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lfunc_lfunctions • Show schema
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{'Lhash': '864288497078248504709974530618', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [1.5374015770252258, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 66.11613287362019, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [23, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '8280.1', 'coefficient_field': 'CDF', 'conductor': 8280, 'conductor_radical': 690, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.5374015770252258, 0], [7.0, 0]], [[1.0, 0], [-0.8608058531117034, 0], [11.0, 0]], [[1.0, 0], [-0.13919414688829662, 0], [13.0, 0]], [[1.0, 0], [5.5076144052846585, 0], [17.0, 0]], [[1.0, 0], [-5.259013283248633, 0], [19.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 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[113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 27, 'label': '2-8280-1.1-c1-0-27', 'leading_term': '1.87799162625543801256635310056', '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/8280/2/a/bl/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [1.877991626255438, 1.8685635982662034, 1.8402758215984303, 1.7931236601380784, 1.7271204079824474, 1.6423272798750141, 1.538892460462184, 1.4170965881391262, 1.2774016905382926, 1.1205004402576308, 0.9473626408511685, 0.7592760492598877, 0.5578789509565932, 0.34518228938591416, 0.12357958011061777, -0.10415671018229349, -0.3348931829041384, -0.5651683313957455, -0.7912401218379812, -1.0091478335047468, -1.2147872151859316, -1.4039975765748838, -1.5726590077459166, -1.7167975140711194, 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'4.98473578067983757012324953543694', '5.66912112607525873254510319463331', '6.48875422682276677752665038971973', '7.31167015427148941395512174423970', '7.62972022752656823369229699300993'], 'prelabel': '2-8280-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.131182747523278, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.68180340617725493237626046191', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.75996223251628944686473893423', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.63118188237224067983570784240', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 66.11613287362019, 'bad_primes': [2, 3, 5, 23], 'central_character': '1.1', 'conductor': 8280, 'conductor_radical': 690, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8280/2/a/bl/1/2'], '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': '2-8280-1.1-c1-0-27', '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': '2-8280-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.131182747523278, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.68180340617725493237626046191', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '864288497078248504709974530618', 'Lhash_array': ['864288497078248504709974530618'], 'label': '2-8280-1.1-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8280/2/a/bl/1/2'}