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lfunc_lfunctions • Show schema
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{'Lhash': '1668120073819045295051386712552', 'a10': [-3.5615528128088303, 0.0], 'a2': [1.0, 0.0], 'a3': [-1.0, 0.0], 'a4': [1.0, 0.0], 'a5': [-3.5615528128088303, 0.0], 'a6': [-1.0, 0.0], 'a7': [0.0, 0.0], 'a8': [1.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 30.518823652533378, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '3822.1', 'coefficient_field': 'CDF', 'conductor': 3822, 'conductor_radical': 546, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [3.5615528128088303, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.5615528128088303, 0], [11.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-6.68465843842649, 0], [17.0, 0]], [[1.0, 0], [-4.68465843842649, 0], [19.0, 0]], [[1.0, 0], [5.56155281280883, 0], 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'group': 'GL2', 'index': 54, 'label': '2-3822-1.1-c1-0-54', '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/3822/2/a/bo/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-1.2105709407714252e-60, 0.1711022917238008, 0.3414316335805159, 0.5101767237908185, 0.6764517859264118, 0.8392647531461724, 0.9974915546358779, 1.149857921563298, 1.2949297004203184, 1.4311122240063767, 1.5566588803007728, 1.6696886611167687, 1.7682121770792831, 1.8501653935020894, 1.9134501658546776, 1.9559805224069815, 1.9757335432741745, 1.9708036089739547, 1.9394587301447193, 1.8801976189393041, 1.7918061205870732, 1.6734115920231278, 1.5245337964515402, 1.3451308824660289, 1.135639038559979, 0.8970044630716127, 0.6307063698379103, 0.3387698642044908, 0.023767674569800668, 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'7.42590511407383774850594312249116', '7.83442632807584960067983105142170'], 'prelabel': '2-3822-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.5243844591531985, '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': '1.31591471145023310684852207232', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.86985591270793636190150429916', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.59844997507620280971808870077', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 30.518823652533378, 'bad_primes': [2, 3, 7, 13], 'central_character': '1.1', 'conductor': 3822, 'conductor_radical': 546, 'degree': 2, 'index': 54, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3822/2/a/bo/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': '2-3822-1.1-c1-0-54', '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': '2-3822-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.5243844591531985, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.31591471145023310684852207232', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1668120073819045295051386712552', 'Lhash_array': ['1668120073819045295051386712552'], 'label': '2-3822-1.1-c1-0-54', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3822/2/a/bo/1/1'}