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lfunc_lfunctions • Show schema
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{'Lhash': '1993803960299794733558427652786', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.7187096903919148, 0.0], 'a4': [0.0, 0.0], 'a5': [0.39138238063090086, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-0.046037000152928616, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 67.96866220051389, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-1.0, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 7, 19], 'central_character': '8512.1', 'coefficient_field': 'CDF', 'conductor': 8512, 'conductor_radical': 266, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.7187096903919148, 0], [3.0, 0]], [[1.0, 0], [-0.39138238063090086, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-3.064055070869887, 0], [11.0, 0]], [[1.0, 0], [2.782764761261802, 0], [13.0, 0]], [[1.0, 0], [6.220184142045631, 0], [17.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], 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[[1.0, 0], [-19.785713664569233, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 200, 'label': '2-8512-1.1-c1-0-200', '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/8512/2/a/bj/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-2.0042484752330122e-60, 0.2792607879249233, 0.5572303046024208, 0.8325661801732658, 1.1038277633155114, 1.3694364792623173, 1.6276468095235161, 1.876530242243272, 2.1139737039155517, 2.3376931201573425, 2.545261934356414, 2.7341536869865743, 2.90179715174551, 3.045642044504175, 3.163232960552029, 3.252288940388445, 3.3107858979214364, 3.3370390528745157, 3.329782481020328, 3.2882429257804233, 3.212205101159927, 3.102065860373736, 2.9588748099639655, 2.784359219059237, 2.580931410068774, 2.351677220970135, 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'5.35371292017920075780715973889257', '6.10288505403354802736893225827615', '6.91134600153018472074665403871461', '7.50245093263258689196475894612180'], 'prelabel': '2-8512-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.244310899069363, 'root_angle': 0.5, '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': '1.57283399695533435773204712778', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.24055631838275322536401146455', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.95908749824610114709844453550', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 67.96866220051389, 'bad_primes': [2, 7, 19], 'central_character': '1.1', 'conductor': 8512, 'conductor_radical': 266, 'degree': 2, 'index': 200, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8512/2/a/bj/1/3'], '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': '2-8512-1.1-c1-0-200', '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': '2-8512-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.244310899069363, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.57283399695533435773204712778', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1993803960299794733558427652786', 'Lhash_array': ['1993803960299794733558427652786'], 'factors': ['2-8512-1.1-c1-0-200'], 'label': '2-8512-1.1-c1-0-200', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8512/2/a/bj/1/3'}