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lfunc_lfunctions • Show schema
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{'Lhash': '1607596970409195969493782445807', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.652836810670971, 0.5178131683252296], 'a4': [0.0, 0.0], 'a5': [-2.529171444591497, 0.44596116451888534], 'a6': [0.0, 0.0], 'a7': [1.4078935840328097, -1.677862236761439], 'a8': [0.0, 0.0], 'a9': [2.463739045417975, 1.7117213313162063], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.4495373673193144, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.652836810670971, -0.5178131683252296]]]], 'bad_primes': [2, 3], 'central_character': '432.47', 'coefficient_field': 'CDF', 'conductor': 432, 'conductor_radical': 6, 'conjugate': '2157560847083260542153402780054', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.652836810670971, -0.5178131683252296]], [[1.0, 0], [2.529171444591497, -0.44596116451888534], [4.698463103929542, -1.7101007166283437]], [[1.0, 0], [-1.4078935840328097, 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-0.8899157238153719, -0.2952994543093314, 0.4875634990434043, 1.1862457173543286], 'positive_zeros': ['1.26817040130755446162177919606850', '3.18267482322682430884824684866088', '3.73400628478469041279065715083215', '5.30039477768763743443051896344709', '6.43264365588052050009757919718420', '7.918972840623806277253021711392059', '8.220716732810443187392806272746405', '8.797659298960346412201132827549057', '10.18330553858597210280653740320553', '11.20453820749951211318885122074473'], 'prelabel': '2-432-108.47-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.857293021394124, 'root_angle': -0.19156275920350213, 'root_number': '0.8243110394856865 - 0.5661371831826868*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0957813796018', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.26817040130755446162177919607', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.18267482322682430884824684866', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.73400628478469041279065715083', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.4495373673193144, 'bad_primes': [2, 3], 'central_character': '108.47', 'conductor': 432, 'conductor_radical': 6, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/432/2/be/c/47/6'], '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': '2-432-108.47-c1-0-8', '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': '2-432-108.47-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.857293021394124, 'root_angle': -0.09578137960175107, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.26817040130755446162177919607', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1607596970409195969493782445807', 'Lhash_array': ['1607596970409195969493782445807'], 'label': '2-432-108.47-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/432/2/be/c/47/6'}