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lfunc_lfunctions • Show schema
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{'Lhash': '436947060287875596929136791175', 'a10': [0, 0], 'a2': [0, 0], 'a3': [429.4615206811522, 429.4615206811522], 'a4': [0, 0], 'a5': [2473.083165706088, 2473.083165706088], 'a6': [0, 0], 'a7': [-198740.09997071637, 0], 'a8': [0, 0], 'a9': [0, -162566.6045084646], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 116.99120861136457, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '6.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]]], 'bad_primes': [2], 'central_character': '128.31', 'coefficient_field': 'CDF', 'conductor': 128, 'conductor_radical': 2, 'conjugate': '1172729629214234144521698851076', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-429.4615206811522, -429.4615206811522], [0, 531441.0]], [[1.0, 0], [-2473.083165706088, -2473.083165706088], [0, 244140625.0]], [[1.0, 0], [198740.09997071637, 0], [13841287201.0, 0]], [[1.0, 0], [-1130312.2427904082, 1130312.2427904082], [0, -3138428376721.0]], [[1.0, 0], [1221424.8848571272, 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'1.551809656976453268891566873780311906878808658555831398', 'load_key': 'CMFs-workshop', 'motivic_weight': 12, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [12], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/128/13/f/b/31/16', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [1.5518096569764532, 1.317844268113159, 1.0556003193687116, 0.771062203543046, 0.4706154245493248, 0.16091030644064458, -0.15127954154156426, -0.45920106204095934, -0.7562648946337315, -1.0361848412651882, -1.2931107301174694, -1.5217518798012957, -1.7174885459504239, -1.8764689658955076, -1.9956899001797748, -2.0730588973731088, -2.1074368751732635, -2.098660009570251, -2.047540347591923, -1.9558449999366123, -1.8262542192385687, -1.6622991190613299, -1.4682802290295018, -1.2491685038033065, -1.0104907990064165, -0.7582021871608607, -0.49854780305159174, -0.2379171732617172, 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'8.804798511998655159968861934519007', '9.553185691473356910754332188604946', '10.57387558253091618792150780218094'], 'prelabel': '2-2e7-16.11-c12-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.816247436674356, 'root_angle': -0.5680921319769524, 'root_number': '-0.2122899626392139858111106972269939656581671714945587066 - 0.9772067190531597701147002965912892381415871571737376335*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2840460659884762', 'prec': 64}, 'spectral_label': 'c12-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.34469045351235356258450486148', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.74568769707477572497412848656', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.80124501422855180466366660304', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 116.99120861136457, 'bad_primes': [2], 'central_character': '16.11', 'conductor': 128, 'conductor_radical': 2, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/128/13/f/b/31/16'], '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': '2-2e7-16.11-c12-0-8', 'motivic_weight': 12, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [12], 'order_of_vanishing': 0, 'prelabel': '2-2e7-16.11-c12-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.816247436674356, 'root_angle': -0.2840460659884762, 'self_dual': False, 'spectral_label': 'c12-0', 'z1': {'__RealLiteral__': 0, 'data': '0.34469045351235356258450486148', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '436947060287875596929136791175', 'Lhash_array': ['436947060287875596929136791175'], 'label': '2-2e7-16.11-c12-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/128/13/f/b/31/16'}