj/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': '2-1008-1.1-c5-0-0', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-1008-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.714829545514345, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.12879740626776010187684498022', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '163270109363165208747062283486', 'Lhash_array': ['163270109363165208747062283486'], 'factors': ['2-1008-1.1-c5-0-0'], 'label': '2-1008-1.1-c5-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1008/6/a/bj/1/1'}