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lfunc_lfunctions • Show schema
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{'Lhash': '452785590537317595501332857206', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-15.556349186104045, -1.0], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [241.0, 31.11269837220809], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 61.587386808184576, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [15.556349186104045, 1.0]]]], 'bad_primes': [2, 3], 'central_character': '384.191', 'coefficient_field': 'CDF', 'conductor': 384, 'conductor_radical': 6, 'conjugate': '1212829830196002220860352512286', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [15.556349186104045, 1.0]], [[1.0, 0], [0, 0], [3125.0, 0]], [[1.0, 0], [0, 0], [-16807.0, 0]], [[1.0, 0], [0, -474.0], [-161051.0, 0]], [[1.0, 0], [0, 0], [-371293.0, 0]], [[1.0, 0], [0, 1419.8704166225875], [-1419857.0, 0]], [[1.0, 0], [-1264.306924761547, 0], [2476099.0, 0]], [[1.0, 0], [0, 0], [6436343.0, 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'index': 16, 'label': '2-384-24.11-c5-0-16', 'leading_term': '0.995901290169507867661415180691193906305407944241416008', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/384/6/f/b/191/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [0.9959012901695079, 0.8535433500886286, 0.6934251874873326, 0.5187822050792846, 0.3331295184374942, 0.14021185513523005, -0.05605002657763397, -0.2516160838088323, -0.44238654099310376, -0.6242638309223112, -0.7932164357579041, -0.9453440544426414, -1.076943428721721, -1.1845740594053422, -1.2651229415307585, -1.3158673462225727, -1.3345345832207682, -1.319357596419421, -1.2691251806029356, -1.1832255660701483, -1.0616821039290831, -0.9051798030104733, -0.7150815234399169, -0.493432724969171, -0.24295380225711402, 0.03298078466724574, 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'8.400160401555777302243441414643973', '9.568220370796130472585592724621884', '10.45206608194364388914571999408022'], 'prelabel': '2-384-24.11-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.847763172279383, 'root_angle': -0.4795663800765182, 'root_number': '0.0641500299099584182787943089446619395164001945855696529 - 0.9979402655783318177840786971024001967268674921193841264*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2397831900382591', 'prec': 64}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.35718485082229875548867360965', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.55529597136221000885224437089', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.32898853573931163213926122579', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 61.587386808184576, 'bad_primes': [2, 3], 'central_character': '24.11', 'conductor': 384, 'conductor_radical': 6, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/384/6/f/b/191/1'], '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': '2-384-24.11-c5-0-16', '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': '2-384-24.11-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.847763172279383, 'root_angle': -0.2397831900382591, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.35718485082229875548867360965', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '452785590537317595501332857206', 'Lhash_array': ['452785590537317595501332857206'], 'label': '2-384-24.11-c5-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/384/6/f/b/191/1'}