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lfunc_lfunctions • Show schema
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{'Lhash': '2726200305235111316122256085012', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.5, -0.8660254037844386], 'a4': [0.0, 0.0], 'a5': [-0.5, 2.179449471770337], 'a6': [0.0, 0.0], 'a7': [2.6374586088176875, -0.2093133697914896], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.1179056282979258, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0.5, -2.179449471770337]]], [7, [[1.0, 0], [-2.6374586088176875, 0.2093133697914896]]]], 'bad_primes': [2, 5, 7], 'central_character': '140.9', 'coefficient_field': 'CDF', 'conductor': 140, 'conductor_radical': 70, 'conjugate': '2856740267848795463285298499511', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.5, 0.8660254037844386], [1.5, -2.598076211353316]], [[1.0, 0], [0.5, -2.179449471770337]], [[1.0, 0], [-2.6374586088176875, 0.2093133697914896]], [[1.0, 0], [1.1374586088176875, 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[-12.04983443527075, 6.956975154893989], [33.5, -58.023702053557386]], [[1.0, 0], [-10.54983443527075, 0], [71.0, 0]], [[1.0, 0], [-1.8625413911823125, 1.0753387735759283], [36.5, -63.21985447626402]], [[1.0, 0], [0.13745860881768743, -0.2380852944099699], [-39.5, -68.41600689897065]], [[1.0, 0], [0, -5.672323011526571], [-83.0, 0]], [[1.0, 0], [3.5, -6.06217782649107], [-44.5, -77.07626093681505]], [[1.0, 0], [0, -6.928203230275509], [-97.0, 0]], [[1.0, 0], [0.7749172176353748, 1.3421959926043785], [-50.5, 87.4685657822283]], [[1.0, 0], [2.225082782364625, 1.2846521433674178], [51.5, 89.20061658979718]], [[1.0, 0], [12.04983443527075, 6.956975154893989], [53.5, 92.66471820493493]], [[1.0, 0], [-1.774917217635375, -3.0742468001732557], [-54.5, 94.39676901250381]], [[1.0, 0], [0, -13.01915298138506], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-140-35.9-c1-0-2', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 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False, 'root_analytic_conductor': 1.0573105637881075, 'root_angle': 0.02640139469829123, 'root_number': '0.9965622483466144 + 0.08284736067214639*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0132006973491', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.15059284060156860198596146756', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.21641432278640671822632457388', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.87039846142984731138562535907', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.1179056282979258, 'bad_primes': [2, 5, 7], 'central_character': '35.9', 'conductor': 140, 'conductor_radical': 70, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/140/2/q/b/9/2'], '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': '2-140-35.9-c1-0-2', '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': '2-140-35.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0573105637881075, 'root_angle': 0.013200697349145614, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.15059284060156860198596146756', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2726200305235111316122256085012', 'Lhash_array': ['2726200305235111316122256085012'], 'label': '2-140-35.9-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/140/2/q/b/9/2'}