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lfunc_lfunctions • Show schema
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{'Lhash': '1676579955993005304995709766015', 'a10': [-2.947637170221976, -1.1451790745231865], 'a2': [0.2212317420824743, 1.3968022466674206], 'a3': [-1.543268569769601, -0.7863346117024802], 'a4': [-1.902113032590307, 0.6180339887498949], 'a5': [-1.1258498051628834, 1.9319581300366468], 'a6': [0.7569339580671207, -2.329603181472081], 'a7': [0.3125957127348594, 0.3125957127348594], 'a8': [-1.2840790438404124, -2.520147021340202], 'a9': [1.7633557568774194, 2.4270509831248424], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.791024121276825, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.2212317420824743, -1.3968022466674206]]], [3, [[1.0, 0], [1.543268569769601, 0.7863346117024802]]], [5, [[1.0, 0], [1.1258498051628834, -1.9319581300366468]]]], 'bad_primes': [2, 3, 5], 'central_character': '600.437', 'coefficient_field': 'CDF', 'conductor': 600, 'conductor_radical': 30, 'conjugate': '327843067099452548520226315095', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.2212317420824743, -1.3968022466674206]], [[1.0, 0], [1.543268569769601, 0.7863346117024802]], [[1.0, 0], [1.1258498051628834, -1.9319581300366468]], [[1.0, 0], [-0.3125957127348594, -0.3125957127348594], [0, 7.0]], [[1.0, 0], [4.081736761651094, 2.9655553454624], [3.3991869381244215, 10.46162167924669]], [[1.0, 0], [0, 0], [12.363734711836996, 4.017220926874317]], [[1.0, 0], [0, 0], [-9.992349288972044, 13.753288904374106]], [[1.0, 0], [0, 0], [-15.371322893124, -11.16791979355699]], [[1.0, 0], [0, 0], [-21.874299874788534, 7.1073908706237905]], [[1.0, 0], [-5.086696511825936, 1.6527678854514674], [23.461492836873475, -17.04577231648172]], [[1.0, 0], [-3.406737174786834, 10.484858918324372], [-25.079526825623372, -18.221342821066667]], [[1.0, 0], [0, 0], [-35.189091102920685, -11.433628791873055]], [[1.0, 0], [0, 0], [-12.669696769372845, 38.9933171681013]], [[1.0, 0], [0, 0], [0, 43.0]], [[1.0, 0], [0, 0], 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[[1.0, 0], [-0.7267337772485979, -0.7267337772485979], [0, 107.0]], [[1.0, 0], [0, 0], [33.68285238686927, -103.66516027617173]], [[1.0, 0], [0, 0], [107.46938634135235, 34.91892036436906]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 51, 'label': '2-600-600.437-c1-0-51', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/600/2/bp/b/437/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.39717396412163225, 0.5422645050882916, 0.6618117219482017, 0.7553471155364823, 0.8190022272119959, 0.8462072962819845, 0.8288447147098394, 0.7586480733083844, 0.6286904459457966, 0.434848258347571, 0.1771373027808709, -0.1391951056076647, -0.5029542730859953, -0.8967957132250888, -1.2976568041785448, -1.6779014027114858, -2.00718984610661, -2.255000278947127, 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'3.09598333981143800711123192881803', '4.53825400194687121635534544263664', '4.78212457935231248537617025479113', '5.81128745063747023926422587951952', '7.30437110854902658579351700625324', '8.405325360254808446771018081582547', '9.291580781071736789969273399794297', '10.26122085890541836877070849195407', '10.67767113546251873538441198940143'], 'prelabel': '2-600-600.437-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.188840816797061, 'root_angle': 0.27590578315102504, 'root_number': '0.6472816093128774 + 0.7622509548995866*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.137952891576', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.32258838176004630155984715683', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.09598333981143800711123192882', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.53825400194687121635534544264', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.791024121276825, 'bad_primes': [2, 3, 5], 'central_character': '600.437', 'conductor': 600, 'conductor_radical': 30, 'degree': 2, 'index': 51, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/600/2/bp/b/437/1'], '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': '2-600-600.437-c1-0-51', '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': '2-600-600.437-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.188840816797061, 'root_angle': 0.13795289157551252, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.32258838176004630155984715683', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1676579955993005304995709766015', 'Lhash_array': ['1676579955993005304995709766015'], 'label': '2-600-600.437-c1-0-51', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/600/2/bp/b/437/1'}