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lfunc_lfunctions • Show schema
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{'Lhash': '1625129382625685813769094578920', 'a10': [1.5615528128088303, 0.0], 'a2': [1.0, 0.0], 'a3': [-2.5615528128088303, 0.0], 'a4': [1.0, 0.0], 'a5': [1.5615528128088303, 0.0], 'a6': [-2.5615528128088303, 0.0], 'a7': [-1.0, 0.0], 'a8': [1.0, 0.0], 'a9': [3.5615528128088303, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 40.35639318155513, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [7, [[1.0, 0], [1.0, 0]]], [19, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 7, 19], 'central_character': '5054.1', 'coefficient_field': 'CDF', 'conductor': 5054, 'conductor_radical': 266, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [2.5615528128088303, 0], [3.0, 0]], [[1.0, 0], [-1.5615528128088303, 0], [5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [6.56155281280883, 0], [11.0, 0]], [[1.0, 0], [-0.4384471871911697, 0], [13.0, 0]], [[1.0, 0], [-2.0, 0], [17.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 117, 'label': '2-5054-1.1-c1-0-117', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/5054/2/a/m/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-1.2202944021430833e-60, 0.17723622444056075, 0.3534560462897576, 0.527604600889282, 0.6985527170077211, 0.8650661258813725, 1.0257818200861428, 1.1791932023901985, 1.3236451433493568, 1.4573395306973007, 1.5783513860947083, 1.6846551748259182, 1.7741605564427418, 1.8447565214961374, 1.8943626248676042, 1.9209858486459637, 1.9227814948283186, 1.8981164098264698, 1.8456327714031706, 1.764310620381986, 1.6535272937132681, 1.513111914305615, 1.343393120277659, 1.1452382766634461, 0.9200825109196136, 0.6699460540610206, 0.3974385550173244, 0.10574926848286403, 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'6.83648146032189259053632856542968', '7.67612270193975430926223395278475'], 'prelabel': '2-5054-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.352668193881617, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.28200103587936256617730006073', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.56603192282416082164874650039', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.20169500745029864967524845650', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 40.35639318155513, 'bad_primes': [2, 7, 19], 'central_character': '1.1', 'conductor': 5054, 'conductor_radical': 266, 'degree': 2, 'index': 117, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5054/2/a/m/1/1'], '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': '2-5054-1.1-c1-0-117', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-5054-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.352668193881617, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.28200103587936256617730006073', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1625129382625685813769094578920', 'Lhash_array': ['1625129382625685813769094578920'], 'label': '2-5054-1.1-c1-0-117', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5054/2/a/m/1/1'}